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1. Introduction This manual describes the usage, files and the theoretical background of aftertreatment modeling and simulation using the AVL simulation codes BOOST and FIRE.
1.1. Scope This document is for users of the FIRE/BOOST Aftertreatment Module and anyone interested in catalyst theory and modeling.
1.2. Symbols The following symbols are used throughout this manual. Safety warnings must be strictly observed during operation and service of the system or its components. Caution: Cautions describe conditions, practices or procedures which could result in damage to, or destruction of data if not strictly observed or remedied. Note: Notes provide important supplementary information. Convention
Meaning
Italics
For emphasis, to introduce a new term.
monospace
To indicate a command, a program or a file name, messages, input/ output on a screen, file contents or object names.
MenuOpt
A MenuOpt font is used for the names of menu options, submenus and screen buttons.
1.3. Configurations Software configurations described in this manual were in effect on the publication date of this manual. It is the user's responsibility to verify the configuration of the equipment before applying procedures in this manual.
4
FIRE BOOST Aftertreatment
2. Overview
2. Overview The FIRE/BOOST Aftertreatment Module enables the simulation of the chemical and physical processes occurring in various types of • honeycomb type catalytic converter • wall-flow type particle filter • pipes (for BOOST). The models account for the simulation of the fluid flow within these elements, for heterogeneous chemical reaction, for adsorption and desorption of species on the catalysts' surface and also for heterogeneous soot regeneration reactions. The solution of continuity, momentum, species and energy balances in the gas phase coupled with the solid phase energy conservation and chemical reactions models delivers detailed results resolved in time and space. Typical results are for example: • flow velocities inside the channels and overall pressure drop • species mass fractions and pollutant conversion • gas/solid temperatures and thermal behavior • reaction rates and chemical behavior • heat and mass transfer • soot decomposition and regeneration With the FIRE/BOOST aftertreatment models and their results, a broad range of aftertreatment applications can be investigated, developed and optimized: Catalytic Converter
Particle Filter
Three-way catalyst
Particle filter loading
Diesel oxidation catalyst
Bare trap regeneration
NOx storage catalyst
Fuel additive regeneration
Selective Catalytic Reduction (SCR) catalyst
Low temperature NO2 regeneration
Reformer catalyst
Catalytic supported regeneration
In order to model all the different chemical reactions given by these various types of applications, FIRE offers a general chemical reaction input language which has similar functionality to the CHEMKIN software package. Thus the user can set up his own chemical reaction models containing gas phase species and species stored on the surface. The kinetic rate equations are defined via a standard Arrhenius type rate law or via user models. The chemical equilibrium and sticking coefficient formulation is also considered. The FIRE Aftertreatment Module allows definition of different kinetic parameter sets that can be assigned to any number of different catalysts in one geometric model. Additionally, FIRE and BOOST offer pre-defined reaction sets. For the simulation of catalytic reactions Langmuir-Hinshelwood approaches were setup. The user has access to all kinetic parameters and therefore can adapt all pre-defined models to different types of catalysts. In the same way pre-defined soot regeneration models are implemented for all the regeneration types listed above. Free access to any reaction model, with an arbitrary number of reactions and species, is offered by user-routines that can be linked to BOOST and FIRE.
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3. Theory
3. Theory 3.1. Catalytic Converter Model Availability BOOST AT: Catalyst
page [187]
FIRE: Catalyst Specification
page [100]
3.1.1. Principle of Heterogeneous Catalytic Reactions In this section effects are discussed that should be considered when a mathematical formulation for the description of surface kinetics is developed. Catalytic combustion reactors are heterogeneous reactors because they contain a gas phase (reactants and products) and solid catalyst. Since the catalytic reactions occur on the catalyst, the reactants have to be transported to the external gas-solid interface. Modeling the overall combustion process therefore requires the consideration of both the physical transport and chemical kinetic steps. • Generally there is a boundary layer between the bulk fluid stream and the solid surface. Within this boundary layer there are variations in velocity, concentration and temperature. Species transport from the bulk fluid stream to the solid surface can have limiting effect on the rate of the catalytic reaction. • Most catalysts are porous materials. Much of the chemical reactions occur inside the porous catalyst, which in some cases can have significant effect on the complexity of the problem. Figure 1. Steps of a Catalytic Reaction
page [95]
The above figure (adapted from Hayes et al. [21 ]) shows the individual steps taking place page [95] during a heterogeneous catalytic reaction. As discussed by Froment and Bischoff [14 ] the following steps can be distinguished: 1. Transport of the reactants from the bulk gas phase to the external solid surface across the boundary layer. 2. Diffusion of the reactants into the porous catalyst. Since the main part of the catalyst is located inside the porous material (washcoat) the reactants must diffuse into it. 3. Adsorption of the reactants onto the surface. 4. Catalytic reaction at the surface. 5. Desorption of the products of the reaction. 6. Diffusion of the products to the surface of the catalyst. 6
FIRE BOOST Aftertreatment
3. Theory 7. Transport of the products into the bulk gas phase. Steps 1, 2, 6 and 7 are mass transport steps while steps 3, 4 and 5 are chemical kinetic steps. To account for these effects properly, the FIRE/BOOST Aftertreatment Module distinguishes the following types of species: • Gas phase species: • : Concentration in the bulk gas flow (Species transport equation) • : Concentration directly above the surface of the catalyst • Stored (adsorbed) species: A stored species occupies one 'site' of the catalytic surface. The number of sites is conserved. This allows to model steps 4, 5 and 6 either separately (i.e. Oxygen storage on the surface) or in one step (i.e. Langmuir-Hinshelwood-Hougen-Watson reaction model for 3 way catalysts). FIRE Example: Three-way catalyst:
CO + 0.5*O2 = CO2 C3H6 + 4.5*O2 = 3*CO2 + 3*H2O H2 + 0.5*O2 = H2O
This mechanism accounts for the catalytic oxidation of CO, C3H6 and H2 as proposed by page [97] page [95] numerous authors in literature (i.e. Voltz et al. [65 ], Chen et al. [11 ] and Wanker page [97] et al.[67 ]). The reactions are global reactions and do not contain any stored species. Therefore the influence of adsorption and desorption of species on the surface has to be considered in the formulation of the reaction rates (kinetics). Most commonly the LangmuirHinshelwood-Hougen-Watson type rate equations are used in literature for these reactions. FIRE Example: Oxygen storage:
O2 + 2*PT_s = 2*O_s
The above reaction accounts for the effect of Oxygen storage on the catalyst. The Oxygen molecule dissociates to two Oxygen atoms that are stored on the surface, which is indicated by the identifier "_s" added to "O". Since two surface sites are occupied by the two Oxygen atoms, the expression "2*PT_s" must appear on the left hand side of the reaction definition line. PT is a dummy identifier for one surface site.
3.1.2. General Approaches and Assumptions In the following section general approaches considering catalytic converter modeling are briefly summarized. For more detailed information please refer to the literature cited. 3.1.2.1. Cell Specification of Honeycomb-Type Catalytic Converter The Honeycomb-type catalytic converter consists of hundreds (thousands) of individual channels. The exhaust gas flows through these channels and reacts catalytically. The catalytic reactions take place at active sites that are spread within the so-called washcoat of the monolith. This washcoat is a porous solid layer that covers the solid substrate as shown in the following figure.
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3. Theory Figure 2. Structure of a Squared Cell Monolith
As shown, the total thickness of the monolith's wall
results to (1)
where wall is the thickness of the substrate wall and wcl,tot is the thickness of the washcoat layers. The repeat distance s of the monolith can be derived from the cell density CPSM according to: (2)
where CPSM is defined as the number of channels per square meter cross sectional area. Catalysts are often specified with the CPSI number determining the number of channels per square inch. With given CPSI number one obtains CPSM with equation (3)
Based on this information (CPSI, wall and washcoat thickness) FIRE/BOOST calculates the hydraulic channel diameter dhyd, open frontal area OFA and the geometric surface area GSA as shown below. Hydraulic channel diameter: (4) Monolith's open frontal area (= fluid volume fraction
g)
results from: (5)
Geometric surface area (= channel wetted perimeter) GSA given in surface per monolith volume is calculated as: (6)
In the same way as the dhyd, OFA and GSA are derived from the cell density CPSM and the total wall thickness , the latter can be calculated from the first three data. Therefore the above given equations have to be inverted. The cell density is given by (7)
and the total wall thickness of the monolith is (8)
8
FIRE BOOST Aftertreatment
3. Theory
The washcoat layer thickness ( wcl,tot) of the monolith is assumed to be zero and therefore the page [8] page [8] total thickness is equal to the substrate thickness wall. Eq.7 and Eq.8 show that three different equations can be used for the evaluation of the cell density and the wall thickness. The difference between them is that only a pair of two values out of the three data (dhyd, OFA page [8] and GSA) is required. FIRE/BOOST uses the first term on the right hand side of Eq.7 and page [8] Eq.8 where the hydraulic diameter dhyd and the open frontal area OFA are needed. The above calculated values of CPSM and wall are exact for squared cells. If other geometries (round, sinusoidal channel) are given, the derived values of CPSM and wall have to be understood as approximate values. Deviations do not matter since the calculation kernel of FIRE/ BOOST use the values of dhyd, OFA and GSA in any case. 3.1.2.2. Conservation Equations of Mass or Moles In general the balance of mass or moles is equivalent and therefore leads to the exact same results. Due to chemical reactions the number of moles in the system changes, but their overall mass remains constant. Therefore mass balances are often preferred. In a mole balance equation, the change of the total number of moles has to be taken into account by an additional correction term. A second reason to use mass balances is the fact that many physical properties such as enthalpies or caloric values of combustibles are given as a function of their mass. The molar mass which is necessary to transform mass specific values to mole specific data is not always completely accessible. 3.1.2.3. Volume Fraction, Density and Mass Fraction Catalytic converter models have to describe a system consisting of two different phases (gas and solid substrate) with two different volumes. The volume of the gas phase in this system is given by means of an overall volume fraction. This volume fraction of gas phase in the entire system is defined as follows: (9)
where g is the volume fraction of the phase g(as) in the entire volume V. The volume of the solid phase Vs is evaluated by Vs=(1- g)V = sV. Note, the fluid volume fraction g is identical to the open frontal area OFA. If one phase comprises several different species, a cumulative density consisting of the densities of all species can be defined. For this purpose the next relation is used: (10)
The density of the entire phase g is the sum of the densities of all different species k in it. In an additional step the mass fraction wk,g of one species in a system can be defined as the fraction of the density of the species k,g and the total density g (11)
The relation given by these two equations defines that the sum of all mass fractions always has to be equal to one.
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3. Theory 3.1.2.4. Equation of State and Ideal Gas Law If conservation equations for a gaseous phase are given, a general relation between the intensive variables of the gas is necessary. Pressures and temperatures observed during typical catalytic converter applications lie within moderate ranges (p<10bar, T<3000K). Thus, the ideal gas law is sufficient as equation of state in the present models. (12)
The mass density g is directly proportional to the pressure pg, the total molar mass Mg, and it is indirectly proportional to the temperature Tg and the ideal gas constant R. The molar mass is a function of the composition of the different species k in the considered phase: (13)
Mk,g represents the molar mass of the species k in the gas phase.
3.1.3. FIRE Balance Equations The modeling of the balance equation for the solid energy is presented in this section. These equations are solved in addition to all other transport equations (momentum, gas phase enthalpy, turbulence quantities, species transport ...) if the aftertreatment module is activated. 3.1.3.1. Solid Energy Balance Equation The following basic equation rules the anisotropic heat conduction within the solid part of the porous medium: (14)
where K is the anisotropic heat conduction matrix, kh is the gas-solid heat transfer coefficient, GSA the geometric surface area per unit volume, Tg and Ts the gas and solid temperature, Sr the chemical reaction source, V the cell volume, Vs the solid volume part of the cell and As the surface of the solid part of the cell. 3.1.3.1.1. Anisotropic Heat Conduction Matrix The presence of channels implies that the conduction does not have the same magnitude in cross-stream (radial) as in streamwise direction; in other words in the porous medium, the solid heat conduction is anisotropic. 3.1.3.1.1.1. Anisotropic Conduction Factor The default approach assumes that crosstream and streamwise solid thermal conductivity are linearly linked; i.e. they differ only from a so-called anisotropy factor. The matrix solid heat conduction K reads (15)
where is the conduction matrix in the genuine catalyst reference frame and Q and its inverse are transfer matrices from the genuine catalyst reference frame to the Cartesian reference frame. s is the physical solid thermal conductivity and G is the anisotropic conductivity factor. 10
FIRE BOOST Aftertreatment
3. Theory 3.1.3.1.1.2. Effective Thermal Conductivity including Radiation This approach intends to model the cross-stream thermal conductivity based on the heat transfer modes that in reality take place in the monolith: conduction and radiation. The following figure shows the heat transfer modes within a catalyst squared unit cell. The walls have a width and d is the hydraulic diameter. The length s is the unit cell width of the catalyst derived from the density number (cpsi) N as: . The heatflux exchanged between faces at temperature T1 and T2 can be written (16)
where L is the catalyst length and is the effective radial thermal conductivity. Figure 3. Heat Transfer within a Catalyst Squared Unit Cell
The heatflux is composed of the heat conduction within the wall along length s and width (flux QL, orange zone in the above figure), the conduction along length and width d (flux Qs1, green zone) and the radiation through the channel (flux Qs2, blue zone). Following composition of thermal resistance rules, the last two are treated in serial and are in parallel with the first one, i.e: (17)
In the above equation, the radiation term has been linearized and the term between parentheses is the effective thermal conductivity . This relation describes the heat exchange within a unit cell. If one assumes thermal equilibrium of all unit cells contained into a mesh cell, the relation extends to mesh cells as: (18)
where h is the distance between two mesh cell centers. Based on relation (4) one can build the anisotropic heat conduction matrix as follows: (19)
The model can be applied as it is on catalyst or particulate filters. No specific modeling is associated to the channel shapes.
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3. Theory 3.1.3.1.1.3. Solid Surfaces The diffusion fluxes must be computed along the solid surface of the cells As . For monoliths with a preferential flow direction (e.g. monoliths with channel shaped geometry: DPFs, catalysts) the solid surface vectors are calculated different than for catalytic blocks without any preferential flow direction (e.g. undirected porosities: packed beds). For the first case one can create the following assumption: If one considers a cell face A normal to the main catalyst direction, then is for the fluid and the complement for the solid. If one considers a face tangent to the main direction, all the surface is solid. The solid surface vectors are then computed by the general relation: (20)
where is the surface reduction matrix in the genuine catalyst reference frame. For the second case of catalytic blocks with undirected porosities, the surface reduction is uniform in all directions. Thus, the solid surface vectors are computed by the relation: (21)
3.1.3.1.2. Diffusion Terms Calculation The following formula is used to compute the diffusion fluxes on the cell face j. It is derived from the isotropic relation generally used in FIRE. (22)
The first term on the right-hand side determines the diffusion coefficient, while the second term is the cross-diffusion part and is added in the source terms. is the interpolated cell-face temperature gradient. dj is the distance between cell centers Pj and Pi. 3.1.3.1.3. Boundary Conditions As the walls are in contact with the solid part of the catalyst, the thermal wall boundary conditions are removed from the gas enthalpy equation and added to the solid temperature equation. The page [12] boundary fluxes are computed according to the boundary version of the relation (Eq.22 ). The local wall heat transfer coefficient is then proportional to the solid thermal conductivity and inversely proportional to the wall distance. Post-processing the solid heat transfer coefficient can be confusing as it can be very high due to the dependence on the wall distance. But it is physical. When reducing the wall distance the solid heat transfer coefficient increases but the wall to cell solid temperature difference decreases, giving a wall heat flux of same order. The interfaces between the catalyst and the gas are presumed adiabatic for the solid temperature. 3.1.3.2. Source Terms in the Gas Phase Balance Equations 3.1.3.2.1. Sources in the Enthalpy Conservation Equation The term Sr (W) accounts for heat sources due to catalytic chemical reactions. It is calculated using the species' reaction rates and the corresponding enthalpies of formation using the following formula: (23) 12
FIRE BOOST Aftertreatment
3. Theory
3
where is the reaction rate of species k (kmol/(m ·s)) and species k at 298 K.
is the formation enthalpy of
3.1.3.2.2. Sources in the Species Conservation Equations The following sources are added for each species k to the right-hand side of the corresponding species transport equation: (24) where
3
is the reaction rate of species k (kmol/(m ·s)).
3.1.4. BOOST Balance Equations, Single Channel Model Under the assumption that radial transport effects of a honeycomb-type catalytic converter are small compared to the heat transport in axial direction, the entire converter can be represented by one single channel. The physical situation of such a channel is sketched in the following figure. The effects taking place are convective, diffusive and conductive transport in the gas phase, mass and energy transfer through the boundary layer, diffusion and catalytic conversion in the wash-coat, and conduction in the solid phase. Neglecting radial gradients in the channel, transient and 1D (in axial direction) conservation equations suffice to describe the thermo- and fluid dynamics. Figure 4. Scheme of One Single Channel in a Honeycomb-type Catalytic Converter
The differential conservation equations for mass momentum and energy of a single channel can be written as shown in the following section. The continuity equation of the gas phase is (25)
where g is the density of the gas phase, t is the time, vg is the interstitial gas velocity and z is the spatial coordinate in axial direction. The momentum conservation equation is given by the steady-state Darcy equation (see Kaviani page [96] [26 ]) (26)
where pg is the pressure of the system. The Darcy constant AD can be described by: (27)
dhyd represents the hydraulic channel diameter and is a friction coefficient. The factor is called Fanning friction factor and takes into account deviations from round channel cross sections. It has values as summarized in the following table. The friction factor is typically described as a function of the Reynolds Number Re and changes depending on the flow regime (laminar, transition or turbulent): (28)
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3. Theory The bounds for the transition region from laminar to turbulent are set by Reynolds numbers of Relam = 2300 and Returb = 5000. In the turbulent region, turb is considered as a constant input value. In the laminar region lam is given by (29)
where a and b are input values. These two parameters are supplied with default values (a=64, b=-1) according to the Hagen-Poisseuille-Law for laminar tube flow. page [97] Table 3-1: Fanning Friction Factor (see VDI ,Lb7 [64 ] Channel Cross Section Round
1.00
Square
0.89
Equilateral Triangle
0.83
Sinusoidal (duct open height to open width ratio 0.425)
0.69
The species conservation equation is given by (30)
wk,g is the mass fraction of species k and Deff is an effective diffusion coefficient. Diffusion is usually small compared to convection but becomes important for small Peclet numbers of mass transfer. represents the molar reaction rate of the catalytic surface reactions with their stoichiometric coefficients vi,k. Homogeneous gas phase reactions are not considered, since their rates are negligible in the temperature range which is typical for automotive applications. Assuming that viscous dissipation can be neglected, the energy balance of the gas phase is written as (31)
where Tg is the gas temperature and h k the total enthalpy of the component k. Conductive heat transport in the gas phase is modeled by Fourier's law using the thermal conductivity g. This effect is usually small compared to convection but becomes important for small Peclet numbers of heat transfer. The third term on the right side takes into account the enthalpy transport due to species diffusion. kh is the heat transfer coefficient between the gas phase and the solid walls, and GSA represents the total channel surface area per unit of substrate volume. The heat of reaction of the catalytic surface reactions is represented by h i . This heat is released in the solid phase and convected into the gas phase. Thus, the heat of reaction that is implicitly taken into account by the combined solution of the gas species and energy conservation equations has to be deducted from the gas phase (minus sign before the last term) and subsequently added to the solid phase energy balance equation. 14
FIRE BOOST Aftertreatment
3. Theory The solid phase energy balance equation is given by (32)
where Ts is the temperature of the catalyst wall, s is its thermal conductivity, and considers a general radial heat transport between radially distributed channels as they are defined by the page [15] Discrete Channel Method (see Section Total and Diffusive Velocity ). The heat loss to the surrounding is captured with . There are two different models available: 1. a simplified heat loss model as described in section Boundary Conditions page [19], where the heat loss of the overall canning and insulation is lumped into a 0D model. 2. In the second modeling approach a 1D model for the multi-layered wall is set-up according page [65] to section Multi-Layered Wall Model . Thermal radiation is not taken into account in the energy conservation equation due to the low temperature range, as it is given by 'standard' operation conditions. Thus, radiation does not significantly affect the exit conversion and ignition/extinction bounds. Due to the chemical reactions occurring on the surface of a catalyst, the concentrations of the species directly above the catalytic surface are not equal to the concentration of species in the bulk. This effect is accounted for by solving additional balance equations for the individual species concentrations at the solid surface. Therefore it is possible to take into account for the two cases of chemical and mass transfer limitation. Under the assumption of quasi steady-state conditions, the rates of the catalytic surface reactions balance the diffusive transport from the bulk gas to the surface. Thus, the molar surface L concentration (c k of the component j can be evaluated using (33)
B
where ck,g is the molar concentration of species k in the bulk gas, and kk,m is the mass transfer coefficient of the individual species. The amount of a certain species stored on the surface is represented by a surface fraction . The conservation of this species on the surface is accounted for by the following equation, (34)
where the product ( ·GSA) of the site density and the geometrical reaction surface GSA is a measure for the entire storage capacity. The right hand side of the equations represents a general reaction term depending on the applied storage model. 3.1.4.1. Total and Diffusive Velocity In systems where the fluid flow is modeled, the velocity of the system and of different species in it is an important property. In the current model, the following definition is chosen. One species moves with its proper velocity vk in one direction of the space domain. The mean velocity (see Bird et al. [6
page [95]
]) of all the species or the entire continuum is given by the following equation: (35)
The mean velocity vg is the sum of all species velocities vk,g multiplied by their mass fraction wk,g. In that way, a mass specific mean velocity or 'mass-averaged velocity' is determined. The
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3. Theory difference between the velocity of the mass continuum and that of one single species is called D diffusive velocity vk . The mathematical relation is given by: (36) D
v k,g represents a general diffusive velocity that has to be quantified by additional diffusion models. In the presented model Fick's first law of diffusion is used (see Taylor and Krishna [62 page [97] ]). This decision was made due to the fact that in typical catalytic converter applications, convective fluxes have more influence than diffusive. Thus, errors in the modeling of diffusion have only minor importance and simplified models are sufficient. Fick's law states that the D diffusive velocity vk of a component k of concentration wk,g, across a surface of unit area, is proportional to the concentration differential multiplied by a system constant Dk, and is expressed by: (37)
The system constant Dk,g is called diffusion coefficient of the species k. 3.1.4.2. Enthalpy and Heat Capacity If a considered phase consists of different species, the mass-specific enthalpy hg of the entire phase can be described as the weighted sum of all the enthalpies hk,g of the different species k: (38)
The heat capacity of the entire gas is defined as partial derivative of the total enthalpy with respect to temperature assuming constant composition and pressure (39)
and the species heat capacity is given by (40)
page [95]
Assuming ideal gas mixtures (see Barin [4 ]) the species enthalpy hk,g also can be defined as the partial derivative of the total enthalpy with respect to the species mass fraction: (41)
3.1.4.3. Heat Conduction and Fourier's Law Fourier's law states that the area specific heat flow q through a homogeneous phase is directly proportional to the temperature difference along the path of heat flow multiplied by a system constant g. In order to comply with the second law of thermodynamics, the negative sign in the following equation is used. Heat only flows from higher to lower temperature: (42)
Where Specific heat flow Thermal conductivity 16
FIRE BOOST Aftertreatment
3. Theory Temperature 3.1.4.4. BOOST Multi-Channel Model and Discrete Channel Method (DCM) The Discrete-Channel-Method (DCM), developed in BOOST (see Wurzenberger and Peters page [97] page [97] [77 , 76 ]) describes the spatial distribution of the converter by locating several channels along each radial direction as sketched in the following figure. Figure 5. Setup of Four Radially Distributed Single Channels for 2D Catalyst Simulation
The thermal and fluid dynamic behavior of each channel in the above figure is represented by conservation equations for mass, momentum and energy as summarized in Section BOOST page [13] Balance Equations, Single Channel Model . Hence, the solution of these differential balance equations describes the catalytic converter locally very accurately. This can be understood as solution at fine scale of the individual channel. The distribution of the temperature (Ts) in the radial directions of an entire catalytic converter as the coarse scale is assumed to depend on the heat flux through the web walls as shown in Fig. 6 page [17] . Figure 6. Radial Heat Transfer in a Catalytic Converter
The comparison of the heat conductivity of the wall material ( s) and the gaseous phase ( g), respectively, shows that the transport of heat in radial direction through gas and ring walls is negligible. On this coarse scale, therefore, the converter can be treated as a homogeneous reactor with locally dependent heat sources. These heat sources are determined by the catalytic conversion reactions as described by the single channel model and the fine scale. An analytical investigation of such radial heat conduction reaction problems, as given by (43)
delivers a shape function for radial temperature profiles: (44)
The radial distribution of the solid temperature Ts(r) is determined by a polynomial function of the order M that corresponds to the number of single channels models considered. The polynomial page [17] coefficients am are determined by solving Eq.44 with the known temperatures given at each single channel. Once the radial temperature profile is known, the heat fluxes at arbitrary positions can be estimated by applying the gradient of this spatial temperature distribution. The fluxes entering and leaving each channel in radial directions complete the energy balance and thus, couple the channels. This makes it possible to take into account the spatial behavior of a
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3. Theory converter through a spatial distribution of temperatures. The benefit of using the above sketched page [17] shape function (Eq.44 ) is computational efficiency. By using an analytically derived shape function within the numerical solution procedure, the solution of the radial temperature profile is a priori 'pushed' into the right direction and therefore only very few radial grid points (i.e. single channel simulations) are required to get converged results. 3.1.4.5. Thermodynamic and Transport Properties Thermodynamic and transport properties are required for the simulation of catalytic converters page [10] and the solution of all model equations summarized in Section FIRE Balance Equations . In the present model all physical properties of the fluid change with the temperature, pressure and composition of the gas. The following table briefly summarizes how properties are calculated and on which reference they are based. For more detailed information see the cited references and basic literature of fluid mechanics. Table 3-2: Physical Properties and Calculation Approach Species
Unit
Reference
Molecular weight
(kmol/kg)
tabulated from literature
Specific heat/ Enthalpy/ Entropy
(kJ/(kg·K))
Polynomial fits from Barin [4
page [95]
Thermal conductivity
(W/(m·K))
Polynomial fits from VDI [64 page [97] Reid et al. [60 ]
page [97]
Viscosity
(Pa·s)
Polynomial fits from VDI [64 page [97] Reid et al. [60 ]
page [97]
Diffusion coefficients
(m /s)
2
]
], and
], and
page [95]
Binary acc. to Fuller et al. [15 ], page [97] mixture acc. to Perry et al. [56 ] (Wilke Method)
The properties given above are internally stored by BOOST for a list of 34 species, as given in the following table. A detailed description of how the fluid properties are treated by FIRE is given in the Species Transport Manual. Table 3-3: Gas Species of Internal Database Species C2H2
C5H12
H2
NO3
C2H4
C6H10
H2O
O
C2H6
C6H14
HCl
O2
C3H4
C6H6
N
OH
C3H6
CH3OH
N2
SO
C3H8
CH4
N2O
SO2
C4H10
CO
NH3
SO3
C4H6
CO2
NO
C4H8
H
NO2
3.1.4.6. Initial and Boundary Conditions page [10] The equations given in Section FIRE Balance Equations and Section Total and Diffusive page [15] Velocity represent a set of coupled partial differential equations with independent 18
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3. Theory variables time (t), axial position (z) and radial position (r). In order to solve the entire system, initial and boundary conditions have to be defined. 3.1.4.6.1. Boundary Conditions The boundary conditions at the catalyst inlet/outlet in axial directions have to be defined by the user. For the solution of the continuity and momentum balance equations, the model is set up in a way that at one side (inlet) a mass flux has to be defined and at the other side (outlet) a pressure has to be given. If the direction of the flow should change, negative mass fluxes can be applied. The restriction here is that the simulated pressure drop over the entire catalyst is not bigger than the pressure at the outlet. Inlet-temperatures and species mass fractions have to be given for the solution of the energy and species balance equations. At the outlet either an adiabatic back flow option can be chosen or also outlet temperatures and species mass fraction can be set. For the solution of the solid energy balance adiabatic conditions were chosen at the inlet and outlet of the converter. In radial direction adiabatic boundaries can be chosen or 'heat loss conditions' have to be defined. Figure 7. Radial Heat Loss to the Ambient
The overall heat transfer in radial direction, as sketched in the above figure, is evaluated considering transfer through an insulation material, a shell and a boundary layer. Therefore the following correlation is applied for overall heat flux given in Watt: (45)
Where Overall heat flux Solid temperature at the border (in 1D simulation this radial dependency is not required) Overall heat loss coefficient Diameter of the monolith Environment temperature The overall heat loss coefficient
, is defined by: (46)
Where
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19
3. Theory Thermal conductivity of the material Thermal conductivity of the shel Material position Shell position Heat transfer coefficient between the outer surface of the shell and environment 3.1.4.6.2. Initial Conditions In the present catalytic converter model all initial conditions are derived from the inlet boundary conditions and set automatically. Thus, if constant boundary conditions of temperatures or species mass fractions are given, these values are used in order to initialize the entire spatial domain of the converter. If the boundary conditions change as a function of time, the value corresponding to the start of integration time is used for the initialization. The initial temperature of the solid is assumed to be identical to the one of the gas phase. The initial pressure and velocity field is evaluated using the inlet mass flux, the outlet pressure and the pressure drop of the entire converter.
3.1.5. Washcoat Layer Pore Diffusion 3.1.5.1. Pore Diffusion Model page [6] page [6] Fig. 1 in section Principle of Heterogeneous Catalytic Reactions describes the principle of the heterogeneous catalytic reactions. Most catalysts are porous materials where the chemical reactions take place in a certain catalytically active layer, the washcoat. Other catalysts consist of extruded ceramics where the whole porous material is catalytically active. The noble metals responsible for the catalytic reactions are distributed in the porous reactive material, and the reactants must diffuse into it. As an example, the following figure shows a catalyst coated page [95] with three different washcoat layers. According to Hayes et al. [21 ], mass transfer of the reactants takes place from the bulk gas onto the solid surface across the boundary layer. Via pore diffusion the reactants are further transported through and into the washcoat layers where the adsorption of the reactants, the chemical reactions and the desorption of the products take place. Further diffusion causes the transport of the products back to the solid surface, and the mass transfer through the boundary layer transports the products back to the bulk gas phase. Figure 8. Square Cell Catalyst with Washcoat Layers
BOOST/FIRE offers two different approaches to model heterogeneous reactions. In the standard model approach, the pore diffusion through the washcoat layer(s) is neglected. This assumption is valid for unlimited diffusion, where pore diffusion is so fast that every reactant and every product is uniformly distributed over the whole washcoat layer. This is the reason why the chemical reaction rate of any reaction i can be related to the catalytic surface area in [kmol/ 2 (s·m _cat)]. By multiplication with the geometrical surface area GSA, the reaction rate 20
FIRE BOOST Aftertreatment
3. Theory 3
page [15]
is related to the catalyst volume in [kmol/(s·m _cat)], as solved in Eq.32 . In the advanced model approach, pore diffusion is taken into account. Therefore, every washcoat layer is discretized in the direction perpendicular to the catalyst solid surface (y-direction). The following assumptions are made: • Uniform temperature Ts over the whole washcoat layer in y-direction. • Diffusion of the species through the washcoat layer in y-direction is the only transport mechanism, convective transport is neglected. • Diffusive transport in axial direction (z-direction) is not accounted for. • No species diffusion in the monolith, since the ceramic substrate is assumed to be catalytically inert. • Transport of the species from the bulk gas to the solid surface (y=0) across the boundary layer is modeled via a Sherwood number based on mass transfer correlation. The balance equation for species k, solved for every computational cell and obtained from the washcoat layer discretization over all layers, is described by (47)
L
where wcl is the porosity (gas void fraction) of the considered washcoat layer. is the density L of the gas mixture in the washcoat layer cell, and w k is the mass fraction of species k. The left hand side describes the transient change of mass of species k in the washcoat layer. The second term on the right hand side is the species source/sink through chemical reactions, where M k is the molecular weight of species k, i,k is the stoichiometric coefficient of species k in reaction i, 3 and is the reaction rate per unit volume washcoat [kmol/(s·m _wcl)]. The first term on the right hand side is the diffusive transport of the species. The transport model, as described in section page [21] Transport Models , is used to determine the effective diffusion coefficient Dk,eff. The boundary condition at the solid surface (y=0) is determined by the balance of diffusive flux and mass transfer through the boundary layer from the bulk gas to the solid surface and vice versa, as described by (48)
B
kk,m is the mass transfer coefficient of the individual species k, is the bulk gas density, and w B is the mass fraction of the species in the bulk gas. The second boundary condition at the total k washcoat layer thickness (y= wcl,tot) is simply described by (49)
leading to no diffusive flux out of the last washcoat layer. The total or entire washcoat layer thickness wcl,tot is the sum of the individual layer thicknesses wcl,ilay, as described by (50)
3.1.5.2. Transport Models In a simplifying way the porous structure of a catalyst washcoat can be seen as complex network of individual channels of different diameters, lengths and shapes. Diffusive transport in such systems can be described by the general Fick's law where the applied diffusion coefficients need to be appropriately chosen. The pure gas phase diffusion coefficients do no longer apply in small pores with diameters in range of the mean free path of the diffusing molecules. Here
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21
3. Theory diffusion is not dominated by fluid-fluid collisions but it changes to fluid-solid collision driven diffusion where – according to kinetic gas theory – the 'Knudsen' diffusion takes place, Froment page [95] and Bischoff [14 ]. As discussed by the same authors, models for effective pore diffusion coefficients in porous systems are widely spread in the literature. They reach from simple models incorporating solely the porosity and tortuosity of solid the structure to complex descriptions of the pore-network including multi-component diffusion considerations as used in the dusty gas page [96] model applied by Khinast [29 ]. 3.1.5.2.1. Effective Pore Diffusion Model A simple approach to take into account the hindered molecular movement in the porous medium is described by the effective pore diffusion model. The interaction of the gas molecules with the solid walls result in a higher diffusion resistance and longer diffusion paths. The tortuosity wcl describes the locally averaged ratio of actual diffusion length to direct diffusion length. Thus, the effective diffusion coefficient Dk,eff of the species is smaller than the free gas diffusion coefficient Dk,g of species k, as described by the equation (51)
In the numerical implementation for two-component mixtures Dk,g is the binary diffusion coefficient, and for multi-component mixtures Dk,g is calculated according to Wilke's approach (see Froment and Bischoff [14 other species
page [95]
]) assuming diffusion of species k through the stagnant
3.1.5.2.2. Parallel Pore Model An often cited model for the effective diffusion coefficient in porous structures is the parallel pore page [97] model (PPM) described by Wheeler [73 ]. The model composes the transport effects of the pure gas phase and Knudsen diffusion assuming both transport effects taking place in parallel. With this, the effective diffusion coefficient is defined as (52)
where DKn is the Knudsen diffusion coefficient depending on pore diameter dpor, molar mass M of the considered species and temperature Ts, as described by the equation (53)
3.1.5.2.3. Random Pore Model A more complex approach to describe an effective diffusion coefficient is given by the random page [97] pore model (RPM) developed by Wakao and Smith [66 ]. Assuming that the washcoat features two distinct characteristic pore size diameters, called macro- and micro-pores, the approach of the PPM is first applied to both pores sizes individually. In a second step, the two macro and micro pore diffusion coefficients, DM and , are combined applying probabilistic and geometrical considerations. This leads to an effective diffusion coefficient according to the equations (54)
22
FIRE BOOST Aftertreatment
3. Theory
3.1.5.3. Reference for Chemistry Data This topic describes why and how reaction mechanisms formulated with respect to converter surface are to be converted to washcoat volume. Conversion of reaction rates from converter surface based to washcoat volume based page [77] The reaction rates in the available Kinetic Models for catalytic conversions are formulated with respect to the inner surface area of a converter in units of the other hand, the reaction rate
in Eq.47
page [21]
. On
is related to the washcoat layer volume and
has units of . Consequently, the converter surface based reaction rates need to be converted from converter surface based to washcoat volume based units. This conversion is done by multiplying the converter surface based reaction rates with the specific reactive surface area per unit volume of washcoat, in units of : (55) This conversion is valid, but for any calibrated reaction mechanism related to converter surface its application in a different catalyst model (variation of converter type and/or washcoat thickness) using the WCL model does not correctly predict the conversion behavior. In order to resolve this issue either all kinetic parameters would have to be transformed to washcoat layer volume, which would be a huge effort, or a complete new set of kinetic parameters would be necessary for the WCL model, which would make the comparison with the surface reaction model very difficult. Hence a characteristic number - the reference washcoat layer volume - may be introduced with which the conversion of converter surface based reaction rates shall be simplified. The reference washcoat layer volume The reference washcoat layer volume is used to convert reaction rates and a particular set of kinetic parameters considering the reference converter whose conversion behavior is characterized by this parameter set. It is denoted by and shall be defined as the ratio of washcoat volume to total monolith volume of the reference converter. can be interpreted as a reciprocal measure of the noble metal density in the washcoat layer volume. By taking into account some geometrical transformations, the reference washcoat layer volume for layer ilay can be calculated with (56)
2
where CPSM is the cell density per square meter calculated with CPSM = CPSI / (0.0254) . The reference washcoat layer volume is used to scale the geometric surface area of a converter to account for the reference converter's washcoat volume: (57)
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3. Theory Tip: The reference washcoat layer volume determines the reference washcoat layer volume (thickness) for which the kinetic parameters are valid. If one uses the same kinetic parameter set, but varies the washcoat layer thicknesses and consequently the washcoat layer volumes, one has to have the same value of to obtain reasonable conversion rates. Example An example shall demonstrate the effect of the reference washcoat layer volume in different page [24] layer configurations. Fig. 9 shows three catalysts A, B, and C with different washcoat layer coatings. Only the species conversion in the coating called Diesel Oxidation Catalyst (DOC) is considered. Unlimited diffusion is assumed and the same set of kinetic reaction parameters page [23] of the DOC is applied for all three catalysts. Eq.55 is solved for all species and the conversion of species k, e.g. C3H6 is compared. In coating INERT present in catalyst C only diffusion takes place (no chemical reactions). Figure 9. Example for catalytic conversion in three different washcoat layers
The three samples have the following geometrical parameters: Parameter
To characterize the conversion of the three samples the following two cases shall be highlighted: 1. The absolute amount of noble metals is the same in all samples: When assuming that the absolute amount of noble metals is the same in catalyst A, B and C it can be expected that the conversion of C3H6 is the same for all three samples. The reference washcoat layer volumes for the three samples are:
24
FIRE BOOST Aftertreatment
3. Theory
Comparing the overall reaction rate in the DOC layer one finds that all samples lead to the same C3H6 conversion:
The same result would have been achieved if the reaction rate wouldn't have been converted using the reference washcoat layer volume of the related reference converter:
2. The noble metal density is the same in all samples: In the case of having the same noble metal density in the DOC coating of catalyst A, B and C, the C3H6 conversion of catalyst A and C will be the same, whereas it will be twice as large for catalyst B. As the noble metal density is the same in all catalysts, the reference washcoat layer volume for the three samples is the same, namely the one from catalyst A:
Comparing the overall reaction rate in the DOC layer one finds that the expectation is met when using the proper reference washcoat layer volume:
The reason for this behavior can be found in the way how the kinetic parameters related to the catalyst surface are transferred into the rates of reactions which take place in a certain washcoat layer volume. The kinetic parameters contain the information of how many noble metals are located within the washcoat layer. Using the same parameter set and calculating the specific
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25
3. Theory page [23]
reference volume for both catalysts, A and B, with Eq.56 , means that the same amount of noble metals is distributed for catalyst A in volume and for catalyst B in volume 2· . Although the washcoat layer volume of catalyst B is twice as big as that of catalyst B, the noble metal density is only half. Thus for comparison of washcoat layer coatings of varying thickness with the same set of kinetic parameters, it is indispensable to use the same value of the specific reference washcoat volume. Related Information Where can I find the reference washcoat layer volume of a catalyst?
3.1.6. General Chemical Reaction Rate Calculation According to Coltrin et al. [12
page [95]
] a chemical reaction can be written in the general form (58)
th
where are stoichiometric coefficients and is the chemical symbol for the k species. K is the total number of species (gas phase and stored) in the system, I is the total number of chemical reactions considered. The stoichiometric coefficient of species k in reaction i is defined as: (59) The rate of production of species k is: (60)
The reaction rate rates:
of reaction i is defined by the difference of forward and backward reaction (61)
, and are the exponents of concentration of the gas phase species in reaction i. For elementary reactions these exponents are equal to the stoichiometric coefficients: (62)
The definition of ck,g depends on the phase the species is part of. For gas phase species ideal gas is assumed. (63)
For stored species the following definition is used: (64)
The forward reaction rate constant dependence:
is defined by the following Arrhenius temperature (65)
26
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3. Theory
For irreversible reactions the backward rate constant is zero by definition. For reversible reactions, the backward reaction rate is evaluated with the forward reaction rate and the equilibrium constants as: (66)
page [95]
is the equilibrium constant in concentration units for reaction i. Coltrin et al. [12 ] notes that in some cases there are experimental data that indicate the Arrhenius expression for the reaction rate constant is modified by the coverage (concentration) of some surface species, as described by: (67)
, , and are the three coverage parameters for the surface site species k and the reaction i. The -term enhances the Arrhenius expression so that the pre-exponential factor A and the activation energy E can be written as: (68)
In general, the equilibrium constant formation:
is obtained from the standard state Gibbs free energy of (69)
where (70)
(71)
Finally
is obtained from
via: (72)
For the cases where no stored species are considered the second term in this equation becomes '1'.
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3. Theory 3.1.6.1. Sticking Coefficients For some simple surface reactions, the rate of the reaction can be calculated via the 'sticking coefficient' formulation. The sticking coefficient expresses the probability that adsorption of the molecule on the surface takes place (sticking) when a collision occurs. The sticking coefficient form of the rate equation is allowed for the simple case of a surface reaction in which there is exactly one gas phase reactant species. The sticking coefficient is calculated via the following expression: (73)
The three parameters A i , b i , E i are the Arrhenius parameters, but in this case A i and b i are dimensionless and E i is in (kJ/(kmol·K)). In order to convert the rate constants given in sticking coefficient formulation to the kinetic rate constants the following equation is used: (74)
where Mk,g is the molecular weight of the reaction gas phase species, tot is the total surface site concentration and m is the sum of all the stoichiometric coefficients of reactants that are surface page [26] species. The rate of progress is calculated using Eq.61 .
3.1.7. Transfer Coefficients The FIRE/BOOST Aftertreatment Module calculates the transfer coefficients for mass ( j) and heat ( ) inside the catalytic monoliths based on empirical relations for Nusselt and Sherwood numbers. Generally the following functional relations apply (75)
where Re is the Reynolds number, Pr is the Prandtl number, and Sc is the Schmidt number. For channel shaped monoliths dhyd represents the hydraulic channel diameter and l is the channel length. For granulated materials (undirected porosities) dhyd represents the characteristic pore length, e.g. the solid particle diameter while l is meaningless in that case. The transport coefficients for heat kh and species mass kk,m finally result from (76)
where, g is thermal conductivity of the gas mixture and Dk,g is the diffusion coefficient of species k in the gas mixture. 3.1.7.1. Transfer Coefficients for Directed Porosities For laminar flow in circular catalyst channels, literature offers a plethora of functional relationships to calculate the actual Nusselt and Sherwood numbers as a function of catalyst length and operating conditions. Most of them are based on the definition of the dimensionless Graetz numbers for heat and mass transfer: (77) 28
FIRE BOOST Aftertreatment
3. Theory
3.1.7.1.1. Sieder/Tate page [97] FIRE/BOOST suggests the Sieder/Tate relationship (see Perry[56 ]) as a default: (78)
In addition to the Sieder/Tate approach, FIRE offers additions to the Nusselt/Sherwood relations. 3.1.7.1.2. Hausen page [97] The more general Hausen equation (Perry [56 ]) is described by (79)
3.1.7.1.3. Hawthorn page [95] The Hawthorn's equation which is suggested by more recent papers (i.e. Ahn et al. [1 ]) is described by: (80)
3.1.7.1.4. Martin model page [97] VDI [64] (Chapter Gb) suggests for the heat transfer of a hydraulic and thermal page [96] developing flow in a pipe a correlation from Martin. Kirchner and Eigenberger [30] extend this correlation also to describe the mass transfer between the gas phase and the solid wall surface. The approaches are given by: (81)
3.1.7.1.5. Constant and User Defined Transfer Coefficients In addition to these, FIRE/BOOST offer the possibility to set constant values for kh and kk,m. The FIRE user can also define his own correlation by using the user subroutine use_cattra.f. The BOOST user can define his own correlation by using the user subroutine cat_dimless_numbers.f90.
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29
3. Theory 3.1.7.2. Transfer Coefficients for Undirected Porosities FIRE offers the possibility to simulate the reactive flow through undirected porosities like packed beds or granulated materials. These materials are represented by undirected porosities with arbitrary flow direction through the pores. The following models for the heat and mass transfer coefficients are available: 3.1.7.2.1. VDI Packed Bed The transfer coefficient in a packed bed increases within the first particle layers and approaches a final value rapidly. The heat transfer coefficient in packed beds consisting of spheres of uniform size is much higher than that of a single sphere. The reason for this is the production of swirl when the fluid flows through the interstices between the spheres. page [95] As described in the book for Baehr and Stephan [2] , the averaged Nusselt number in the packed bed is proportional to the Nusselt number of a single sphere Nusph: (82) The shape factor
depends on the fluid volume fraction
g
according to equation (83)
page [30]
Eq.82 can be also applied for packed beds consisting of non-spherical particles. In page [97] VDI [64] (Chapter Gh) one can found a list for the shape factors of different particle geometries: Table 3-4: Shape Factor of Packed Beds Particle
valid for
Cylinder length L, diameter d
1.6
0.24 < L/d < 1.2
Cube
1.6
0.6
Raschig ring
2.1
Pr = 0.7, Sc = 0.6
page [95]
According to Baehr and Stephan [2] page [30] required for Eq.82 is calculated by
Pr, Sc
1300
the Nusselt number for a single sphere Nusph (84)
The Reynolds number Re is calculated with the equivalent particle diameter dP and the interstitial velocity vg, as described by (85)
For non-spherical particles, dP is defined as the diameter of a sphere with the same surface area as the particle. If the specific surface area GSA and the number of particles per unit volume nP are known, dP is simple determined by (86)
30
FIRE BOOST Aftertreatment
3. Theory The Sherwood number for the mass transfer coefficient is calculated by applying the analogy of heat and mass transfer by replacing Nusselt with Sherwood number as well as Prandtl with Schmidt number. The Sherwood number of the packed bed is proportional to the Sherwood number of the single sphere, as described by (87) The Sherwood number of the single sphere
can be calculated by (88)
3.1.7.2.2. Constant and User Defined Transfer Coefficients FIRE offers the possibility to set constant values for kh and kk,m. Furthermore, the FIRE user can also define his own correlation by using the user subroutine use_cattra.f.
As previously mentioned in section Transfer Coefficients for Undirected Porosities FIRE offers the possibility to simulate the reactive flow through undirected porosities. This model – also called Reactive Porosity – can be used to simulate devices such as coated wiremesh mixers or catalysts where gas can flow, to some extent, in a radial direction. In such devices the interaction with urea-water liquid sprays can be complex and requires models more detailed than a simple stop of Lagrangian particles at porosity inlet. The spray - reactive porosity interaction model is composed of three submodels: • The collision submodel checks the probability of collision between the Lagrangian particles and the solid part of the porous medium. • The interaction submodel, when a collision occurs, considers the type of interaction performed (deviation, splashing, deposition, …) • The enhancement of evaporation and thermolysis in the porous medium and the redistribution of evaporation energy sources to the solid part of the medium. A user function cyuse_rpor.f has been added allowing self-modeling of spray-porosity submodels. 3.1.8.1. The Collision Submodel The modeling of the collision of a Lagrangian particle with the solid part of porous medium page [97] follows the lines of the O'Rourke particle collision model [55 ]. More details about this model can be found in the Spray Manual. The porous surface is assimilated to a sphere of diameter where GSA is the geometrical surface area of the porosity and V the volume of the cell where the droplet is located. The collision frequency between the wall and a droplet of diameter is then evaluated as: (89)
where is the droplet velocity. During a time step , the spray particle motion is calculated within a subcycling loop, each iteration of this loop being associated with a specific parcel time step . Following O'Rourke, one assumes that the probability that n collisions occur between the droplet and the porous medium follows a Poisson distribution (90)
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3. Theory
Thus the probability of no collision is where c is a calculation parameter. A random number R is then computed to decide whether a collision takes place or not. • If 0 R P0 then no collision is calculated. • If R > P0 then the spray-porosity interaction submodel is applied. The higher the parameter c is, the closer to zero is P0 and therefore the more probable is the collision. 3.1.8.2. The Interaction Submodel Once a collision between a particle and the porous medium is assessed, the interaction is treated page [96] following the lines of the Kuhnke 46 wall-interaction model (especially developed for the interaction of urea-water mixture, see the Spray Manual). The Kuhnke model considers four alternative treatments of the interaction depending on the values of two parameters (as shown in the following figure): (91)
Where We is the Weber number and La the Laplace number. Figure 10. Regime Map for Spray-Wall Interaction According to Kuhnke
In the porous medium, the role of Twall is played by the solid temperature Ts. One cannot use the wallfilm model within the reactive porosity because the liquid film must be generated on the wall boundary faces of the mesh while the porous domain is essentially composed of internal faces and cells. Therefore the modeling of deposition is not easy. In a first approximation, the regimes lying below the adimensioned temperature T* - which include deposition - are neglected and we assume that a particle undergoes only rebound or thermal breakup. In the case of thermal breakup, one assumes that the whole mass of the incident particles goes into the secondary droplets. One then uses the Kuhnke correlations to estimate the mass, diameter and velocity of these droplets. Mass conservation is ensured by adapting the number of droplets in parcel in the secondary droplets. The number ns of secondary droplets per collision is a calculation parameter. The angle of the collision is calculated randomly by a Gaussian law assuming the normalto-the-wall collision is the most probable (top of the Gaussian curve). This angle is used for the determination of several characteristics of the rebound/secondary droplets. However, the direction of the droplet extracted from this estimation is not directly used because the probability to obtain droplets moving back to the inlet would be too high and this is not realistic. Instead a transformation is performed, imposing that the direction of the droplet(s) after collision is oriented with a maximum angle max from the gas direction. The max angle is reached when normal collision is selected from the Gaussian law (a in the following figure). On the other hand the angle is zero when a tangential collision occurs (b in the following figure). This generates a cone of possible directions with the gas direction as the centerline and the angle selected randomly from the Gaussian law. Furthermore the direction of the rebound/secondary droplets orthogonal to the gas direction is calculated randomly. 32
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3. Theory Figure 11. Droplet Direction after Collision in Porous Medium
left: angles calculated from Gaussian law, right: angles used in the interaction submodel 3.1.8.3. Enhancement of Evaporation & Energy Redistribution In some devices that can be modeled via the reactive porosity approach - such as wiremesh mixers - the spray evaporation is enhanced compared to the evaporation level in free gas flow. In FIRE the spray model includes evaporation and thermolysis enhancement parameters which act on reactive porosity regions and can be modified by the user. Using these evaporation enhancement parameters can lead to a rapid decrease of gas temperature and consequently to a quite limited thermolysis of urea. In order to reduce this side effect, one takes into consideration the idea that the energy used to evaporate the liquid might come partly from the solid and partly from the gas. The spray energy source added to the gas enthalpy ( ) equation is calculated as follows: (92) The first term on the right hand side is the enthalpy source associated to the gain of vapor mass. Its numerical discretization is implicit. The second term Senerg is the enthalpy source exchanged between the liquid and gas phases, including the heat exchange due to the difference of temperature between liquid and gas, and to the latent heat of evaporation. The numerical treatment is explicit. The redistribution of the source term to gas and solid enthalpy equations reads: (93)
where is the porosity (gas volume fraction) and e is a tuning parameter. The function f is continuous with regards to both and e. For example, for =0 (full solid) the function is zero and all energy required for the evaporation is extracted from the solid and vice versa for =1 (full gas). For e =0, the function equals 1 and all energy is extracted from the gas. For high values of e, the function tends to zero. Note that this treatment influences only the sources terms of the gas and solid enthalpy equations. The spray evaporation routine, which makes use of the gas enthalpy and gas temperature and modifies them locally, is not changed with respect to the use of solid enthalpy.
3.1.9. Nomenclature Units a
Constant in the laminar friction approach
(-)
ai
Arrhenius parameter
(variable)
am
Polynomial coefficient of radial temperature shape function (variable)
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3. Theory A
Temperature Dependency Factor
(-)
Ai
Pre-exponential factor of the rate constant of reaction i
(variable)
AD
Darcy Constant
(kg/(m ·s))
AS
Surface of the solid part in a computation cell
(m )
2 2
3
Awcl,spec Specific reactive surface area per unit volume washcoat
(m _cat/m _wcl)
b
Constant in the laminar friction approach
(-)
bi
Temperature exponent in the rate constant of reaction i
(-)
ci
Arrhenius parameter
(kJ/kmol)
Concentrations of species k in the reactive surface layer
(kmol/m )
ck,g
Concentration of species k in the gas phase
(kmol/m )
cp,k
Specific heat at constant pressure of species k in the gas phase
(kJ/(kmol·K))
cp
Specific heat at constant pressure of the entire gas phase
(kJ/(kmol·K))
cp,s
Specific heat of the solid phase
(kJ/(kg·K))
CPSI
Number of channels per square inch
(1/in )
CPSM
Number of channels per square meter
(1/m )
d
Diameter
(m)
dmat
Diameter of the insulation mat
(m)
dmon
Diameter of the monolith
(m)
dP
Solid particle diameter
(m)
dshell
Diameter of the shell
(m)
Dk,g
Diffusion coefficient of species k in gas mixture
(m /s)
Deff
Effective mean diffusion coefficient
(m /s)
dd
Droplet diameter
(m)
dp
Equivalent diameter of solid part in the porous medium
(m)
Ei
Activation energy of the rate constant of reaction i
(kJ/kmol)
Shape factor for packed beds
(-)
Fo
Forward reaction order
(-)
G
Anisotropic heat conduction factor
(-)
GSA
Geometrical surface area (=reactive surface area) of the catalyst
(m /m )
Gzmass
Graetz number for mass transfer
(-)
GSA
Geometry surface area of the catalyst (=atrans)
(m /m )
hg
Enthalpy of the entire gas phase
(kJ/kmol)
hk,g
Enthalpy of species k in the gas phase
(kJ/kmol)
ck
34
3
L
3 3
2
2
2 2
FIRE BOOST Aftertreatment
2
3
2
3
3. Theory Hf,k
Heat of formation of the species k
(kJ/kmol)
Hk
Enthalpy of species k in the gas phase
(kJ/kmol)
hi
Heat of reaction i
(kJ/kmol)
Hi
Enthalpy of reaction i
(kJ/kmol)
kh
Heat transfer coefficient
(W/(m ·K))
kk,m
Mass transfer coefficient of species k
(m/s)
kf i
Forward rate constant of reaction i
(variable)
kr i
Backward rate constant of reaction i
(variable)
kout
Heat transfer coefficient to the environment
(W/(m ·K))
K
K-number (adimensioned)
(-)
K
Anisotropic heat conduction matrix
(W/(m·K))
Kci
Equilibrium constant in concentration units for reaction i
(variable)
Kpi
Equilibrium constant in pressure units for reaction i
(variable)
l
Channel, monolith length
(m)
La
Laplace number
(-)
m
Sum of all stoichiometric coefficients
(-)
Evaporated liquid mass
(kg)
Mg
Molar mass of the entire gas phase
(kg/kmol)
Mk,g
Molar mass of the species k in the gas phase
(kg/kmol)
n
Normal Vector to the surface cell
(-)
ns
Number of secondary droplets after collision
(-)
nP
Particle number density
(1/m )
N
Cell density
(1/in ), (1/cm )
Nu
Nusselt Number
(-)
OFA
Open frontal area of the catalyst (=fluid volume fraction
pg
Pressure
(Pa)
P0
Probability of no collision
(-)
Pn
Probability that n collisions occur
(-)
Pr
Prandtl number
(-)
Rate of progress of reaction i
(kmol/(m ·s))
Heat flux
(W/(m ·K))
Rotation matrix
(-)
Radial heat loss flux
(W/m)
m
Q
2
2
3
2
g)
3
2
3
(m /m )
2
2
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3. Theory r
Radial coordinate
(m)
General reaction source term
(kmol/(m ·s))
Reaction rate of reaction i per catalyst surface
(kmol/(m _cat·s))
Reaction rate of reaction i per washcoat unit volume
(kmol/(m _wcl·s))
Reaction rate of reaction i per catalyst unit volume
(kmol/(m _cat·s))
Reaction rate of species k
(kmol/(m ·s))
R
Radius of the monolith
(m)
R
Universal gas constant
(kJ/(kmol·K))
Re
Reynolds number
(-)
Ro
Backward reaction order
(-)
s
Monolith repeat thickness
(m)
S
Surface of the solid part of a computational cell
(m )
Sg
Gas enthalpy source term (from spray evaporation)
(W)
Ss
Solid enthalpy source term (from spray evaporation)
(W)
Senerg
Spray enthalpy loss due to evaporation
(W)
Sk
Entropy of species k
(kJ/(kmol·K))
Sr
Energy source term
(W)
Sw,k
Mass source term of the species k
(kg)
Sc
Schmidt number
(-)
Sh
Sherwood number
(-)
Entropy of reaction i
(kJ/kmol)
Time
(s)
Droplet calculation time step
(s)
Tenv
Environment temperature
(K)
Tg
Gas temperature
(K)
Ts
Solid temperature
(K)
Tsat
Saturation temperature
(K)
Twall
Wall temperature
(K)
T*
Adimensioned solid temperature
(-)
ud
Droplet velocity
(m/s)
vg
Mean mass weighed gas velocity
(m/s)
Si t td
36
3
2
3
3
3
2
FIRE BOOST Aftertreatment
3. Theory vk,g
Velocity of the species k in the gas phase
(m/s)
vk,g
Diffusive velocity of the species k in the gas phase
(m/s)
V
Volume of a computational cell
(m )
Vg
Volume of a computational cell (gaseous part)
(m )
Vs
Volume of a computational cell (solid part)
(m )
Specific reference volume of the washcoat layer
(m /m )
Specific volume of the washcoat layer (per catalyst unit volume)
(m /m )
We
Weber number
(-)
yk,g
Molar fraction of species k in the gas phase
(mol/mol)
z
Spatial coordinate in Cartesian coordinates
(m)
Length of a calculation cell
(m)
D
z
3 3 3 3
3
3
3
Greek Letters c
User-defined collision factor
(-)
e
User-defined energy redistribution factor
(-)
out
Heat transfer coefficient between shell and environment
(W/m )
Sticking coefficient of the reaction i
(-)
Total surface site concentration
(mol/m )
Monolith total wall thickness
(m)
wall
Monolith wall thickness
(m)
wcl
Washcoat layer thickness
(m)
g
Fluid volume fraction in catalyst (=open frontal area OFA) (m /m )
k
Surface coverage parameter of surface site species k
(-)
Solid volume fraction in catalyst
(m /m )
Porosity of the washcoat layer (void fraction)
(-)
Surface coverage parameter of surface site species k
(-)
Friction factor
(-)
Fanning friction factor
(-)
k
Symbol for the species k
(-)
mat
Thermal conductivity of the insulation mat
(W/(m·K))
g
Thermal conductivity of gas
(W/(m·K))
s
Thermal conductivity of solid
(W/(m·K))
tot
s wcl k
FIRE BOOST Aftertreatment
2
2
3
3
3
3
37
3. Theory Thermal conductivity of the shell
(W/(m·K))
Heat conduction matrix
(W/(m·K))
g
Viscosity
(Pa·s)
k
Surface coverage parameter of surface site species k
(-)
k,g
density of the species k in the gas-phase
(kg/m )
g
Density of the entire gas phase
(kg/m )
Solid density
(kg/m )
Collision frequency
(-)
Stoichiometric coefficient of species k in reaction i
(-)
Surface coverage fraction
(-)
Maximum deviation angle authorized within sprayporosity interaction
(deg)
Site density
(kmol/m )
Tortuosity of the washcoat layer
(-)
shell
s
i,k
max
wcl
3 3 3
2
Indices
38
ambient
Ambient
B
Bulk gas
cat
Catalyst
D
Darcy
D
Diffusion
eff
Effective
env
Environment
f
Forward
g
Gas
h
Heat
hyd
Hydraulic
i
Reaction index
I
Total number of reactions
ilay
Washcoat layer index
K
Total number of species
Kgas
Number of gas species
Kstor
Total number of stored species
L
Layer at the reactive surface
FIRE BOOST Aftertreatment
3. Theory lam
Laminar
Lay
Total number of washcoat layers
loss
Radial heat loss
m
Index of radially distributed channels and polynomial coefficients
mass
Mass
mat
Insulation mat
mon
Monolith
M
Total number of coefficients in polynomial fits
out
Outside
por
Pore
r
Reverse
rad
Radial
reac
Reaction
s
Solid substrate
shell
Shell
sph
Sphere
stor
Storage
tot
Total
trans
Transfer
turb
Turbulent
wall
Wall
wcl
Washcoat layer
3.2. Particulate Filter Model Availability BOOST AT: Particulate Filter
page [224]
FIRE: Particulate Filter Specification
page [144]
3.2.1. Introduction Modeling and numerical simulation of diesel particulate filters (DPF) has been performed for page [96] many years. Konstandopoulos et al. [39 ] presented an overview of the state-of-the-art and progress in diesel particulate filter simulation. The models reach from simple analytically solvable page [96] page [97] pressure drop correlation (e.g. Konstandopoulos et al., [41 ]; Ogyu et al., [52 ]) over a broad variety of 1D filter flow and regeneration models to 3D models considering one page [96] representative pair of filter channels with CFD methods (e.g. Konstandopoulos et al. [43 ]; page [95] Guo and Zhang, [18 ]). Focusing on 1D models in literature, one can roughly distinguish between different approaches describing the DPF flow and different concepts to capture the page [95] effect of soot regeneration. Bissett [9 ] presented a steady-state and isothermal flow
FIRE BOOST Aftertreatment
39
3. Theory model assuming that the thickness of the soot layer is small compared to the channel width. page [96] page [96] Koltsakis and Stamatelos [31 ] or Konstandopoulos et al. [38 ] chose the same page [97] simplification in their publications. Mohammed et al. [51 ] applied a model from Huynh page [96] page [97] et al. [24 ] considering the impact of depth and cake filtration (see Opris [54 ]) page [95] regimes on the pressure drop during transient loading phases. Gaiser and Mucha [16 ] investigated the influence of ash and different ash distributions on the filter pressure drop. A regeneration model considering bare trap, and catalytically supported regeneration mechanisms page [96] page [96] was applied by Konstandopoulos et al. [38 ]. Millet et al. [49 ] presented a soot page oxidation mechanism taking into account the impact of fuel additive. Haralampous et al. [19 [95] ] extended a soot regeneration approach by catalytic conversion reactions as they take place in the wall of coated filters. The Particulate Filter (PF) model implemented in BOOST/FIRE combines in one overall solution the most detailed and pragmatic approaches for filter flow, soot filtration and regeneration proposed by several different research groups in the literature. In addition, the model offers extended approaches to take into account the influence of ash and asymmetric channel structures.
3.2.2. Overall Modeling Concept The geometrical situation for a squared cell PF given by a pair of inlet and outlet channels loaded with soot and ash is sketched in the following figure. The inlet channel is plugged at the end of the filter and the outlet channel is plugged at the inlet. BOOST/FIRE can handle many different inlet channel geometries, e.g. squared, hexagonal, octagonal, n-gonal, rectangular, etc. shaped channels. For the squared cell PF in the following figure, the diameters of the inlet channel and outlet channel are given by d1 and d2, respectively. Figure 12. Pair of PF Channels
As shown in the sketch, soot is split into two distinct layers – a depth filtration and a cake filtration layer – and therefore the model distinguishes between soot located within the porous filter wall and soot forming a cake above it. With the introduction of distinct depth and cake layer balance equations the regeneration behavior of coated filters can additionally be modeled in a more precise way. An increased soot combustion rate can be simulated in the depth filtration layer by applying catalytically supported regeneration mechanisms. As soon as the amount of soot in the depth layer is smaller than the maximum load, two different approaches can be chosen. Either soot from the cake layer slides down and therefore also converts catalytically, or the cake layer remains and cavities develop until the entire depth layer is converted. The second approach typically shows smaller overall conversion rates since only the amount of soot in the depth layers is exposed to the faster catalytic reaction scheme. 40
FIRE BOOST Aftertreatment
3. Theory Ash, which may be present in aged filters, is treated in the model as ash plug at the end of the inlet channel, as ash cake layer over the entire length of the filter, or as combination of both. The presence of an ash layer increases the overall pressure drop as there is additional flow resistance and a reduced free frontal surface in the inlet channel. In models where soot needs to be described by a depth and cake filtration layer, the ash layer can be understood as barrier between the two soot layers. Thus, soot cannot be deposited in the depth filtration layer as soon as an ash layer is present. The existence of an ash plug leads to a reduced effective filtration length and therefore to an increased pressure drop. The effective filtration length is also reduced by the length of the inlet and outlet plugs. Compared to the entire length, these two lengths are typically negligible. In order to provide a most generic model, they are included in BOOST/FIRE. Assuming that radial gradients (within the channels and the entire monolith) are of minor importance, a transient 1D model in axial direction z is sufficient to describe the entire thermo and fluid dynamics. A comparison of the time scales given by the entire filter system, in particular by the flow velocities and by the growth of the soot layer, reveals that the gas phase processes can be assumed as quasi-steady. Thus, the present model distinguishes between two sub-models for: • filter flow • soot deposition/ regeneration The two sub-models, discussed in the following, are also treated separately in their numerical solution procedures. The individual solutions are updated on a given time step basis and coupled page [57] with the help of a lumped filter model (see Section Modeling Glueing Zones in SIC PFs ). 3.2.2.1. Cell Structures of Particulate Filters The Honeycomb-type cell structure of particulate filters consist of hundreds (thousands) of individual channels. The most common PF types have squared inlet and outlet channels, as shown in the following figure. There, the numbers of inlet and outlet channels are identical and the geometry is defined by the channel diameters d1 and d2, respectively. In the case of filters composed of individual segments, like the SiC filter, the growth of ash/soot behaves differently depending on the location of the considered inlet channel. Inlet channels directly adjacent to the cement stripes have either three or, if they are located in the corners, two active filtration walls. Consequently, the PF model should be able to consider the impact of the different channel geometries on loading and regeneration. Figure 13. PF Structure made of Single Segments
The PF model of BOOST/FIRE can handle many different channel geometries. While the channel shape of the outlet channels guiding the gas out of the PF is of minor importance, the channel shape of the inlet channels is significant, since it determines the formation and structure of the soot and ash layers. Thus, for the correct calculation of the soot and ash heights, a detailed specification of the inlet channel geometry is necessary. For the calculation of the outlet channel flow velocity, the heat transfer and the outlet channel pressure drop, it is enough to specify the outlet channel cross-section and the outlet channel perimeter. The general PF approach of BOOST/FIRE can handle any inlet channel geometry which can be reproduced by multiple reflection of a general quadrilateral (see the following figure), here called General Symmetry Element (GSE). The GSE is the geometrical base of all PF channel geometries in BOOST/FIRE. The following figure shows the GSE and the unity cell for a PF with octagonal inlet channels. The unity cell determines the smallest repetitive element for reflection to represent the PF geometry consisting of inlet and outlet channels.
FIRE BOOST Aftertreatment
41
3. Theory In the present example the unity cell is defined by a square and contains a single outlet channel and a single inlet channel (four times one fourth of an inlet channel). The general symmetry element of the octagonal inlet channel is drawn on the right hand side in the following figure. It is defined by the center corner angle + , the right corner angle , the left corner angle , and the side lengths on the wall, l1 and l2. The octagonal inlet channel requires eight GSEs to obtain the specified geometry. Thus, the number of general symmetry elements per inlet channel nC is eight. Figure 14. Unity Cell and General Symmetry Element in a PF with Octagonal Inlet Channels
Another example for hexagonal inlet and outlet channels is shown in the following figure. The unity cell is an equilateral hexagon containing a single outlet and two inlet channels. The inlet channel with the side lengths, a and b, is produced by reflecting the GSE six times. PFs with page [95] hexagonal channel shape are further discussed by Becker et al. [5 ]. Figure 15. Unity Cell and General Symmetry Element in a Hexahex PF
By variation of the specification parameters of the general symmetry element, one can obtain many different inlet channel geometries, e.g. squared, hexagonal, octagonal, n-gonal, rectangular, etc. The following figure shows the soot and ash layers in an arbitrary general symmetry element where sc and ac represent soot cake and ash heights respectively. sd represents the soot height in the depth filtration layer. The free perimeter of the empty inlet channel is defined by the equation (94) and the cross-section of the inlet channel is defined by the cross-section of the single general symmetry element AGSE and the number of GSE per inlet channel nC, as described by (95) To consider the case where not the entire side length is available for filtration, the reduced side lengths and are applied. They can be expressed as fraction of the actual side lengths, as described by (96)
where Feff,1 and Feff,2 are filtration efficiency factors. These factors are model parameters and allow to take into account the reduced soot and ash deposition along channel walls which are not located adjacent to an outlet channel. For example, since in the inlet channel of the Hexahex PF, depicted in the previous figure, is located adjacent to another inlet channel, it can be expected that only a fraction of its side length is used for filtration.
42
FIRE BOOST Aftertreatment
3. Theory Figure 16. Soot and Ash Layers in the General Symmetry Element
The next two figures show the general symmetry elements together with the soot and ash layers for selected types of inlet channels. The following figure demonstrates that the three different channel types in segmented PFs leading to four, three, and two active filtration walls can be applied by adequate specifications of the GSEs. Figure 17. General Symmetry Elements of PF Inlet Channels with 4 (left), 3 (middle), and 2 (right) Filtra
The following figure shows the GSEs for two different hexagonal and for one octagonal inlet channel. Figure 18. General Symmetry Elements of Hexagonal PF inlet Channels a-b-a-b-a-b (left), a-a-b-b-a-a (m
The following table gives an overview of the different channel geometries and their specification parameters, which can be specified by the GSE approach in the PF model of BOOST/FIRE. Table 4-1: GSE Parameters for Different Inlet Channel Geometry Types Nr.
Inlet channel geometry type
nc
l1
1
Square (a a a a)
4
90
o
90
o
90
o
2
Rectangular (a b a b)
4
90
o
90
o
90
o
3
Hexagonal (Hexahex) (a b a b a b)
6
60
o
90
o
90
o
FIRE BOOST Aftertreatment
l2
43
3. Theory a
90
o
60
o
90
o
45
o
90
o
90
o
90
o
67.5
4
Hexagonal Hex3 (a a b a a b)
4
5
Octagonal, alternating (a b a b a b a b)
8
6
Octagonal, double side (a a b b a a b b)
4
7
N-gonal, equilateral (a a . . . . . a)
N
90
o
90
o
8
N-gonal, alternating a b (a b a . . . . b)
N
90
o
90
o
9
Square, 2 sided (a a)
1
a
10
Square, 3 sided (a a a)
2
a
11
Rectangular, 2 sided (a b)
1
a
12
Rectangular, 3 sided (a b a)
2
a
a
b
a
b
o
67.5
o
90
o
90
o
90
o
90
o
90
o
90
o
90
o
90
o
90
o
90
o
90
o
90
o
Based on the inlet channel geometry, given by the general symmetry element, the PF solver of BOOST/FIRE determines the free channel cross-section. Furthermore, for a given ash mass distribution overlain with a soot mass distribution (varying during the loading and regeneration process), the heights of the soot and ash layers are calculated. The layer heights strongly influence the transition velocity of the exhaust gas through the filter wall and consequently the pressure drop of the PF as well as the progress of the regeneration. 3.2.2.2. Main Geometry Parameters of Particulate Filters The cell density of a PF is defined by the CPSI number indicating the total number of Channels Per Square Inch. One can distinguish between the cell density of the inlet channels CPSIinl and the cell density of the outlet channels CPSIout, where the sum has to satisfy the equation (97) The cell density per square meter CPSM is defined by (98)
In general a unity cell contains Iinl inlet channels and Iout outlet channels. Consequently the CPSM numbers of the inlet and outlet channels are determined by the equations (99)
and (100)
44
FIRE BOOST Aftertreatment
3. Theory
page [44]
By replacing CPSM with CPSI, Eq.99 and Eq.100 densities per square inch, CPSIinl and CPSIout. The cross-section of the unity cell can be calculated by
page [44]
can be also applied for the cell
(101)
The open frontal area of all inlet channels is determined by (102)
and the open frontal area of the outlet channels is given by (103)
The total open frontal area is obtained from the sum of OFAInl and OFAOut, as described by (104) The heat transfer between solid and gas as well as the wall flow are mainly influenced by the overall geometrical surface area (GSA) of the PF. For the determination of the GSA the perimeters of both, the inlet and outlet channels are considered. The GSA of all inlet channels is described by (105)
and the GSA of the outlet channels is given by (106)
The total geometrical surface area is obtained by the sum of the individual GSAs for inlet and outlet, GSAInl and GSAOut, as described by (107)
3.2.2.3. Squared Cell Channels Symmetric or asymmetric square-shaped channels represent the most common geometry in particulate filters. This section discusses the geometry parameters of the selected channel shape. Other inlet channel geometries, e.g. hexagonal or octagonal have to be treated analogously. As sketched in the following figure, two different channel diameters are required to describe asymmetric channel structures. In addition, although it is not commonly used for particulate filters, a washcoat thickness is considered in the set of equations given below.
FIRE BOOST Aftertreatment
45
3. Theory Figure 19. Squared Cell PF with Asymmetric Cell Structure
As shown, the total thickness of the monolith's wall
is given by (108)
where w is the thickness of the substrate wall and wc is the thickness of the washcoat. The repeat distance s for structures with different channel diameters is given by (109) and determines the side length of the unity cell. d1 and d2 represent the diameters of the inlet and outlet channel, respectively. The cross section of the unity cell simply equals (110) and the perimeters of the inlet and outlet channels are described by (111)
The numbers of inlet and outlet channels per unity cell, Iinl and Iout, are two, respectively. By page [44] page [45] page [46] combining Eq.99 , Eq.101 and Eq.110 , one obtains the correlation between the cell density and the cell distance s by the equation (112)
With the help of the channel diameter ratio (113)
the hydraulic diameter of both channels can be evaluated using (114)
With the calculated hydraulic diameters BOOST/FIRE further evaluates the open frontal area (OFA) and the geometric surface area (GSA) with respect to the inlet channel, with respect to the page [45] page [45] outlet channel and with respect to both channels. Based on Eq.102 , Eq.103 and page [45] Eq.104 the open frontal areas are described by (115)
46
FIRE BOOST Aftertreatment
3. Theory
and the geometrical surface areas, based on Eq.105 can be calculated by the equations
page [45]
, Eq.106
page [45]
and Eq.107
page [45]
(116)
The OFA considering both channel diameters defines the solid fraction of the filter that is used in the energy balance equations. The GSA is used to specify the heat transfer between the gas and solid phase. 3.2.2.4. Soot and Ash Layer Geometries of Squared Channels This section describes the layer geometries leading to correlations for the soot and ash heights of the squared channels. The correlations for other inlet channel geometries, e.g. hexagonal or octagonal, are derived in an analogous manner. page [48] The solution of the filter wall flow model (see Section Filter Flow Model ) and soot/ash deposition and regeneration model (see Section Deposition and Regeneration of Soot and page [52] Ash ) requires a correlation between the soot/ash loading (mass per filter volume) and the height of the soot depth layer, ash and soot cake. These values depend, beside the above mentioned geometrical issues, on the number of active filtration walls per inlet channel. For PFs made out of cordierite the value of active filtration walls per inlet channel is normally four. If SiC PFs are considered, this value depends on the position related to the glueing stripes (e.g. page [41] cement) which connect the single segments. As shown in Fig. 13 , inlet channels which are directly adjacent to the cement stripes have either three or, if they are located in the corners, two active filtration walls. Inlet channels which are not in close vicinity to the glueing stripes have four filtration walls. Simple geometrical considerations are applied to calculate the heights of the soot depth, ash and soot cake layer considering these geometrical constraints. The height of the soot in the depth filtration layer of a channel with 4 filtration walls is given by (117)
where msd is the soot loading in the depth layer, Afront represents the frontal surface of the filter. n1 is the number of inlet channels (four, three, or two), sd is the packing density of the soot in the depth layer, nfw is the number of active filtration walls and d1 represents the diameter of the inlet channel. The soot packing density in the depth layer is derived from the maximum depth filtration loading and the corresponding depth layer thickness. Thus, this density should to be viewed as a scaling factor rather than as a real physical density value. page [50] Assuming that the cake layers of soot and ash form a trapezoidal shape (see Fig. 20 ), the soot cake height for an inlet channel is given by (118)
FIRE BOOST Aftertreatment
47
3. Theory
where msc is the soot cake loading, and sc represents the packing density of the cake. mac,layer is the local ash loading deposited in the ash layer and ac represents the packing density of the ash cake. The geometrical factors Fnfw,1 and Fnfw,2 depend on the number of active filtration walls in the inlet channel. Fnfw,1 is 1 for four filtration walls, 1.5 for three filtration walls and 2 for two filtration walls. The corresponding values for Fnfw,2 are 1, 2 and 4 respectively. The height of the ash layer ac required in this equation can be further derived from (119)
The amount of ash in the layer is calculated by the total amount of ash, mac, and a layer-plugdistribution factor lpd. This factor is defined by (120)
The amount of ash in the plug is consequently given by (121) With the known ash load in the plug, the length of the plug lash-plug is calculated. It is (122)
where VPF is the volume of the entire filter and OFAinl represents the open frontal area evaluated page [46] with respect to the inlet channel diameter (see Eq.115 ). The calculated ash plug length page [40] together with any specified length of inlet/outlet plugs (see Fig. 12 ) is also used in order to derive the effective filtration length in the PF.
3.2.3. Filter Flow Model page [40]
As sketched in Fig. 12 , the entire filter can be split into several flow regions. These are regions for the inlet/outlet flow, regions for the channel flow neighboring plugs and the region for the effective filtration flow. The first two regions are described by algebraic corrections page [51] summarized in Section Overall Pressure Drop and Pressure Drop Contributions . The latter is described by 1D steady-state balance equations of continuity and momentum for a representative pair of inlet and outlet channels. 3.2.3.1. 1D Continuity and Momentum Balance 3.2.3.1.1. General Conservation Equations The steady-state continuity equations of the gas phase in the inlet and outlet channel is (123)
(124)
where g,n is the density of the gas phase and vg,n is the gas velocity in the inlet (n=1) and outlet (n=2) channel, respectively. z is the spatial coordinate in axial direction. 48
FIRE BOOST Aftertreatment
3. Theory AF,n represents the free channel cross section that is available for the gas flow. This cross section is constant in the outlet channel but changes in the inlet channel depending on the local height of the ash and soot cakes. It is essential to have AF,1 inside the spatial derivative. Soot loadings up to 20 g/l lead to significant reductions of the free inlet channel cross-section (see page [96] Millet et al. [49 ]) and therefore the complete neglect of the cake height may lead to oversimplified models. PS,n is the wet perimeter of the free channel cross section of the nth channel. This value is constant in the outlet channel but also changes in the inlet channel as a function of the cake height. vw,n represents the wall velocity lateral to the axial direction. The difference between the wall velocity of inlet vw,1 and of the outlet channel vw,2 at the same axial position can be derived by continuity considerations as discussed later in this section. The steady-state momentum balance equations of the gas phase in the pair of channels is given by (125)
(126)
where g,n represents the pressure in the inlet and outlet channel, respectively. The frictional pressure loss along the channels is approached as a linear function of the local channel velocity page [49] scaled by a friction coefficient Fn and the dynamic viscosity . The last term of Eq.125 describes a momentum sink due to mass sinks in the inlet channel. The term can be understood as additional contribution to the channel friction and therefore is often dropped in literature. Nevertheless, omitting this term in inviscid flows (F1 1) leads to an increase of the stagnation pressure over the filter length, and therefore breaks the second law of thermodynamics. 3.2.3.1.2. Squared Channel Structure Under the assumption of a squared cell structure, the free channel cross section and the wet perimeter of the two channels are derived from geometrical considerations according to (127)
(128) (129) (130) dn is the diameter of the individual channels. sc and ac represent the heights of the soot and ash cake and Fnfw,A, Fnfw,B and Fnfw,C are again geometrical factors, which distinguish between inlet channels with four, three and two active filtration walls. The corresponding values for a channel with four, three or two active filtration walls are 4, 3 and 2 for Fnfw,A , 8, 4, and 2 for Fnfw,B and 4, 2 and 1 for Fnfw,C, respectively. page [43] page [43] For non-squared channel geometries (see Fig. 17 and Fig. 18 ), the required geometrical parameters, AF,1, AF,2, PS,1, and PS,2, are determined in an analogous manner. 3.2.3.2. Wall Flow and Wall Pressure Drop The inlet and outlet channels are connected by the porous wall through which the gas passes, whereupon the filtered soot builds a depth filtration and cake layer. This porous media flow is described by Darcy's law assuming that the pressure drop is a linear function of the local
FIRE BOOST Aftertreatment
49
3. Theory flow velocity. For squared channels, the cake (ash or soot) builds a trapezoidal shape, as sketched in the following figure. Deviations from this cake geometry, given especially in the corners of non-squared channels, are lumped into the trapezoidal shape. This approximation seems reasonable since the cake grows over the entire internal surface area of the inlet channel page [97] (compare experimental investigations from Ogyu et al., [52 ]). This issue is also addressed page [96] in more detail by Konstandopoulos et al. [39 ], who concluded that the flow follows the path with the lowest resistance which is not necessarily the smallest geometrical distance between the inlet and outlet channel. Figure 20. Soot and Ash Cake
Assuming that changes of the gas density are negligible over the cake height, a continuity consideration leads to the flow velocity expressed by (131)
where x describes the coordinate from top of the cake down to the wall. The wall velocity entering the outlet channel is one solution of the previous equation where additionally changing gas densities in the inlet and outlet channel are taken into account (132)
The total 'wall pressure drop' is the sum of individual pressure drops given by the wall, a soot depth filtration layer, an ash cake layer and a soot cake layer. The application of Darcy's law over the different layers with their individual flow velocities leads to (133)
where kw, ksd, kac and ksc represent the permeability of the wall, the soot depth layer, the ash cake and soot cake layer, respectively. Assuming that the depth filtration height is small compared to the entire wall thickness, the latter is held constant in the applied pressure drop correlation. Soot Permeability page When setting the soot permeability to "Formula" in the GUI, ksc is calculated according to [41 [96] ]: 50
FIRE BOOST Aftertreatment
3. Theory (134)
where f( ) is the Kuwabara function, is the porosity, dprimary is the primary particle diameter, SCF is the Stokes-Cunningham Factor, Kn the Knudsen number and the gas mean free path. is evaluated using the following equation: (135)
where
g
is the kinematic viscosity of the exhaust gas, and MW is the molecular weight.
3.2.3.3. Overall Pressure Drop and Pressure Drop Contributions page [48] page [50] The set of flow model equations (Eq.123 to Eq.133 ) can be solved together with the following four boundary conditions (136) (137) (138) (139) where the inlet velocity and filter back pressure are assumed to be known. The geometrical situation leads to the boundary conditions of the velocities in the inlet and outlet channel. The inlet velocity at the end of the inlet channel, and the outlet velocity at the beginning of the outlet page [48] page [50] channel is zero. The solution of Eq.123 to Eq.133 leads to the spatial distribution of the velocities, pressures in the inlet and outlet channels (vg,1(z), vg,2(z), p g,1(z), pg,2(z)), and of the wall velocity vw(z). The pressure drop over the entire effective filtration length is one solution of the calculated pressure profiles. It is given by (140) where p g,1 (z = 0) is the inlet channel pressure at the inlet and p g,2 (z = leff)is the outlet channel pressure at the end of the effective filter length. This pressure drop can be further split into its individual contributions. Therefore, the different pressure drops over the wall, soot depth layer, ash, and soot cake (see page [50] Eq.133 ) are simply evaluated as mean values over the effective filter length. The viscous pressure drop of the inlet and outlet channel is given by (141)
(142)
FIRE BOOST Aftertreatment
51
3. Theory where the pressure differences from one position z in the filter to inlet and outlet, respectively, are evaluated and averaged over the entire effective filter length. Outside the effective filtration length there are two regions where pure channel flow can be assumed. This is the entrance region in the inlet channel adjacent to the inlet channel plug and the rear region in the outlet channel neighboring the outlet and ash plug. Assuming laminar flow, the pressure drops for both regions are given by (143)
(144)
where is a general channel shape factor. For squared channels is typically 0.89, for hexagonal channels 0.95, and for octagonal channels 0.98. is the length of the inlet and outlet plug and represents the length of the ash plug. At the inlet and outlet of the filter, changing cross sections lead to contraction and expansion effects of the flow. In order to describe additional pressure losses caused by the flow acceleration and slowdown, two correlations are considered in the present model. These are (145)
(146)
where the given dynamic pressure is scaled by a general friction loss coefficient . The total pressure drop over the entire filter is simply the sum of the individual pressure losses page [51] page [52] given by Eq.140 to Eq.145 . The pressure drops given by the plug regions are typically small compared to the proper filter pressure drop. The inlet and outlet pressure losses, on the contrary, have a decisive impact on higher mass flows because of their quadratic velocity dependency.
3.2.4. Deposition and Regeneration of Soot and Ash The following figure shows a zoom on the different soot, ash and wall layers as they are used and understood in the present soot deposition and regeneration approach. The model considers three reactive layers where soot regeneration and catalytic reactions can take place. These are the soot cake, the soot depth layer and the wall itself. The ash layer is assumed to be inert with respect to chemical reactions and mass changes. It is reasonable to keep the ash mass constant (i.e. solve no dedicated ash balance equations) since no noticeable changes of the ash mass are expected within the time ranges given by soot loading and regeneration events. Figure 21. 1D Slice of Soot Cake, Ash Cake, Soot Depth Layer and Filter Wall
3.2.4.1. Soot Cake and Depth Layer Balance Equation Two distinct balance equations are applied to capture the transient changing soot mass in both the cake and depth layer. These are 52
FIRE BOOST Aftertreatment
3. Theory (147)
(148)
where msc(z) and msd(z) are the volume specific soot mass (soot loading with respect to the filter volume) in the cake and depth layer at each axial position of the filter, respectively. Rsd and Rsc describe general soot reaction source terms in the different layers. vw,dl(z) represents a page [53] dimensionless wall velocity (see Eq.149 ) at each axial position, and msoot,inl is the specific soot mass flow entering the filter. Ssd is a binary switch to steer soot deposition in the depth filtration layer. Soot deposition in the depth layer is switched off as soon as an ash or soot cake is present or the depth filtration capacity is reached. The binary switch Ssc controls the soot deposition in the cake layer. Soot deposition in the cake is switched on as soon as the depth filtration layer has reached its full capacity. The application of switches to steer the soot loading either in depth or cake layers needs to be understood as a coarse phenomenological approach. Under the assumption that all soot particulates follow the streamlines in the inlet channel, the wall velocity can be used as 'weighting function' in order to distribute the entire incoming soot mass over the effective filter length. Therefore a dimensionless wall velocity defined by (149)
is used in the present approach. The crucial characteristic of the new velocity is that its shape is similar to the original velocity and that its integral sum over the entire effective filter length is equal to one. With this approach it is possible to describe the effect that higher soot deposition rates are given at spatial locations with lower soot heights (i.e. lower pressure drops and higher wall velocities). 3.2.4.2. LLD Concept and Regeneration Reactions The soot regeneration and catalytic wall reaction schemes summarized in Section Filter page [90] page [92] Regeneration with Oxygen - Filter CSF Catalytic Reactions comprises soot combustion and catalytic conversion reactions to describe: • Bare trap regeneration with O2 • fuel additive regeneration • low temperature regeneration with NO2 • catalytically supported NO2 regeneration • CSF conversion of CO, C3H6, C3H8 and NO in the catalytic filter wall and in the outlet channel • CSF Selective Catalytic Reduction in the catalytic filter wall and in the outlet channel 3.2.4.2.1. Soot Regeneration and CSF Reactions in the filter wall The reaction schemes take place along the streamlines of gas flow passing through the soot cake layer, the soot depth layer and the wall. Provided that transport effects are negligible in directions other than those given by the wall velocity, a 1D isothermal steady-state fixed-bed page [52] model (direction x in Fig. 21 ) can be applied for small soot slices (Local Layers) given by an axial discretization. The advantage of this Local Layer Discretization is its computational performance and its flexible application to various types of reaction mechanisms taking place with different reaction layers. The balance equation for the gas phase continuity is given by (150)
FIRE BOOST Aftertreatment
53
3. Theory where vw is the wall velocity at each axial position, g is the gas density and x represents the spatial coordinate over the height of the soot cake, soot depth layer and filter wall. Mj is the molar mass of the species j and S denotes the total number of species. The stoichiometric coefficient of the species j in there action i is given by i,j that multiplies the molar reaction rate r i (yg,Ts) of the ith reaction. The total number of reactions is represented by R. Catalytic conversion without surface storage reactions have no impact on the global continuity of the gas phase. Reactions where solid soot or stored solid species are involved contribute to the continuity source. Thus, the right-hand side of page [53] Eq.150 directly equals to changes of the solid soot/stored solid species mass. The species conservation equation over the height of the soot cake, soot depth layer and wall is (151)
where wg,k represents the gas mass fraction of species k. The first term on the right side considers changes in the species composition due to all reactions involved. The second term on the right side (chain rule) is the spatial derivative of the gas density at constant species fractions. page [53] page [54] Eq.150 and Eq.151 represent an initial value problem that can be integrated from the top of the soot cake down to the bottom of the filter wall. The initial conditions at the topmost layer are given by (152) (153) assuming that the species gas composition does not change significantly over the length of the inlet channel. In low mass flow bare trap or fuel additive regeneration cases, where the assumption of a constant O2 concentration along the inlet channel is not valid due to O2 diffusion into the soot layer, a 1D isothermal steady-state model is applied for the inlet channel gas flow. Sinks for this model are the convective mass flow through the wall and a diffusive oxygen mass flow into the soot layer. The oxygen diffusion term, there, is proportional to an artificial diffusion coefficient and a concentration gradient which comes from the local oxygen concentration in the inlet channel and the corresponding concentration at the bottom of the soot layer, a result from the Local Layer model described above. This model approach represents an initial value problem that can be integrated over the particulate filter length giving an oxygen profile along the inlet channel as well as diffusive oxygen fluxes into local soot slices given by the axial discretization. These results are used as an input for the Local Layer regeneration model described above. page [53] page [54] The solution of the 1D fixed-bed model (Eq.150 to Eq.154 ) delivers overall soot reaction source terms for both the cake and the depth layer. Therefore the model is integrated (154)
(155)
over the individual heights of the two layers. The sources Rsc and Rsd are applied in the transient page [53] page [53] balance equations of two soot layers, Eq.147 and Eq.149 .
54
FIRE BOOST Aftertreatment
3. Theory 3.2.4.2.2. CSF Reactions in the PF Inlet and Outlet Channels While passing through the inlet and outlet channels, the exhaust gas comes into contact with the catalytic surface of the filter wall. As an example in particulate filters (PF), which are (zone) coated in the rear part, the unconverted gas which passes the filter wall in the front part comes into contact with the catalytic surface in the outlet channel rear part and reacts there. To describe the species conversion in the inlet and outlet channel, 1D isothermal steady-state models are applied. The discretization is given by the PF monolith discretization in axial direction. Below the conservation equation for the outlet channel is derived as representative example. The same applies to the inlet channel with one exception - the sign of the wall flow term, which is leaving the inlet channel. Figure 22. 1D Slice of the Outlet channel
The steady-state species conservation equation of the PF outlet channel is given by (156)
where j,g,2 is the density of the gas phase species j in the outlet channel and vg,2 is the gas velocity. z is the spatial coordinate in axial direction. AF,2 represents the free channel cross section that is available for the gas flow and PS,n is the wet perimeter of the free channel cross section of the outlet channel. j,g,w is the density of the gas phase species j at the bottom of the filter wall entering the outlet channel and vw,2 represents the corresponding wall velocity lateral to the axial direction. Mj is the molar mass of the species j and S notes the total number of species. The stoichiometric coefficient of the species j in the reaction i is given by i,j that multiplies the molar reaction rate r i (cj,g,L,Ts) of the ith reaction. Beside the temperature, the reaction rates depend on the species concentrations cj,g,L on the surface of the outlet channel filter wall. The total number of reactions is represented by R. Due to the chemical reactions occurring on the surface of the catalytic filter wall and due to the gas flow coming from the inlet channel passing through the filter wall, the concentrations cj,g,L of the species directly above the catalytic outlet channel surface are not equal to the concentration of species in the outlet channel bulk. This effect is accounted for by solving additional balance equations for the individual species concentrations at the outlet channel surface, taking into account the mass transfer limitation. Under the assumption of quasi steady-state conditions and neglecting the gas flow through the filter wall in a first step, the rates of the catalytic surface reactions balance the diffusive transport from the bulk gas to the surface. Thus, the molar surface concentration (cj,g,L of the component j can be evaluated using (157)
where cj,g,2 is the molar concentration of species j in the bulk gas, and kj,m,corr is a mass transfer coefficient of the individual species.
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55
3. Theory The impact of the gas flow passing through the filter wall on the species surface concentrations cj,g,L is considered in the calculation of the mass transfer coefficients kj,m,corr. These coefficients are evaluated with a Sherwood correlation and then corrected with a wall flow term (158) The equations above represent an initial value problem that can be integrated from the beginning of the outlet channel to the end. The initial conditions at the first layer are given by (159)
3.2.4.3. LLD Sources for Lumped Filter Model page [53] By integrating the LLD model of Section LLD Concept and Regeneration Reactions over page [52] the entire height of all layers (from x=0 to x=xwall in Fig. 21 and over the outlet channel), source terms for the continuity, species and energy balance equations can be derived. The overall source term of species j is given by (160)
This source term comprises the impact of reactions taking place within all different reaction layers (cake, depth, wall, outlet channel). The source term of the gas phase continuity equation is the sum of all species sources. It is given by (161)
page [54]
where this equation comprises the sum of the two soot sources from the depth (Eq.154 ) page [54] and cake (Eq.155 ) filtration layer as well as the sources from stored surface species. The enthalpy source term results to (162)
where hg,j represents the enthalpy of species j. The source terms summarized in this section are applied in the framework of transient nonisothermal, two-phase models solved by BOOST/FIRE in order to capture the transient behavior of loading and regeneration. More details on this integration are given in Section Modeling page [57] Glueing Zones in SIC PFs .
3.2.5. Soot Migration At elevated flow velocities and increased soot heights soot migration can cause redistribution of soot. Figure 23. Forces on Soot Particles
The interaction between flow and soot particles due to migration forces causes the particles, in particular those in the vicinity of the surface of the soot layer, to be transported along the 56
FIRE BOOST Aftertreatment
3. Theory channel. This leads to a redistribution of already deposited soot. Assuming the soot redistribution depends on the local soot height and the given inlet channel velocity, the impact of migration can be expressed by (163)
where cm is a general migration constant. The soot migration model does not apply on ash. The model is solved at each integration step after the solution of the PF flow (Section Filter Flow page [48] Model ) and solution of the soot deposition and regeneration (Section Deposition and page [52] Regeneration of Soot and Ash ) model.
3.2.6. Modeling a Partial Wall Flow Filter Removing plugs from the inlet face of a regular ceramic particle filter qualifies the substrate to be called a partial wall flow filter plugged at the rear. page [57] The functioning principle of such a rear-plugged particle filter is illustrated in Fig. 24 . Figure 24. Scheme of a rear plugged particulate filter
The exhaust gas is distributed in the inlet and outlet channels depending on the pressure resistance along the flow path. At the inlet of both filter channels the total pressures are the same. The pressure decreases along the length of the non filtering outlet channel to ambient at its exit. The flow model equations to describe the pressure drop and filtering behaviour of the partial page [48] page [50] wall flow filter are the same as for the full wall flow filter (Eq.123 to Eq.133 ). The boundary conditions are derived from the above mentioned assumption, that the total pressure at both filter inlet channels is the same: (164) (165) (166) The solution of the model equations leads to the spatial distribution of the velocities, pressures in the inlet and outlet channels (vg,1(z), vg,2(z), p g,1(z), pg,2(z)), and of the wall velocity vw(z). The pressure drop over the entire filter is given by the difference of the static pressure directly in front of the filter and the outlet channel pressure at the end of the effective filter length. This pressure drop can be further split into its individual contributions (see Overall Pressure Drop and page [51] Pressure Drop Contributions ).
3.2.7. Modeling Glueing Zones in SIC PFs SiC PFs are composed of segments connected together with glueing stripes (cement, see Fig. page [41] page [58] 13 and Fig. 25 ). In FIRE, two methods exist which allow modeling these glueing zones.
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57
3. Theory Figure 25. Modeling SIC PF Glueing Zones in FIRE
The basic model locates the glueing zones via face selections and works out a reduction of the heat conduction fluxes in the solid energy equation. The idea is to take into account the thermal resistance due to the presence of the cement. However, this approach does not model the thermal inertia of the glueing zones, which gives rise to strong temperature gradients on these locations. The advanced glueing zones model (called Glueing zones in the solver GUI) allows a full thermal, dynamical and chemical modeling of these regions. The cement is first included into the mesh (as shown in the following figure) and the calculation of the solid energy is extended there. However, the fluid dynamics and the chemistry are not. For the gas, the boundaries of the glueing zones behave like walls. It is a conjugate heat transfer approach. Furthermore, it is possible to take into account the reduced number of active filtration walls in channels directly adjacent to the cement. Either two or three active filtration walls are counted if page [41] the channels are located along the cement or in the corner (Fig. 13 ). The consequence is that during a soot loading phase, the soot mass stored into these channels is lower than in channels having four active walls. The chemical kinetics is also affected during the regeneration phase, as less active area is available. This model however is theoretically consistent only when the mesh size of the cells adjacent to the glueing zones is in the range of one inlet channel size. Figure 26. Modeling SiC PF Glueing Zones in FIRE - Mesh Detail
3.2.8. Particulate Filter Model Integration in FIRE and BOOST The models discussed in the previous section account for the variation of flow, soot layer height and pressure drop along one inlet and outlet channel with a high level of accuracy. Nevertheless, page [48] the models for the PF fluid flow (Section Filter Flow Model ) and for the soot regeneration page [52] (Section Deposition and Regeneration of Soot and Ash ) are setup one-dimensionally and steady-state. In order to perform multi-dimensional (FIRE) and transient (FIRE/BOOST) simulations, the PF specific models are coupled to existing solver structures given by FIRE and BOOST. Thus, in the context of the overall PF simulation, the PF channel flow and regeneration are understood as sub-models linked to FIRE/BOOST flow-solver as sketched in the following figure. In order to account for variations in all directions inside the particulate filter (heat losses 58
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3. Theory to the ambient, flow distribution, soot distribution ...) this model is coupled to FIRE. As sketched in the following figure, one row of cells (structured mesh) of the CFD mesh represents a portion of the filter. All inlet/outlet channels inside this row are assumed to have equal properties (soot loading, temperature, pressure, ...). Typically, one row of cells stands for 5 inlet/outlet channels (depending on the cell size). The applied numerical concept is an implicit/explicit coupling of the PF sub-models and 3D-CFD code FIRE and the 1D-code BOOST, respectively. By using this procedure the computational effort is reduced dramatically. The pressure drop, obtained from the solution of the 1D filter flow model for each row of cells (see below), is taken as a (stepwise constant) source term for the three-dimensional flow equations. Hence, the CFD solution is de-coupled from the local effects of deposition, regeneration or pressure drop in the filter and thus, improves the robustness of the solution process significantly. In BOOST, the results of the stepwise calculated PF sub-models are transferred to its catalytic converter model (see Section BOOST Balance Equations, Single page [13] Channel Model ) where all the required balance equations are solved. Figure 27. Integration Concept of the PF Submodel in the FIRE/BOOST Solver
From the basic solution concept sketched, a detailed simulation procedure can be derived as summarized in the following table. Table 4-2: Integrate PF Flow and Regeneration Solutions in BOOST/FIRE I) Solve 1D PF Flow Model for Each Row of Cells Input
Output
pressure and mass flow at the outlet
pressure drop for each row
temperature (solid) distribution
inlet channel velocity distribution
soot distribution
wall velocity distribution
II) Solve PF Reaction and Deposition Model for Each Cell Input
Output
actual soot distribution
local soot masses according to wall velocity distribution
actual temperature (solid) distribution
source terms for the continuity equation (mass of regenerated soot is added to gas phase)
actual wall velocity distribution
source terms for all species transport equations
actual mass flow in the corresponding row
source terms for the solid equation balance
stoichiometry and chemical kinetics III) Solve 1D Soot Layer Migration Equation for Each Row of Cells Input
Output
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59
3. Theory actual inlet channel velocity distribution
new soot distribution
actual soot distribution
Figure 28. 1D PF Flow Model in a 3D CFD Mesh
3.2.9. Nomenclature Latin Letters Units
60
2
AF,1
Free inlet channel cross section
(m )
AF,2
Free outlet channel cross section
(m )
Afront
Frontal surface of the filter
(m )
AGSE
Cross section of the general symmetry element
(m )
Ainl
Cross section of the single inlet channel
(m )
Aout
Cross section of the single outlet channel
(m )
Aunity
Unity cell cross section
(m )
a
Side length of the inlet channel wall
(m)
b
Side length of the inlet channel wall
(m)
cdr
Channel diameter ratio
(-)
cm
Migration constant
(-)
CPSIinl
Number of inlet channels per square inch
(in )
CPSIout
Number of outlet channels per square inch
(in )
CPSI
Total number of channels per square inch
(in )
CPSMinl
Number of inlet channels per square meter
(m )
CPSMout
Number of outlet channels per square meter
(m )
CPSM
Total number of channels per square meter
(m )
d1
Diameter of the inlet channel
(m)
d2
Diameter of the outlet channel
(m)
dprimary
Primary soot particle diameter
(m)
F1
Friction coefficient in the inlet channel
(-)
2 2 2 2 2 2
-2 -2 -2
-2 -2 -2
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3. Theory F2
Friction coefficient in the outlet channel
(-)
Feff,1
Filtration efficiency of l1
(-)
Feff,2
Filtration efficiency of l2
(-)
GSAinl
Geometry surface area for inlet channel
(m /m )
GSAout
Geometry surface area for outlet channel
(m /m )
GSA
Geometry surface area for both channels
(m /m )
Kn
Knudsen number
(-)
ksc
Permeability of the soot cake
(m )
ksd
Permeability of the soot depth layer
(m )
kw
Permeability of the wall
(m )
l1
First side length of the general symmetry element
(m)
Reduced first side length available for filtration
(m)
Second side length of the general symmetry element
(m)
Reduced second side length available for filtration
(m)
lash-plug
Length of the ash plug
(m)
leff
Effective filtration length
(m)
lplug
Length of the inlet/outlet plug
(m)
lpd
Ash layer-plug-distribution factor
(-)
mac
Overall ash loading
(kg/m )
mac,layer
Ash loading in the ash layer
(kg/m )
mac,plug
Ash loading in the plug
(kg/m )
msc
Soot loading in the cake layer
(kg/m )
msd
Soot loading in the depth layer
(kg/m )
msoot,inl
Specific soot inlet mass flow
(kg/m )
M
Molar Mass
(kg/kmol)
n1
Number of inlet channels in the filter
(-)
nC
Number of general symmetry elements per single inlet channel
(-)
OFAinl
Open frontal area for inlet channel
(m /m )
OFAout
Open frontal area for outlet channel
(m /m )
OFA
Open frontal area for both channels
(m /m )
Pinl
Perimeter of the empty inlet channel
(m)
Pout
Perimeter of the empty outlet channel
(m)
PS,1
Wet perimeter of the free inlet channel
(m)
l2
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2
3
2
3
2
3
2 2 2
3 3 3 3 3 3
3
3
3
3
3
3
61
3. Theory PS,2
Wet perimeter of the outlet channel
(m)
pg,1
Pressure in the inlet channel
(Pa)
pg,2
Pressure in the outlet channel
(Pa)
pout
Pressure at the filter outlet
(Pa)
Pressure loss of the ash cake
(Pa)
pac
62
pchannel,inl Pressure loss in the inlet channel
(Pa)
pchannel,out Pressure loss in the outlet channel
(Pa)
peff
Pressure loss over the effective filter length
(Pa)
pinl
Pressure loss at the filter inlet
(Pa)
pout
Pressure loss at the filter outlet
(Pa)
pplug,inl
Pressure loss over the inlet plug
(Pa)
pplug,out
Pressure loss over the outlet plug
(Pa)
psc
Pressure loss of the soot cake
(Pa)
psd
Pressure loss of the soot depth layer
(Pa)
pw
Pressure loss of the wall
(Pa)
R
Total number of reactions
(-)
Rsc
Soot regeneration rate in the cake layer
(kg/(m ·s))
Rsd
Soot regeneration rate in the depth layer
(kg/(m ·s))
Rcontinuity
LLD source term for gas phase continuity
(kg/(m ·s))
Renthalpy
LLD source term for solid enthalpy
(J/(m ·s))
Rspecies,j
LLD source term for species j
(kg/(m ·s))
S
Total number of species
(-)
r
General reaction rate
(kmol/(m ·s))
SCF
Stokes-Cunningham factor
(-)
Ssc
Switch for soot depth layer deposition
(-)
Ssd
Switch for soot cake layer deposition
(-)
s
Cell distance of a PF base cell
(m)
t
Time
(s)
Ts
Solid temperature
(K)
VPF
Filter volume
(m )
vg,1
Velocity in the inlet channel
(m/s)
vg,2
Velocity in the outlet channel
(m/s)
vinl
Velocity at the filter inlet
(m/s)
vout
Velocity at the filter outlet
(m/s)
vw
Wall velocity
(m/s)
3 3 3
3
3
3
3
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3. Theory vw,dl
Dimensionless wall velocity
(-)
vw,1
Wall velocity in the inlet channel
(m/s)
vw,2
Wall velocity in the outlet channel
(m/s)
w
Channel wall thickness
(m)
wg,j
Mass fraction of the species j
(kg/kg)
wg,j,inl
Mass fraction of the species j at top of soot cake
(kg/kg)
x
Cartesian coordinate in direction of the wall height
(m)
yg
Mole fraction
(mol/mol)
z
Cartesian coordinate in direction of the filter length
(m)
Greek Letters Total thickness of the filter wall and washcoat
(m)
ac
Height of the ash cake
(m)
sc
Height of the soot cake
(m)
sd
Height of the soot depth layer
(m)
w
Thickness of the filter wall
(m)
wc
Thickness of the washcoat
(m)
Porosity of the soot cake
(-)
Channel shape factor
(-)
Mean free gas path
(m)
Viscosity
(Pa·s)
Stoichiometry coefficient
(-)
ac
Packing density of the ash cake
(kg/m )
g
Gas density
(kg/m )
g,1
Gas density in the inlet channel
(kg/m )
g,2
Gas density in the outlet channel
(kg/m )
inl
Gas density at the filter inlet
(kg/m )
out
Gas density at the filter outlet
(kg/m )
sc
Packing density of the soot cake
(kg/m )
sd
Packing density of the soot depth layer
(kg/m )
in
Pressure loss coefficient at the filter inlet
(-)
out
Pressure loss coefficient at the filter outlet
(-)
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3 3 3 3 3 3 3 3
63
3. Theory
3.3. Pipe Model Availability BOOST AT: Aftertreatment Pipe
page [240]
Overview Pipes are a major component of aftertreatment systems, connecting aftertreatment devices such as catalytic converters or particulate filters. Assuming that radial effects within the gas phase of pipes are of minor importance, a transient 1D model is sufficient to describe its entire thermo- and fluid dynamics covering the effects of convection in axial direction and heat transfer in perpendicular (radial) direction to the solid wall. Axial gas phase conduction is assumed to be negligible due to the high flow velocities typical of engine exhaust systems. In a very generic consideration, the wall of a pipe consists of opaque layers such as steel walls or insulation mats and of transparent layers representing air gaps. The following figure sketches such a pipe consisting of three wall layers, an insulation mat and an air gap. Although this configuration may not represent real-life pipes, it will point out the capabilities of the generic model offered by BOOST. The main effects taking place within the pipe wall are heat transfer from the exhaust gas, heat conduction in axial and radial direction, heat radiation between the surfaces neighboring transparent layers and heat transfer to the ambient due to convection and radiation. Figure 29. Main Transport Effects in a Pipe Consisting of Different Wall Layers
In the following section the basic equations of a transient 1D compressible pipe flow model with variable cross sections are presented, followed by the balance equations of a solid wall consisting of an arbitrary number of different wall layers. In the absence of chemical reactions, the solution of species transport equations may look redundant. These equations are kept in the model to provide a correct transient species transport between reacting components that are linked by a pipe.
3.3.1. Gas Phase Balance Equation The continuity equation of the gas phase is (167)
where is the density of the gas phase, is the time, is the gas velocity, and is the spatial coordinate in axial direction. represents the hydraulic gas cross section in the pipe. This term is part of the spatial derivative in order to consider variable cross sections as given in conical pipe sections. page [96] The pressure drop in the channel is described by Darcy's law (see Kaviany [26 ]) (168)
64
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3. Theory where by
is the system pressure and
is a friction coefficient. This coefficient can be described (169)
where is the hydraulic channel diameter and is called Fanning friction factor which takes into account deviations from round channel cross sections (e.g. round=1, square=0.89, Equilateral Triangle=0.83). is a generic friction coefficient. This coefficient is given by (170)
where the Reynolds number
is used to distinguish between laminar
and turbulent flow regimes. and are laminar and turbulent friction coefficients, respectively. If the turbulent friction characteristics are described by a relative surface roughness the turbulent friction coefficient is calculated from the Colebrook equation. page [96] This equation (see Liu et al. [48 ]) is given by (171)
where represents the relative surface roughness of the pipe wall. The species conservation equation is given by (172)
where represents the gas mass fraction of species . The energy balance of the gas phase is (173)
where is the total enthalpy of a component . It is summed up over all species using their individual mass fractions as weighting factor in order to express the overall gas phase enthalpy. is the heat transfer coefficient between the gas phase and the solid wall. and represent the gas temperature and the wall temperature at the inner side of the innermost wall layer. is the geometrical surface area of the pipe wall inner side.
3.3.2. Multi-Layered Wall Model The thermal behavior of pipe walls is modeled by a transient 2D energy balance equation covering heat transfer in axial and radial direction. The full 2D approach is well accepted in the page [96] literature (see for example Liu and Hoffmanner [48 ]). It is required to provide a correct description of the transient behavior of dual-wall pipes where a radially uniform temperature profile cannot be assumed. Thus, any lumping of the 2D system into a 1D description leads to wrong transient responses. The wall energy balance equation is given by (174)
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65
3. Theory where is the temperature of the catalyst wall. and represent the radial and axial coordinates, respectively. Wall density , wall heat capacity and its thermal conductivity are given within the time and space derivatives in order to consider their temperature dependence. All three properties are marked with the index to distinguish between the page [64] properties of different wall layers as sketched in Fig. 29 . The boundary conditions of the 2D heat conduction field are given by (175)
(176)
(177)
(178)
where and represent the heat transfer coefficients between gas and wall and between wall and ambient, respectively. The first is evaluated using a Nusselt correlation, the latter is used as model input parameter in a simplifying approach. is the ambient temperature and is the radiation sink temperature which is not necessarily equal to the ambient temperature. represents the emissivity of the outer surface of the outermost wall layer and is the Stefanpage [66] page [66] Boltzmann constant. According to Eq.175 and Eq.176 no heat losses in axial page [66] direction are assumed. At the wall inner side (Eq.177 ) a boundary heat flux is given by convective heat transfer between the gas and the wall. At the outer surface of the pipe wall page [66] (Eq.178 ), convective and radiative heat transfer to the ambient are taken into account. 3.3.2.1. Air-Gaps If i.e. air-gaps are part of the model, it is additionally necessary to consider radiative heat transfer between the opaque walls neighboring a transparent layer. This radiative heat exchange, taken page [97] from VDI [64 ], is evaluated according to (179)
page [64]
where and represent (see Fig. 29 ) the emissivities at the outer surface , of the inner layer and at the inner surface of the outer layer, respectively. is the viewing factor from the outer (inner) side of the inner (outer) layer to the inner (outer) side of the inner (outer) page [97] layer. Both viewing factors are evaluated according to VDI [64 ] assuming finite length coaxial cylinders. The conductive/radiative heat transfer within air-gaps is typically augmented by free convection. page [97] Therefore, an effective heat conductivity taken from Wilde [74 ] is applied in the model. It is given by (180)
where the effective heat conductivity is calculated as a function of the Grashof and Prandtl number. The Grashof number is defined according to (181) 66
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3. Theory
where is the thickness of the gap and g the gravimetric acceleration. (temperature page [97] dependent data are taken from VDI [64 ]) represents the isobaric expansion coefficient of air and is its kinematic viscosity. 3.3.2.2. Gas-Wall Heat-Transfer The convective heat transfer between the exhaust gas and the pipe wall is modeled by a Nusselt number (182)
Where is the heat transfer coefficient for heat exchange between the gas phase and the solid wall. dhyd is the hydraulic diameter of the pipe inner side and represents the heat conductivity of the gas phase. page [96] Based on Lienhard and Lienhard [47 ] BOOST offers the following approaches for the definition of the Nusselt number: Re-Analogy: (183)
Colburn: (184) Pethukov: (185)
Gnielinski: (186)
3.3.2.3. Corrections for Pulsating Flow and Bended Pipes In order to take into account the influence of flow pulsations and/or pipe bends on the gas/wall heat transfer, the Nusselt number is augmented by two additional factors: (187) represents an additional augmentation factor (pulsation factor taken from Wendland [72 [97] ]) in order to consider the effect of gas pulsation given in engine exhausts. The factor takes into account increased heat transfer conditions within bended pipes. page [96] Therefore, the following correlation (see Liu and Hoffmanner [48 ]) is used
page
(188)
where
is the pipe diameter and
represents the bending radius.
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3. Theory 3.3.2.4. Wall-Ambient Heat-Transfer page The external heat transfer model applies Nusselt approaches for cross-flow take from VDI [64 [97] ]. The correlation considers free and forced convection. It is given by: (189) page [97]
Please refer to VDI [64 ] (section Fa and section Ge) for details on the definition of the Nusselt numbers for free and forced convection.
3.3.3. Nomenclature Units
68
2
3
ageo
Geometrical surface area
(m /m )
Ag
Cross section of the gas phase
(m )
Ai
Inner surface of outer wall layer
(m )
Ao
Outer surface of inner wall layer
(m )
cp
Specific heat capacity of the exhaust gas
(J/(kg·K))
cp,l,w
Specific heat capacity of the wall layer l
(J/(kg·K))
dhyd
Hydraulic diameter
(m)
F
Factor in Nusselt correlation
(-)
FP
Factor for flow pulsation
(-)
FB
Factor for bended pipes
(-)
KD
Darcy friction coefficient
(kg/(m ·s))
g
Gravimetric acceleration
(m/s )
Grashof number in air gap of width
(-)
hg
Enthalpy of the entire gas phase
(kJ/kmol)
hk,g
Enthalpy of species k in the gas phase
(kJ/kmol)
LPipe
Pipe length
(m)
Nu
Nusselt Number
(-)
2 2 2
3
2
Nuforced Nusselt Number for forced convection
(-)
Nufree
Nusselt Number for free convection
(-)
pg
Pressure
(Pa)
Pr
Prandtl number
(-)
Prair
Prandtl number of air
(-)
Radiative heat flux between walls neighboring an air gap
(W)
r
Spatial coordinate in radial direction
(m)
rgw
Inner radius of pipe wall (gas to wall)
(m)
rwa
Outer radius of pipe wall (wall to ambient)
(m)
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3. Theory Rel
Laminar Reynolds number
(-)
Ret
Turbulent Reynolds number
(-)
Re
Reynolds number
(-)
Sh
Sherwood number
(-)
t
Time
(s)
Tamb
Ambient Temperature
(K)
Tg
Gas temperature
(K)
Trad
Radiation sink temperature
(K)
Tw
Wall temperature
(K)
Tw,i
Wall temperature at inner side of wall layer
(K)
Tw,o
Wall temperature at outer side of wall layer
(K)
vg
Mean mass weighed gas velocity
(m/s)
wk,g
Mass fraction of the species k in the gas phase
(kg/kg)
z
Spatial coordinate in Cartesian coordinates
(m)
Greek Letters 2
gw
Heat transfer coefficient between gas and wall
(W/m )
wa
Heat transfer coefficient between wall and ambient
(W/m )
air
Isobar expansion coefficient of air
(1/K)
Thickness of air gap
(m)
Pipe roughness
(m)
g
Open frontal area fraction
(-)
i
Emissivity at inner surface of a wall layer
(-)
o
Emissivity at outer surface of a wall layer
(-)
Friction factor
(-)
Laminar friction factor
(-)
Turbulent friction factor
(-)
Fanning friction factor
(-)
io
Viewing factor from inner to outer pipe in air gap
(-)
io
Viewing factor from outer to inner pipe in air gap
(-)
air
Thermal conductivity of air
(W/(m·K))
eff
Effective thermal conductivity in air gap
(W/(m·K))
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2
69
3. Theory g
Thermal conductivity of exhaust gas
(W/(m·K))
l,w
Thermal conductivity of wall layer l
(W/(m·K))
Stefan Bolzman constant
(W/m /K )
g
Density of the entire gas phase
(kg/m )
l,w
Density of wall layer l
(kg/m )
air
Kinematic viscosity of air
(m /s)
g
Kinematic viscosity of the exhaust gas
(m /s)
2
4
3 3
2 2
3.4. Injector Model Availability page [243] BOOST AT: Aftertreatment Injector Overview The Aftertreatment Injector element offers the possibility to inject multi-component fluids into the exhaust aftertreatment system at any position between the inlet and outlet boundary elements. The following features are addressed: • injection of gas mixture (1,2) • injection of liquid mixture (1,2,3) • injection of liquid mixture and wallfilm modeling (1,2,3,4,5) The numbers in brackets refer to the effects covered: 1. add mass to the system 2. add enthalpy to system 3. consider heat of evaporation in gas phase 4. mass transfer between wallfilm and gas phase (storage, evaporation) 5. heat transfer between wallfilm on the one hand and gas phase and pipe wall on the other
3.4.1. Injector Model The injector consists of a small pipe with an injection orifice. The pipe works as a coupling element for upstream and downstream elements. Its length is standardized. If an additional pipe is attached downstream to the injector, its entire specification is adopted for the injector's pipe (except for the length). On the other hand: if no pipe is attached downstream, a standard specification is assumed. The pipe is modeled as described in the previous chapter. Figure 30. Injector Geometry, Injection Process and Wallfilm Modeling
3.4.2. Injection Process The injected fluid can be chosen as either gaseous or liquid and can be a multi-component mixture in both cases. In the gas phase instantaneous evaporation is assumed, i.e. no fluid phase (spray) is modeled, and heat of evaporation is taken from the gas phase. 70
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3. Theory Injection of a liquid fluid requires a mapping to be specified onto which gas species a certain liquid gets split. This mapping process represents conversion reactions or thermal break-up taking place in the gas phase. In these cases the specified heat of evaporation should include also heat needed for these reactions. The mapping can also cover consumption of a gas species, e.g. UREA breaks up into NH3 and CO2 consuming H2O: (190) Consuming a certain species requires its availability. If wallfilm modeling is disabled, the injection mass flux gets reduced by that amount which cannot evaporate due to missing consumed species; otherwise, this amount is directly stored in the wallfilm. Additionally, a portion of the liquid may be chosedn to be transported downstream as droplets.
3.4.3. Wallfilm Modeling Modeling a wallfilm requires a pipe to be attached downstream the injector. Then the downstream pipes specification is adopted for the injector's pipe. Beside a user defined fraction (1-x) which is stored directly in the wallfilm during the injection process, the wallfilm can cumulate mass which cannot evaporate to the gas phase ( ), when consumed species are not available. 3.4.3.1. Balance Equations The mass of liquid component stored in the wallfilm is increasing due to injection and storage of non-evaporating mass and decreasing due to evaporation: (191)
The wallfilm exchanges heat with the gas phase and the solid wall: (192)
3.4.3.2. Wallfilm Evaporation In general the wallfilm can be a multi-component liquid mixture. The wallfilm evaporation rate of a page [95] liquid component is calculated as follows (see [7 ]): (193) The product determines the components specific surface in the wallfilm. is the mass transfer coefficient of component , and is its Spalding number of mass transfer: (194)
The thermal break-up of urea is starting at its melting point of 406 K. Its wallfilm evaporation rate page [95] is calculated according to the following Arrhenius law (see [8 ]): (195)
is the number of urea particles with a diameter
contained in the wallfilm.
3.4.3.3. Heat Transfer The wallfilm exchanges heat with the gas phase: (196)
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3. Theory
and with the solid wall (see [7
page [95]
]): (197)
Urea particles are assumed to exchange heat mainly with the gas phase because of their page spherical shape. This is described by the following expression (as discussed in principle in [8 [95] ]): (198)
3.4.4. Nomenclature Units AF
(m )
Spalding number of mass transfer of liquid component
(-)
Wallfilm specific heat
(kg/m )
Specific heat of liquid component
(J/(kg·K))
dF
Wallfilm thickness
(m)
DF
Wallfilm diameter
(m)
dhyd
Hydraulic diameter
(m)
dSL1
Thickness of the inner most solid wall layer
(m)
Durea
Urea particle diameter
(m)
E
Activation energy in urea thermolysis rate
(J/mol)
Mass transfer coefficient of liquid component
(m/s)
Heat transfer factor wallfilm
gas phase
(W/K)
solid wall
(W/K)
cp,film
kfilm,gas
3
kfilm,solid Heat transfer factor wallfilm Kurea,gas Heat transfer factor urea
72
2
Wallfilm contact area with gas phase / solid wall
gas phase
(W/K)
K
Frequency factor in urea thermolysis rate
(kg/(m·s))
Nurea
Number of urea particles in wallfilm
(-)
Wallfilm evaporation rate of liquid component
(kg/s)
Urea thermolysis rate
(kg/s)
Injection mass flux
(kg/s)
FIRE BOOST Aftertreatment
3. Theory Injected mass stored in wallfilm due to missing consumed species
(kg/s)
Pr
Prandtl number
(-)
R
Universal gas constant
(J/(mol·K))
Re
Reynolds number
(-)
Tfilm
Wallfilm temperature
(K)
Tg
Gas temperature
(K)
Tinj
Injection temperature
(K)
Tsolid
Temperature of inner most solid wall layer
(K)
VF
Wallfilm volume
(m )
3
Mass fraction of liquid component x
in wallfilm
Fraction of injected mass evaporating instantaneously in gas phase
(-) (-)
Greek Letters film
Thermal conductivity of wallfilm
(W/(m·K))
g
Thermal conductivity of exhaust gas
(W/(m·K))
solid
Thermal conductivity of inner most solid wall layer
(W/(m·K))
film
Density of wallfilm
(kg/m )
g
Density of the entire gas phase
(kg/m )
3 3
3.5. Temperature Sensor Model Availability BOOST AT: Temperature Sensor
page [246]
Physical Model For the purpose of measuring gas temperatures a great variety of temperature sensors is available that ranges over a broad band of technical working principles. However, in order to derive a general physical model for a temperature sensor or thermocouple some basic characteristics common to all of them may be assessed. page [73] In figure Fig. 31 the schematic of a thermocouple is shown: Figure 31. Thermocouple
The base physical phenomena which have to be considered when modeling a thermocouple device are:
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3. Theory 1. convective heat transfer between the gas phase and the thermocouple, 2. heat conduction within the solid substrate of the thermocouple, 3. heat radiation between the solid surface of the thermocouple and the inner solid surface of the device into which the thermocouple is placed. These phenomena translate into the following transient balance equation for the temperature TTHC of the thermocouple: (199)
The temperature sensor model is a 1D model with the discretization axis being the thermocouple axis. For flow in pipes the velocity and temperature profile is assumed to be of parabola shape: • Due to friction the gas flow has zero velocity at the wall and its maximum in a pipe's center. As a consequence the convective heat transfer coefficient is spatially dependent. • Additionally one can generally assume a temperature gradient between pipe wall and the gas flow in the pipe center. The heat transfer between gas flow and pipe wall leads to a radial gradient in the temperature field, that again results in spatially dependent heat transfer between gas and thermocouple. The assumed shape of velocity and temperature field is shown in the below figure: Figure 32. Velocity and temperature profile in a pipe.
On the other hand, when looking at a converter the flow (velocity as well as gas temperature) within the channels can be assumed to be constant across the cross-section. page [74] The balance equation Eq.199 is solved in BOOST by linear discretization with respect to the spatial dimension x and with respect to time. After each time step the balance equation is solved providing the current thermocouple temperature. During the solution for the thermocouple temperature the gas temperature is assumed to remain constant. The physical properties of the thermocouple are in general temperature dependent and therefore dependent on the spatial position x. The time step is split into sub time steps determined by the sampling rate with which the thermocouple signal is sampled by the measurement equipment. The top of the thermocouple located in the gas flow is assumed to be adiabatic, whereas at the end of the thermocouple heat is ideally conducted between thermocouple and wall. The thermocouple is assumed not to change the amount of heat in the gas phase nor in the wall, and also its influence on the gas velocity and pressure drop is neglected.
3.5.1. Nomenclature Units
74
2
A
Outer area of the thermocouple
m
cp
Specific heat capacity of the thermocouple
J/(kg.K)
rPipe
Pipe radius
m
Tg
Gas temperature
K
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3. Theory TTHC
Thermocouple temperature
K
TW
Wall temperature
K
V
Thermocouple volume
m
vg
Gas velocity
m/s
x
Spatial dimension used for discretizing the thermocouple
m
3
Greek Letters 2
Heat transfer coefficient
W/(m .K)
Emissivity of the thermocouple
-
Heat conductivity of the thermocouple
W/(m.K)
Density of the thermocouple
kg/m
Stefan-Boltzmann constant
W/(m .K )
3 2
4
3.6. Liquid Species Transport Availability BOOST AT Overview Liquid species, e.g. water or urea, may be transported as a separate phase with the gas flow (e.g. droplets). Important: The liquid phase does not interact with the gas phase, i.e. it is passively transported, it does not add to the gas mass, nor change the gas' properties. Liquid species may either be introduced at the inlet boundary or via an aftertreatment injector. These species may then be transported downstream and be deposited onto a catalyst substrate using an AUCI mechanism. In case the liquid species have been introduced via an injector, the temperature difference between the injection temperature and the solid substrate will be accounted for upon deposition, i.e. a cooling effect of the substrate can be observed if the injection temperature is below the substrate's temperature.
Overview Adjacent aftertreatment elements can be coupled thermally to each other by enabling the switch Couple to Upstream Element. A coupled pair of elements may consist of any combination of Pipe, Catalyst and Particulate Filter (PF). For all of these elements, heat conduction occurs via the walls of the elements. Thermal Coupling of Walls For the heat conduction between the walls of the elements to have an effect, at least one of the page [193] coupled elements must have its Variable Wall Temperature model enabled. If one of
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3. Theory page [191]
page [191]
the elements is set to 'Adiabatic Simulation ' or the simplified heat loss model is activated, this element's (wall) temperature will not be updated, it will still serve as a heat source/ sink for the wall of the other element. Figure 33. Example Temperature Profile of a System Pipe-Catalyst-Pipe.
Each element has its variable wall temperature model activated. When the elements are not thermally coupled, the temperature profile shows discontinuities at the boundaries between the catalyst and the attached pipes. With thermal coupling enabled, however, the temperature profile is smooth. The substrate's temperature is slightly lower in the coupled case because of the heat flow toward the pipes. When coupling elements which both have the variable wall temperature model enabled, but with a different number of wall layers, the mean temperature over all non-air wall layers is used for calculating the heat flux. This is illustrated in the following figure. Figure 34. Thermal Coupling of Multilayer Walls
Layers 1 and 3 of Pipe 1 at axial position 1.0 have the same temperature as layer 1 of Pipe 2 at axial position Thermal Coupling of Substrates When two elements possessing a monolith (Catalyst, PF) are coupled (i.e. when Couple to Upstream Element is active), heat conduction may additionally occur between the substrates page [76] (Fig. 35 a). The thermal coupling of the elements' monoliths can be suppressed by enabling the switch Consider Air Gap between Elements. In this case only heat conduction page [76] over the elements' shells (walls) occurs (Fig. 35 b). Figure 35. Thermal coupling of walls and substrates.
a) Substrates are thermally coupled. b) Substrates are thermally separated by an air gap. The walls of the catalysts are thermally coupled in both c
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3.8. Kinetic Models In FIRE and BOOST arbitrary kinetic models can be applied in the catalyst and filter models. Pre-Defined Kinetic Models To simplify and speed up the setup procedures for aftertreatment calculations, FIRE/BOOST offers pre-defined kinetic models for catalysts and particulate filters available in the graphical user interface. Note: All pre-defined reaction parameters given below are set for one typical application of a catalytic converter and a particulate filter respectively. Thus if other types of catalyst/ filter are modeled, these parameters can change and must be supplied by the user. Custom Kinetic Models With an interface to the AVL User Coding Interface (AUCI) it is possible to load arbitrary catalytic and regeneration mechanisms. The pre-defined kinetic models are available as AUCI models and it is possible to adjust their rate formulation and add further reactions to them. Besides the pre-defined kinetic models AUCI also provides further reaction mechanisms. Details can be found in the related documentation.
3.8.1. DOC Catalyst Reactions Availability BOOST FIRE AVL User Coding Interface Overview For the simulation of 'Diesel Oxidation Catalysts' three pre-defined reactions rates are available. page [96] page [96] The rate equations and kinetic parameters are mainly based on literature, [32 , 33 ]. Kinetic Model R1 R2 R3, approach 1 R3, approach 2 The corresponding reaction rates for the reactions 1 and 2 are defined as follows: (200)
(201)
where (202)
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3. Theory
(203)
The corresponding reaction rate for the reaction 3 is defined as follows: (204) approach 1: (205) approach 2: where: (206)
(207)
(208)
3.8.2. TWC Catalyst Reactions Availability BOOST FIRE AVL User Coding Interface Overview The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the simulation of 3-way-catalysts and oxidation catalysts. This pre-defined reaction model comprises page [95] page [96] page [96] page 21 reactions based on publications presented in literature [23 , 32 ,33 , 63 [97] ]. Kinetic Model R1 R2 R3 R4 R5, approach 1 R5, approach 2 R6 78
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3. Theory R7 R8 R9 Cerium Storage Reactions: R10 R11 R12 R13 Rhodium Storage Reactions: R14 R15 R16 R17 R18 R19 Barium Storage Reactions: R20 R21 Hydrocarbon (HC) Storage Reaction: R22 The corresponding reaction rates are defined as follows: (209)
The equilibrium constants in reactions 6, 8 and 9 are determined by: (232)
80
FIRE BOOST Aftertreatment
3. Theory
(233)
(234)
The rate for reaction 5 results from: approach 1:
approach 2: where: (235)
(236)
(237)
The rate for reaction 22 (HC storage) is defined as: (238)
where
is obtained from the correlation: (239)
3.8.3. HSO-SCR Catalyst Reactions, Steady-State Approach Availability BOOST FIRE AVL User Coding Interface Overview This pre-defined reaction model is dedicated to the simulation of HSO (Hydrolysis-SCR-Oxidation) systems. These type of NOx reduction systems consist of three different coating sections in one (or more) catalyst(s) that are designed to support individual reactions. These are the hydrolysis of isocyanic acid, the selective catalytic reduction of NOx with ammonia and the oxidation of ammonia. For steady-state applications Eley-Rideal kinetic approaches are commonly accepted in the literature. The following pre-defined reaction model
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3. Theory comprises seven reactions based on publications presented in the literature [75 [98] ].
page [97]
, 78
page
Kinetic Model R1 R2 R3 R4 R5 R6 R7, approach 1 R7, approach 2 The corresponding reaction rates for the reactions 1-6 are defined as follows: (240) (241)
(242)
(243)
(244) (245) where: (246)
The rate for reaction 7 results from: approach 1:
approach 2: where: (247)
82
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3. Theory (248)
(249)
3.8.4. HSO-SCR Catalyst Reactions, Transient Approach Availability BOOST FIRE AVL User Coding Interface Overview This pre-defined reaction model is dedicated to the simulation of HSO (Hydrolysis-SCR-Oxidation) systems. These types of NOx reduction systems consist of three different coating sections in one (or more) catalyst(s) that are designed to support individual reaction. These are the hydrolysis of isocyanic acid, the selective catalytic reduction of NOx with ammonia and the oxidation of ammonia. The model explicitly takes into account the ad/ desorption of ammonia at the solid surface and therefore is dedicated to resolve transient operating conditions. The stored amount of ammonia influences the three different SCR reactions, the oxidation of ammonia and the oxidation of nitric monoxide. Additionally steadystate rate approaches are used for the reactions in the hydrolysis and oxidation catalyst section. The pre-defined reaction model comprises nine reactions that are discussed in more detail in [78 page [98] ]. Kinetic Model R1 R2 R3 R4 R5 R6 R7 R8 R9, approach 1 R9, approach 2 R10 The corresponding reaction rates for the reactions 1-8 are defined as follows: (250) (251)
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3. Theory (252) (253)
(254)
(255)
(256) (257) where: (258)
The rate for reaction 9 results from: approach 1:
approach 2: where: (259)
(260)
(261)
The rate for reaction 10 results from:
3.8.5. Lean NOx Trap Availability BOOST FIRE 84
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3. Theory AVL User Coding Interface Overview This pre-defined reaction model describes a Lean NOx Trap catalyst considering catalytic reactions, O2 surface storage reactions and NOx storage reactions. The last reaction set can be chosen as either an ash core model approach or as surface storage reactions. BOOST/FIRE take into account the following 16 reactions: Kinetic Model R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 For all reaction rates the following definition applies: (262)
The corresponding reaction rates for the catalytic reactions 1-10 are defined as follows: (263)
(264)
(265)
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3. Theory
(266)
(267) (268)
(269) (270)
(271)
(272)
Storage and release of O2 is described by reaction 11 and depends on the surface oxygen ratio: (273) (274) where the engine lambda eng is evaluated from the species composition in the bulk gas page [95] according to Brinkmeier [10 ] is described by the equation (275)
A fuel CHx with ratio of x=1.814 is assumed and the mole fraction of oxygen in air yO2,air is assumed to be 0.2095. 3.8.5.1. Nitric Oxides Storage Approach Two approaches are available for the reactions 12 to 16 describing the NOx storage and release of barium carbonate.
86
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3. Theory 3.8.5.1.1. First approach - Ash Core Model The first approach follows the ash-core model approach developed by ICVT Stuttgart (see also page [97] page [95] [63 ] and [20 ], where NOx is stored as barium nitrate Ba(NO3)2 forming a so called ash growing into barium carbonate BaCO3 clusters. The corresponding reaction rates are: (276) (277) (278) (279) (280)
Here
=r/RBa,p is the relative ash core front position in the barium cluster particle (as shown
in the following figure) which varies between 0 and 1, and is the fraction of barium nitrate (ash) at the current ash front position in the ash core. The specific particle surface area as function of the particle front position results from an empirical approach and is described by (281)
where p,min and p,max are the minimum and the maximum values of the particle surface area per catalyst unit volume, and Ba,p is the ratio between p,max and p,min. The same approach is applied for the catalytic surface area of the NOx storage and regeneration, geo,F , which is (282) trans
is the geometrical surface area of the catalyst. One can show that there is the following
relation between the fraction of barium nitrate in the ash core coverage fraction of barium nitrate which yields
and the surface site (283)
The specific storage volume of the barium cluster particle is evaluated by the integration over the particle radius RBa,p, as described by (284)
In general the mole number of barium nitrate cluster particles is described by (285) where
2
(kmol/m ) is the storage capacity of the barium carbonate surface site. Furthermore, must fulfill the following relation, described by (286)
Ba,p
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3. Theory 3
where cBa,p (mol/m ) is the molar density of the barium cluster particle. By combining equations page [87] page [87] page [87] (Eq.284 ), (Eq.285 ), and (Eq.286 ) cBa,p is determined by (287)
Figure 36. Growing of Barium Nitrate Ash Core Front into Barium Carbonate Cluster during NOx Stora
Depending on the excess oxygen ratio EOR, the model distinguishes between NOx storage and NOx regeneration, where NOx storage may occur after full or after incomplete regeneration depending on the front position of the previous storage . The excess oxygen ratio is the amount of molecular oxygen in the gas divided by the amount of required oxygen for full combustion of carbon and hydrogen minus the provided oxygen in nitric-oxides and other oxygen compounds. It is calculated with the bulk gas composition by the equation (288)
z is the number of oxygen in the molecule AOz where A is an arbitrary element. In the molecule CxHy, x and y are the number of carbon and hydrogen atoms, respectively. For EOR>1 NOx storage and for EOR<1 regeneration occurs. The front position depends on the state of the NOx regeneration. If the previous regeneration was complete, or the actual front position is deeper than the front position of the previous regeneration ( ), it is determined by the equation (289)
If the actual front position is not as deep as front position of the previous regeneration ( ), it is determined by the equation (290)
The storage and regeneration reactions take place on the ash core front in the barium cluster particle. Diffusive transport of the products and educts between the ash core front and catalytic surface layer takes place. For every species of the gas phase an additional ordinary differential front equation has to be solved to determine the species mole fraction on the ash core front yk , as described by the equation (291)
88
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3. Theory
-4
is the volume fraction of the barium cluster particle which is assumed to be 10 , DBa.p is the pore diffusion coefficient, i,k is the stoichiometric coefficient of species k in reaction i, and is the reaction rate of reaction i. Quasi-steady conditions are assumed to determine the L species mole fraction in the catalytic surface layer yk . Ba,p
3.8.5.1.2. Second approach - Surface Storage In the second approach NOx is stored on the surface. Depth-growth processes are not taken into account. Here, the corresponding reaction rates are: (292) (293) (294) (295) (296)
3.8.6. NOx Trap Catalyst Reactions Availability FIRE Overview The following set of four reactions is applied in this pre-defined kinetic model: Kinetic Model R1 R2 R3 R4 The corresponding reaction rates for the reactions 1-4 are defined as follows: (297)
where: (298)
(299)
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3. Theory
(300) (301) (302)
(303) (304)
3.8.7. Filter Regeneration with Oxygen Availability BOOST FIRE AVL User Coding Interface Overview The regeneration (removal of the deposited soot) of a loaded PF is most commonly facilitated by increasing the temperature to a level where the rates of the relevant regeneration reactions are fast enough to burn-off the soot in a relatively short time. FIRE/BOOST takes into account the following 2 reactions in this pre-defined kinetic model: Kinetic Model R1 R2 The corresponding reaction rates for the reactions 1 and 2 are defined as follows: (305)
(306)
where the temperature dependence of the factor fCO is given by: (307)
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FIRE BOOST Aftertreatment
3. Theory FIRE/BOOST additionally offers to define this regeneration mechanism for two different layers of soot. Therefore a sub-layer can be specified and different kinetic parameters can be applied there.
3.8.8. Filter Regeneration with Oxygen and Nitric Dioxide Availability BOOST FIRE AVL User Coding Interface Overview The soot regeneration with oxygen and nitric dioxide implemented in BOOST considers the following three reactions: Kinetic Model R1 R2 R3 R4 The first two reactions take place at rather high temperature (>900K) whereas the third and the fourth reaction occur at temperatures around 600 K. The set of all four reactions offers the possibility to investigate soot regeneration within a wide range of temperatures. page [90] The reaction mechanism defined in Section Filter Regeneration with Oxygen is applied in this pre-defined reaction set in the same way. The kinetic approach of the third and fourth reaction is given by: (308)
This set of four reactions can be defined in two different soot layer zones with different reaction parameters. With the specification of a sub-layer height, catalytically supported reactions near the filter wall can be modeled.
3.8.9. Filter Regeneration with Oxygen, Nitric Dioxide and NO-Oxidation Availability BOOST FIRE AVL User Coding Interface Overview The soot regeneration with oxygen and nitric dioxide and NO oxidation, implemented in BOOST, considers the following four reactions:
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3. Theory Kinetic Model R1 R2 R3 R4 R5
In addition to the four reactions summarized in Section Filter Regeneration with Oxygen and page [91] Nitric Dioxide , the reversible oxidation of nitric monoxide to nitric dioxide is considered. The rates of the first three reactions are described in Section Filter Regeneration with Oxygen page [91] and Nitric Dioxide and the rate of the fourth reaction is given in Section DOC Catalyst page [77] Reactions .
3.8.10. Filter CSF Catalytic Reactions Availability BOOST FIRE AVL User Coding Interface Overview The predefined CSF Catalytic Reaction model considers the following four reactions: Kinetic Model R1 R2 R3 R4 These (oxidation) reactions are assumed to take place in the catalyzed wall of a PF independently of the presence of soot. The corresponding reaction rates are defined as follows: (309)
(310)
(311)
92
FIRE BOOST Aftertreatment
3. Theory where (312)
(313)
(314)
where (315)
(316)
3.8.11. Nomenclature Units 2
3
2
3
2
3
2
3
2
3
ageo,F
Geometrical surface area on the ash core front (LNT model)
(m /m )
ap,max
Maximum specific particle surface area (LNT model)
(m /m )
ap,min
Minimum specific particle surface area (LNT model)
(m /m )
areac
Reactive surface area of the catalyst
(m /m )
atrans
Geometrical surface area (GSA) of the catalyst
(m /m )
ck
B
Concentrations of species k in the bulk gas
(kmol/m )
ck
L
Concentrations of species k in the reactive surface layer
(kmol/m )
cBa,p
Molar Density of the barium cluster particle
(kmol/m )
D
Term in reaction rate equation
(variable)
DBa,p
Pore diffusion coefficient (LNT model)
(m /s)
fCO
Temperature dependence factor of filter regeneration with oxygen
(-)
k
Arrhenius frequency factor
(variable)
K
Term in reaction rate equation
(variable)
Keq
Equilibrium constant
(variable)
Nk
Mole number of species k
(kmol/m )
p
Pressure
(Pa)
r
Radial coordinate
(m)
Reaction rate of reaction i
(kmol/(m ·s))
Universal gas constant
(kJ/(kmol·K))
R
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3 3 3
2
3
3
93
3. Theory RBa,p
Radius of the barium cluster particle (LNT model)
(m)
TA
Arrhenius activation temperature
(K)
T
Temperature
(K)
VBa,p
Storage volume for the barium cluster particle (LNT model) (m )
3
yk
B
Mole fraction of species k in the bulk gas
yk
L
Mole fraction of species k in the reactive surface of the gas (kmol/kmol) phase
yk
front
Mole fraction of species k on the ash core front (LNT model)
(kmol/kmol)
Surface site coverage fraction of species k
(-)
Coverage fraction of species k on the current ash core front position (LNT model)
(-)
Zk Zk
front
(kmol/kmol)
Greek Letters Ratio of maximum and minimum specific particle surface area (LNT model)
(-)
Surface coverage dependency factor
(-)
Volume fraction of the barium cluster particle in the catalyst (LNT model)
(m /m )
Shift factor from fast to slow SCR reaction (R2, R3, R4 in SCR steady kinetics)
(-)
Excess oxygen ratio
(-)
Stoichiometric coefficient
(-)
F
Dimensionless radius of current ash core front position (LNT model)
(-)
st
Dimensionless ash core front position of previous storage (-) process (LNT model)
Ba,p
Ba,p
3
2
Site density
(kmol/m )
Indices
94
3
atm
Atmospheric
Ba,p
Barium cluster particle (LNT model)
eng
Engine
EOR
Excess Oxygen Ratio
equ
Equilibrium
i
Reaction index
FIRE BOOST Aftertreatment
3. Theory k
Species index
solid
Solid
3.9. Literature 1. Ahn T., Pinczewski V. and Trimm D.L., 'Transient Performance of Catalytic Combustors for Gas Turbine Applications.' Chemical Engineering Science 41, 1986, 55-64. 2. Baehr H. D., Stephan K., 'Waerme- und Stoffuebertragung', Springer, Berlin Heidelberg, New York, 1994. 3. Bardon S., Bouteiller B., Bonnail N., Girot P., Gleize V., Oxarango L., Higelin P., Michelin J., Schuerholz S. and Terres F. "Asymmetric Channels to Increase DPF Lifetime", SAE 2004-01-0950, 2004. 4. Barin I. 'Thermochemical Data of Pure Substances'. 3rd Edition, John Wiley & Sons Inc, New York, London, Sidney, 1985. 5. Becker C., Reinsch B., Strobel M., Frisse H. P. and Fritsch A. 'Particulate Filter Made of Cordierite - Design and Regeneration Management', MTZ 2008-06, Vol. 69, pp. 20-26, 2008. th 6. Bird R. B., Stewart W. E. Lightfoot E. N. 'Transport Phenomena', 6 Edition, John Wiley&Sons Inc., New York, London, Sydney, 1965. 7. Birkhold F., Meingast U., Wassermann P., Deutschmann, O. 'Analysis of the Injection of Urea-water-solution for automotive SCR DeNOx-Systems: Modeling of Two-phase Flow and Spray/Wall-Interaction'. SAE 2006-01-0643, 2006. 8. Birkhold F., Meingast U., Wassermann P., Deutschmann, O. 'Modeling and simulation of the injection of urea-water-solution for automotive SCR DeNOx-systems'. Appl. Catal. B: Environ. 70, pp. 119-127, 2007. 9. Bissett E. J. 'Mathematical model of the thermal regeneration of a wall-flow monolith diesel particulate filter'. Chem. Eng. Sci. , 39:1233-1244, 1984. 10. Brinkmeier C. 'Automotive Three-Way Exhaust Aftertreatment under Transient Conditions Measurements, Modeling and Simulation', 2006, PhD-Thesis, University of Stuttgart. 11. Chen D.K.S. and Cole C.E. 'Numerical Simulation and Experimental Verification of Conversion and Thermal Responses for a Pt/Rh Metal Monolithic Converter'. SAE 890798, 1989. 12. Coltrin M.E., Kee R.J., Rupley F.M. and Meeks E. 'Surface Chemkin III: A Fortran Package for Analyzing Heterogeneous Chemical Kinetics at a Solid Surface - Gas Phase Interface'. Sandia National Laboratories Report, SAND96-8217 Unlimited Release, 1996. 13. DieselNet Technology Guide 'Ceramic Monolith Substrates', May 2001, URL http:// www.dieselnet.com. 14. Froment G. F. and Bischoff K. B. 'Chemical Reactor Analysis and Design', John Wiley&Sons Inc., New York, London, Sydney, 1990. 15. Fuller E.N., Schettler P.D. and Giddings J.C. 'A new method for the prediction of gas phase diffusion coefficients'. Ind. Eng. Chem. 58:19-27, 1966. 16. Gaiser G. and Mucha P. 'Prediction of Pressure Drop in Diesel Particulate Filters Considering Ash Deposit and Partial Regeneration', SAE 2004-01-0158, 2004. 17. Gordon, S. and McBride, B.J. 'Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks and Chapman-Jouguet Detonations'. NASA SP-273, 1971. 18. Guo Z. and Zhang Z. 'Multi-Dimensional Modeling and Simulation of Wall-Flow Diesel Particulate Filter During Loading and Regeneration', SAE 2006-01-0265, 2006. 19. Haralampous O. A., Dardiotis C. K., Koltsakis G. C. and Samaras Z. C. 'Study of Catalytic Regeneration Mechanisms in Diesel Particulate Filters Using Coupled Reaction Diffusion Modeling', SAE 2004-01-1941, 2004. 20. Hauff C. H. 'Implementierung des Modells eines NOx-Speicherkatalysators in das Simulationstool BOOST', Master thesis at ICVT, Stuttgart University, 2007. 21. Hayes, R.E. and Kolackowski, S. 'Introduction to Catalytic Combustion'. Gordon and Breach Science Publishers, Amsterdam, 1997. 22. Herzog P.L., Strigl T., Diewald R., and Wanker R. 'Particlulate filter - a key technology for HSDI diesels: From simulation to series application'. JSAE 20025356, 2002. 23. Hughes K. W. and Floerchinger P., 'Ultra Thinwall Light-off Performance - Varying Substrates, Catalysts, and Flow Rates; Models and Engine Testing', SAE 2002-1-352.
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95
3. Theory 24. Huynh J. H., Cuong T. and Johnson, Yang S.T., Song L. and Bagley and Warner J.R. 'A one-dimensional computational model for studying the filtration and regeneration characteristics of a catalyzed wall-flow diesel particulate filter', SAE 2003-01-0841, 2003. 25. Johnson T. V. 'Diesel Emission Control in Review', SAE 2000-01-0184, 2000. 26. Kaviani M. 'Principles of Heat Transfer in Porous Media', Mechanical Engineering Series, Springer, Berlin Heidelberg, New York, 1991. 27. Kee R.J., Dixon Lewis, G., Warnatz J., Coltrin M.E. and Miller J.A. 'A Fortran Computer Package for the Evaluation of Gas Phase Multicomponent Transport Properties'. Sandia National Laboratories Report, SAND86-8246, 1986. 28. Kee R.J., Rupley F.M. and Miller J.A. 'The Chemkin Thermodynamic Database'. Sandia National Laboratories Report, SAND87-8215, 1987. 29. Khinast J., 'Kinetik, Reaktionsmechanismus und Simulation eines trockenen Rauchgasentschwefelungsverfahren', PhD-thesis, Technical University Graz, 1995. 30. Kirchner T. and Eigenberger G., 'Optimization of the Cold-Start Behaviour of Automotive Catalysts Using an Electrically Heated Pre-Catalyst', Chemical Engineering Science 51, 1996, 2409-2418. 31. Koltsakis G. C. and Stamatelos A. M. 'Modes of Catalytic Regeneration in Diesel Particulate Filters', Ind. Eng. Chem. Res., 36(10):4155-4165, 1997. 32. Koltsakis G. C. and Stamatelos, A. M. 'Modeling dynamic phenomena in 3-way catalytic converters', Chemical Engineering Science 54, 1999, 4567-4578. 33. Koltsakis G. C., Konstantinidis, P.A. and Stamatelos A. M.. 'Development and application range of mathematical models for 3-way catalysts',Applied Catalysis B. Environmental 12, 1997, 161-191. 34. Koltsakis G.C. and Stamatelos A.M., 'Modes of catalytic regeneration in diesel particle filters'. Ind. Eng. Chem. Res. , 36:4155-4165, 1997. 35. Konstandopoulos A. G. 'Flow Resistance Descriptors for Diesel Particulate Filters: Definitions, Measurements and Testing', SAE 2003-01-0846, 2003. 36. Konstandopoulos A. G. and Kostoglou M., 'Periodically reversed flow regeneration of diesel particulate traps'. SAE 1999-01-0469 , 1999. 37. Konstandopoulos A. G., Kostoglou M. and Housiada P. 'Spatial Non-Uniformities in Diesel Particulate Trap Regeneration', SAE 2001-01-0908, 2001. 38. Konstandopoulos A. G., Kostoglou M., Skaperdas E., Papioannou E., Zarvalis D., and Kladopoulou E., 'Fundamental studies of diesel particulate filters: Transient loading, regeneration and ageing'. SAE 2000-01-1016 , 2000. 39. Konstandopoulos A. G., Kostoglou M., Vlachos N. and Kladopoulou E. 'Progress in Diesel Particulate Filter Systems', SAE 2005-01-0946, 2005. 40. Konstandopoulos A. G., Skaperdas E. and Masoudi M. 'Interial Contributions to the Pressure Drop of Diesel Particulate Filters', SAE 2001-01-0909, 2001. 41. Konstandopoulos A. G., Skaperdas E. and Masoudi M. 'Microstructural Properties of Soot Deposits in Diesel Particulate Traps', SAE 2002-01-1015, 2002. 42. Konstandopoulos A. G., Skaperdas E., Warren J., and Allansson R. 'Optimise filter design and selection criteria for continuously generating diesel particulate traps'. SAE 1999-01-0468 , 1999. 43. Konstandopoulos A. G., Vlachos N., Housiada P. and Kostoglou M. 'Simulation of Triangular-Cell-Shaped Fibrous Wall-Flow Filters', SAE 2003-01-0844, 2003. 44. Konstandopoulos A.G. and Kostoglou M., 'Reciprocating flow regeneration of soot filters. Combustion and Flame', 121:488-500, 2000. 45. Konstandopoulos A.G.and Johnson J.H., 'Wall-flow diesel particulate filter - their pressure drop and collection efficiency'. SAE 890404 , 1989. 46. Kuhnke D., Spray Wall Interaction Modelling by Dimensionless Data Analysis, PhD thesis, Technische Universitaet Darmstadt, 2004. 47. Lienhard John H. IV and Lienhard John H. V 'A Heat Transfer Text Book Phlogiston Press, Cambridge Massachusetts, 3rd edition, 2003. 48. Liu Zheji and Hoffmanner Albert L. 'Exhaust Transient Temperature Response', SAE 950617, 1995. 49. Millet C. N., Menegazzi P., Martin B., Colas H. and Bourgeois C. 'Modeling of Diesel Particulate Filter, Regeneration: Effect of Fuel-Borne Catalyst', SAE 2002-01-2786, 2002. 50. Missy S., Thams J., Bollig M., Tatschl R., Wanker R., Bachler G., Ennemoser A., and Grantner H. 'Computer-aided optimisation of the exhaust gas aftertreatment system of the new BMW 1.8-litre valvetronic engine'. MTZ Journal , 11:18-29, 2001. 96
FIRE BOOST Aftertreatment
3. Theory 51. Mohammed H., Triana A. P., Yang S. L. and Johnson J. H. 'An Advanced 1D 2-Layer Catalyzed Diesel Particulate Filter Model to Simulate: Filtration by the Wall and Particulate Cake, Oxidation in the Wall and Particulate Cake by NO2 and O2, and Regeneration by Heat Addition', SAE 2005-01-0467, 2005. 52. Ogyu K., Ohno K., Hong S. and Komori T. 'Ash Storage Capacity Enhancment of Diesel Particulate Filter', SAE 2004-01-0949, 2004. 53. Ohno K., Shimato N., Taoka K., Hong S., Ninomiya T., Komori T. and Salvat O., 'Characterization of SiC-DPF for Passenger Car', SAE 2000-01-0185, 2000. 54. Opris C. N. 'A Computational Model Based on the Flow, Filtration, Heat Transfer and Reaction Kinetics Theory in a Porous Ceramic Diesel Particulate Trap', PhD thesis, Michigan Technological University, 1997. 55. O'Rourke, P.J. 'Statistical Properties and Numerical Implementation of a Model for Droplet Dispersion in Turbulent Gas', J. Comput. Physics 83, 1989. 56. Perry R. and Green D., 'Perry's Chemical Engineer's Handbook'. New York, McGraw Hill Book Company, 6. Edition, 1984. 57. Peters B. and Dziugys A., 'Numerical modeling of electrified particle layer formation on the surface of filtration fabric'. Environmental Engineering , 9:4:191-197, 2001. 58. Peters B. and Dziugys A., 'Numerical simulation of the motion of granular material using object-oriented techniques'. Comput. Methods Appl. Mech. Eng. , 191:1983-2001, 2002. 59. Peters B. J., Wanker R., Muenzer A. and Wurzenberger J. C. 'Integrated 1D to 3D simulation Workflow of Exhaust Aftertreament Devices', SAE 2004-01-1132, 2004. 60. Reid R.C., Prausnitz J.M. and Poling B.E. 'The properties of gases and liquids'. 4th Edition, Mc Graw Hill, New York, 1988. 61. Shah R. K. and London A. L. 'Laminar flow forced convection in ducts: a sourcebook for compact heat transfer exchange analytical data'. Academic Press, 1978. 62. Taylor R., and Krishna R. 'Multicomponent Mass Transfer', John Wiley&Sons Inc., New York, London, Sydney, 1993. 63. Tuttlies U., Schmeisser V. and Eigenberger G. 'A mechanistic simulation model for NOx storage catalyst dynamics', Chemical Engineering Science, 59, 2004, 4731-4738. 64. Verein Deutscher Ingenieure (Ed.) VDI-Waermeatlas, Berechnungsblaetter fuer den th Warmeuebergang. 7 Edition, VDI Verlag, Duesseldorf, 1994. 65. Voltz E.V., Morgan C.R. and Liederman, D. and Jacob, S.M. 'Kinetic Study of Carbon Monoxide and Propylene Oxidation on Platinum Catalysts'. Ind. Eng. Chem. Prod. Res. Develop. 12:4, 1973, 294-301. 66. Wakao W., Smith J.M, 'Diffusion in catalyst pellets', Chemical Engineering Science 17 (1962): 825-834, 1962. 67. Wanker R. and Peters B., 'DPF pressure drop vs. soot mass during regeneration and loading'. Technical report, AVL Internal Communication, 2001. 68. Wanker R., Granter H., Bachler G., Rabenstein G., Ennemoser A., Tatschl R., and Bollig M. 'New physical and chemical models for the CFD simulation of exhaust gas lines: A generic approach'. SAE 2002-01-0066 , 2002. 69. Wanker R., Granter H., Tatschl R., and Bollig M. '3D CFD simulation of exhaust lines: A new approach to account for current and future challenges'. JSAE 20025336 , 2002. 70. Wanker R., Raupenstrauch H. and Staudinger G. 'A fully distributed model for the simulation of catalytic converter' Chemical Engineering Science 55, 2000, 4709-4718. 71. Wanker R., Wurzenberger J. C. and Higbie D. '1d and 3d CFD Simulation of Exhaust-Gas Aftertreatment Devices: Parameter Optimization via Genetic Algorithm', Proceedings of 5th ASME/JSME Int. Symposium on Computational Technologies for Fluid/Thermal/Stress Systems with Industrial Applications, San Diego, 2004 72. Wendland Daniel W. 'Automobile Exhaust-System Steady-State Heat Transfer', SAE 931085, 1993. 73. Wheeler A., In P.H. Emmett (Ed.), Catalysis, Reinhold New York, Vol II: 105, 1955. 74. Wilde Karl 'Erzwungene und freie Stroemung', Dietrich Steinkopff Verlag, Darmstadt, 2nd edition, 1978. 75. Winkler C. and Floerchinger P., Patil, M.D., Gieshoff, J., Spurk, P., Pfeifer, M., 'Modeling of SCR DeNOx Catalyst - Looking at the Impact of Substrate Attributes', SAE 2003-01-0845. 76. Wurzenberger J. C. and Peters B. 'Catalytic Converter in a 1D Cycle Simulation Code Considering 3D Behavior', SAE 2003-01-1002, 2003. 77. Wurzenberger J. C. and Peters B. 'Design and Optimization of Catalytic Converters taking into Account 3D and Transient Phenomena as an Integral Part in Engine Cycle Simulations', 97 FIRE BOOST Aftertreatment
3. Theory ICES 2003-611, Proceedings of STC2003, ASME Internal Combustion Engine Division, 2003. 78. Wurzenberger J. C. and Wanker R. 'Multi-Scale SCR Modeling, 1D Kinetic Analysis and 3D System Simulation', SAE 2005-01. 79. Wurzenberger J. C., Muenzer A., Peters B. and Wanker R. '1D/3D Simulation Workflow Optimization of Exhaust Gas Aftertreatment Devices', ATZ-Worldwide, 106(7-8):27-44, 2004. 80. Silvis, W. 'An Algorithm for Calculating the Air/Fuel Ratio from Exhaust Emissions', SAE Technical Paper 970514, 1997.
3.10. Appendix 3.10.1. Analysis Formulae (317)
(318)
A is an arbitrary element, z the number of oxygen atoms in the molecule AOz. x and y are the number of carbon and hydrogen atoms in an arbitrary composition of a hydrocarbon CxHy, respectively. (319)
A is an arbitrary element, z the number of oxygen atoms in the molecule AOz. x and y are the number of carbon and hydrogen atoms in an arbitrary composition of a hydrocarbon CxHy. (320)
(321)
(322)
(323)
98
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3. Theory 3.10.2. Conversion of Mole and Volume Fractions and ppm's to Mass Fractions and Vice Versa The correlation between mole fractions, volume fractions and parts per million (ppm) is given by: • One mole fraction is identical to one volume fraction 6 • One mole fraction is 10 ppm The evaluation of mass fractions out of mole (or volume) fractions is given by (324)
where wk is the mass fraction, yk is the mole fraction and Mk is the molar mass of the species k. The equation shows that for the evaluation of the individual k species mass fractions, the molar masses of the K species have to be known. For a system consisting of H2 and O2 with identical mole fractions (i.e. yH2=0.5, MH2 = 2 kg/kmol and yO2= 0.5, MO2 = 32 kg/kmol) the mass fractions are given by: (325)
The evaluation of mole (or volume) fractions out of mass fractions is given by the following formula (326)
For a system consisting of H2 and O2 with identical mass fractions (i.e. wH2 = 0.5, MH2 = 2 kg/ kmol and wO2=0.5, MO2 = 32 kg/kmol) the mole fractions are given by: (327)
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4. FIRE Aftertreatment
4. FIRE Aftertreatment In this section the application FIRE Aftertreatment is presented.
4.1. Input Data This chapter explains how catalyst input data can be generated within the FIRE Workflow Manager and describes the data in the Solver Steering File for the FIRE Aftertreatment Module. Aftertreatment examples are available in the Examples Manual and in the installation package.
4.1.1. Run Mode Select Run mode in the parameter tree to access the Run mode pull-down menu and then select Timestep or Steady. Note: Steady simulations of chemical reactions require the specification of the Pseudo time step for aftertreatment at Run mode. For steady pressure drop simulations without chemical reactions, the pseudo time step is not necessary.
4.1.2. Module Activation Select Module activation in the parameter tree to access the Aftertreatment toggle switch. Turn on toggle switch to activate. Note: The Aftertreatment Module cannot be activated without the Species Transport Module (General).
4.1.3. Aftertreatment The Aftertreatment parameter tree is displayed in the Modules folder as follows: Figure 37. Aftertreatment Parameter Tree
Click on Aftertreatment TNG with the right mouse button to access the following options: • Import from BOOST • Catalyst: Insert • DPF: Insert • Reactive Porosity: Insert page [101] Refer to the corresponding sections Catalyst Specification , General Particulate Filter page [144] page [165] Specification, Reactive Porosity Specification and Aftertreatment-Device Import page [178] from BOOST for further details.
4.1.4. Catalyst Specification To add a catalyst to the project, click on Aftertreatment TNG in the parameter tree with the right mouse button and select Catalyst: Insert from the submenu. To delete a catalyst from the project, click on the name of the catalyst (i.e. Catalyst[1]) with the right mouse button and select Remove from the submenu. The specification of a catalyst comprises data over its geometry, its fluid and thermodynamic behavior and the conversion reactions taking place. 100
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment Copy from CAT allows the complete set of input data to be copied from Catalyst[X] to the present catalyst. Figure 38. Copy from CAT Function
This input data is discussed in the following sub-sections. 4.1.4.1. Catalyst Specification Select Catalyst specification in the parameter tree to access the following input fields: 4.1.4.1.1. Catalyst Specification Typical Values and Ranges Cell selection
Supply a cell selection that defines the geometry of the catalyst.
NoSelection (default)
Inlet face selection
Supply a face selection that defines the inlet plane of the catalyst.
NoSelection (default)
Outlet face selection
Supply a face selection that defines the outlet plane of the catalyst.
NoSelection (default)
Monolith initialization temperature
Determines the initial temperature of the catalyst.
Determines the type of monolith: Number of 2 channels per in = N.
100-900 (1/in )
Wall thickness
Determines the thickness of the monolith's walls = Wall.
0.006-0.015 (in)
Washcoat thickness
Determines the thickness of the washcoat = WC. For activated Activate Washcoat Layer (WCL) Model a value greater than zero is required.
0-0.003 (m)
4.1.4.1.3. Catalyst Type: General Catalyst Typical Values and Ranges Open frontal area (OFA)
Determines the open frontal area (= fluid volume fraction) of monolith ( ).
0.50-0.75 (-)
Hydraulic diameter
Determines the hydraulic diameter dhyd of the monolith.
0.001-0.005 (m)
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101
4. FIRE Aftertreatment 4.1.4.2. Pressure Drop Specification The pressure loss of the flow within a catalytic converter is determined by a flow-resistance model and corresponding parameters, which have to be supplied by the user. All necessary input data are summarized in the following sections. 4.1.4.2.1. Pressure Drop Models Four different pressure drop models are available to calculate the pressure drop within the catalyst: 4.1.4.2.1.1. Tube Friction The Tube Friction pressure drop model is especially applicable for flow through catalysts where empirical data of the pressure drop are not available. The pressure drop is based on the flow of fluid along the channels of the catalyst and the pressure drop is calculated due to the wall friction within pipes: (328)
The notation used is as follows: Pressure gradient within porous material dh
wi
Mean hydraulic diameter = A
Non-circular cross-sectional area
Lper
Wetted perimeter
Interstitial (local) velocity components in the tubes (
)
Laminar tube friction (HAGEN-POISEUILLE) = 1.0 for cross sections with circular shapes = 0.89 for cross sections with quadratic shapes (user-supplied input) Turbulent tube friction (BLASIUS) Reynolds number
To activate the Tube friction pressure drop model, select Tube friction from the Pressure drop model pull-down menu to access the following input fields: Typical Values and Ranges Shape factor
This specifies a shape factor for the laminar tube friction. In the laminar case the tube friction is dependent on the shape of the cross-sectional area. = 1.0 for cross sections with circular shapes. = 0.89 for cross sections with quadratic shapes.
0.8-1 (-)
4.1.4.2.1.2. Forchheimer If Forchheimer is chosen as pressure drop model, then the pressure gradients within the catalyst channels are calculated with following equation 102
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment (329)
The linear and the quadratic term take into account the viscous losses and the inertial losses, respectively, of the flow inside the catalyst channels. Pressure gradient within porous material 2
i
Viscous loss coefficient (x-, y- and z-components) (1/m ) 2
Molecular (laminar) dynamic viscosity of domain fluid (Ns/m ) wi
Interstitial (local) velocity components in porous medium according to the local volume-fraction Inertial loss coefficient (1/m) Domain fluid density
To activate the Forchheimer pressure drop model, select Forchheimer from the Pressure drop model pull-down menu to access the following input fields: Typical Values and Ranges Zeta-value
This specifies the parameter ( ) defining the dependency between the velocity and the pressure loss per unit length of porous material.
0-100 (1/m)
Alpha value
This specifies the parameter ( i) defining the dependency between the velocity in the i direction, the laminar viscosity, and the pressure loss per unit length of porous material. Only if Undirected is selected for Porosity Type, direction dependent alpha values ( i) can be defined to simulate an unisotropic porous media.
0-10 (1/m )
7
2
Instead of the direct specification of the pressure drop model parameters Alpha and Zeta, a set of corresponding measured pressure drop / velocity pairs and the corresponding reference density and viscosity could be specified. During a pre-processing step FIRE then fits Alpha and Zeta from this data. Typical Values and Ranges 3
Reference Density
This specifies the density of the medium which is used in the experiment, where the pressure/velocity data specified in the table are evaluated.
0.5-50 (kg/m )
Reference Viscosity
This specifies the viscosity of the medium which is used in the experiment, where the pressure/velocity data specified in the table are evaluated.
5.10 -5.10 (Ns/ 2 m )
-7
-4
Velocity Pressure Drop Table - Forchheimer
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103
4. FIRE Aftertreatment Typical Values and Ranges Interstitial velocity This specifies the measured interstitial velocities w (for fitting Alpha and Zeta, at least three different velocities are necessary). Pressure Gradient dp/dx
0-50 (m/s)
This specifies the measured pressure gradients -400000-0 (N/ 3 corresponding to the different velocities (for positive m ) pressure drops over the monolith length, the pressure gradients are negative!)
4.1.4.2.1.3. Re formulation If Re formulation is chosen as pressure drop model, the pressure gradients within the catalyst channels are calculated with following equation: (330)
The notation used is as follows: Pressure gradient within porous material dh
Mean hydraulic diameter = A
Non-circular cross-sectional area
Lper
Wetted perimeter
wi
Interstitial (local) velocity components in porous medium according to the local volume-fraction
f
General Re-number dependent correlation for the friction factor Reynolds Number
(square:0.89)
Fanning friction factor
The friction factor f is described as a function of the Reynolds Number Re and changes depending on the flow regime (laminar, transition or turbulent): (331) The bounds for the transition region from laminar to turbulent are set by Reynolds numbers of Relam = 2300 and Returb = 5000. In the turbulent region, fturb is considered as a constant input value. In the laminar region flam is given by (332)
To activate the Re formulation pressure drop model, select Re formulation from the Pressure drop model pull-down menu to access the following input fields: Typical Values 104
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment Coefficient a
Input for the calculation of the general Re number dependent correlation for the friction factor.
64 (-)
Coefficient b
Input for the calculation of the general Re number dependent correlation for the friction factor.
-1 (-)
Turbulent
Turbulent Friction Factor
0.019
Channel Shape
Input for the Fanning Friction Factor
Square: 0.89
4.1.4.2.1.4. Power Law For catalysts where empirical data of the pressure drop are available, the power law option may be suitable. The empirical pressure drop is used to prescribe the user-supplied pressure drop coefficients: (333)
The notation used is as follows: Pressure gradient within porous material wi ,
Interstitial (local) velocity components through porous material Power law parameters
To activate the power law pressure drop model, select Power law from the Pressure drop model pull-down menu to access the following input fields: Typical Values and Ranges alpha-value
This specifies the parameter defining the 0.1-1000 (-) dependency between velocity and the pressure loss per unit length of porous material.
beta-value
0-2 (-) This specifies the parameter defining the dependency between the velocity and the pressure loss per unit length of porous material.
4.1.4.2.1.5. User If User is chosen as pressure drop model, the pressure drop is calculated according to the coding in the user routine usepor_pres.f. 4.1.4.2.2. Turbulence Treatment Within the single channels of a catalytic converter, the turbulence kinetic energy k is calculated by the standard transport equation. To take into account the laminarization process within the single channels the dissipation rate is calculated from the algebraic equation shown below: (334)
Crel is a relative turbulent length scale, which is multiplied with the hydraulic channel diameter dhyd and estimates the turbulence characteristics inside the monolith channels. Crel is a problem dependent quantity which has to be specified by the user.
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105
4. FIRE Aftertreatment Typical Values and Ranges Rel. turb. length scale Crel
Relative turbulent length scale which is multiplied with the hydraulic channel diameter to estimate the turbulence characteristics within monolith channels.
0.0001-0.02 (-)
4.1.4.3. Catalyst Physical Properties Select Catalyst Physical Properties in the parameter tree to access the following input fields: 4.1.4.3.1. Catalyst Physical Properties Typical Values and Ranges Density
Determines the bulk density of the monolith material considering the volume in the pores.
400-2000 (kg/ 3 m )
Thermal conductivity
Determines the thermal conductivity of the monolith material (= bulk solid material considering the volume in the pores). The thermal conductivity can either be specified as a constant value or as a table where the value changes as a function of temperature. Click on
0.1-50 (W/(m·K))
to define table data. Specific heat
Determines the specific heat of the monolith material 500-2000 (J/ (= bulk solid material considering the volume in the (kg·K)) pores). The specific heat can either be specified as a constant value or as a table where the value changes as a function of temperature. Click on table data.
Anisotropic cond. Factor
to define
Corrects the diffusion coefficients of the solid temperature equation normal to axial direction. A value of 1.0 simulates an isotropic conductivity. A value of 0.5 would be a good choice for monoliths. The anisotropic conduction factor is not used if the user-defined parameter ATM_ACTIV_RADIATION is specified and the current catalyst is selected as shown in the following figure. Then the effective thermal conductivity including radiation is used instead of the default anisotropic model (see section page [10] Anisotropic Heat Conduction Matrix )
0-10 (-)
Figure 39. User Defined Parameters for Effective Heat Conduction Specification
4.1.4.3.2. Mass Transfer Model FIRE allows to specify mass and heat transfer models independently. The following mass transfer models are available: 106
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4. FIRE Aftertreatment Typical Values and Ranges Type of transport coefficients
Mass Transfer Multiplier
Sieder/Tate: The Sieder/Tate correlation is used to calculate heat page [29] and mass transfer coefficients (Eq.78 ). Hawthorn: The Hawthorn correlation is used to calculate heat page [29] and mass transfer coefficients (Eq.80 ). Hausen: The Hausen correlation is used to calculate heat and page [29] mass transfer coefficients (Eq.79 ). constant: Constant values which have to be defined by the user are taken as heat and mass transfer coefficients.
Sieder/Tate (default)
Mass transfer coefficient Martin: The Martin correlation is used to calculate heat and page [29] mass transfer coefficients (Eq.81 ). user: The user can specify the transfer coefficients in use_cattra.f.
0.1-10 (m/s)
Specify a factor by which the gas diffusion coefficient of the mass transfer model is scaled. Possible input is constant (mass transfer of every species is scaled in the same way) or table (mass transfer of selected species is scaled).
0.01-10 (-)
4.1.4.3.3. Heat Transfer Model The following heat transfer models are available: Typical Values and Ranges Type of transport coefficients
Sieder/Tate: The Sieder/Tate correlation is used to calculate heat page [29] and mass transfer coefficients (Eq.78 ). Hawthorn: The Hawthorn correlation is used to calculate heat page [29] and mass transfer coefficients (Eq.80 ). Hausen: The Hausen correlation is used to calculate heat and page [29] mass transfer coefficients (Eq.79 ). constant: Constant values which have to be defined by the user are taken as heat and mass transfer coefficients.
Sieder/Tate (default)
Heat transfer coefficient Martin: The Martin correlation is used to calculate heat and page [29] mass transfer coefficients (Eq.81 ).
5-500 (W/(m ·K))
FIRE BOOST Aftertreatment
2
107
4. FIRE Aftertreatment user: The user can specify the transfer coefficients in use_cattra.f. Heat Transfer Multiplier
Specify a factor by which the heat transfer is scaled.
0.1-10 (-)
4.1.4.3.4. Catalyst Segmentation FIRE provides a simple model to take into account perforations in the catalyst. If Repeat turbulent inlet region is activated, the distance to the channel inlet in the heat and mass transfer models (Sieder/Tate, Hausen, Hawthorn and Martin) is reset at every location of a page [28] perforation (see length l in section Transfer Coefficients ). Typical Values and Ranges Repeating Length Determines the repeating length of the uniformly distributed perforations.
0.001-0.2 (m)
4.1.4.3.5. External Heat Source FIRE allows to specify constant heat sources for arbitrary cell selections. The specification is done for catalyst, reactive porosity and particulate filter separately. A warning check is performed, if a cell selection is specified more than one time. Select Activate at External heat source and click New external heat source for every heat source selection to be specified: Figure 40. Specification of External Heat Sources
Select HeatSource_X to open the window for the heat source specification. To delete a heat source select the check box at delete? and click Delete external heat source. Figure 41. Specification of External Heat Sources
Typical Values and Ranges Cell selection
Determines the cell selections for which the constant heat sources are applied. Click on table or formula data.
Heat Source 108
NoSelection
to define
Determines the quantity of heat introduced.
FIRE BOOST Aftertreatment
8
3
0-10 (W/m )
4. FIRE Aftertreatment 4.1.4.4. Washcoat Two different approaches are available to model heterogeneous reactions. In the standard model approach, the pore diffusion through the washcoat layer(s) is neglected. In the advanced model approach, pore diffusion is taken into account. Therefore, every washcoat layer is discretized in the direction perpendicular to the catalyst solid surface. The standard approach is equivalent to the advanced approach with only one washcoat layer of one computational cell. Therefore, the former specification at Conversion Reactions is now done at the My_Reaction branch. The advanced approach, taking into account pore diffusion through the washcoat layers, requires the specification of Transport Model and Reaction Model for each washcoat layer respectively. Note: For a deactivated button Activate Washcoat Layer (WCL) Model, the set-up of the Conversion Reactions is located in the first reaction branch My_Reaction. For the activated washcoat layer model one has to specify conversion reactions as well as a transport model for every layer separately. Note: The washcoat layer (WCL) model requires a Washcoat Thickness greater than zero to be specified at Catalyst Specification. Figure 42. Washcoat - Activated Washcoat Layer (WCL) Model
If Activate Washcoat Layer (WCL) Model is selected, the following input data has to be specified: Typical Values and Ranges -6
Layer Thickness
Determines the dimensionless layer thickness for every washcoat layer. The sum over all layer thicknesses must be 1.0. The dimensioned layer thickness is determined by multiplication with the Washcoat Thickness.
10 -1 (-)
No. Grid Points
Determines the number of computational cells of each washcoat layer.
1-10 (-)
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4. FIRE Aftertreatment Ref. WCL Volume
Determines the specific reference washcoat 0.01 (-) layer thickness as described in section page [20] Pore Diffusion Model . With Calculate Spec. Washcoat Layer Volume, a reasonable default value based on the geometrical specification is calculated.
Density
Determines the bulk density of the washcoat layer materials. Together with the density specified at Catalyst Physical Properties, a solid mixture density is calculated.
400-2000 (kg/m )
Reaction Model
User-given name of the reaction model for each washcoat layer.
My_Reaction (default)
Transport Model
User-given name of the transport model for each washcoat layer.
My_Transport (default)
3
4.1.4.4.1. Reaction Model (Conversion Reactions) Several different reaction models are available. Either no reactions are taken into account, pre-defined reaction models are chosen or the application of user-defined models is possible. If Activate Washcoat Layer (WCL) Model is selected, one has to specify a reaction model for each washcoat layer separately. More detailed information about the individual reaction page [77] mechanisms is given in Section DOC Catalyst Reactions . The pre-defined reaction models use global kinetic approaches given by Langmuir Hinshelwood equations and also transient mechanisms where adsorption and desorption steps are explicitly taken into account. All reaction models are supplied with default values for the individual kinetic parameters. The user can use the kinetic model and adjust all kinetic parameters. Note that the suggested reaction parameters have been successfully applied to several validation simulations, but they may have to be adjusted for use in other types of catalysts. In this case it is recommended to apply the pre-defined reaction model and to supply it with adequate reaction parameters. The following pre-defined reaction models are available: 1. Diesel Oxidation Catalyst (DOC). This model is dedicated for DOCs comprising the three major oxidation reactions of CO, HC and NO. 2. Three Way Catalyst (TWC). This model is a dedicated TWC model comprising seven conversion reactions and surface storage reactions on cerium, rhodium and barium. By selecting specific reactions and adapting the related kinetic parameters, this model also can be applied to other catalysts such as DOCs. 3. Selective Catalytic Reduction (SCR), Steady Kinetics. This model comprises seven reaction rates which can be enabled/disabled individually for three different reaction sections in the catalyst. The SCR rates use Eley-Rideal mechanisms, thus it assumes steady-state conditions for the reaction steps of adsorption, catalytic reaction and desorption. 4. Selective Catalytic Reduction (SCR), Transient Kinetics. This model comprises nine reactions that can be enabled/disabled individually for three different reaction sections in the catalyst. The transient effect of ad-/desorption is explicitly taken into account. 5. NOx Trap Catalyst Reactions. This model comprises two conversion reactions for NO and the surface storage of NO2 on barium. 6. Lean NOx Trap. This model comprises ten conversion reactions and surface storage on cerium. Furthermore, it offers two approaches of storing nitric oxides: an ash core model approach, developed by ICVT Stuttgart, and a surface storage approach. 4.1.4.4.1.1. Diesel Oxidation Catalyst (DOC) This reaction model offers a set of three oxidation reactions. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. page [77] More detailed information about this model is given in section DOC Catalyst Reactions . 110
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4. FIRE Aftertreatment The different reactions can be en/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. R1: CO Oxidation
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of carbon monoxide. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
R2: C3H6 Oxidation
R3: NO Oxidation
K1 - K5
Determines the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determines the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of propane as representative of hydro carbons. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5
Determines the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determines the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
A reversible rate mechanism is commonly accepted in the literature for the oxidation of nitric monoxide. Two rate approaches are available. The reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy. Approach 1
Approach 2
K
Determines the frequency factors used in the pre-defined reversible power-law conversion mechanism.
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111
4. FIRE Aftertreatment E
Determines the activation temperatures used in the pre-defined reversible power-law conversion mechanism.
A
Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism.
4.1.4.4.1.2. Three Way Catalyst (TWC) This reaction model offers a set of nine conversion reactions and surface storage mechanisms at three different surface sites. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. page [78] More detailed information about this model is given in Section TWC Catalyst Reactions . The different reactions can be enabled/disabled individually by clicking the corresponding check boxes. When enabled, several sub-pages for the detailed specification of the reaction parameters become enabled. R1: CO Oxidation
R2: C3H6 Oxidation
R3: CO-NO Redox Reaction
112
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of carbon monoxide. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of propene as representative of hydrocarbons. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of carbon monoxide and reduction of nitric monoxide. The denominator takes into account an inhibition effect of carbon monoxide. Each reaction constant is evaluated using Arrhenius'
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment law. The reaction order of carbon monoxide is a function of the carbon monoxide concentration itself and therefore the order changes between lean and rich conditions.
R4: H2 Oxidation
R5: NO Oxidation
m
Determines the reaction order of nitric monoxide in the pre-defined reaction approach.
n
This is a tuning value in order to determine the reaction order of carbon monoxide (n) in the pre-defined reaction approach. There are two possibilities, either a constant value for n (activate Reaction Order and specify n), or the evaluation of the Shift Function (activate Shift Function and specify o).
K1 - K2
Determine the frequency factors used in the predefined conversion mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of hydrogen. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
A reversible rate mechanism is commonly accepted in the literature for the oxidation of nitric monoxide. Two rate approaches are available. The reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy. Approach 1
Approach 2
FIRE BOOST Aftertreatment
113
4. FIRE Aftertreatment
R6: CO-H20 Shift
R7: C3H8 Oxidation
R8: C3H6-H20 Shift
114
K
Determines the frequency factor used in the pre-defined reversible power-law conversion mechanism.
E
Determines the activation temperature used in the pre-defined reversible power-law conversion mechanism.
A
Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the water gas shift reaction. Its reversible behavior is taken into account by considering the equilibrium constant as part of the rate equation. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of propane. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for water gas shift reactions. Its reversible behavior is taken into account by considering the equilibrium constant as part of the rate equation. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment of the temperature and is derived from the free Gibbs reaction enthalpy.
R9: C3H8-H20 Shift
R10-R13: Ce Storage
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the water gas shift reaction. Its reversible behavior is taken into account by considering the equilibrium constant as part of the rate equation. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Under lean conditions cerium is oxidized by O2 and under rich conditions cerium is reduced by CO, C3H6 and C3H8. All rates are of first order with respect to the participating gas and solid phase components. All reaction constants are evaluated using Arrhenius' law. R10
R11
R12
R13
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115
4. FIRE Aftertreatment
R14-R19: Rh Storage
Cerium Storage Capacity
Determines the maximum amount of oxygen that can be stored on the cerium surface site.
Initial Surface Coverage fraction of CeO2
Determines the coverage fraction of CeO2 at the solid surface. Range: 0-1 (-)
Max Surface Coverage fraction of CeO2
Determines the maximum surface coverage fraction of CeO2 at the solid surface. This property can be specified as a constant value or as a function of temperature. Range: 0-1 (-)
K1 - K4
Determines the frequency factors used in the predefined ad-/desorption mechanisms .
E1 - E4
Determines activation temperatures used in the pre- ad-/desorption mechanisms .
Under lean conditions rhodium is oxidized by O2 or NO and under rich conditions rhodium is reduced by CO, H2, C3H6 and C3H8. All rates are of first order with respect to the participating gas and solid phase components. All reaction constants are evaluated using Arrhenius' law. R14
R15
R16
R17
R18
R19
Rhodium Storage Capacity 116
Determines the maximum amount of oxygen that can be stored on the rhodium surface site.
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment
R20-R21: Ba Storage
Initial Surface Coverage fraction of RhO
Determines the coverage fraction of at the solid surface. Range: 0-1 (-)
Max Surface Coverage fraction of RhO
Determines the maximum surface coverage fraction of at the solid surface. This property can be specified as constant value or as function of temperature. Range: 0-1 (-)
K1 - K6
Determine the frequency factors used in the predefined ad/desorption mechanisms.
E1 - E6
Determine the activation temperatures used in the pre-defined sorption-equilibrium and ad/desorption mechanisms.
In the presence of NO2 and O2, barium carbonate is oxidized to barium nitrate and in the presence of CO, barium nitrate is reduced to barium carbonate. All rates are of first order with respect to the participating gas and solid phase components. All reaction constants are evaluated using Arrhenius' law. R20
R21
Barium Storage Capacity
Determines the maximum amount of nitric oxide that can be stored on the barium surface site.
Initial Surface Coverage fraction of Ba(NO3)2
Determines the coverage fraction of Ba(NO3)2 at the solid surface. Range: 0-1 (-)
Max Surface Coverage fraction of Ba(NO3)2
Determines the maximum surface coverage fraction of Ba(NO3)2 at the solid surface. This property can be specified as constant value or as function of temperature. Range: 0-1 (-)
K1 - K2
Determine the frequency factors used in the predefined ad/desorption mechanisms.
E1 - E2
Determine the activation temperatures used in the pre- ad/desorption mechanisms.
R22: HC Storage
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117
4. FIRE Aftertreatment Metal Storage Capacity
Determines the maximum amount of C3H6 that can be stored on the metallic surface site.
Initial Surface Coverage fraction of C3H6
Determines the coverage fraction of C3H6 at the solid surface. Range: 0-1 (-)
Max Surface Coverage fraction of C3H6
Determines the maximum surface coverage fraction of C3H6 at the solid surface. This property can be specified as constant value or as function of temperature. Range: 0-1 (-)
K1 - K2
Determine the frequency factors used in the predefined sorption-equilibrium and ad/desorption mechanisms.
E1 - E2
Determine the activation temperatures used in the pre-defined sorption-equilibrium and ad/desorption mechanisms.
4.1.4.4.1.3. Selective Catalytic Reduction (HSO SCR), Steady Kinetics This reaction model offers a set of seven conversion reactions that are typically used in SCR converters. This pre-defined model is setup in a way that three different reaction sections can be specified where in each section the reactions can be individually switched on. The name HSO is related to a typical SCR system where three different sections for Hydrolysis, SCR and Oxidation are used in one converter. If only one section is considered, the lengths of the two others sections can be simply set to zero. The model uses steady-state approaches for all SCR reactions as given by the Eley-Rideal mechanism. For the hydrolysis and all oxidation reactions also steady-state power-law reactions are applied. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. More detailed information about this model is given in Section HSO-SCR Catalyst Reactions, page [81] Steady-State Approach . The rate is assumed to be of first order with respect to both water vapor and isocyanic acid. The reaction constant is evaluated using Arrhenius' law. Length of Section 1 Length of Section 2
This is a dimensionless length that is used to specify up to three different reaction sections. The length of the third section is calculated by 1-Length_1-Length_2. If only one section is needed, set the length of section 1 to '1' and section 2 to '0'. Range: 0-1 (-)
The different reactions can be enabled/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. R1: HNCO Hydrolysis
118
The Eley-Rideal kinetic approach is commonly accepted in the literature for the selective reduction of nitric monoxide with ammonia. The denominator takes into account the inhibition effects of ammonia and each reaction constant is evaluated using Arrhenius' law.
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment
R2: NO Reduction
R3: NOx Reduction
R4: NO2 Reduction
R5: NH3 Oxidation 1
K
Determines the frequency factor used in the predefined power law mechanism.
E
Determines the activation temperature used in the pre-defined power law conversion mechanism.
The Eley-Rideal kinetic approach is commonly accepted in the literature for the selective reduction of nitric monoxide and dioxide with ammonia. The denominator takes into account the inhibition effects of ammonia and each reaction constant is evaluated using Arrhenius' law.
K1 - K2
Determine the frequency factors used in the predefined Eley-Rideal conversion mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined Eley-Rideal conversion mechanism.
The Eley-Rideal kinetic approach is commonly accepted in the literature for the selective reduction of nitric monoxide and dioxide with ammonia. The denominator takes into account the inhibition effects of ammonia and each reaction constant is evaluated using Arrhenius' law.
K1 - K2
Determine the frequency factors used in the predefined Eley-Rideal conversion mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined Eley-Rideal conversion mechanism.
The Eley-Rideal kinetic approach is commonly accepted in the literature for the selective reduction of nitric monoxide and dioxide with ammonia. The denominator takes into account the inhibition effects of ammonia and each reaction constant is evaluated using Arrhenius' law.
K1 - K2
Determine the frequency factors used in the predefined Eley-Rideal conversion mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined Eley-Rideal conversion mechanism.
The rate is assumed to be of first order with respect to ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
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119
4. FIRE Aftertreatment
R6: NH3 Oxidation 2
R7: NO Oxidation
K
Determines the frequency factor used in the predefined power law mechanism.
E
Determines the activation temperature used in the pre-defined power law conversion mechanism.
The rate is assumed to be of first order with respect to ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factor used in the predefined power law mechanism.
E
Determines the activation temperature used in the pre-defined power law conversion mechanism.
A reversible rate mechanism is commonly accepted in the literature for the oxidation of nitric monoxide. Two rate approaches are available. Each reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy. Approach 1
Approach 2
K
Determines the frequency factor used in the pre-defined reversible power-law conversion mechanism.
E
Determines the activation temperature used in the pre-defined reversible power-law conversion mechanism.
A
Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism.
4.1.4.4.1.4. Selective Catalytic Reduction (HSO SCR), Transient Kinetics This reaction model offers a set of nine conversion reactions that are typically used in SCR converters. This pre-defined model is setup in a way that three different reaction sections can be specified where in each section the reactions can be individually switched on. The name HSO is related to a typical SCR system where three different section for Hydrolysis, SCR, and Oxidation are used in one converter. If only one section is considered, the lengths of the two other sections simply can be set to zero. The model uses steady-state approaches for the hydrolysis, one of the ammonia and one of the nitric monoxide oxidation reactions. For the SCR reactions explicit ad-/desorption steps of ammonia at the solid surface are taken into 120
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment account. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. More detailed information about this model is given in page [83] Section HSO-SCR Catalyst Reactions, Transient Approach . Length of Section 1 Length of Section 2
This is a dimensionless length that is used to specify up to three different reaction sections. The length of the third section is calculated by 1-Length_1-Length_2. If only one section is needed set the length of section 1 to '1' and of section 2 to '0'. Range: 0-1 (-)
The different reactions can be en/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. R1: HNCO Hydrolysis
R2-R3: NH3 Adsoprtion, Desorption
The rate is assumed to be of first order with respect to both vapor and isocyanic acid. The reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factors used in the predefined power law mechanism.
E
Determines the activation temperatures used in the pre-defined power law conversion mechanism.
The adsorption rate is of first order with respect to ammonia in the gas phase and also proportional to the free site fraction at the surface. The desorption rate is proportional to the amount of ammonia stored at the surface. For the desorption a surface coverage dependency is additionally taken into account. Each reaction constant is evaluated using Arrhenius' law. R2
R3
NH3 Storage Capacity
Determines the maximum amount of ammonia that can be stored at the solid surface site.
Initial Surface Coverage Fraction of NH3
Determines the coverage fraction of NH3 at the solid surface. Range: 0-1 (-)
Coverage Determines a surface coverage dependency in the Dependency pre-defined ad/desorption mechanisms. (epsilon) Max Surface
Determines the maximum surface coverage fraction of NH3 at the solid surface. This property
FIRE BOOST Aftertreatment
121
4. FIRE Aftertreatment Coverage Fraction of NH3
can be specified as constant value or as function of temperature. Range: 0-1 (-)
NH3 Determines the order of NH3 surface coverage Surface fraction in the adsorption rate formulation. Coverage Range: 0-2 (-) Fraction Dependency m
R4: NO Reduction
R5: NOx Reduction
R6: NO2 Reduction
122
K1 - K2
Determines the frequency factors used in the predefined ad/desorption mechanisms.
E1 - E2
Determines the activation temperatures used in the pre- ad/desorption mechanisms.
The reaction rate is of first order with respect to nitric monoxide in the gas phase and it depends on the stored amount of ammonia at the surface. The reaction is additionally limited by a critical surface fraction of ammonia.
Critical Surface Coverage)
Determines a tuning factor that slows down the reaction rate above a critical surface coverage.
K
Determines the frequency factor used in the predefined transient conversion mechanism.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism.
The reaction rate is of first order with respect to nitric dioxide in the gas phase and it depends on the stored amount of ammonia at the surface. The reaction is additionally limited by a critical surface fraction of ammonia.
Critical Surface Coverage)
Determines a tuning factor that slows down the reaction rate above a critical surface coverage.
K
Determines the frequency factor used in the predefined transient conversion mechanism.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism.
The rate is assumed to be of first order with respect to stored ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment
R7: NH3 Oxidation 1
R8: NH3 Oxidation 2
R9: NO Oxidation
Critical Surface Coverage)
Determines a tuning factor that slows down the reaction rate above a critical surface coverage.
K
Determines the frequency factor used in the predefined transient conversion mechanism.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism.
The rate is assumed to be of first order with respect to stored ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factor used in the predefined transient oxidation mechanism.
E
Determines the activation temperature used in the pre-defined transient oxidation.
The rate is assumed to be of first order with respect to stored ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factor used in the predefined power-law oxidation mechanism.
E
Determines the activation temperature used in the pre-power-law transient oxidation.
A reversible rate mechanism is commonly accepted in the literature for the oxidation of nitric monoxide. Two rate approaches are available. The reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy. Approach 1
Approach 2
Temperature Determines the temperature dependency used in Dependency the pre-defined transient and reversible power-law (A) conversion mechanism. K
Determines the frequency factor used in the pre-defined transient and reversible power-law conversion mechanism.
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4. FIRE Aftertreatment
R10: NO2 Formation
E1
Determines the activation temperature used in the pre-defined transient and reversible power-law conversion mechanism.
K
Determines the frequency factor used in the predefined power-law conversion mechanism.
E
Determines the activation temperature used in the pre-defined power-law conversion mechanism.
4.1.4.4.1.5. NOx Trap Catalyst Reactions This reaction model offers a set of two conversion reactions for NO and a surface storage mechanism at one surface site. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. page [78] More detailed information about this model is given in Section TWC Catalyst Reactions . The different reactions can be enabled/disabled individually be clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. R1: CO-NO Redox Reaction
R2: NO Oxidation
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of carbon monoxide and reduction of nitric monoxide. The denominator takes into account an inhibition effect of carbon monoxide. Each reaction constant is evaluated using Arrhenius' law. The reaction order of carbon monoxide is a function of the carbon monoxide concentration itself and therefore the order changes between lean and rich conditions.
m
Determines the reaction order of nitric monoxide in the pre-defined reaction approach.
o
This is a tuning value in order to determine the reaction order of carbon monoxide in the predefined reaction approach.
K1 - K2
Determine the frequency factors used in the predefined conversion mechanism..
E1 - E2
Determine the activation temperatures used in the pre-defined conversion mechanism.
A reversible rate mechanism is commonly accepted in the literature for the oxidation of nitric monoxide. Two rate approaches are available. The reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy.
K
124
Determines the frequency factor used in the pre-defined reversible power-law conversion mechanism.
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4. FIRE Aftertreatment
R3-R4: Ba Storage
E
Determines the activation temperature used in the pre-defined reversible power-law conversion mechanism.
A
Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism.
In the presence of NO2 and O2, barium carbonate is oxidized to barium nitrate and in the presence of CO, barium nitrate is reduced to barium carbonate. All rates are of first order with respect to the participating gas and solid phase components. All reaction constant is evaluated using Arrhenius' law. R3
R4
Barium Storage Capacity
Determines the maximum amount of nitric oxide that can be stored on the barium surface site.
Initial Surface Coverage fraction of Ba(NO3)2
Determines the coverage fraction of Ba(NO3)2 at the solid surface. Range: 0-1 (-)
Max Surface Coverage fraction of Ba(NO3)2
Determines the maximum surface coverage fraction of Ba(NO3)2 at the solid surface. This property can be specified as constant value or as function of temperature. Range: 0-1 (-)
K1 - K2
Determine the frequency factors used in the predefined ad/desorption mechanisms.
E1 - E2
Determine the activation temperatures used in the pre- ad-/desorption mechanisms.
4.1.4.4.1.6. Lean NOx Trap (LNT) This reaction model offers a set of ten conversion reactions, surface storage on cerium and barium. The rate equations and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. The different reactions can be en/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. R1: H2 Oxidation
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
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4. FIRE Aftertreatment E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Reaction Order m
Determines the reaction order of nitric oxide in the pre-defined Langmuir-Hinshelwood conversion mechanism.
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
R2: CO Oxidation
Reaction Determines the reaction order of propene, nitric Orders m, n, oxide and oxygen in the pre-defined Langmuirp Hinshelwood conversion mechanism. R3: C3H6 Oxidation
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Reaction Determines the reaction order of oxygen and nitric Orders m, n oxide in the pre-defined Langmuir-Hinshelwood conversion mechanism. R4: NO Oxidation
126
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
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4. FIRE Aftertreatment Kinetic Determines a kinetic coefficient used in the Coefficient f pre-defined Langmuir-Hinshelwood conversion mechanism. Reaction Determines the reaction order of propene, nitric Orders m, n, oxide and oxygen in the pre-defined Langmuirp Hinshelwood conversion mechanism. R5: NO Reduction H2
K1
Determines the frequency factor used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1
Determines the activation temperature used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
R6: NO Reduction CO
Reaction Determines the reaction order of propene and nitric Orders m, n oxide in the pre-defined Langmuir-Hinshelwood conversion mechanism. R7: NO Reduction C3H6 K1
Determines the frequency factor used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1
Determines the activation temperature used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
R8: NO2 Reduction CO
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127
4. FIRE Aftertreatment E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Reaction Order m
Determines the reaction order of nitric oxide in the pre-defined Langmuir-Hinshelwood conversion mechanism.
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Ce Storage Capacity
Determines the maximum amount of oxygen that can be stored on the cerium surface site.
Initial Surface Coverage Fraction of CeO2
Determines the coverage fraction of CeO2 at the solid surface. This property can be specified as a constant value or as a function of the catalyst length. Range: 0-1 (-)
K1 - K2
Determine the frequency factors used in the predefined ad/desorption mechanism. Determine the frequency factors used in the predefined ad/desorption mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined ad/desorption mechanism.
R9: NO2 Reduction C3H6
R10: Water Gas Shift Reaction
R11: Surface Storage on Cerium
Reaction Determines the reaction order of oxygen stored on Orders m, n, the surface and oxygen ratio at the surface in the p, q pre-defined ad/desorption mechanism. 128
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4. FIRE Aftertreatment R12-R16: Surface Storage on Barium Carbonate
R12
R13
R14
R15
R16
BaCO3 Storage Capacity
Determines the maximum amount of nitric oxides that can be stored on the barium carbonate clusters (rate approach 1) and barium carbonate surface site (rate approach 2).
Initial Surface Coverage Fraction of Ba(NO3)2
Determines the coverage fraction of Ba(NO3)2 at the solid surface. This property can be specified as a constant value or as a function of the catalyst length. Range: 0-1 (-)
Rate approach 1
This activates the sophisticated ash core model where the NO and NO2 molecules are stored as Ba(NO3)2 in barium cluster particles. Additional differential equations are solved to determine mole fractions of all gas phase species on the dimensionless ash core front position in the barium cluster particles. The ash core front moves from the outer radius ( =1) toward the center ( =0) page [88] of the cluster particle (see sketch in Fig. 36
Rate approach 2
This activates the surface storage model where the NO and NO2 molecules are stored as Ba(NO3)2 on the catalytic surface represented by the surface coverage fraction ZBa(NO3)2.
K1 - K5
Determine the frequency factors used in the pre-defined ad/desorption mechanism for Rate approach 1 and Rate approach 2. Determine the frequency factors used in the pre-defined ad/desorption mechanism for Rate approach 1 and Rate approach 2.
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4. FIRE Aftertreatment E1 - E5
Determine the activation temperatures used in the pre-defined ad/desorption mechanism.
Reaction Determines the reaction order of Ba(NO3)2 in the Orders m, n, pre-defined ad/desorption mechanism of Rate p, q, r approach 2. R12-R16: Ash Core Model
The ash core model is activated by Rate approach 1. R12
R13
R14
R15
R16
Particle Radius
Determines the radius RBa,p of the barium cluster particle. Typical Value: 5.0e-8 (m)
Min Specific Surface
Determines the minimum specific particle surface area ap,min. 2 3 Typical Value: 48.4 (m /m )
Max Specific Surface
Determines the minimum specific particle surface area ap,max. 2 3 Typical Value: 452637 (m /m )
Pore Diffusion Coefficient
Determines the diffusion coefficient DBa,p of the barium cluster particle. This property can be specified as constant value or as function of temperature. 2 Typical Value: 2.672e-14 (m /s)
Scaling The LNT model assumes that NOx desorption Factor (regeneration) takes place faster than NOx During adsorption (storage). This factor increases the pore Regeneration diffusion coefficient during regeneration. Typical Value: 10 (-)
130
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4. FIRE Aftertreatment 4.1.4.4.1.7. User Defined Reactions (Without Archive) This reaction model offers the possibility to define an arbitrary number of conversion reactions and surface storage mechanisms at different surface sites. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. More page [78] detailed information about this model is given in Section TWC Catalyst Reactions . 4.1.4.4.1.7.1. Surface Species Select Surface species in the parameter tree and select the Activate surface species toggle switch to access the following input fields: Typical Values and Ranges Number of surface sites
Defines the total number of site types on the catalytic surface. Example: Describe the active surface of a 3-way catalytic converter by using 2 sites, i.e. 'Platinum' and 'Rhodium'.
0-4 (-)
Ratio catalytic/ geometric surface area
Determines the ratio between the catalytic ('reactive') and the geometric surface area of the catalyst.
1-30 (-)
After entering a value >0 for Number of surface sites, the project tree expands and the corresponding input window for each site type appears. Typical Values and Ranges Name
Defines the name of the surface site. This string is arbitrary, e.g. Platinum.
NoName
No. of surface species on site
Determines the number of surface species on this site.
1-3 (-)
Site density
Determines the value of for this site.
in equation (Eq.34
page [15]
)
2
0-0.03 (mol/m )
Select Edit surface species to open a table: Typical Values and Ranges Names
Specifies the name of the species stored on the Surface surface as strings. As for the gas phase species, Species1 FIRE must find the names of all species in the internal thermochemistry database or in the CHEMKIN database thermdat. The number of surface sites occupied by the species is specified as an extra option after the species name encased by two slashes "/". The default value of 1 requires no extra specification. E.g.: H2 /2/ means that H2 is occupied by two surface sites
Initial coverage fractions
Defines the surface coverage fractions at start-up. As for the mass fractions these values must add up to 1.
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0-1 (-)
131
4. FIRE Aftertreatment Note: As for the gas phase species, FIRE must find the names of all surface species in the internal thermochemistry database or in the CHEMKIN database thermdat. 4.1.4.4.1.7.2. Stoichiometry Specification Select Stoichiometry specification in the parameter tree and then enter the following: Typical Values and Ranges Number of reactions
Defines the number of chemical reactions in the case. 0-50 Select Stoichiometry to open a table as shown in the following figure.
Figure 43. Stoichiometry Specification Window
A set of chemical reactions can be entered. The input conventions for each reaction are: • Use one line for each reaction • Only use species defined either as gas phase species or as surface species • Indicate surface species by adding "_S1", "_S2", "_S3", etc to the species' name. The index depends on the actual surface site index, e.g. "_S2" for all surface species on the second surface site. • Separate reactants from products by "=" • Separate species by "+" • Separate species from stoichiometric coefficient by "*" • Use "/" to specify extra options like arbitrary reaction order "RO" or the surface coverage parameters "COV". • Blanks between the separators ("=", "*", "+", and "/") and the species names or values are ignored. • Use UPPERCASE characters for species names • For reversible reactions it is recommended to specify the forward and backward reactions including all extra options separately, if the Equilibrium option of the current reaction is disabled. E.g.: NO + 0.5*O2 = NO2 NO2 = NO + 0.5*O2 132
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment The mass balance and the conservation of surface sites are checked by FIRE at runtime. An example for oxygen storage is O2+2*PT_S1=2*O_S1 Particulate filter model: • "C_P" is the identifier for the solid carbon in the soot layer. An example for the oxidation of solid carbon to carbon dioxide is: C_P+O2=CO2 Arbitrary reaction order: page [26] For elementary reactions the reaction orders (Eq.62 ) are determined by the stoichiometric coefficients. However, often in real-world applications measurements find that the reaction rate is proportional to the concentration of a species raised to some arbitrary power. FIRE allows declaring the reaction order for any species participating in the chemical reaction by specification of the keyword 'RO'. Therefore, the user has to attach the extra options starting with "/", setting the keyword "RO", the species name and the new value of the reaction order, as described by: / RO / RO The following example shows the change of the reaction orders for the NO-oxidation. Forward and backward reactions are specified separately. NO + 0.5*O2 = NO2 / RO NO 1.04 / RO O2 0.46 NO2 = NO + 0.5*O2 / RO NO2 1.03 Note, if the Activation of the current reaction is set to User, the reaction order is not changed automatically, since in this case the reaction rate has to be specified by the user in use_catrat.f or use_dpfrat.f. Surface coverage parameters: FIRE allows modifying the Arrhenius expression for the reaction rate constant by the coverage of some surface species (identified by strings "_S1", "_S2", etc attached to the species name). page [27] There the three surface coverage parameters of reaction i in Eq.66 , , , and can be specified as extra option via the keyword 'COV', as described by: / COV / COV ... The following example shows the set-up of the surface coverage parameters for the ammonia desorption: ME-NH3_S1 = NH3 + ME_S1 / COV ME-NH3 0.0 1.0 -0.256 Here = 0.0, = 1.0 and = -0.256. Note, if the Activation of the current reaction is set to User, the surface coverage parameters are not taken into account automatically, since in this case the reaction rate has to be specified by the user in use_catrat.f or use_dpfrat.f. 4.1.4.4.1.7.3. Kinetic Parameters Specification Select Kinetic parameters specification in the parameter tree to access the following input fields. Typical Values and Ranges Number of kinetic models
Defines the number of reaction kinetic parameter sets. Select Name of kinetic model to open a table: The actual name given to a kinetic model is used for the .fla file output only. A certain model is assigned to a catalyst via its index.
1-3 (-)
In general three flags (activation type, chemical equilibrium, sticking coefficient type) and three parameters (frequency factor, temperature exponent, activation energy) should be supplied for each reaction. Typical Values and Ranges Activation
On:
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On (default) 133
4. FIRE Aftertreatment Activates the standard rate equation (equation Eq.61 ). Off: Completely deactivates the reaction. User: The user can specify the rate of the reaction in use_catrat.f. If the catalyst is assigned to be a particulate filter, the user specifies the rate of the reaction in use_dpfrat.f.
page [26]
Equilibrium
Activates/deactivates the chemical equilibrium for Off (default) this reaction. If active, the equilibrium constant Kc is calculated to determine the backward rate constant kr page [27] page [26] (Eq.66 ) as used in equation Eq.61 . Note, if the Activation of the current reaction is set to User, the equilibrium calculation is skipped, since then the reaction rate has to be specified in use_catrat.f or use_dpfrat.f.
Sticking Coefficient
Activates/deactivates the sticking coefficient type rate equation (surface reactions only). Note, if the Activation of the current reaction is set to User, the equilibrium calculation is skipped since in this case the reaction rate has to be specified in use_catrat.f or use_dpfrat.f.
Off (default)
Frequency factor
Frequency factor kf of the Arrhenius rate law; the actual units depend on the type of reaction.
0-10 s, k)
Use cgs units
When enabled, all frequency factors are interpreted in Disabled the cgs unit system (mol, cm, s). (default)
Temperature Exponent
Temperature exponent b of the Arrhenius rate law.
0-1 (-)
Activation Energy
Activation energy E of the Arrhenius rate law.
0-50000 (kJ/ kmol)
15
(kmol, m,
indicates that the user can input values in a table relating to the number of kinetic models. The following options are available: 1. Constant This is the default setting and specifies that the parameter value entered in the field will remain constant for all kinetic models. 2. Model Select it to open an input table where parameter values can be entered for each kinetic model separately. Select the User parameter toggle switch to activate the following: Default
134
Default
Default
UP_1
0
UP_6
0
UP_11
0
UP_2
0
UP_7
0
UP_12
0
UP_3
0
UP_8
0
UP_13
0
UP_4
0
UP_9
0
UP_14
0
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment UP_5
0
UP_10
0
UP_15
0
The user can input up to 15 user parameters for each reaction. These values are not used by FIRE directly, but they can be accessed by the user in use_catrat.f when supplying his own kinetic models. 4.1.4.4.1.8. Map Based Conversion This model comprises different input of conversion maps, where the user can specify the conversion of selected species depending on several conditions like massflow, substrate temperature and further more. Species conversion maps can be added or removed by clicking the right mouse button on the tree node Map Based Conversion. Conversion Definition The following input data has to be specified: Typical Values and Ranges Species
Enter the name of a General Species whose conversion is specified for. If the species is not contained in the Gas Composition then the Conversion map is ignored.
Conversion
Select the conversion specification Constant: Enter a constant conversion value. Table: Specify the conversion as a function of one of the conversion dependencies. Map: Specify the conversion as a function of two of the conversion dependencies. If Constant is selected, enter a value for constant species conversion.
Table for Conversion of The following input data has to be specified: Typical Values and Ranges Conversion Dependency
The following Conversion Dependencies are available: • Inlet Gas Temperature • Mean Solid Temperature • Inlet Massflow • Inlet Excess Oxygen Ratio • Inlet GHSV
Conversion Table
Specify the conversion as a function of the selected Conversion Dependency.
Map for Conversion of The following input data has to be specified:
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135
4. FIRE Aftertreatment Typical Values and Ranges Conversion Dependency 1 and Conversion Dependency 2
The following Conversion Dependencies are available: • Inlet Gas Temperature • Mean Solid Temperature • Inlet Massflow • Inlet Excess Oxygen Ratio • Inlet GHSV
Conversion Map
Specify the conversion as a function of the selected Conversion Dependency 1 and Conversion Dependency 2.
4.1.4.4.1.9. User Defined Reactions This is an interface to load custom kinetic models developed using the AVL User Coding Interface (AUCI). Loading and maintaining an AUCI Catalytic Reaction Mechanism In general an arbitrary number of AUCI Catalytic Reaction Mechanism models can be loaded. In order to add or delete an AUCI model click Insert and Remove repsectively next to the table. An AUCI model ("Archive") is stored in an ucp and uca file respectively, and the existing predefined kinetic models are available as ucp files in the installation. An already loaded Archive can be enabled or disabled in the simulation by selecting Yes and No respectively in the first column of the table. The buttons below the table provide the following functions: Button
Description
Select Archive
Opens a filebrowser to select an ucp or uca file.
Reload Archive
Reload the Archive from the selected row. In order to reset the Model Parameters with the default values from the AUCI model click "No" in the pop-up box "Keep current parameter values?".
Edit Archive
Launches AUCI Catalytic Reaction Mechanism graphical user interface (GUI). If a row has been selected in the table the AUCI model will be opened in that GUI.
Model Parameters
Interface to access the public model parameters from the selected Archive. In the pop-up window these parameters can be modified and global/local parameters can be assigned to them for access in the Parameter or Case Explorer.
Designing an AUCI Catalytic Reaction Mechanism AUCI is a graphical user interface that supports designing custom kinetic models for catalysts and filters as well as custom transfer models for heat and mass transfer as well as pore diffusion. Please, refer to the related AUCI documentation for more details on using AUCI. 4.1.4.4.2. Transport Model At "My_Transport" different pore diffusion models can be selected. The transport model for the active washcoat layer model determines the calculation of the diffusion coefficient Dk,eff for every species of the pore diffusion model (see section Transport Models 136
page [21]
).
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment Note: For specification of the transport model, Activate Washcoat Layer (WCL) Model must be active. The transport model has to be specified for each washcoat layer separately. The following models are available: 4.1.4.4.2.1. Constant Pore Diffusion For this model constant diffusion coefficients are applied. If Constant Pore Diffusion is selected, the following input data has to be specified: Typical Values and Ranges Layer Porosity
Determines the porosity wcl of the washcoat layer (= gas void fraction).
0-1 (-)
Diffusion Coefficients
Determines the effective diffusion coefficient Dk,eff of every species in the washcoat layer.
10
-14
-5
2
-10 (m /s)
4.1.4.4.2.2. Effective Pore Diffusion The effective diffusion coefficient is calculated with the free gas flow diffusion coefficient adapted with the washcoat layer porosity and tortuosity. A scaling factor allows linear variation of the calculated value for every species. If Effective Pore Diffusion is selected, the following input data has to be specified: Typical Values and Ranges Layer Porosity
Determines the porosity wcl of the washcoat layer (= gas void fraction).
0-1 (-)
Tortuosity
Determines the tortuosity layer.
1-5 (-)
Scaling Factors
Determines the scaling factors multiplied to the calculated effective diffusion coefficient Dk,eff of every species in the washcoat layer.
wcl
of the washcoat
0-100 (-)
4.1.4.4.2.3. Random Pore Diffusion This model assumes that the washcoat features two distinct characteristic pore size diameters, called macro- and micro-pores. The two macro and micro pore diffusion coefficients are combined applying probabilistic and geometrical considerations. If Random Pore Diffusion is selected, the following input data has to be specified: Typical Values and Ranges Macropore Porosity
Determines the porosity (= gas void fraction) of the macro pores.
Micropore Porosity
Determines the porosity (= gas void fraction) of the micro pores.
0-1 (-)
Macropore Diameter
Determines the mean diameter of the macro pores.
10 -10 (m)
Micropore Diameter
Determines the mean diameter of the micro pores.
10 -10 (m)
FIRE BOOST Aftertreatment
M
0-1 (-)
-8
-4
-9
-5
137
4. FIRE Aftertreatment Scaling Factors
Determines the scaling factors multiplied to the calculated effective diffusion coefficient Dk,eff of every species in the washcoat layer.
0-100 (-)
4.1.4.4.2.4. Parallel Pore Diffusion The model combines the transport effects of the pure gas phase and Knudsen diffusion assuming both transport effects are taking place in parallel. If Parallel Pore Diffusion is selected, the following input data has to be specified: Typical Values and Ranges Layer Porosity
Determines the porosity wcl of the washcoat layer (= gas void fraction).
0-1 (-)
Tortuosity
Determines the tortuosity layer.
1-5 (-)
Pore Diameter
Determines the mean pore diameter of washcoat layer.
10 -10 (m)
Scaling Factors
Determines the scaling factors multiplied to the calculated effective diffusion coefficient Dk,eff of every species in the washcoat layer.
0-100 (-)
wcl
of the washcoat
-9
-3
4.1.4.4.2.5. User Pore Diffusion The effective diffusion coefficient is calculated in the user function use_catwcltra.f. An example of the user function can be found in the installation. If User Pore Diffusion is selected, the following input data can be specified: Typical Values and Ranges Layer Porosity
Determines the porosity wcl of the washcoat layer (= gas void fraction).
Parameter Label
Parameter strings which can be used in the user-function for identification of the Transport Parameter.
Transport Parameter
Double precision value which can be used in the user function.
0-1 (-)
4.1.4.5. Catalyst Reaction Solver Specification Select Catalyst Reaction Solver Specification in the parameter tree to access the following input fields. 4.1.4.5.1. Reaction Solver Parameters Typical Values
138
Catalytic reaction Specifies the maximum number of sub-iterations solver: max. no. of that the solver carries out for the catalytic reactions. iterations Normally no changes are required.
20000 (-)
Catalytic reaction solver: relative tolerance
1e-05 (-)
Specifies the relative tolerance for the solution of the reaction rate equation system. Normally no changes are required.
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment Catalytic reaction solver: absolute tolerance
Specifies the absolute tolerance for the solution of the 1e-08 (-) reaction rate equation system. Normally no changes are required.
4.1.4.5.2. General Settings Typical Values and Ranges Implicit solution of Normally the reaction rate equation system is solved chem. kinetics at the beginning of a time step. Depending on the problem (i.e. chemical equilibrium problems) it can be necessary to solve it within the time step also, i.e. th specify 5 to solve it every 5 iteration for large time steps. A value of 0 turns off implicit solver calls.
0-20 (-)
Reaction solver block size
In order to speed up the solution of the chemical 1-50 (-) kinetics, the corresponding equation system is not solved for each cell separately but more cells are considered for each solver call. The number of cells is given here.
Solve catalytic reactions
Activates/deactivates the solution of the kinetic rate equation system and the corresponding source terms for heat and mass. If deactivated, only the heat exchange between the gas and the monolith is calculated without chemical reactions.
Active (default)
Consider enthalpy Activates/deactivates the consideration of the sources from enthalpy sources from the catalytic reactions in the catalytic reactions enthalpy equation for the solid material ('isothermal'). If deactivated, only the species sources from the catalytic reactions are considered.
Active (default)
Activate user Activates/deactivates the user function model for use_catmod.f. This user function is called by FIRE catalytic reactions instead of the FIRE catalyst reaction model. Here (use_catmod.f) the user defines the source terms for the species transport equations and the enthalpy equation. It is typically used by advanced users who have their own models available and need full flexibility for their implementation. Please contact FIRE support for more information on use_catmod.f.
Inactive (default)
4.1.4.5.3. Reaction Solver Flags Select Reaction solver flags in the parameter tree to access the following input fields. Typical Values and Ranges On / Off
Activates/deactivates input flags. The 23 input fields are for AVL internal use only.
Off (default)
4.1.4.6. 2D Output Specification Select 2D Output Specification in the parameter tree to access the following input fields.
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139
4. FIRE Aftertreatment 4.1.4.6.1. Substrate Data Typical Values and Ranges Mean catalyst temperature
Activates/deactivates the output of the mean catalyst temperature to the .fla file and to the .fl2 file.
Active (default)
Maximum catalyst temperature
Activates/deactivates the output of the maximum catalyst temperature to the .fla file and to the .fl2 file.
Active (default)
Minimum catalyst Activates/deactivates the output of the minimum temperature catalyst temperature to the .fla file and to the .fl2 file.
Active (default)
Solid heat capacities
Inactive (default)
Activates/deactivates the output of the minimum, maximum and mean value of the solid specific heat capacity (J/(kg·K)) of the catalyst to the .fla file and to the .fl2 file. Data is only written for temperature dependent values. Click on
Solid thermal conductivities
Activates/deactivates the output of the minimum, Inactive (default) maximum and mean value of the solid thermal conductivity (W/(m·K)) of the catalyst to the .fla file and to the .fl2 file. Data is only written for temperature dependent values. Click on
Gradient of solid temperature
to define table data.
to define table data.
Activates/deactivates the output of the maximum and mean value of the solid temperature gradient (K/m).
Inactive (default)
4.1.4.6.2. Pressure Drop Typical Values and Ranges Catalyst pressure Activates/deactivates the output of the total pressure Active (default) drop drop (Pa) of the catalyst to the .fla file and to the .fl2 file. 4.1.4.6.3. Flow Uniformities Typical Values and Ranges Uniformity index
Activates/deactivates the output of the uniformity index Inactive (default) (-) of the catalyst to the .fla file and to the .fl2 file. The uniformity index is calculated in the first porous cell layer according to the equation where is the cell velocity vector, and is the crosssection area of face adjacent to cell i. Note: In the first porous cell layer, the gas velocity already points in the converter direction .
Centricity index
140
Activates/deactivates the output of the centricity index Inactive (default) (-) of the catalyst to the .fla file and to the .fl2 file.
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment The centricity index is determined at the inlet face selection of the particulate filter according to equation , where the eccentricity
denotes the
distance between the center of the mean mass flow rate and the center of gravity, as described by
is the equivalence radius, determined by the equation
.
is the mass flow rate through face j is the face area is the position vector of the face center. Max./Min. inlet velocities
Activates/deactivates the output of minimum and the Inactive maximum inlet velocity (m/s), and the position of the maximum inlet velocity (m) of the catalyst to the .fla file and to the .fl2 file. The max. and min. inlet velocity are determined in the last non-porous fluid cell layer in front of the particulate filter.
High and low speed inlet area
Activates/deactivates the output of the high and low Inactive (default) speed inlet areas (-) of the catalyst to the .fla file and to the .fl2 file. The high speed inlet area is defined as the inlet area fraction, where the flow velocity is greater than the bound of . The low speed inlet area is the inlet area fraction, where the flow velocity is smaller than . Both the high and the low speed inlet areas are evaluated in the first porous cell layer of the catalyst.
Tangential inlet velocity
Activates/deactivates the output of the mean, the Inactive(default) minimum, and the maximum tangential velocity (m/s) of the catalyst inlet to the .fla file and to the .fl2 file. The tangential inlet velocity is the amount of the velocity components which point into the direction perpendicular to the catalyst direction. It is evaluated in the last non-porous fluid cell layer in front of the catalyst.
Tangential inlet Activates/deactivates the output of the mean, the pressure gradient minimum, and the maximum tangential pressure gradient [Pa/m] of the catalyst inlet to the .fla file and to the .fl2 file. The tangential inlet pressure gradient is the amount of the gradient components which point into the direction
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Inactive (default)
141
4. FIRE Aftertreatment perpendicular to the catalyst direction. It is evaluated in the last non-porous fluid cell layer in front of the catalyst. Gas hourly space Activates/deactivates the output of the gas hourly velocity (GHSV) space velocity at operation conditions (GHSV) (1/h) and the gas hourly space velocity at norm conditions (GHSVn) (1/h) of the catalyst to the .fla file and to the .fl2 file. The gas hourly space velocity is the volume flux of the gas divided by the entire volume of the catalyst or particulate filter. The GHSV at operation conditions is calculated by:
Inactive (default)
The GHSVn at norm conditions is calculated by:
where the gas density 1.013 bar.
is evaluated at 273.15 K and
4.1.4.6.4. Conversions Typical Values and Ranges Species conversions
Activates/deactivates the output of the species' conversions to the .fla file and to the .fl2 file. The conversion C for species k is calculated as:
Surface coverage Activates/deactivates the output of the mean surface fraction coverage fractions (-) of the surface species of the catalyst to the .fla file and to the .fl2 file.
Inactive (default)
Excess oxygen ratio at inlet
Inactive (default)
The excess oxygen ratio is the amount of molecular oxygen in the gas divided by the amount of required oxygen for full combustion of carbon and hydrogen minus the provided oxygen in nitric-oxides and other oxygen compounds. z is the number of oxygen in the molecule AOz where A is an arbitrary element. In the
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Active (default)
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment molecule CxHy is x the number of carbon and y the number of hydrogen atoms respectively. Redox ratio at inlet
Inactive (default)
The redox ratio RR is the amount of oxygen required for full oxidation of carbon and hydrogen divided by the amount oxygen available in the gas-phase. A is an arbitrary element, z the number of oxygen atoms in the molecule AOz. x and y are the number of carbon and hydrogen atoms in an arbitrary composition of a hydrocarbon CxHy. 4.1.4.6.5. Washcoat Layer Results of the washcoat layer (WCL) model can be plotted as mean values over the whole layer, and they can be plotted individually for certain washcoat layer depths of selected mesh cells of the catalyst monolith. Therefore, one has to specify the cells at Select monolith cells for detailed 2D result output. The following results are available for both enabled and disabled washcoat layer model. The following input fields are available: Typical Values and Ranges WCL Mole Fraction
Activates/deactivates the mean value output and the selected cell output of the species' mole fractions to the .fla file and to the .fl2 file.
Inactive (default)
WCL Mass Fraction
Activates/deactivates the mean value output and the selected cell output of the species' mass fractions to the .fla file and to the .fl2 file.
Inactive (default)
WCL Species Concentration
Activates/deactivates the mean value output and the selected cell output of the species' concentrations fractions to the .fla file and to the .fl2 file.
Inactive (default)
WCL Effective Diffusion Coefficient
Activates/deactivates the mean value output and the selected cell output of the species' effective diffusion coefficients to the .fla file and to the .fl2 file. Only available for enabled washcoat layer model.
Inactive (default)
WCL Species Rate
Activates/deactivates the mean value output and the Inactive (default) selected cell output of the species' rates to the .fla file and to the .fl2 file.
WCL Reaction Rate
Activates/deactivates the mean value output and the Inactive (default) selected cell output of the reaction rates to the .fla file and to the .fl2 file.
WCL Stored Species Fraction
Activates/deactivates the mean value output and the selected cell output of the stored species' fractions to the .fla file and to the .fl2 file.
Inactive (default)
WCL Stored Species Loading
Activates/deactivates the mean value output and the selected cell output of the stored species' loadings to the .fla file and to the .fl2 file.
Inactive (default)
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4. FIRE Aftertreatment 4.1.5. Particulate Filter Specification To add a Particulate Filter (DPF) to the project, click on Aftertreatment TNG in the parameter tree with the right mouse button and select DPF: Insert from the submenu. To delete a DPF from the project, click on the name of the DPF (i.e. DPF[1]) with the right mouse button and select Remove from the submenu. The specification of the particulate filter follows the input concept of the catalytic converter page [100] presented in Section Catalyst Specification . Figure 44. DPF Specification Parameter Tree
Copy from DPF allows the complete set of input data to be copied from DPF[X] to the present DPF. Figure 45. Copy from DPF function
4.1.5.1. General Particulate Filter Specification Select DPF specification in the parameter tree to open the following window: Figure 46. DPF Specification Window
4.1.5.1.1. Particulate Filter Specification Typical Values and Ranges
144
Cell selection
Supply a cell selection that defines the geometry NoSelection of the particulate filter. (default)
Inlet face selection
Supply a face selection that defines the inlet plane of the particulate filter.
NoSelection (default)
Outlet face selection
Supply a face selection that defines the outlet plane of the particulate filter.
NoSelection (default)
Monolith initialization temperature
Determines the initial temperature of the particulate filter.
293.15-1500 (K)
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment 4.1.5.1.2. Square Cell + Asymmetrical Cell PF Click on Square + Asymmetrical Cell PF to obtain the parameter specification of the square cell PF. Typical Values and Ranges 2
Cell density (CPSI) Determines the type of monolith: Number of channels 2 per in .
100-900 (1/in )
Wall thickness
0.006-0.015 (in)
Determines the thickness of the monolith's walls = Wall.
Enable Enables the calculation for asymmetrical channel Asymmetrical diameters. Channel Diameters
Off (default)
Ratio of Channel Diameters
1-1.4 (-)
Determines the ratio of the channel diameters (d1/d2, page [144] see Fig. 46 ).
4.1.5.1.3. Simplified Square Cell PF Click on Simplified Square Cell PF to obtain the parameter specification of the square cell PF with equal inlet and outlet channel diameter. The simplified square cell PF corresponds to a Square + Asymmetrical Cell PF with diameter ratio of 1. Typical Values and Ranges Open frontal area (OFA)
Determines the open frontal area (= fluid volume fraction) of monolith ( g).
0.5-0.75 (-)
Hydraulic diameter
Determines the hydraulic diameter of the monolith (d). 0.001-0.005 (m)
4.1.5.1.4. Hexahex Click on Hexahex to obtain the following parameter specification. Typical Values and Ranges 2
Cell density (CPSI) Determines the total number of inlet and outlet 2 channels per in .
200-500 (1/in )
Wall thickness
Determines the thickness of the monolith's walls = Wall.
0.004-0.015 (in)
Inlet Channel Side Ratio (a/b)
Determines the ratio between the side lengths a and b of the hexagonal inlet channel.
0.666 (-) (default)
Perimeter Efficiency (a)
Since the side length a is located adjacent to another inlet channel wall of side length a, it is expected that there is reduced filtration along this wall. The Perimeter Efficiency determines the fraction of the side length used for filtration and is in the range between 0. and 1. 1. soot deposition along the entire wall 0. no soot deposition along this wall
0.0-1.0 (-)
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4. FIRE Aftertreatment 4.1.5.1.5. Hex3 Click on Hex3 to obtain the following parameter specification. Typical Values and Ranges 2
Cell density (CPSI) Determines the total number of inlet and outlet 2 channels per in .
200-500 (1/in )
Wall thickness
Determines the thickness of the monolith's walls = Wall.
0.004-0.015 (in)
Inlet Channel Side Ratio (a/b)
Determines the ratio between the side lengths a and b of the hexagonal inlet channel.
0.81 (-) (default)
Perimeter Efficiency (a)
Since the side length a is located adjacent to another inlet channel wall of side length a, it is expected that there is reduced filtration along this wall. The Perimeter Efficiency determines the fraction of the side length used for filtration and is in the range between 0. and 1. 1. soot deposition along the entire wall 0. no soot deposition along this wall
0.0-1.0 (-)
4.1.5.1.6. General Cell PF Click on General Cell PF to obtain the parameter specification of any arbitrary inlet channel geometry which can be reproduced by multiple reflection of the general symmetry element (GSE). Note, the GSE is the geometrical base of the PF inlet channel geometries in BOOST/ FIRE since it determines the formation and structure of the soot and ash layer. The Unity Cell represents the smallest repetitive element for reflection to represent the PF geometry consisting of inlet and outlet channels. Typical Values and Ranges 100-900 (1/in )
Nr of Inlet Determines the number of inlet channels per unity Channels per Unity cell. Cell
1-3 (-)
Nr of Outlet Determines the number of outlet channels per unity Channels per Unity cell. Cell
1 (-)
Nr of GSEs per Inlet Channel
Determines the number of general symmetry elements per single inlet channel.
1-12 (-)
Wall thickness
Determines the thickness of the monolith's walls = wall.
0.004-0.015 (-)
Center Corner Determines the sum of the angles Angle (alpha+beta) general symmetry element.
146
2
Cell density (CPSI) Determines the total number of inlet and outlet 2 channels per in .
and
of the
45-90 (deg)
Right Corner Angle (gamma)
Determines the angle
of the GSE.
45-90 (deg)
Left Corner Angle (phi)
Determines the angle
of the GSE.
45-90 (deg)
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment Side length (l1)
Determines the length of the first side along the channel wall of the GSE.
0.1-1 (mm)
Side length (l2)
Determines the length of the second side along the channel wall of the GSE.
0.1-1 (mm)
Filtration Efficiency at l1
The Filtration Efficiency determines the faction of the side length l1 used for filtration and is in the range between 0. and 1. 1. soot deposition along the entire wall 0. no soot deposition along this wall.
0-1 (-)
Filtration Efficiency at l2
The Filtration Efficiency determines the fraction of 0-1 (-) the side length l2 used for filtration and is in the range between 0. and 1. 1. soot deposition along the entire wall 0. no soot deposition along this wall.
Channel Shape Factor
Determines the difference of the pressure drop due to the gas flow in the channels between the present channel and a channel of circular shape. The shape factor is 0.89 for squared channels 0.95 for hexagonal channels 0.98 for octagonal channels, and 1.0 for channels with circular cross-section.
Outlet Channel Perimeter
Determines the perimeter of the single outlet channel. 1-10 (mm)
Outlet Channel Cross Section
Determines the cross-section of the single outlet channel.
0.5-1 (-)
2
0.5-5 (mm )
4.1.5.1.7. Physical Properties Select DPF Physical Properties in the parameter tree to access the following input fields. Typical Values and Ranges Density
Determines the bulk density of the monolith material considering the volume in the pores.
400-2000 (kg/ 3 m )
Thermal conductivity
Determines the thermal conductivity of the monolith material (= bulk solid material considering the volume in the pores). The thermal conductivity can either be specified as a constant value or as a table where the value changes as a function of temperature. Click on
0.1-50 (W/(m·K))
to define table data. Specific heat
Determines the specific heat of the monolith material 500-2000 (J/ (= bulk solid material considering the volume in the (kg·K)) pores). The specific heat can either be specified as a constant value or as a table where the value changes as a function of temperature. Click on table data.
Anisotropic cond. Factor
to define
Corrects the diffusion coefficients of the solid temperature equation normal to axial direction. A
FIRE BOOST Aftertreatment
0-10 (-) 147
4. FIRE Aftertreatment value of 1.0 simulates an isotropic conductivity. A value of 0.5 would be a good choice for monoliths. The anisotropic conduction factor is not used if the user-defined parameter ATM_ACTIV_RADIATION is specified and the current catalyst is selected (Fig. page [106] 39 ). Then the effective thermal conductivity including radiation is used instead of the default anisotropic model (see section Anisotropic Heat page [10] Conduction Matrix ). 4.1.5.1.7.1. Glueing Zones Typical Values and Ranges On/Off
Activates the consideration of glueing zones within particulate filters (e.g. SIC-PFs).
Off (default)
Selection
Specifies the glueing zone cell selection. This selection must not additionally be defined as particulate filter cell selection.
NoSelection (default)
Initialization temperature
Determines the initial temperature of the glueing material.
293.15-1500 (K)
Density
Determines the density of the glueing material.
400-2000 (kg/ 3 m )
Thermal Conductivity
Determines the thermal conductivity of the glueing material.
0.1-50 (W/(m·K))
Specific Heat
Determines the specific heat of the glueing material.
500-2500 (J/ kgK)
Filter area reduction
Activates the consideration of the filter area reduction of inlet channels which are directly adjacent to the glueing zones. A correct treatment of the filter area reduction requires a mesh size of these cells in the range of the inlet channel size.
Off (default)
4.1.5.1.7.2. Reduction of Heat Conduction Typical Values and Ranges
148
On/Off
Activates the local reduction of the heat conduction on a certain region in the particulate filter defined by a face selection of internal faces. Before the glueing zone model was available, this model was the only rough approximation of the heat transfer change in segmented particulate filters.
Off (default)
Selection
Face selection of internal faces on which the head conduction is multiplied with the factor defined at Reduction factor.
NoSelection (default)
Reduction factor
Heat reduction factor.
0-1 (-)
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment 4.1.5.1.8. External Heat Source FIRE allows to specify constant heat sources arbitrary cell selections. The setup is the same as page [108] for the catalyst which is explained in section External Heat Source . 4.1.5.2. Soot and Filter Properties Select Soot and Filter Properties in the parameter tree to access the following input fields. The soot and filter properties comprise thermodynamic data of the soot and fluid mechanic information of the soot and the filter. Additionally a particle mass can be specified that is used as initial condition for all soot mass balances. 4.1.5.2.1. Soot Layer Properties Typical Values and Ranges 3
Layer Packing Density
Determines the packing density of the soot.
5-30 (kg/m )
Migration Constant
Determines the impact of soot migration due to a convective transport.
1E-15-1E-5 (-)
4.1.5.2.2. Pressure Drop Typical Values and Ranges 2
Wall Permeability
Determines the permeability of the filter wall.
1E-15-1E-12 (m )
Soot Permeability
Determines the permeability of the soot bed. This property may be specified as one of: • Constant • Table (dependent on temperature or wall velocity) • Map (dependent on both, temperature and wall velocity) • Formula (see. Soot Permeability page [50])
1E-16-1E-13 (m )
Enable Depth Filtration
Enables the application of a depth filtration layer in addition to a cake filtration layer
Off (default)
Sublayer Thickness
Determines the thickness of the depth flirtation layer.
10-100 (micron)
Depth Filtration Threshold
Determines the maximum soot loading that can be deposited within the depth filtration layer
0-3 (g/l)
Depth Filtration Permeability
Determines the permeability of the soot depth filtration layer
1E-16-1E-13 (m )
Inlet Loss Coefficient
Friction factor for pressure losses at the inlet.
0.5-10 (-)
Outlet Loss Coefficient
Friction factor for pressure losses at the outlet.
0.5-10 (-)
Consider Inlet/ Outlet Plugs
Enables the specification of inlet and outlet plugs closing the inlet and outlet channel at one site.
Off (default)
Length of PF Inlet- Determines the length of the inlet and outlet plugs. Outlet Plugs
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2
2
0-20 (mm)
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4. FIRE Aftertreatment 4.1.5.2.3. Filter Inlet Boundary Condition Typical Values and Ranges Csoot [kg Particles/kg Gas]
Defines the concentration of soot in the gas phase at the inlet of the particulate filter. It has units [kg particles/kg gas]. Choose between constant, table and formula.
Defines the initial particle mass and distribution in the filter. Choose between constant, table and formula. Particle mass
0-20 [kgsoot / 3 m Filter]
Distribution type Constant 0 uniform distribution 1 linearly increasing 2 linearly decreasing 3 all soot is distributed close to inlet (first 50% of filter length) 4 all soot is distributed close to outlet (second 50% of filter length) 5 parabolic distribution (minimum in the middle of the filter) 6 parabolic distribution (maximum in the middle of the filter) 7 constant in first 50% of filter, decreasing to outlet 8 constant in second 50% of filter, decreasing to inlet
0 (default)
Distribution type Table Click on
to define table or formula data.
Scaling factor for The scaling factor is multiplied by the existing soot soot mass (restart) mass in every particulate filter cell after the restart. This factor allows to adjust the total soot mass of a regeneration simulation restarted from a loading simulation. Extended Output
1.0-100 (-)
Activates an extended soot and filter property output On (default) to the file at the beginning of the calculation.
4.1.5.3. Ash Properties Select Ash Properties in the parameter tree to access the following input fields. Typical Values and Ranges Enable Ash Model 150
If On/Off is selected, the ash model is activated.
FIRE BOOST Aftertreatment
Off (default)
4. FIRE Aftertreatment 3
Ash Packing Density
Determines the packing density of the ash layer.
100-500 (kg/m )
Ash Permeability
Determines the permeability of the ash layer.
1E-15-1E-13 (m )
Specify Ash Plug Fraction
Enables the distribution of the ash mass into a Layer and a Plug fraction
Off (default)
2
Ash Layer/Plug Determines the ratio of ash that is stored in the Distribution Factor ash layer to ash stored in the ash plug. A factor of 1 means all the ash is stored in the layer. A factor of 0 means all the ash is stored in the ash plug. If the ash loading is not specified as constant value but as function of the filter length, the shape of the axial profile is kept but scaled down by the ashdistribution factor.
(0-1) (-)
Ash Mass
0-100 (g/l)
Determines the initial ash loading in the filter. This property can be specified as a constant value, as a function of the filter length or as a formula. Click on
to define table or formula data.
4.1.5.4. Chemical Reactions BOOST has four different pre-defined reaction models for the simulation of soot regeneration. The reaction model can be applied to two different reaction zones, an upper and a catalytic sub-layer. For both layers one and the same reaction approach is applied, where the user has access to all reaction parameters. The reaction scheme in the sub layer can only be activated if the Depth Filtration Model is also enabled. The parameters can be defined separately for each reaction layer. Additionally the user can specify an arbitrary number of coating zones which are applied to all catalytically supported reactions (depth filtration layer, filter wall and outlet channel). Each kinetic parameter of a chosen catalytically supported reaction can be individually specified for each Coating Zone. Together with the O2-thermal and O2-fuel-additive Soot Regeneration Mode the Oxygen diffusion into the soot layer can be considered. Therefore a lumped diffusion coefficient has to be specified. In the catalytic wall layer, a pre-defined reaction model is available with full access to all reaction parameters. Furthermore there is the possibility for the user to define a kinetic model with an page [132] arbitrary number of catalytic reactions (see section Stoichiometry Specification and page [133] section Kinetic Parameters Specification ). Note that all reaction parameters were chosen for one type of regeneration simulation. For other filter applications these reaction parameters may change and therefore have to be supplied by the user. Enable O2 Diffusion into Soot Layer Lumped DiffusionCoefficient
On /Off -6
-5
2
Coefficient for the concentration gradient driven O2 10 -10 (m /s) diffusion from the inlet channel into the soot layer.
Soot Regeneration Mode None
No reactions are taken into account. In this case sub-layer reactions cannot be specified.
O2-thermal
A reaction mechanism (see Section Filter Regeneration with Oxygen [90] ) consisting of two reactions is applied. Soot is oxidized depending on the temperature range either to CO or to CO2.
page
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4. FIRE Aftertreatment O2-fuel-additive
The same reaction mechanism as given by O2-thermal is set up.
O2-NO2
In addition to the reaction mechanism of O2-thermal, a soot oxidation reaction in presence of NO2 can be used and specified. Details of this NO2 reaction are explained in Section Filter Regeneration with Oxygen page [91] and Nitric Dioxide .
O2-NO2-NO2catalytic
In addition to the reaction mechanism of O2-NO2 the reversible oxidation of NO to NO2 is taken into account. As explained in Section page [92] Filter CSF Catalytic Reactions , this reaction is catalytically supported and takes place in the sub-layer that can be specified. In the upper layer the reaction can be switched off by setting the appropriate reaction constants.
User Defined
This enables the possibility to supply user-defined soot regeneration models. The specification of these models is described in section page [132] Stoichiometry Specification and section Kinetic Parameters page [133] Specification .
PF Zone Coating Table
An arbitrary number of Coating Zones can be inserted for which dimensionless section lengths have to be defined. The sum of all section lengths has to be one.
Regeneration Mode Sublayer Toggle switch
This enables or disables the application of soot sub-layer reactions. The switch only can be activated if the Depth Filtration Model is also enabled.
Catalytic Wall Reactions None
No catalytic wall reactions are taken into account.
CO-HC-NOConversion
A pre-defined reaction mechanism for the catalytically supported conversion of CO, C3H6, C3H8 and NO is enabled.
Selective Catalytic Reduction
A predefined reaction mechanism for the catalytically supported SCR reactions is enabled.
User Defined
This enables the possibility to supply user-defined wall reaction models. The specification of these models is described in section Stoichiometry page [132] page [133] Specification and section Kinetic Parameters Specification .
Fraction of Catalytic Wall Height
Determines a fraction of the entire wall height that is catalytically active. A fraction of 1 comprises the entire wall height.
0-1 (-)
Catalytic Reactions Outlet Channel Enable Outlet Channel Reactions Mass Transfer Scaling Factor
This specifies a factor for the linear scaling of the mass transfer from the outlet channel bulk to the catalytic filter wall.
On/Off
Note: The activation of Regeneration Mode Sublayer is only possible if depth filtration is activated (Enable Depth Filtration at Soot and Filter Properties). 152
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4. FIRE Aftertreatment 4.1.5.4.1. Soot Regeneration Mode O2 - Thermal
O2 - Fuel Additive
K
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
kf
Determines a frequency factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
qf
Determines an exponential factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
Ef
Determines an activation energy in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
K
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
kf
Determines a frequency factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
qf
Determines an exponential factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user
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4. FIRE Aftertreatment can choose the table option to specify individual values for each coating section. Ef
O2 - NO2
Determines an activation energy in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
O2 K1
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E1
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
kf
Determines a frequency factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
qf
Determines an exponential factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
Ef
Determines an activation energy in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
NO2
154
K3
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E3
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
FIRE BOOST Aftertreatment
4. FIRE Aftertreatment O2 - NO2-NO2-Catalytic O2 K1
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E1
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
kf
Determines a frequency factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
qf
Determines an exponential factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
Ef
Determines an activation energy in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
NO2 K3-K4
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E3-E4
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
NO2- Catalytic K5
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table
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4. FIRE Aftertreatment option to specify individual values for each coating section. E5
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
4.1.5.4.2. Catalytic Wall Reactions The different reactions can be enabled/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. The string "all" means that a certain reaction is activated in all PF Coating Sections, but it is also possible to replace "all" with specific coating section numbers separated by commas (e.g. "1,3,4"). 4.1.5.4.2.1. CO, HC and NO Oxidation R1: CO Oxidation
R2: C3H6 Oxidation
R3: C3H8 Oxidation
156
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion
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4. FIRE Aftertreatment mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section. R4: NO Oxidation
K
Determines the frequency factor used in the pre-defined reversible power-law conversion mechanism (see Section TWC Catalyst Reactions page [78] ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined reversible power-law conversion mechanism (see Section TWC Catalyst Reactions page [78] ). The user can choose the table option to specify individual values for each coating section.
Determines the maximum amount of ammonia that can be stored at the solid surface site (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
Initial Surface Coverage Fraction of NH3
Determines the coverage fraction of NH3 at the solid surface. This property can be specified as constant value or as function of the catalyst length. The user can choose the table option to specify individual values for each coating section. Typical Values & Ranges: 0-1[-]
Coverage Determines a surface coverage dependency in Dependency the pre-defined ad-/desorption mechanisms (see (epsilon) Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section. Typical Values & Ranges: 0-1[-] Max Surface Coverage Fraction of NH3
Determines the maximum surface coverage fraction of NH3 at the solid surface. This property can be specified as constant value or as function of temperature. The user can choose the table option to specify individual values for each coating section.
NH3 Surface Coverage Fraction Dependency m
Determines the adsorption rate dependence of the NH3 surface coverage fraction. The user can choose the table option to specify individual values for each coating section.
K1 - K2
Determine frequency factors used in the predefined ad/desorption mechanisms (see Section HSO-SCR Catalyst Reactions, Transient Approach
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4. FIRE Aftertreatment page [83]
). The user can choose the table option to specify individual values for each coating section.
R3: NO Reduction
R4: NOx Reduction
R5: NO2 Reduction
158
E1 - E2
Determine the activation temperatures used in the pre-defined ad-/desorption mechanisms (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
Critical Surface Coverage
Determines a tuning factor that slows down the reaction rate above a critical surface coverage (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
K
Determines the frequency factor used in the predefined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
Critical Surface Coverage
Determines a tuning factor that slows down the reaction rate above a critical surface coverage (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
K
Determines the frequency factor used in the predefined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
Critical Surface Coverage
Determines a tuning factor that slows down the reaction rate above a critical surface coverage (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table
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4. FIRE Aftertreatment option to specify individual values for each coating section.
R6: NH3 Oxidation (Transient Approach)
K
Determines the frequency factor used in the predefined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
K
Determines the frequency factor used in the pre-defined transient oxidation mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient oxidation (see Section HSOpage SCR Catalyst Reactions, Transient Approach [83] ). The user can choose the table option to specify individual values for each coating section.
R7: NH3 Oxidation K (Steady-State Approach)
Determines the frequency factor used in the predefined power-law oxidation mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-power-law transient oxidation (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
R8: NO Oxidation
Rate Approach 1 K
Determines the frequency factor used in the pre-defined transient and reversible power-law conversion mechanism (see Section HSO-SCR page [83] Catalyst Reactions, Transient Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient and reversible power-law conversion mechanism (see Section HSO-SCR page [83] Catalyst Reactions, Transient Approach ).
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4. FIRE Aftertreatment The user can choose the table option to specify individual values for each coating section. A
Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism see Section HSO-SCR Catalyst page [83] Reactions, Transient Approach ). The user can choose the table option to specify individual values for each coating section.
Rate Approach 2
R9: NO2 Formation
K, KR
Determine the frequency factors used in the pre-defined transient and reversible power-law conversion mechanism, respectively (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
E, ER
Determine the activation temperatures used in the pre-defined transient and reversible power-law conversion mechanism, respectively (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
A, AR
Determine the temperature dependencies used in the pre-defined transient and reversible power-law conversion mechanism, respectively (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
m
Modifies the NH3 dependency. The user can choose the table option to specify individual values for each coating section.
K
Determines the frequency factor used in the predefined power-law conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined power-law conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
4.1.5.4.2.3. Catalytic Outlet Channel Reactions page [156] The same reaction set as defined in the Catalytic Wall Reactions Model is selected. Sub-pages for the detailed specification of the reaction parameters appear. The user can choose the table option to specify individual values for each coating section.
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4. FIRE Aftertreatment 4.1.5.5. Reaction Solver Specification Select PF Reaction Solver Specification in the parameter tree to access the following input fields. 4.1.5.5.1. Reaction Solver Parameters Typical Values Regeneration reaction solver: max. no. of iterations
Specifies the maximum number of sub-iterations that the solver carries out for the catalytic reactions. Normally no changes are required.
20000 (-)
Regeneration reaction solver: relative tolerance
Specifies the relative tolerance for the solution of the reaction rate equation system. Normally no changes are required.
1e-05 (-)
Regeneration Specifies the absolute tolerance for the solution of the 1e-08 (-) reaction solver: reaction rate equation system. Normally no changes absolute tolerance are required. 4.1.5.5.2. General Settings Typical Values and Ranges Implicit DPF flow solution
Normally the PF flow solver and regeneration 0-100 (-) reactions are called once per time step at the beginning. Depending on the problem it can be useful to perform these calls more frequently, i.e. specify 5 th to call them every 5 iteration for large time steps. A value of 0 turns off implicit solver calls.
Scaling factor for The pressure drop calculation by the PF flow solver is 0.2-5 (-) dp underrelaxation separated from the CFD flow solution. The calculated pressure drop value is then impressed as source term in the momentum equation of the CFD flow solver. The scaling factor for dp underrelaxation enables to increase/decrease the underrelaxation of the pressure drop source. A value of 1 means that the default underrelaxation is used. Values greater than 1 increase, values less than 1 decrease the underrelaxation. Recommended values are in the range between 0.2 and 5. Refinement factor for DPF flow solution
Specifies the refinement factor of the PF flow solution. The PF flow solver is only called, if the changes of the flow conditions at the filter inlet since the last solver call exceed a certain tolerance value. By specifying a value greater than 1.0, this tolerance is reduced by the reciprocal of the refinement factor, and consequently the PF flow solver is called more often. This leads to smoother pressure curves, but increases simulation time.
0.2-10 (-)
4.1.5.5.3. Reaction Solver Flags Select Reaction solver flags in the parameter tree to access the following input fields.
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4. FIRE Aftertreatment Typical Values and Ranges On / Off
Activates/deactivates input flags. The 23 input fields are for AVL internal use only.
Off (default)
4.1.5.6. 2D Output Specification Select 2D Output Specification in the parameter tree to access the following input fields. 4.1.5.6.1. Substrate Data Typical Values and Ranges Mean DPF temperature
Activates/deactivates the output of the mean particulate filter temperature to the .fla file and to the .fl2 file.
Active (default)
Maximum DPF temperature
Activates/deactivates the output of the maximum particulate filter temperature to the .fla file and to the .fl2 file.
Active (default)
Minimum DPF temperature
Activates/deactivates the output of the minimum particulate filter temperature to the .fla file and to the .fl2 file.
Active (default)
Solid heat capacities
Activates/deactivates the output of the minimum, Inactive (default) maximum and mean value of the solid specific heat capacity (J/kgK) of the particulate filter to the .fla file and to the .fl2 file. Data is only written for temperature dependent values. Click on
Solid thermal conductivities
to define table data.
Activates/deactivates the output of the minimum, Inactive (default) maximum and mean value of the solid thermal conductivity (W/(m·K)) of the particulate filter to the .fla file and to the .fl2 file. Data is only written for temperature dependent values. Click on table data.
Gradient of solid temperature
to define
Activates/deactivates the output of the maximum and mean value of the solid temperature gradient (K/m).
Inactive (default)
4.1.5.6.2. Pressure Drop Typical Values and Ranges DPF pressure drop values
162
Activates/deactivates the output of all pressure drop Active (default) contributions (Pa) of the particulate filter to the .fla file and to the .fl2 file. The following data is written: • Overall DPF pressure drop • Converter pressure drop • Soot cake layer pressure drop • Soot depth layer pressure drop • Ash layer pressure drop • Wall pressure drop • Inlet pressure drop
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4. FIRE Aftertreatment • • • • •
Outlet pressure drop Inlet channel pressure drop Outlet channel pressure drop Inlet plug pressure drop Outlet plug pressure drop
4.1.5.6.3. Soot Typical Values and Ranges Total particle mass
Activates/deactivates the output of the total particle mass [kg] of the entire particulate filter to the .fla file and to the .fl2 file.
Inactive (default)
Specific particle mass
Activates/deactivates the output of the specific particle mass (g/l) of the entire particulate filter to the .fla file and to the .fl2 file.
Active (default)
Particle deposition rate
Activates/deactivates the output of the particle deposition rate [kg/s] of the entire particulate filter to the .fla file and to the .fl2 file.
Inactive (default)
4.1.5.6.4. Flow Uniformities Typical Values and Ranges Uniformity index
Activates/deactivates the output of the uniformity Inactive (default) index (-) of the particulate filter to the .fla file and to the .fl2 file. The definition of the uniformity index is described in the 2D results of the catalyst in section 2D Output page [139] Specification .
Centricity index
Activates/deactivates the output of the centricity index (-) of the particulate filter to the .fla file and to the .fl2 file. The definition of the centricity index is described in the 2D results of the catalyst in section 2D Output page [139] Specification .
Max./Min. inlet velocities
Activates/deactivates the output of minimum and the Inactive (default) maximum inlet velocity (m/s), and the position of the maximum inlet velocity (m) of the particulate filter to the .fla file and to the .fl2 file. The max. and min. inlet velocity are determined in the last non-porous fluid cell layer in front of the particulate filter.
High and low speed inlet area
Activates/deactivates the output of high and low speed Inactive (default) inlet areas (-) of the particulate filter to the .fla file and to the .fl2 file. The definition of the high and low speed inlet areas are described in the 2D results of the catalyst in section 2D page [139] Output Specification .
Tangential inlet velocity
Activates/deactivates the output of the mean, the Inactive (default) minimum, and the maximum tangential velocity (m/s) of
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Inactive (default)
163
4. FIRE Aftertreatment the particulate filter inlet to the .fla file and to the .fl2 file. The tangential inlet velocity is described in the 2D results of the catalyst in section 2D Output page [139] Specification . Tangential inlet Activates/deactivates the output of the mean, the pressure gradient minimum, and the maximum tangential pressure gradient [Pa/m] of the particulate filter inlet to the .fla file and to the .fl2 file. The tangential inlet pressure gradient is described in the 2D results of the catalyst in section 2D Output page [139] Specification .
Inactive (default)
Gas hourly space Activates/deactivates the output of the gas hourly velocity (GHSV) space velocity at operation conditions (GHSV) (1/h) and the gas hourly space velocity at norm conditions (GHSVn) (1/h) of the particulate filter to the .fla file and to the .fl2 file. The definition of the GHSV is described in the 2D results of the catalyst in section 2D Output page [139] Specification .
Inactive (default)
4.1.5.6.5. Conversions Typical Values and Ranges Species conversions
Activates/deactivates the output of the species' conversions to the .fla file and to the .fl2 file. The species conversion is described in the 2D results page of the catalyst in section 2D Output Specification [139] .
Active (default)
Excess oxygen ratio at inlet
Activates/deactivates the output of the excess oxygen Inactive (default) ratio at the inlet to the .fla file and to the .fl2 file. The excess oxygen ratio is described in the 2D results of page [139] the catalyst in section 2D Output Specification
Redox ratio at inlet
Activates/deactivates the output of the redox ratio at the inlet to the .fla file and to the .fl2 file. The redox ratio is described in the 2D results of the catalyst in page [139] section 2D Output Specification
Inactive (default)
4.1.5.6.6. Filter flow model 2D results Typical Values and Ranges Filter flow model 2D results
If On/Off is selected, FIRE writes (for a given row number and a given output frequency) the results of the PF flow model as column data to ASCII files:
Off (default)
Output frequency (time steps)
50
Row number (particulate filter)
5
column no. data 164
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E.g.:
4. FIRE Aftertreatment 1 axial coordinate (m) 2 wall velocity (-) 3 V1 (m/s) 4 V2 (m/s) 5 h_soot (m) 6 Gas temperature (K) 7 Solid temperature (K) 8 Cell number
4.1.6. Reactive Porosity Specification To add a reactive porosity (RPOR) to the project, click on Aftertreatment TNG in the parameter tree with the right mouse button and select Reactive Porosity: Insert from the submenu. To delete a RPOR from the project, click on the name of the RPOR (i.e. RP[1]) with the right mouse button and select Remove from the submenu. The specification of a reactive porosity comprises data over its geometry, its fluid and thermodynamic behavior and the conversion reactions taking place. Figure 47. Reactive Porosity Specification Parameter Tree
Copy from RPOR allows the complete set of input data to be copied from RPOR[X] to the present reactive porosity. Figure 48. Copy from RPOR Function
4.1.6.1. General Reactive Porosity Specification Select RPOR specification in the parameter tree to access the following input fields. 4.1.6.1.1. Reactive Porosity Specification Typical Values and Ranges Cell selection
Supply a cell selection that defines the geometry NoSelection of the reactive porosity. (default)
Mesh requirements fulfilled
Specify if the mesh requirements for the RPOR cell selection which are summarized in section page [175] Mesh Requirements are fulfilled or not. The options available are: Yes and NO.
Yes (default)
Specified inlet/outlet of reactive porosity
Select this option for directed porosities. This option enables the user more heat and mass transfer models for selection including those are available for catalysts. Also, enables specification of an inlet and outlet face selection for additional 2D output.
Active (default)
Inlet face selection
If the geometry allows it, supply a face selection that defines the inlet plane of the reactive
NoSelection (default)
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4. FIRE Aftertreatment porosity. Only available for activated Specified inlet/outlet of reactive porosity. Outlet face selection
If the geometry allows it, supply a face selection that defines the outlet plane of the reactive porosity. Only available for activated Specified inlet/outlet of reactive porosity.
NoSelection (default)
RPOR initialization temperature
Determines the initial temperature of the reactive porosity.
293.15-1500 (K)
4.1.6.1.2. Reactive Porosity Type Typical Values and Ranges Fluid volume fraction (porosity)
Determines the fluid volume fraction (=porosity) of the RPOR porosity block.
0.1-0.95 (-)
Geometric surface area (GSA)
Determines the geometric surface area.
100-10000 (m / 3 m )
2
4.1.6.2. Pressure Drop Specification 4.1.6.2.1. Pressure Drop Models Two different pressure drop models and a user access are available to calculate the pressure drop within the RPOR block which is an undirected porosity. 4.1.6.2.1.1. Forchheimer If Forchheimer is chosen as pressure drop model, the pressure gradients within the reactive porosity are calculated with following equation (335)
The linear term and the quadratic terms take into account the viscous and the inertial losses, respectively, of the flow through the reactive porosity. Pressure gradient within porous material 2
i
Viscous loss coefficient (x-, y- and z-components) (1/m ) 2
Molecular (laminar) dynamic viscosity of domain fluid (N·s/m ) wi
Interstitial (local) velocity components in porous medium according to the local volume-fraction Inertial loss coefficient (x-, y- and z-components) (1/m) Domain fluid density
To activate the Forchheimer pressure drop model, select Forchheimer from the Pressure drop model pull-down menu to access the following input fields: Typical Values and Ranges 166
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4. FIRE Aftertreatment Zeta-value
This specifies the direction dependent parameters ( ) 0-100 (1/m) defining the dependency between the velocity and the pressure loss per unit length of porous material.
Alpha value
This specifies the direction dependent parameters ( i) 0-10 (1/m ) defining the dependency between the velocity in the i direction, the laminar viscosity, and the pressure loss per unit length of porous material.
7
2
4.1.6.2.1.2. Carman-Kozeny If Carman-Kozeny is chosen as pressure drop model, then the pressure gradients within the reactive porosity is calculated with following equation (336)
CCK is the Carman-Kozeny constant usually 150, is the molecular dynamic viscosity of domain 2 fluid in (N·s/m ), ui is the superficial and wi is the interstitial velocity in (m/s), is the fluid volume fraction (porosity) in (-), and dp is the equivalent solid particle diameter. To activate the Carman-Kozeny pressure drop model, select Carman-Kozeny from the Pressure drop model pull-down menu to access the following input fields: Typical Values and Ranges Model constant C1 Specifies the Carman-Kozeny constant.
0-1500 (-)
Equivalent particle Specifies the diameter of an equivalent solid sphere diameter for calculating the pressure drop.
0.0001-0.005 (m)
4.1.6.2.1.3. User If User is chosen as pressure drop model, the pressure drop is calculated according to the coding in the user routine usepor_pres.f. 4.1.6.2.2. Turbulence Treatment Within the interstices of the porosity the turbulence kinetic energy k is calculated by the standard transport equation. To take into account the laminarization process within the pores, the dissipation rate is calculated from the algebraic equation shown below: (337)
Crel is a relative turbulent length scale, which is multiplied with the hydraulic pore diameter dhyd and estimates the turbulence characteristics inside the porosity block. Crel is a problem dependent quantity which has to be specified by the user. Typical Values and Ranges Rel. turb. length scale Crel
Relative turbulent length scale Crel in equation page [167] Eq.337 to estimate the turbulence characteristics within the pores of the block.
0.0001-0.02 (-)
Hydraulic pore diameter dhyd
Hydraulic pore diameter dhyd in equation Eq.337 [167] to estimate the turbulence characteristics within the pores of the block.
page
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0.0001-0.005 (m)
167
4. FIRE Aftertreatment 4.1.6.3. Physical Properties of Reactive Porosities Select RPOR Physical Properties in the parameter tree to access the following input fields. 4.1.6.3.1. RPOR Physical Properties Typical Values and Ranges Density
Determines the density of the reactive porosity material.
Thermal conductivity
Determines the thermal conductivity of 0.1-50 (W/(m·K)) the reactive porosity material. The thermal conductivity can either be specified as a constant value or as a table where the value changes as a function of temperature. Click on table data.
Specific heat
to define
Determines the specific heat of the reactive 500-2000 (J/ porosity material. The specific heat can either be (kg·K)) specified as a constant value or as a table where the value changes as a function of temperature. Click on
Anisotropic cond. Factor
400-2000 (kg/ 3 m )
to define table data.
Corrects the diffusion coefficients of the solid 0-10 (-) temperature equation normal to a preferential block direction. The default value of 1.0 means that there is no preferential block direction. This is reasonable for packed beds, granulated materials, etc. However, for blocks with preferential flow direction one can specify an anisotropic conductivity factor different from 1. Then the thermal conductivity matrix is calculated so that there is different thermal diffusion between block direction and the direction normal to the block direction. The preferential block direction vector is calculated from the center points of inlet and outlet face selection. (Inlet and outlet face selections have to be specified).
4.1.6.3.2. Mass Transfer Models 4.1.6.3.2.1. Constant Constant values which have to be defined by the user are taken as mass transfer coefficients. Typical Values and Ranges Mass transfer coefficient
Constant value of the species mass transfer coefficient.
4.1.6.3.2.2. VDI Packed Bed The VDI packed bed correlation is used to calculate mass transfer coefficients. 168
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0.1-10 (m/s)
4. FIRE Aftertreatment Typical Values and Ranges Equivalent particle Specifies the diameter of an equivalent solid sphere diameter of the granulated material.
0.0001-0.005 (m)
Shape factor mass Specifies the shape factor of the Sherwood number transfer for the mass transfer according to fe in section VDI page [30] Packed Bed .
1-2.1 (-)
4.1.6.3.2.3. User The user can specify the transfer coefficients in use_cattra.f. 4.1.6.3.3. Heat Transfer Models 4.1.6.3.3.1. Constant Constant values which have to be defined by the user are taken as heat transfer coefficients. Typical Values and Ranges Heat transfer coefficient
Constant value of the heat transfer coefficient.
2
5-500 (W/(m ·K))
4.1.6.3.3.2. VDI Packed Bed The VDI packed bed correlation is used to calculate heat transfer coefficients. Typical Values and Ranges Equivalent particle Specifies the diameter of an equivalent solid sphere diameter of the granulated material. Shape factor heat transfer
0.0001-0.005 (m)
Specifies the shape factor of the Nusselt number for 1-2.1 (-) the heat transfer according to fe in section VDI Packed page [30] Bed .
4.1.6.3.3.3. User The user can specify the transfer coefficients in use_cattra.f. 4.1.6.3.4. RPOR Segmentation FIRE provides a simple model to take into account perforations in the reactive porosities. The page [108] setup is the same as for catalysts explained in section Catalyst Segmentation . 4.1.6.3.5. External Heat Source FIRE allows to specify constant heat sources for arbitrary cell selections. The setup is the same page [108] as for catalysts explained in section External Heat Source . 4.1.6.4. Conversion Reactions FIRE offers the possibility to compute chemical reactions inside the reactive porosity. Either no reactions are taken into account or the application of user defined models is possible. 4.1.6.4.1. User Defined Kinetic Reactions The specification of the user defined kinetic reactions is identical to that of the catalyst described page [131] in section User Defined Reactions (Without Archive) .
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4. FIRE Aftertreatment 4.1.6.5. Reactive Porosity Reaction Solver Specification Select RPOR Reaction Solver Specification in the parameter tree to access the following input fields. 4.1.6.5.1. Reaction Solver Parameters Typical Values Reactive porosity solver: max. number of iterations
Specifies the maximum number of sub-iterations that the solver carries out for the catalytic reactions. Normally no changes are required.
20000 (-)
Reactive porosity solver: relative tolerance
Specifies the relative tolerance for the solution of the reaction rate equation system. Normally no changes are required.
1e-05 (-)
Reactive porosity solver: absolute tolerance
Specifies the absolute tolerance for the solution of the 1e-08 (-) reaction rate equation system. Normally no changes are required.
4.1.6.5.2. General Settings Typical Values and Ranges Implicit solution of Normally the reaction rate equation system is solved chem. kinetics at the beginning of a time step. Depending on the problem (i.e. chemical equilibrium problems) it can be necessary to solve it within the time step also, i.e. th specify 5 to solve it every 5 iteration for large time steps. A value of 0 turns off implicit solver calls. Reaction solver block size
0-100 (-)
In order to speed up the solution of the chemical 1-50 (-) kinetics, the corresponding equation system is not solved for each cell separately but more cells are considered for each solver call. The number of cells is given here.
Consider enthalpy Activates/deactivates the consideration of the sources from enthalpy sources from the catalytic reactions in the chemical reactions enthalpy equation for the solid material ('isothermal'). If deactivated, only the species sources from the catalytic reactions are considered.
Active (default)
Activate user Activates/deactivates the user function Inactive (default) model for use_catmod.f. This user function is called by the catalytic reactions CFD solver instead of the RPOR reaction model. Here (use_catmod.f) the user defines the source terms for the species transport equations and the enthalpy equation. It is typically used by advanced users who have their own models available and need full flexibility for their implementation. Please contact FIRE support for more information on use_catmod.f.
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4. FIRE Aftertreatment 4.1.6.6. Spray Particle Interaction Select Spray particle interaction in the parameter tree. If the Spray module is deactivated, the button Activate is greyed out, otherwise one clicks on Activate to access the following input fields. 4.1.6.6.1. Collision Typical Values and Ranges O'Rourke based
Selects the spray-porosity collision submodel based On (default) on the O'Rourke spray particle-particle collision model
User
Selects a user-defined spray-porosity collision submodel. The user submodel must be coded in the user function cyuse_rpor.f
Off (default)
Collision factor
Specifies the user-defined collision factor c. The higher the value is, the more probable a dropletporosity collision is.
1 (-) (default)
4.1.6.6.2. Interaction with solid Typical Values and Ranges Kuhnke based
Selects the spray-porosity interaction submodel based on the Kuhnke spray-wall interaction model.
On (default)
User
Selects a user-defined spray-wall interaction submodel. The user submodel must be coded in the user function cyuse_rpor.f
Off (default)
Maximum deviation angle
Specifies the maximum deviation angle max from the gas direction that a particle can undergo after a collision with the solid part of the porous medium.
65-85 (deg)
Number of secondary droplets
Specifies the number of secondary droplets ns generated after a splashing of a particle on the solid part of the porous medium.
2-4 (-)
4.1.6.6.3. Enhancement of evaporation Typical Values and Ranges Enhancement factor
Specifies the multiplication factor used for the evaporation massflow of each component.
1-5 (-)
Energy redistribution factor
Specifies the factor e used in the redistribution of 2-6 (-) the energy sink required to evaporate the liquid spray. The higher the factor is, the more energy is extracted from the solid for the evaporation.
4.1.6.7. 2D Output Specification Select 2D Output Specification in the parameter tree to access the following input fields.
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4. FIRE Aftertreatment 4.1.6.7.1. Substrate Data Typical Values and Ranges Mean porosity temperature
Activates/deactivates the output of the mean porosity temperature to the .fla file and to the .fl2 file.
Active (default)
Maximum porosity temperature
Activates/deactivates the output of the maximum porosity temperature to the .fla file and to the .fl2 file.
Active (default)
Minimum porosity temperature
Activates/deactivates the output of the minimum porosity temperature to the .fla file and to the .fl2 file.
Active (default)
Solid heat capacities
Activates/deactivates the output of the minimum, maximum and mean value of the solid specific heat capacity (J/(kg·K)) of the RPOR to the .fla file and to the .fl2 file. Data is only written for temperature
Inactive (default)
dependent values. Click on Solid thermal conductivities
Activates/deactivates the output of the minimum, Inactive (default) maximum and mean value of the solid thermal conductivity (W/(m·K)) of the RPOR to the .fla file and to the .fl2 file. Data is only written for temperature dependent values. Click on
Gradient of solid temperature
to define table data.
to define table data.
Activates/deactivates the output of the maximum and mean value of the solid temperature gradient (K/m).
Inactive (default)
4.1.6.7.2. Pressure Drop Typical Values and Ranges Pressure drop of reactive porosity
Activates/deactivates the output of the total pressure Active (default) drop (Pa) of the RPOR to the .fla file and to the .fl2 file. Output is only available if Specified inlet/outlet of reactive porosity is active.
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Uniformity index
Activates/deactivates the output of the uniformity index Inactive (default) (-) of the RPOR to the .fla file and to the .fl2 file. Output is only available if Specified inlet/outlet of reactive porosity is active. The definition of the uniformity index is described in the 2D results of the catalyst in section 2D Output page [139] Specification .
Centricity index
Activates/deactivates the output of the centricity index (-) of the RPOR to the .fla file and to the .fl2 file. Output is only available if Specified inlet/outlet of reactive porosity is active.
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4. FIRE Aftertreatment The definition of the centricity index is described in the 2D results of the catalyst in section 2D Output page [139] Specification . Max./Min. inlet velocities
Activates/deactivates the output of minimum and the Inactive (default) maximum inlet velocity (m/s), and the position of the maximum inlet velocity (m) of the RPOR to the .fla file and to the .fl2 file. The max. and min. inlet velocity are determined in the last non-porous fluid cell layer in front of the RPOR. Output is only available if Specified inlet/outlet of reactive porosity is active.
High and low speed inlet area
Activates/deactivates the output of high and low speed Inactive (default) inlet areas (-) of the RPOR to the .fla file and to the .fl2 file. Output is only available if Specified inlet/ outlet of reactive porosity is active. The definitions of the high and low speed inlet areas are described in the 2D results of the catalyst in page [139] section 2D Output Specification .
Tangential inlet velocity
Activates/deactivates the output of the mean, the minimum, and the maximum tangential velocity (m/s) of the RPOR inlet to the .fla file and to the .fl2 file. Output is only available if Specified inlet/outlet of reactive porosity is active. The tangential inlet velocity is described in the 2D results of the catalyst in section 2D Output page [139] Specification .
Inactive (default)
Tangential inlet Activates/deactivates the output of the mean, the pressure gradient minimum, and the maximum tangential pressure gradient (Pa/m) of the RPOR inlet to the .fla file and to the .fl2 file. Output is only available if Specified inlet/outlet of reactive porosity is active. The tangential inlet pressure gradient is described in the 2D results of the catalyst in section 2D Output page [139] Specification .
Inactive (default)
Gas hourly space Activates/deactivates the output of the gas hourly Inactive (default) velocity (GHSV) space velocity at operation conditions (GHSV) (1/h) and the gas hourly space velocity at norm conditions (GHSVn) (1/h) of the RPOR to the .fla file and to the .fl2 file. Output is only available if Specified inlet/ outlet of reactive porosity is active. The definition of the GHSV is described in the 2D results of the catalyst in section 2D Output page [139] Specification . 4.1.6.7.4. Conversions Typical Values and Ranges Species conversions
Activates/deactivates the output of the species' Active (default) conversions to the .fla file and to the .fl2 file. Output is only available if Specified inlet/outlet of reactive porosity is active.
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4. FIRE Aftertreatment The species conversion is described in the 2D results page of the catalyst in section 2D Output Specification [139] . Surface coverage Activates/deactivates the output of the mean surface fraction coverage fractions (-) of the surface species of the RPOR to the .fla file and to the .fl2 file.
Inactive (default)
Excess oxygen ratio at inlet
Activates/deactivates the output of the excess oxygen Inactive (default) ratio at the inlet to the .fla file and to the .fl2 file. The excess oxygen ratio is described in the 2D results of page [139] the catalyst in section 2D Output Specification . Output is only available if Specified inlet/outlet of reactive porosity is active.
Redox ratio at inlet
Activates/deactivates the output of the redox ratio at Inactive (default) the inlet to the .fla file and to the .fl2 file. The redox ratio is described in the 2D results of the catalyst in page [139] section 2D Output Specification . Output is only available if Specified inlet/outlet of reactive porosity is active.
4.1.7. 3D Output Specification Select 3D Output Specification in the parameter tree to access the following input fields. 4.1.7.1. Standard Typical Values and Ranges Monolith temperature
Activates/deactivates the output of the monolith temperature.
Active (default)
Surface coverage fraction
Activates/deactivates the output of the surface coverage fraction.
Active (default)
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Heat transfer coefficients
Activates/deactivates the output of the heat transfer coefficient.
Inactive (default)
Solid heat capacity
Activates/deactivates the output of the specific solid heat capacity.
Inactive (default)
Solid thermal conductivity
Activates/deactivates the output of the solid thermal conductivity.
Inactive (default)
Mass transfer coefficients
Activates/deactivates the output of the mass transfer coefficients for each species.
Inactive (default)
Rates of user defined chemical reaction
Activates/deactivates the output of the rates for each user defined reaction.
Inactive (default)
Production/ depletion rates of chemical species
Activates/deactivates the output of the reaction rates for each species.
Inactive (default)
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Activates/deactivates the output of the velocity Inactive (default) components perpendicular to the monolith direction. The tangential velocity is plotted only in the fluid layer in front of the monolith inlet.
Tangential inlet pressure gradient
Activates/deactivates the output of the pressure gradient in the direction perpendicular to the monolith direction. The tangential pressure gradient is plotted only in the fluid layer in front of the monolith inlet.
Inactive (default)
Gradient of solid temperature
Activates/deactivates the output of the solid temperature gradient.
Inactive (default)
4.1.7.3. Washcoat Layer The washcoat layer (WCL) model is available for catalysts only. Note: 3D WCL results are plotted for every specified washcoat layer depth (YdPos). This may lead to a huge number of results and large result files. Typical Values and Ranges WCL Mole Fraction
Activates/deactivates the output of the species' mole fractions for all cells over all washcoat layers
Inactive (default)
WCL Mass Fraction
Activates/deactivates the output of the species' mass fractions for all cells over all washcoat layers
Inactive (default)
WCL Species Concentration
Activates/deactivates the output of the species' concentrations for all cells over all washcoat layers
Inactive (default)
WCL Effective Diffusion Coefficient
Activates/deactivates the output of the species' effective diffusion coefficients for all cells over all washcoat layers
Inactive (default)
WCL Species Rate
Activates/deactivates the output of the species rates in each cell of the washcoat layer.
Inactive (default)
WCL Reaction Rate
Activates/deactivates the output of the reaction rates for all activated reactions in each cell of the washcoat layer.
Inactive (default)
WCL Stored Species Fraction
Activates/deactivates the output of the stored species fraction in each cell of the washcoat layer.
Inactive (default)
WCL Stored Species Loading
Activates/deactivates the output of the stored species loading in each cell of the washcoat layer.
Inactive (default)
4.1.8. Mesh Requirements and MPI Decomposition 4.1.8.1. Mesh Requirements In aftertreatment simulations the cell selections for the catalyst, the reactive porosity (RPOR) and the particulate filter are defined internally as porosity blocks. It is no longer necessary (since FIRE v8.5) to activate the Porosity module in the GUI. Nevertheless, some mesh requirements have to be taken into account:
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4. FIRE Aftertreatment 4.1.8.1.1. Mesh Requirements for Catalyst and Particulate Filter The flow through a catalyst or a particulate filter is determined by the channel shaped structure of the monolith. Thus, the monolith is modeled as directed porosity for which the following mesh requirements have to be taken into account: • Arbitrary interfaces are not allowed within the porosity (catalyst or particulate filter) blocks. • The distance between arbitrary interfaces and the porosity/fluid interfaces must be at least two cell layers (see the following figure). • The catalyst or the particulate filter block must be a structured, direction-aligned grid. Porosity/fluid interfaces must be plane and normal to the porosity direction. Figure 49. Mesh Requirements for Catalysts and Particulate Filters
4.1.8.1.2. Mesh Requirements for Reactive Porosities In general there is no preferential flow direction in reactive porosities. Thus, they are modeled by undirected porosities for which the Mesh Requirements can be set to Yes (=fulfilled) or No (=not fulfilled). For not fulfilled mesh requirements no special treatment is necessary. For fulfilled mesh requirements the following conditions must be taken into account: • The distance between arbitrary interfaces and porosity/fluid interfaces must be at least two cell layers. • The face selection determining the porosity/fluid interface must be a smooth surface without protruded cells. However, it is recommended to create computational grids with fulfilled mesh requirements whenever possible. 4.1.8.2. MPI Decomposition 4.1.8.2.1. MPI Decomposition for Catalyst In general the computational effort for catalyst cells is higher than that for ordinary fluid cells. In addition to the transport equations, the chemical reactions and the solid temperature equation have to be solved for the porous cells of the catalyst. To achieve a good load balance in MPI simulations, FIRE offers the capability of weighted MPI decomposition. This means that if the user specifies a cell selection with the name "_decomp_weight_", then instead of the ordinary cell count, the cell count for the generated MPI domains is determined by the factor specified at . The weight must be an integer greater than 0. For all cells outside such cell selections, a weight of 1 is assigned. For example, if there is a cell selection specified with the name "CAT01_decomp_weight_3", during the MPI decomposition the cells contained by this selection have the weight 3, while the cells outside of this selection have the weight 1. For catalysts it is recommended to apply the weighting to all cells of the porous block. The quantity of the weighting factor depends on the setup of the simulated case, i.e. how many chemical reactions are active, how often the reaction solver is called (see Implicit solution of page [138] chem. kinetics in section Reaction Solver Parameters ), etc. For many cases a weighting factor of 3 seems to be a good choice.
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4. FIRE Aftertreatment Note: Any "_indivisible" or "_domain_"-selections and arbitrary-interface-cell-layers are processed afterwards. 4.1.8.2.2. MPI Decomposition for Particulate Filter Contrary to the catalyst selection the MPI decomposition of PF blocks is not arbitrary. The MPI interface must be aligned along the porosity block direction. This means that the PF cell rows in porosity direction (representing a certain number of PF channels) must not be located on different domains. Note: The MPI decomposition of PF blocks is not arbitrary. To avoid PF channels splitting onto different domains, the decomposition must be topologically normal to the front surface of the PF. By specification of "_domain_"-selections one can influence the MPI decomposition. The following figure shows the specification of the selections for the domain decomposition of a simulation with 4 CPUs. Figure 50. Example of Manual Domain Decomposition of a PF for 4 CPUs
If the cell selections are specified in that way, PF channels are not distributed onto more than one domain and the decomposition requirement for PF is fulfilled. The names of the selections are composed by the selection name plus the domain extensions "_domain_X" starting at index zero (e.g. mesh_domain_0, mesh_domain_1, mesh_domain_2, mesh_domain_3,..). This method is sophisticated and leads to an excellent load balance, since the user specifies exactly on which domain which PF channel row is calculated. However, the creation the cell selections may be circuitous, and if one changes the number of processors of the simulation, one has to create new selections. Therefore, FIRE offers a more convenient way for the domain decomposition. If face-selections with the names "_decomp_struct_front_" and "_decomp_struct_end" are found, then they are considered as the front and back sides of a structured cell-block, where the decomposition is performed only topologically normal to the front surface. If there is no "_decomp_struct_end" face selection, the structured block ends at the mesh boundary or as soon as a non-sweepable cell is encountered, the suffix specifies the cell count weighting factor, similar to that already described in section MPI Decomposition for page [176] Catalyst for the catalysts. The specified weight is assigned to the cells in the structured block. If no specific weight will be assigned, the suffix can be omitted. The prefix may be any name, but any "decomp_struct_end"-selection must have the same prefix as the corresponding "decomp_struct_front"-selection. An arbitrary number of such "decomp_weight"- or "decomp_struct_front"-selections may exist, but the structured cell-blocks must not overlap. Also here, any "_indivisible" or "_domain_"-selections and arbitrary-interface-cell-layers are processed afterwards. The quantity of the weighting factor depends on the set-up of the PF model, i.e. if there are chemical reactions active or not and if yes, how many chemical reactions are active, which PF
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4. FIRE Aftertreatment models are active (Depth filtration), etc. For many cases a weighting factor of 2 seems to be a good choice. The following figure shows an example of the face selections applied for weighted decomposition. The prefix "DEC_DPF_0" and the suffix "2" determine the names of the front and backside selections "DEC_DPF_0_decomp_struct_front_2" and "DEC_DPF_0_decomp_struct_end". For correct decomposition, these selections are located one cell layer before and after the PF block. Figure 51. Face Selections for Weighted MPI Decomposition of a PF
4.1.9. Aftertreatment-Device Import from BOOST To import Aftertreatment devices from BOOST, click on Aftertreatment in the parameter tree with the right mouse button, select Import from BOOST from the submenu and choose the corresponding .bwf file. After the import function is executed, all Aftertreatment devices (Catalysts and Particulate Filters) from the chosen BOOST project are added to the FIRE Case. If only one of multiple Aftertreatment devices specified in the BOOST project is needed, the redundant devices can be deleted from the project by clicking on the name of the catalyst or particulate filter with the right mouse button and selecting Remove from the submenu. Since the specification of Aftertreatment devices in the FIRE Solver GUI is not completely identical to the specification in the BOOST GUI, the following items have to be considered when using the Import from BOOST feature: • If more than one Case is specified in BOOST, the active one is chosen for the import. All parameters which are set in BOOST are resolved to values. • All imported values are highlighted orange. • All values which are not imported (i.e. the monolith cell selections with no corresponding entries in BOOST) are default (black) and have to be modified by the user. • Log files are written in the Case directory (ImportDataFromBoost_Match.log and ImportDataFromBoost_NO_Match.log), where the success of the data mapping procedure is recorded (Note: Quantities which are not imported because corresponding entries do not exist in BOOST, do not appear in the log file). • The highlighting of imported values disappears after saving the FIRE Project.
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use_catrat.f
This example shows how to program a user defined rate law (Langmuir-Hinshelwood kinetics for three-way catalyst). Refer to the User Functions Code Manual for details.
use_cattra.f
This example shows how to program a user defined calculation of mass and heat transfer coefficients in the catalyst. Refer to the User Functions Code Manual for details.
use_dpfrat.f
This example shows how to program a user defined rate law (Oxidation of soot (solid carbon) with oxygen to CO and CO2
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4. FIRE Aftertreatment in the cake as well as in the depth layer. Refer to the User Functions Code Manual for details.
4.1.11. Homogenous Gas Phase Reactions - Input data The Homogenous Gas Phase Reactions chemistry interpreter needs a text based chemistry input file with an arbitrary name, where the stoichiometries of the reactions, the kinetic Parameters (A, b and E) and – optionally – auxiliary data are defined. The reaction specification part begins with 'REACTIONS' and ends with 'END'. The number of blanks or empty lines between specification blocks/lines is arbitrary. Comment lines beginning with '!' are allowed. Example for such a chemistry input file:
REACTIONS 2O+M<=>O2+M 1.200E+17 -1.000 .00 H2/2.40/ H2O/15.40/ CH4/2.00/ CO/1.75/ CO2/3.60/ C2H6/3.00/ AR/ .83/ O+H+M<=>OH+M 5.000E+17 -1.000 .00 H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ AR/ .70/ O+H2<=>H+OH 3.870E+04 2.700 6260.00 END The chemistry interpreter reads this input file during the preprocessing and creates an Info file ('input_file_name'_out.dat in the input file directory) with the specified chemistry. Currently about 95% of the auxiliary-keywords known by the CHEMKIN-II Version 4.9, April 1994, DOUBLE PRECISION are considered by the interpreter. Therefore it is capable of reading and interpreting the corresponding chem.inp files.
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5. BOOST Aftertreatment
5. BOOST Aftertreatment In this section the application BOOST Aftertreatment is presented. General information about how to use the BOOST pre- and post-processor is available in the BOOST Users Guide and the IMPRESS Chart Users Guide. Aftertreatment examples are available on the installation media and described in the BOOST AT Examples Manual. A detailed step by step explanation of how to use BOOST Aftertreatment Analysis is available in the BOOST Aftertreatment Primer and on the installation media. Note: The values and ranges specified in the right column of all tables in this chapter are taken for 'typical' automotive applications. Its purpose is to give the user an idea in which range the considered value lies. The application of data outside this range is additionally checked by the GUI for physical reasonability. The aftertreatment simulation can be performed either completely decoupled from any BOOST cycle simulation or as an integrated part of a BOOST model as shown in the following figures.
Catalytic Converter Model
Particulate Filter Model
Pipe Model
Combined Exhaust System Model: Pipe, DOC, Pipe, DPF, Pipe and SCR
Figure 52. BOOST Aftertreatment Models Figure 53. BOOST Cycle Simulation Model with Aftertreatment Analysis Simulation
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5. BOOST Aftertreatment The aftertreatment connection visualizes the connection of aftertreatment elements (catalytic converter or particulate filter) with aftertreatment boundary conditions. It does not feature any specific data of its own. An arbitrary number of catalytic converters, particulate filters and pipes can be linked with aftertreatment connections to aftertreatment boundary conditions. Using these elements a complete aftertreatment analysis model is specified.
5.1. Input Data This section explains how the input data can be generated within BOOST.
5.1.1. Aftertreatment Solver For every BOOST Aftertreatment simulation general run information like for example simulation time and results writing as well as solver options have to be specified. This input data and the available ATM Solver output and databus channels are discussed in the following sub-sections: 5.1.1.1. Run Information Run information is defined in Simulation | Control, which can be accessed directly via the button . Different BOOST simulation tasks are available – the Aftertreatment Analysis toggle switch should be activated to run simulations in aftertreatment analysis mode. In this case the transient behavior of the catalyst is simulated. The specification of the aftertreatment simulation is located in the global tree element Aftertreatment Analysis as shown in the following figure. Figure 54. Aftertreatment Analysis - General Simulation Control
The following data concerning the integration horizon is required: Typical Values and Ranges Start Time
Determines the beginning of the simulation and therefore start time of the integration.
0 (s)
End Time
Determines the end of the simulation and therefore the end time of the integration.
0-1800 (s)
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5. BOOST Aftertreatment Time Step
Determines the interval for the stepwise integration. Note that larger time steps will increase the simulation speed but may lead to instabilities of the numerical procedure. Here it is recommended to specify the size of the time step according to the transient changing of the aftertreatment boundary conditions (section page [185] Boundary Conditions ). The time step may be variable, i.e. a table containing time step information may be set up. In this table, for different simulation periods, different time steps may be entered. The time steps entered here will be effective starting from the corresponding time. E.g. for a Variable Time Step Size table: Table 1: Time (X)
Time Step Size (Y)
0
0.5
60
5
0-End Time/30 (s)
the time step will be 0.5 s at the start of the simulation, and starting from second 60, a time step size of 5 s will be used for the rest of the simulation (i.e. the next output will be 65 s). Note: The values in the table will be interpreted as a step function (i.e. no interpolation between the values will take place). When employing the user-defined parameter ATM_PeriodicTimeSteps YES (see User Defined page [184] Parameters ) the data in the table will be interpreted as being periodic. In this case, the last entry in the table will only serve to mark the end of the period but its value will be ignored (when the new period begins, the first value in the table will be used instead). Output After ... Time Steps
Determines at which time step results of the simulation should be written to the results file. '1' each time step, '2' each second time step, ...
Use Enables the user to specify an external database Thermodynamic file for thermal gas properties. Please refer to the Property Database BOOST Users Guide for a detailed description of the expected input format. page [181]
1 (-)
-
As shown in Fig. 54 , the gas composition consisting of gaseous species and solid particles has to be specified. This is defined as global information since the gas flow links all elements considered in the aftertreatment simulation and therefore the number and type of any species has to be identical. The input of solid species is restricted to particulate filters since in the case of catalyst simulations any solid flows through without any impact or interaction. 182
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5. BOOST Aftertreatment The following species specifications are required: Typical Values Gas Composition
Determines the number and type of gas species transported through the system. The user can choose between 2 and 36 species from a popup menu. The list can be stored to an ASCII-file and also loaded from external files.
CO, CO2 O2, N2...
Solid Species
Determines the number and type of solid components transported by the gas flux. The species names can be chosen from a pulldown menu. The list can be stored to an ASCII-file and also loaded from external files.
C(s)
When the Engine A/F Ratio input at the inlet Aftertreatment Boundary is chosen (cf. section page [185] Boundary Conditions ), the reference fuel used for calculating emissions from the given Engine A/F Ratio needs to be specified by enabling Fuel Composition. In this case the following input is required: Typical Values C
Carbon content in fuel.
H
Hydrogen content in fuel.
O
Oxygen content in fuel.
The specification of the Homogenous Gas Phase Reactions, which can be considered in pipes page [181] and catalysts, is shown in Fig. 54 . The list of chemistry models is either typed in (by using the Insert/Remove options) or read in from an ASCII input file. For each chemistry model an arbitrary key (string) is defined. In the BOOST model a specific chemistry model is referred through this key. Typical Values Homogenous Gas Phase Reactions: Key
The key is an arbitrary string which is defined for each chemistry set. In the BOOST model a specific chemistry model is referred by this key.
e.g. CH4_autoignition
Homogenous Gas Phase Reactions: Chemistry
The file name of the chemistry set has to be specified here. The file has to be saved either in the Case or in the Project directory. More info about the format of such a chemistry input file can be found in Appendix Homogenous Gas Phase page [179] Reactions - Input data .
e.g. CH4_ignit.txt
The Restart Control section allows a restart file to be written during a simulation and/or a simulation to be restarted from an existing restart file: Typical Values Restart Simulation YES: Choose this option in order to run a restart simulation. This requires a valid restart file to be available. NO:
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5. BOOST Aftertreatment This is the standard mode for simulations. Write Restart File
Enable this option in order to write a restart file during the simulation: After Termination: A restart file is written after the simulation has been terminated by the user or due to a solver error (e.g. convergence error). After ... Time Steps: Two restart files are written in turn every ... time steps.
-
In the Solver Options section general solver settings can be set: Typical Values Enable HighRobustness Option
This option can lead to better performance especially in the simulation of numerically challenging models which show for example instability.
-
Tolerance Specify a factor in order to refine the default solver 0.1-100 Refinement Factor tolerances. Values > 1 lead to smaller tolerances (-) (more strict solver iteration abort criteria), and values < 1 lead to higher tolerances. Disable Result Writing
Choose this option in order to disable results collection and writing of gid files.
-
5.1.1.2. User Defined Parameters These can be used in order to supply the boost calculation kernel with additional input information. To do so, a Parameter Key and a corresponding Value may be specified. In this chapter, some user-defined parameters specific to BOOST Aftertreatment will be treated. For additional information about this feature please contact [email protected].
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Parameter Key
Value
Description
ATM_AMEND_INPUT_TABLES
NO
Do not amend input tables which are missing a value at the simulation start time with a copy of the first given value, i.e. switch back to the old default behavior (default: YES, i.e. do take the first given value to be valid at the simulation start time in case its time is past the simulation start time; the new default behavior is useful when employing raw sensor data, which may be missing a value at t=0 s, which is usually the simulation's start time).
ATM_RUNNING_AVERAGE
<# points>
Apply a running (moving) average to the input boundary tables using a window size of <# points> (> 1). For details and options, page [186] see Running Average
ATM_PeriodicTimeSteps
YES
Interpret user-defined variable time step page table as periodic data, see Time Step [182] .
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5. BOOST Aftertreatment Example The following figure shows the input of optional parameters. This page allows to specify model page [14] parameters in a general way. As shown, two values (see Eq.29 ) for the friction model of the catalyst are specified. If no optional parameter is set, the simulation uses its default settings. Figure 55. User Defined Parameters
5.1.2. Boundary Conditions In order to run an aftertreatment simulation in analysis-mode, aftertreatment boundary conditions (symbol ) at the inlet and at the outlet of the element have to be defined. At the inlet a mass flux and at the outlet a pressure has to be defined. In order to change the flow direction, negative mass fluxes at the inlet can be set. If no detailed information about the outlet conditions are given then the Adiabatic Backflow conditions can be chosen where no temperature and species mass fraction gradients are assumed. All boundary conditions either can be defined as constant values, or as tables where the boundary value changes as function of the time. Click on to define data in tables. Data can be entered directly in all input tables. If data is stored to a file it can be reloaded by providing the filename and path. The species composition can be defined as mass or mole fractions. At the inlet the following data is required: Typical Values and Ranges Temperature
Determines the temperature of the gas flux entering the aftertreatment element.
Inlet Flow Specification
Determine unit of inlet flow: • Mass Flux • Volume Flow
Mass Flux
Determines the mass entering the aftertreatment element. Negative values cause a change of the flow direction.
Volume Flow
Determines the gas volume entering the aftertreatment element. Negative values cause a change of the flow direction.
Gas Mass/Mole Fractions
Determines the mass or mole fractions of all the 0-1 (kg i /kggas) gas species defined. The sum of all mass fractions has to be '1'.
Solid Mass Fractions
Determines the mass flux of the solid species as a fraction of the gas mass flux. Soot, for example,
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0 (kg/s) depends on the catalyst size
0-1 (kgs/kggas)
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5. BOOST Aftertreatment is required for the simulation of particulate filter loading. Engine A/F Ratio
The optional input of an inlet engine A/F ratio allows the calculation of selected emissions. For the following species the inlet gas fractions can be calculated from the given A/F ratio: CO2, H2O, O2 and N2. In addition, a species from the gas composition needs to be selected to which the correction of sum of fractions is applied. Note: Any value of one of the selected species is overruled by the calculated emissions. Note: A reference fuel needs to be specified in Simulation Control Aftertreatment Analysis (cf. page [181] section Run Information ).
If the Adiabatic backflow toggle switch is selected, only the outlet pressure is required: Typical Values and Ranges Pressure
Determines the pressure at the outlet of the aftertreatment element. In the case of negative flow directions this pressure has to be larger than the pressure loss of the element.
1-5 (bar)
If the Adiabatic backflow toggle switch is deselected (user-defined), the following data is required in addition to Pressure: Typical Values and Ranges Temperature
Determines the temperature of the gas flux entering the aftertreatment element in the case of a reversed flow direction.
300-1500 (K)
Gas Mass/Mole Fractions
Determines the mass or mole fractions of all the 0-1 (kg i /kggas) gas species defined in the case of reversed flow conditions. The sum of all mass fractions has to be 1.
Solid Mass Fractions
Determines the mass flux of the solid species as a fraction of the gas mass flux. This data is only required for particulate filter simulation in the case of a changed flow direction.
0-1 (kgs/kggas)
5.1.2.1. Running Average The data in the boundary input tables may be smoothed applying a running (moving) average method. This may improve solver stability in case of noisy input data. Generally speaking, the smoothed y values are calculated as a mean of the n y values inside the averaging window to be applied, and are centered between the first and the last time value of that averaging window. Since centering the time values would move the first and last given data point forward and backward in time, respectively, these end values are amended by default using the original first and last data points (this behavior may be turned off, although it is not recommended). Multiple averaging passes may be applied. Furthermore, the window size may be reduced by a given factor, in each subsequent pass. 186
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5. BOOST Aftertreatment Currently, this can be achieved by employing a user-defined parameter ATM_RUNNING_AVERAGE. The parameter has several options to control the smoothing procedure which are described in the following table. Parameter Key
Value
Description
ATM_RUNNING_AVERAGE
<# points>
Apply a running (moving) average to the input boundary tables using a window size of <# points>. The method is only applied if <# points> is at least two.
PASSES
<# passes>
Number of sequential averaging passes (default: 1, i.e. one pass).
FACTOR
Factor by which to divide the averaging window in each subsequent pass (default: 1.0, i.e. do not change the window size in subsequent passes).
AMEND
NO
Do not amend the start and end points using the original data points (default: YES, i.e. do amend the end points).
NO
Turn off the running average method selectively for the given input table, where: PRESSURE: pressure (outlet boundary) TEMP: temperature MFRAC: species mass/mole fractions SFRAC: solid mass fraction INFLOW: mass/volume flux
Example: The User Defined Parameters table: Parameter Key
Value
ATM_RUNNING_AVERAGE
40
PASSES
3
FACTOR
1.3371
MFRAC
NO
PRESSURE
NO
would apply a three-pass running average with window sizes of 40, 30, and 22 points to all input tables, except for the species mass/mole fractions and the pressure tables, and amend the end points afterwards. Giving e.g. ATM_RUNNING_AVERAGE 20 as the only parameter would apply a one-pass running average with an averaging window of 20 points.
5.1.3. Catalyst The specification of the catalyst ( ) comprises data of its geometry, its fluid and thermodynamic behavior and the conversion reactions taking place. This input data is discussed in the following sub-sections:
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5. BOOST Aftertreatment 5.1.3.1. General In order to simulate the chemical processes in the catalyst - either heterogeneous or homogeneous reactions - the switch Chemical Reactions needs to be activated. As a consequence the input pages to define the required input for the single-channel converter model are activated as well. If deactivated, no chemical reactions can be modeled and default values will be considered for the numerical and physical properties for the single-channel converter model. Furthermore the basic geometry has to be defined by the following data: Typical Values and Ranges 3
Monolith Volume
Determines the volume of the monolith, comprising both, the volume of the gas phase and the solid substrate.
1-10 (dm )
Length of Monolith
Determines the length of the monolith.
0.1-0.5 (m)
Inlet Collector Volume
Determines the volume of the inlet cone. This information is only required for the Cycle Simulation task.
1 (dm )
Outlet Collector Volume
Determines the volume of the inlet cone. This information is only required for the Cycle Simulation task.
1 (dm )
Couple to upstream element
Select to thermally couple the catalyst to an upstream element via wall heat conduction (see page [75] Thermal Coupling for details).
-
Consider Air Gap between the Substrates
When deselected, thermal coupling to an upstream element's substrate (e.g. another catalyst or a particulate filter) is active. Select to suppress this thermal coupling (see Thermal page [76] Coupling (Substrates) for details).
-
3
3
Note: Relevant only when Couple to upstream element is active. 5.1.3.2. Initialization The monolith (solid phase) initial temperature can be defined by the user: Typical Values and Ranges Initial Solid Temperature
Determines the initial temperature of the solid substrate as constant or as a function of the catalyst length.
273-1000 (K)
5.1.3.3. Type Specification The cell structure of the monolith can either be defined assuming Squared Cell Catalysts in a simplified way or within any geometrical assumptions for General Catalysts. If Square Cell Catalyst is selected, the following input data has to be defined: Typical Values and Ranges
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Cell density (CPSI)
Determines the type of monolith using the 2 number of channels per in .
100-900 (1/in )
Wall Thickness
Determines the thickness of the monolith's walls.
0.006-0.015 (in)
If General Catalyst is selected, the following input data has to be defined: Typical Values and Ranges Open Frontal Area (OFA)
Determines the open frontal area (= fluid volume fraction) of monolith.
0.50-0.75 (-)
Hydraulic Diameter (Hydraulic Area)
Determines the hydraulic unit (diameter or area) of the monolith channels.
0.001-0.005 (m)
5.1.3.4. Friction The friction of the catalytic converter model can either be specified by Target Pressure Drop or by a friction Coefficient. If the catalyst is simulated in the aftertreatment analysis mode, only the specification of a friction coefficient can be used. For a standard BOOST cycle simulation both input variants can be used. If Target Pressure Drop is selected, the following data is required: Typical Values and Ranges Inlet Mass Flow
Determines the inlet mass flow, as reference value 0 (kg/s) for the evaluation of a friction coefficient. depends on the catalyst size
Inlet Temperature
Determines the inlet temperature, as reference value for the evaluation of a friction coefficient.
300 (K)
Inlet Pressure
Determines the inlet pressure, as reference value for the evaluation of a friction coefficient.
1 (bar)
Target Pressure Drop
Determines the pressure drop of the element as basis for the evaluation of a friction coefficient.
0.003 (bar)
For more detailed information about the input variant Pressure Drop refer to the BOOST Users Guide. If Coefficient is selected, the following input data is required: Typical Values and Ranges Laminar Coefficient a
Determines a laminar friction coefficient according page [14] to Eq.29 .
64 (-)
Laminar Coefficient b
Determines a laminar friction coefficient according page [14] to Eq.29 .
-1 (-)
Turbulent (Friction Determines a turbulent friction coefficient. The Coefficient) friction coefficient can be specified as constant or
0.01-0.04 (-)
table value (see typical values below). The latter value is defined as a function of the monolith length.
Determines a dimensionless factor that considers 0.04-1 (-) the influence of the channel shape in the case of laminar flow. The multiplier either can be chosen for different channel geometries (see section BOOST Balance Equations, Single Channel Model page [13] ) or setup completely freely.
5.1.3.5. Discretization The required input of the discretization does not concern the physical situation of the catalyst, but is required in order to setup and 'tune' its numerical model. Typical Values and Ranges Model Dimension
Determines the dimension of the catalyst model. Here either 1D or 2D can be set. Note that for adiabatic radial heat loss conditions 2D models are page [191] reduced to 1D (refer to section Heat Loss ).
1D/2D
Axial Direction
Number of Grid Point: Determines the number of calculation cells in axial direction. Grid Shape Factor: Determines the allocation of the axial grid points. Values below 1 produce a grid which gets more dense toward the boundaries (according to a geometrical series), whereas values greater than 1 increase the grid density toward the middle of the catalyst.
10-100 (-) 0.8 (-)
If a 2D simulation is chosen, the following data should be set in addition to the radial direction: Typical Values and Ranges Radial Direction
Number of Channels: 2-7(-) Determines the number of channels located in radial direction 0.5 (-) Grid Shape Factor: Determines the allocation of the radial channels. Values below 1 produce a grid along the radius which is more dense toward the center and the shell of the catalyst (according to a geometrical series), whereas values greater than 1 yield a grid which is more dense in the middle of the radius.
5.1.3.6. Catalyst Physical Properties Physical properties of the catalyst's solid phase are required in order to model the thermal behavior of the converter. Typical Values and Ranges Density
190
3
Determines the bulk density of the monolith material 400-2000 (kg/m ) considering the volume in the pores.
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5. BOOST Aftertreatment Thermal Conductivity
Determines the thermal conductivity of the monolith 0.1-50 (W/(m·K)) material (= bulk solid material considering the volume in the pores). This property can specified as constant value or as a function of temperature.
Specific Heat
Determines the specific heat of the monolith 500-2000 (J/ material (= bulk solid material considering the (kg·K)) volume in the pores). This property can specified as constant value or as a function of temperature.
Anisotropic Corrects the diffusion coefficients of the solid Conduction Factor temperature equation normal to axial direction. A value of 1.0 simulates an isotropic conductivity. A value of 0.5 would be a good choice for monoliths. This value is only needed for 2D simulations.
0-10 (-)
Heat Transfer Model
Determines different approaches for calculating the heat transfer through the boundary layer (see page [28] Section Transfer Coefficients ). If 'Constant' is chosen, a heat transfer coefficient needs to be specified.
Sieder-Tate (default)
Heat Transfer Coefficient
Determines a constant heat transfer coefficient through the boundary layer.
5-500 (W/m2)
Heat Transfer Multiplier
Specify a factor by which the heat transfer is scaled. 0.1-10 (-)
Mass Transfer Model
Determines different approaches for calculating the mass transfer through the boundary layer (see page [28] Section Transfer Coefficients ). If 'Constant' is chosen, a mass transfer coefficient needs to be specified.
Sieder-Tate (default)
Mass Transfer Coefficient
Determines a constant mass transfer coefficient through the boundary layer.
0.01-0.1 (kg/ (m2s))
Mass Transfer Multiplier
Specify a factor by which the mass transfer is 0.01-10 scaled. Possible input is 'Constant' (mass transfer (-) of every species is scaled in the same way) or 'Table' (mass transfer of selected species is scaled).
Catalysts whose substrates are axially structured in a way that there is heat- and mass-transfer between channels, can be modeled using the options from the Catalyst Segmentation section: Typical Values and Ranges Repeat Turbulent Inlet Region
Enable this option in order to consider recurrent turbulent inlet regions along the catalyst's axial direction.
-
Repeating Length
Specify a length at which the turbulent inlet region is 0.001-0.1 (m) repeated.
5.1.3.7. Heat Loss In the current model, Adiabatic Simulation can be chosen, or the radial heat transfer to the environment can be either specified in a simplified model or by using a multi-layered wall model. In the case of a simplified model the required input data must be specified as shown
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5. BOOST Aftertreatment in the following figure. More detailed information on how the radial heat transfer is modeled page [19] can be found in Section Boundary Conditions . In the second case, where the canning and insulation can be modeled in detail by specifying individual wall layers, Variable Wall Temperature needs to be enabled and the required input data can be provided on the related sub-page. Detailed information on the multi-layered wall model can be found in sectionMultipage [65] Layered Wall Model . Figure 56. Heat Loss - Specification of Radial Heat Transfer Conditions
The following input data has to be specified: Typical Values and Ranges
192
Variable Wall Temperature
Enables the specification of a multi-layer wall model around the monolith and disables the input for the simplified heat-loss-to-ambient model below.
External Heat Transfer Coefficient
Determines the heat transfer between the shell and the environment. This property can be defined as constant or as function of the simulation time.
10-100 (W/(m ·K))
Thickness, Shell
Determines the thickness of the shell.
0-5 (mm)
Thickness, Insulation
Determines the thickness of the insulation mat.
0-30 (mm)
Thermal Conductivity, Shell
Determines the thermal conductivity of the shell.
10-100 (W/(m·K))
Thermal Conductivity, Insulation
Determines the thermal conductivity of the insulation mat.
0.01-0.1 (W/(m·K))
Environment Temperature
Determines the temperature of the environment. This property can be defined as constant or as function of the simulation time. This (i.e. the temperature of the medium surrounding the catalyst) may be specified as a function of time. The temperature profile is considered to be periodic if not the entire integration time is covered by the input data.
298-350 (K)
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5. BOOST Aftertreatment 5.1.3.7.1. Variable Wall Temperature Typical Values and Ranges Solid Material Table
Add a solid wall layer by clicking on Insert.
Solid Material
Determines a solid material for a given wall layer. Click in the input field and select a material from the selection field. The properties of the solid material can be specified in the pull-down menu . The first line in the table represents the innermost wall layer and the last line the outermost wall layer.
Layer Thickness
Determines the thickness of each individual wall layer.
No. of Grid Points
Determines the numerical discretization of each wall 3-10 (-) layer in radial direction.
Ambient Temperature
Determines the temperature of the ambient. This value is a constant or a function of simulation time.
Radiation Sink Temperature
Determines the temperature used for the evaluation 273-1000 (K) of radiative heat transfer. This value is a constant or a function of simulation time.
Convection Model
Enables the application of a convection model for the external heat transfer from the outer wall layer surface to the ambient.
Convection Coefficient
Enables the application of a convection coefficient for the external heat transfer from the outer wall layer surface to the ambient.
Coolant
Determines a fluid which is assumed to flow around the outer wall layer. Fluid properties of air and water are available.
Characteristic Determines the velocity of the coolant flowing Velocity of Coolant around the outer wall layer. A cross-flow regime is assumed. Convection Coefficient
0.1-30 (mm)
273-1000 (K)
0.1-30 (m/s)
2
Determines a convective heat transfer coefficient for 7-100 (W/(m ·K)) the external heat transfer. This value is constant or a function of simulation time.
5.1.3.8. Washcoat At "Washcoat" the physical properties of the washcoat material, as well as the reaction mechanism and mass transfer models are specified. Two different approaches are available to model heterogeneous reactions in the catalyst's washcoat: In the Surface Reaction Model approach, the mass transfer, i.e. pore diffusion, through the washcoat layer(s) is neglected. In the Washcoat Layer (WCL) Model approach, pore diffusion is taken into account. Therefore, every washcoat layer is discretized in the direction perpendicular to the catalyst solid surface, resulting in a 1D+1D simulation model. The Surface Reaction Model approach is equivalent to the WCL Model approach with only one washcoat layer of one computational cell.
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5. BOOST Aftertreatment A single Catalyst can consider either the Surface Reaction Model or the WCL Model; they cannot be mixed. Surface Reaction Model The necessary input for the Surface Reaction Model is the thickness of the washcoat, as well as the reaction mechanism describing the chemical behavior of the converter. The set-up of the page [197] Conversion Reactions is located in the first reaction branch My_Reaction . The input of Washcoat Layer Thickness can be done directly in the Catalyst component mask, by selecting "Washcoat Layer Thickness" or it can be taken from an AUCI Catalytic Reaction Mechanism. Details on making use of washcoat properties from custom models can be found in page [221] the related section Washcoat Properties from AUCI Custom Models . Typical Values and Ranges Washcoat Thickness Washcoat Thickness (direct GUI input)
Specify the thickness of the washcoat.
>0-0.003 (m)
From AUCI Catalytic Indicate that the thickness of the washcoat Reaction Mechanism shall be taken from an AUCI custom kinetic page [197] model loaded at subnode My_Reaction . Additionally specify from which custom model it shall be taken by typing its row index in the User Defined Reactions table. Extruded Catalyst
The entire converter is modeled as an extruded catalyst. The washcoat thickness is calculated out page of the input from subnode Type Specification [188] . Tip: An example for extruded catalyst modeling can be found in the related section in the BOOST Aftertreatment Application Examples Guide.
The washcoat thickness is used in the calculation of the hydraulic diameter in case of a "Square Cell Catalyst" and the fraction of solid substrate in the overall converter volume in case of a page [188] "General Catalyst" (cf. Type Specification ). Washcoat Layer (WCL) Model In the WCL Model an arbitrary number of washcoat layers can be defined. This is done in the related table of washcoat layers that is editable as soon as the WCL model has been selected. For each washcoat layer a separate row is added to the table. The required input for the simulation is done on related subnodes: For each washcoat layer the following subnodes are created: 1. My_Layer page [195]: Specify the physical properties of the washcoat material and input required for the numerical simulation model. 2. My_Reaction page [197]: Specify the reaction mechanism taking place in the related washcoat layer. 3. My_Transport page [219]: Specify the pore diffusion model that describes the mass transfer within the washcoat layer.
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5. BOOST Aftertreatment Tip: The labels of these subnodes may be changed within the table listing all washcoat layers; for example "My_Layer" at washcoat layer #1 could be renamed to "Top_Layer": Simply double-click the related input field and enter a new label. 5.1.3.8.1. Washcoat Layer Specification At "My_Layer" physical properties of the washcoat layer as well as numerical simulation model input is given. Below, the required input for single washcoat layer (WCL) is described. Some of the WCL properties may either be typed-in directly at this input pages or an AUCI custom model may be indicated as source. Details on this treatment are given in the related section Washcoat page [221] Properties from AUCI Custom Models . Dimension For each washcoat layer its thickness needs to be indicated. Note that the washcoat layer thickness needs to be greater than zero. The following input possibilities are available: Typical Values and Ranges Washcoat Layer Thickness Washcoat Layer Thickness (direct GUI input)
Specify the thickness of the washcoat layer.
>0-0.003 (m)
From AUCI Catalytic Indicate that the thickness of the washcoat layer Reaction Mechanism shall be taken from an AUCI custom kinetic page [197] model loaded at the related My_Reaction subnode for this WCL. Additionally specify from which custom model it shall be taken by typing its row index in the User Defined Reactions table. From AUCI Transfer Model
Indicate that the thickness of the washcoat layer shall be taken from an AUCI custom pore diffusion model loaded at the related page [219] My_Transport subnode for this WCL.
Extruded Catalyst
The entire converter is modeled as an extruded catalyst. The washcoat thickness is calculated out page of the input from subnode Type Specification [188] . Note: In order to use this option in the Washcoat Layer Model there is only a single washcoat layer allowed in the catalyst. Tip: An example for extruded catalyst modeling can be found in the related section in the BOOST Aftertreatment Application Examples Guide.
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5. BOOST Aftertreatment Reference for Chemistry Data Optionally, reference data can be provided to specify the ratio of washcoat layer volume to converter volume of the particular catalyst for which the kinetic parameters have been calibrated. page [23] More details on this topic can be found in the related section Reference for Chemistry Data . Typical Values and Ranges Specify a Reference WCL Volume
Select this option to type-in the reference washcoat layer volume.
>0-0.01 (-)
Discretization The following input is required for the computational model. Typical Values and Ranges Number of Grid Points
Specify the number of computational cells of each washcoat layer.
1-10 (-)
Washcoat Physical Properties The following physical properties of the washcoat layer material can be specified. Typical Values and Ranges Washcoat Bulk Density WCL Bulk Density (direct GUI input)
Specify the density of the washcoat layer material.
3
400-2000 (kg/m )
From AUCI Catalytic Indicate that the bulk density of the washcoat Reaction Mechanism layer material shall be taken from an AUCI custom kinetic model loaded at the related page [197] My_Reaction subnode for this WCL. Additionally specify from which custom model it shall be taken by typing its row index in the User Defined Reactions table. Washcoat Porosity WCL Porosity (direct GUI input)
Specify the porosity of the washcoat layer material.
From AUCI Catalytic Indicate that the porosity of the washcoat layer Reaction Mechanism material shall be taken from an AUCI custom kinetic model loaded at the related My_Reaction page [197] subnode for this WCL. Additionally specify from which custom model it shall be taken by typing its row index in the User Defined Reactions table. From AUCI Transfer Model
196
Indicate that the porosity of the washcoat layer material shall be taken from an AUCI custom pore diffusion model loaded at the related page [219] My_Transport subnode for this WCL.
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0-1 (-)
5. BOOST Aftertreatment 5.1.3.8.2. Reaction Model (Conversion Reactions) At "My_Reaction" several different reaction models are available. Either no reactions are taken into account, pre-defined or custom kinetic models are chosen or the application of map based conversion is possible. Pre-Defined Kinetic Models The pre-defined reaction models use global kinetic approaches given by Langmuir Hinshelwood equations and also transient mechanisms where adsorption and desorption steps are explicitly taken into account. All reaction models are supplied with default values for the individual kinetic parameters. The user can use the kinetic model and adjust all kinetic parameters. Note: The suggested reaction parameters have been successfully applied to several validation simulations, but they may have to be adjusted for use in other types of catalysts. In this case it is recommended to apply the pre-defined reaction model and to supply it with adequate reaction parameters. The following pre-defined reaction models are available: • Diesel Oxidation Catalyst (DOC) This model is dedicated for DOCs comprising the three major oxidation reactions of CO, HC and NO. • Three Way Catalyst (TWC) This model is a dedicated TWC model comprising seven conversion reactions and surface storage reactions on cerium, rhodium and barium. By selecting specific reactions and adapting the related kinetic parameters, this model also can be applied to other catalysts such as DOCs. • Selective Catalytic Reduction (SCR), Steady Kinetics This model comprises seven reaction rates which can be enabled/disabled individually for three different reaction sections in the catalyst. The SCR rates use Eley-Rideal mechanisms, thus it assumes steady-state conditions for the reaction steps of adsorption, catalytic reaction and desorption. • Selective Catalytic Reduction (SCR), Transient Kinetics This model comprises nine reactions that can be enabled/disabled individually for three different reaction sections in the catalyst. The transient effect of ad-/desorption is explicitly taken into account. • Lean NOx Trap This model comprises ten conversion reactions and surface storage on cerium. Furthermore, it offers two approaches of storing nitric oxides: an ash core model approach, developed by ICVT Stuttgart, and a surface storage approach. Detailed information about the individual reaction mechanisms is given in section Kinetic Models page [77] . Custom Kinetic Models In addition to providing the above pre-defined reaction mechanism custom kinetic models can be simulated as well. For that two interfaces are available: • User Defined Reactions (Without Archive) Here, a custom kinetic model programmed in the FORTRAN file mod_userdef_cat.f90 can be activated. For details on using this approach of custom kinetic models contact the BOOST Support. Restriction: This type of custom kinetic model cannot be combined with any other kinetic model in the same surface or washcoat layer model. Note: This type of custom kinetic model is deprecated. It is recommended to use "User Defined Reactions" and AUCI for designing custom models.
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5. BOOST Aftertreatment • User Defined Reactions Using this option custom kinetic models designed in AUCI Catalytic Reaction Mechanism can be activated. Details in AUCI can be found in the related documentation. This type of custom kinetic model can be combined with the pre-defined models in the same surface or washcoat layer model. Map Based Conversion As an alternative to kinetic models in the catalyst, its conversion can also be modeled by providing maps that comprise the species conversion as a function of different parameters (e.g. temperature, space velocity), that are to be detailed at the related sub-page. In addition to these conversion maps it is also possible to use control elements to define conversion dependencies and to actuate a species' conversion. Restriction: None of the kinetic models can be combined with Map Based Conversion. Further input Typical Values and Ranges Effective Catalyst Loading
This dimensionless value is a measure for > 0 [-] the content of precious group metals (PGM) in the washcoat. It is used as a multiplier to all conversion reactions that are related to PGM. Hence one can model • different PGM loading in the washcoat, by increasing or decreasing the effective catalyst loading relative to a base set of kinetic parameter, assuming that the impact of loading can be linearly covered in the frequency factors, • aging or poising by choosing a value smaller 1.0. Note: Reactions involving surface site species (type "Storage") are not affected by this multiplier.
Tolerate Undefined Species
198
Each reaction requires the educts and products, and optionally those species that are being used in the rate formulation (e.g. as inhibitors), to be present in the Gas Composition (cf. Run page [181] Information ). Hence, if a required species is missing the solver will stop indicating to add that species to the Gas Composition. By checking this switch it is possible to continue the simulation without having all species required by the reaction mechanism available in the gas composition.
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5. BOOST Aftertreatment Attention: If species required by the stoichiometry as products are being omitted, mass conservation is broken and simulation results may be considered with care.
5.1.3.8.2.1. Diesel Oxidation Catalyst (DOC) This reaction model offers a set of three oxidation reactions. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. page [77] More detailed information about this model is given in section DOC Catalyst Reactions . The different reactions can be en/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. R1: CO Oxidation
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of carbon monoxide. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
R2: C3H6 Oxidation
R3: NO Oxidation
K1 - K5
Determines the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determines the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of propane as representative of hydro carbons. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5
Determines the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determines the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
A reversible rate mechanism is commonly accepted in the literature for the oxidation of nitric monoxide. Two rate approaches are available. The reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy. Approach 1
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Approach 2
K
Determines the frequency factors used in the pre-defined reversible power-law conversion mechanism.
E
Determines the activation temperatures used in the pre-defined reversible power-law conversion mechanism.
A
Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism.
5.1.3.8.2.2. Three Way Catalyst (TWC) This reaction model offers a set of nine conversion reactions and surface storage mechanisms at three different surface sites. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. page [78] More detailed information about this model is given in Section TWC Catalyst Reactions . The different reactions can be enabled/disabled individually by clicking the corresponding check boxes. When enabled, several sub-pages for the detailed specification of the reaction parameters become enabled. R1: CO Oxidation
R2: C3H6 Oxidation
200
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of carbon monoxide. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of propene as representative of hydrocarbons. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
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R3: CO-NO Redox Reaction
R4: H2 Oxidation
R5: NO Oxidation
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of carbon monoxide and reduction of nitric monoxide. The denominator takes into account an inhibition effect of carbon monoxide. Each reaction constant is evaluated using Arrhenius' law. The reaction order of carbon monoxide is a function of the carbon monoxide concentration itself and therefore the order changes between lean and rich conditions.
m
Determines the reaction order of nitric monoxide in the pre-defined reaction approach.
n
This is a tuning value in order to determine the reaction order of carbon monoxide (n) in the pre-defined reaction approach. There are two possibilities, either a constant value for n (activate Reaction Order and specify n), or the evaluation of the Shift Function (activate Shift Function and specify o).
K1 - K2
Determine the frequency factors used in the predefined conversion mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of hydrogen. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
A reversible rate mechanism is commonly accepted in the literature for the oxidation of nitric monoxide. Two rate approaches are available.
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5. BOOST Aftertreatment The reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy. Approach 1
Approach 2
R6: CO-H20 Shift
R7: C3H8 Oxidation
K
Determines the frequency factor used in the pre-defined reversible power-law conversion mechanism.
E
Determines the activation temperature used in the pre-defined reversible power-law conversion mechanism.
A
Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the water gas shift reaction. Its reversible behavior is taken into account by considering the equilibrium constant as part of the rate equation. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of propane. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5
202
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
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5. BOOST Aftertreatment E1 - E5
R8: C3H6-H20 Shift
R9: C3H8-H20 Shift
R10-R13: Ce Storage
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for water gas shift reactions. Its reversible behavior is taken into account by considering the equilibrium constant as part of the rate equation. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the water gas shift reaction. Its reversible behavior is taken into account by considering the equilibrium constant as part of the rate equation. The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Under lean conditions cerium is oxidized by O2 and under rich conditions cerium is reduced by CO, C3H6 and C3H8. All rates are of first order with respect to the participating gas and solid phase components. All reaction constants are evaluated using Arrhenius' law. R10
R11
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5. BOOST Aftertreatment
R12
R13
R14-R19: Rh Storage
Cerium Storage Capacity
Determines the maximum amount of oxygen that can be stored on the cerium surface site.
Initial Surface Coverage fraction of CeO2
Determines the coverage fraction of CeO2 at the solid surface. Range: 0-1 (-)
Max Surface Coverage fraction of CeO2
Determines the maximum surface coverage fraction of CeO2 at the solid surface. This property can be specified as a constant value or as a function of temperature. Range: 0-1 (-)
K1 - K4
Determines the frequency factors used in the predefined ad-/desorption mechanisms .
E1 - E4
Determines activation temperatures used in the pre- ad-/desorption mechanisms .
Under lean conditions rhodium is oxidized by O2 or NO and under rich conditions rhodium is reduced by CO, H2, C3H6 and C3H8. All rates are of first order with respect to the participating gas and solid phase components. All reaction constants are evaluated using Arrhenius' law. R14
R15
R16
R17
R18 204
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5. BOOST Aftertreatment
R19
R20-R21: Ba Storage
Rhodium Storage Capacity
Determines the maximum amount of oxygen that can be stored on the rhodium surface site.
Initial Surface Coverage fraction of RhO
Determines the coverage fraction of at the solid surface. Range: 0-1 (-)
Max Surface Coverage fraction of RhO
Determines the maximum surface coverage fraction of at the solid surface. This property can be specified as constant value or as function of temperature. Range: 0-1 (-)
K1 - K6
Determine the frequency factors used in the predefined ad/desorption mechanisms.
E1 - E6
Determine the activation temperatures used in the pre-defined sorption-equilibrium and ad/desorption mechanisms.
In the presence of NO2 and O2, barium carbonate is oxidized to barium nitrate and in the presence of CO, barium nitrate is reduced to barium carbonate. All rates are of first order with respect to the participating gas and solid phase components. All reaction constants are evaluated using Arrhenius' law. R20
R21
Barium Storage Capacity
Determines the maximum amount of nitric oxide that can be stored on the barium surface site.
Initial Surface Coverage fraction of Ba(NO3)2
Determines the coverage fraction of Ba(NO3)2 at the solid surface. Range: 0-1 (-)
Max Surface Coverage
Determines the maximum surface coverage fraction of Ba(NO3)2 at the solid surface. This property can be specified as constant value or as function of temperature.
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5. BOOST Aftertreatment fraction of Ba(NO3)2
Range: 0-1 (-)
K1 - K2
Determine the frequency factors used in the predefined ad/desorption mechanisms.
E1 - E2
Determine the activation temperatures used in the pre- ad/desorption mechanisms.
Metal Storage Capacity
Determines the maximum amount of C3H6 that can be stored on the metallic surface site.
Initial Surface Coverage fraction of C3H6
Determines the coverage fraction of C3H6 at the solid surface. Range: 0-1 (-)
Max Surface Coverage fraction of C3H6
Determines the maximum surface coverage fraction of C3H6 at the solid surface. This property can be specified as constant value or as function of temperature. Range: 0-1 (-)
K1 - K2
Determine the frequency factors used in the predefined sorption-equilibrium and ad/desorption mechanisms.
E1 - E2
Determine the activation temperatures used in the pre-defined sorption-equilibrium and ad/desorption mechanisms.
R22: HC Storage
5.1.3.8.2.3. Selective Catalytic Reduction (HSO SCR), Steady Kinetics This reaction model offers a set of seven conversion reactions that are typically used in SCR converters. This pre-defined model is setup in a way that three different reaction sections can be specified where in each section the reactions can be individually switched on. The name HSO is related to a typical SCR system where three different sections for Hydrolysis, SCR and Oxidation are used in one converter. If only one section is considered, the lengths of the two others sections can be simply set to zero. The model uses steady-state approaches for all SCR reactions as given by the Eley-Rideal mechanism. For the hydrolysis and all oxidation reactions also steady-state power-law reactions are applied. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. More detailed information about this model is given in Section HSO-SCR Catalyst Reactions, page [81] Steady-State Approach . The rate is assumed to be of first order with respect to both water vapor and isocyanic acid. The reaction constant is evaluated using Arrhenius' law. Length of Section 1 Length of Section 2
206
This is a dimensionless length that is used to specify up to three different reaction sections. The length of the third section is calculated by 1-Length_1-Length_2. If only one section is needed, set the length of section 1 to '1' and section 2 to '0'. Range: 0-1 (-)
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment The different reactions can be enabled/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. R1: HNCO Hydrolysis
R2: NO Reduction
R3: NOx Reduction
R4: NO2 Reduction
The Eley-Rideal kinetic approach is commonly accepted in the literature for the selective reduction of nitric monoxide with ammonia. The denominator takes into account the inhibition effects of ammonia and each reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factor used in the predefined power law mechanism.
E
Determines the activation temperature used in the pre-defined power law conversion mechanism.
The Eley-Rideal kinetic approach is commonly accepted in the literature for the selective reduction of nitric monoxide and dioxide with ammonia. The denominator takes into account the inhibition effects of ammonia and each reaction constant is evaluated using Arrhenius' law.
K1 - K2
Determine the frequency factors used in the predefined Eley-Rideal conversion mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined Eley-Rideal conversion mechanism.
The Eley-Rideal kinetic approach is commonly accepted in the literature for the selective reduction of nitric monoxide and dioxide with ammonia. The denominator takes into account the inhibition effects of ammonia and each reaction constant is evaluated using Arrhenius' law.
K1 - K2
Determine the frequency factors used in the predefined Eley-Rideal conversion mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined Eley-Rideal conversion mechanism.
The Eley-Rideal kinetic approach is commonly accepted in the literature for the selective reduction of nitric monoxide and dioxide with ammonia. The denominator takes into account the inhibition effects of ammonia and each reaction constant is evaluated using Arrhenius' law.
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5. BOOST Aftertreatment
R5: NH3 Oxidation 1
R6: NH3 Oxidation 2
R7: NO Oxidation
K1 - K2
Determine the frequency factors used in the predefined Eley-Rideal conversion mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined Eley-Rideal conversion mechanism.
The rate is assumed to be of first order with respect to ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factor used in the predefined power law mechanism.
E
Determines the activation temperature used in the pre-defined power law conversion mechanism.
The rate is assumed to be of first order with respect to ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factor used in the predefined power law mechanism.
E
Determines the activation temperature used in the pre-defined power law conversion mechanism.
A reversible rate mechanism is commonly accepted in the literature for the oxidation of nitric monoxide. Two rate approaches are available. Each reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy. Approach 1
Approach 2
208
K
Determines the frequency factor used in the pre-defined reversible power-law conversion mechanism.
E
Determines the activation temperature used in the pre-defined reversible power-law conversion mechanism.
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment A
Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism.
5.1.3.8.2.4. Selective Catalytic Reduction (HSO SCR), Transient Kinetics This reaction model offers a set of nine conversion reactions that are typically used in SCR converters. This pre-defined model is setup in a way that three different reaction sections can be specified where in each section the reactions can be individually switched on. The name HSO is related to a typical SCR system where three different section for Hydrolysis, SCR, and Oxidation are used in one converter. If only one section is considered, the lengths of the two other sections simply can be set to zero. The model uses steady-state approaches for the hydrolysis, one of the ammonia and one of the nitric monoxide oxidation reactions. For the SCR reactions explicit ad-/desorption steps of ammonia at the solid surface are taken into account. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. More detailed information about this model is given in page [83] Section HSO-SCR Catalyst Reactions, Transient Approach . Length of Section 1 Length of Section 2
This is a dimensionless length that is used to specify up to three different reaction sections. The length of the third section is calculated by 1-Length_1-Length_2. If only one section is needed set the length of section 1 to '1' and of section 2 to '0'. Range: 0-1 (-)
The different reactions can be en/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. R1: HNCO Hydrolysis
R2-R3: NH3 Adsoprtion, Desorption
The rate is assumed to be of first order with respect to both vapor and isocyanic acid. The reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factors used in the predefined power law mechanism.
E
Determines the activation temperatures used in the pre-defined power law conversion mechanism.
The adsorption rate is of first order with respect to ammonia in the gas phase and also proportional to the free site fraction at the surface. The desorption rate is proportional to the amount of ammonia stored at the surface. For the desorption a surface coverage dependency is additionally taken into account. Each reaction constant is evaluated using Arrhenius' law. R2
R3
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5. BOOST Aftertreatment NH3 Storage Capacity
Determines the maximum amount of ammonia that can be stored at the solid surface site.
Initial Surface Coverage Fraction of NH3
Determines the coverage fraction of NH3 at the solid surface. Range: 0-1 (-)
Coverage Determines a surface coverage dependency in the Dependency pre-defined ad/desorption mechanisms. (epsilon) Max Surface Coverage Fraction of NH3
Determines the maximum surface coverage fraction of NH3 at the solid surface. This property can be specified as constant value or as function of temperature. Range: 0-1 (-)
NH3 Determines the order of NH3 surface coverage Surface fraction in the adsorption rate formulation. Coverage Range: 0-2 (-) Fraction Dependency m
R4: NO Reduction
R5: NOx Reduction
210
K1 - K2
Determines the frequency factors used in the predefined ad/desorption mechanisms.
E1 - E2
Determines the activation temperatures used in the pre- ad/desorption mechanisms.
The reaction rate is of first order with respect to nitric monoxide in the gas phase and it depends on the stored amount of ammonia at the surface. The reaction is additionally limited by a critical surface fraction of ammonia.
Critical Surface Coverage)
Determines a tuning factor that slows down the reaction rate above a critical surface coverage.
K
Determines the frequency factor used in the predefined transient conversion mechanism.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism.
The reaction rate is of first order with respect to nitric dioxide in the gas phase and it depends on the stored amount of ammonia at the surface. The reaction is additionally limited by a critical surface fraction of ammonia.
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment
R6: NO2 Reduction
R7: NH3 Oxidation 1
R8: NH3 Oxidation 2
R9: NO Oxidation
Critical Surface Coverage)
Determines a tuning factor that slows down the reaction rate above a critical surface coverage.
K
Determines the frequency factor used in the predefined transient conversion mechanism.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism.
The rate is assumed to be of first order with respect to stored ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
Critical Surface Coverage)
Determines a tuning factor that slows down the reaction rate above a critical surface coverage.
K
Determines the frequency factor used in the predefined transient conversion mechanism.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism.
The rate is assumed to be of first order with respect to stored ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factor used in the predefined transient oxidation mechanism.
E
Determines the activation temperature used in the pre-defined transient oxidation.
The rate is assumed to be of first order with respect to stored ammonia and of zero order with respect to oxygen. The reaction constant is evaluated using Arrhenius' law.
K
Determines the frequency factor used in the predefined power-law oxidation mechanism.
E
Determines the activation temperature used in the pre-power-law transient oxidation.
A reversible rate mechanism is commonly accepted in the literature for the oxidation of nitric monoxide. Two rate approaches are available. The reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy. Approach 1
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5. BOOST Aftertreatment
Approach 2
Temperature Determines the temperature dependency used in Dependency the pre-defined transient and reversible power-law (A) conversion mechanism.
R10: NO2 Formation
K
Determines the frequency factor used in the pre-defined transient and reversible power-law conversion mechanism.
E1
Determines the activation temperature used in the pre-defined transient and reversible power-law conversion mechanism.
K
Determines the frequency factor used in the predefined power-law conversion mechanism.
E
Determines the activation temperature used in the pre-defined power-law conversion mechanism.
5.1.3.8.2.5. Lean NOx Trap (LNT) This reaction model offers a set of ten conversion reactions, surface storage on cerium and barium. The rate equations and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters. The different reactions can be en/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. R1: H2 Oxidation
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Reaction Order m
Determines the reaction order of nitric oxide in the pre-defined Langmuir-Hinshelwood conversion mechanism.
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
R2: CO Oxidation
212
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5. BOOST Aftertreatment E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Reaction Determines the reaction order of propene, nitric Orders m, n, oxide and oxygen in the pre-defined Langmuirp Hinshelwood conversion mechanism. R3: C3H6 Oxidation
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Reaction Determines the reaction order of oxygen and nitric Orders m, n oxide in the pre-defined Langmuir-Hinshelwood conversion mechanism. R4: NO Oxidation
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Kinetic Determines a kinetic coefficient used in the Coefficient f pre-defined Langmuir-Hinshelwood conversion mechanism. Reaction Determines the reaction order of propene, nitric Orders m, n, oxide and oxygen in the pre-defined Langmuirp Hinshelwood conversion mechanism. R5: NO Reduction H2
K1
Determines the frequency factor used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1
Determines the activation temperature used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
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5. BOOST Aftertreatment R6: NO Reduction CO
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Reaction Determines the reaction order of propene and nitric Orders m, n oxide in the pre-defined Langmuir-Hinshelwood conversion mechanism. R7: NO Reduction C3H6 K1
Determines the frequency factor used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1
Determines the activation temperature used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
R8: NO2 Reduction CO
R9: NO2 Reduction C3H6
214
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5. BOOST Aftertreatment Reaction Order m
Determines the reaction order of nitric oxide in the pre-defined Langmuir-Hinshelwood conversion mechanism.
K1 - K4
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism. Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
E1 - E4
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
Ce Storage Capacity
Determines the maximum amount of oxygen that can be stored on the cerium surface site.
Initial Surface Coverage Fraction of CeO2
Determines the coverage fraction of CeO2 at the solid surface. This property can be specified as a constant value or as a function of the catalyst length. Range: 0-1 (-)
K1 - K2
Determine the frequency factors used in the predefined ad/desorption mechanism. Determine the frequency factors used in the predefined ad/desorption mechanism.
E1 - E2
Determine the activation temperatures used in the pre-defined ad/desorption mechanism.
R10: Water Gas Shift Reaction
R11: Surface Storage on Cerium
Reaction Determines the reaction order of oxygen stored on Orders m, n, the surface and oxygen ratio at the surface in the p, q pre-defined ad/desorption mechanism. R12-R16: Surface Storage on Barium Carbonate
R12
R13
R14
R15
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5. BOOST Aftertreatment R16
BaCO3 Storage Capacity
Determines the maximum amount of nitric oxides that can be stored on the barium carbonate clusters (rate approach 1) and barium carbonate surface site (rate approach 2).
Initial Surface Coverage Fraction of Ba(NO3)2
Determines the coverage fraction of Ba(NO3)2 at the solid surface. This property can be specified as a constant value or as a function of the catalyst length. Range: 0-1 (-)
Rate approach 1
This activates the sophisticated ash core model where the NO and NO2 molecules are stored as Ba(NO3)2 in barium cluster particles. Additional differential equations are solved to determine mole fractions of all gas phase species on the dimensionless ash core front position in the barium cluster particles. The ash core front moves from the outer radius ( =1) toward the center ( =0) page [88] of the cluster particle (see sketch in Fig. 36
Rate approach 2
This activates the surface storage model where the NO and NO2 molecules are stored as Ba(NO3)2 on the catalytic surface represented by the surface coverage fraction ZBa(NO3)2.
K1 - K5
Determine the frequency factors used in the pre-defined ad/desorption mechanism for Rate approach 1 and Rate approach 2. Determine the frequency factors used in the pre-defined ad/desorption mechanism for Rate approach 1 and Rate approach 2.
E1 - E5
Determine the activation temperatures used in the pre-defined ad/desorption mechanism.
Reaction Determines the reaction order of Ba(NO3)2 in the Orders m, n, pre-defined ad/desorption mechanism of Rate p, q, r approach 2. R12-R16: Ash Core Model
The ash core model is activated by Rate approach 1. R12
R13
R14 216
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5. BOOST Aftertreatment
R15
R16
Particle Radius
Determines the radius RBa,p of the barium cluster particle. Typical Value: 5.0e-8 (m)
Min Specific Surface
Determines the minimum specific particle surface area ap,min. 2 3 Typical Value: 48.4 (m /m )
Max Specific Surface
Determines the minimum specific particle surface area ap,max. 2 3 Typical Value: 452637 (m /m )
Pore Diffusion Coefficient
Determines the diffusion coefficient DBa,p of the barium cluster particle. This property can be specified as constant value or as function of temperature. 2 Typical Value: 2.672e-14 (m /s)
Scaling The LNT model assumes that NOx desorption Factor (regeneration) takes place faster than NOx During adsorption (storage). This factor increases the pore Regeneration diffusion coefficient during regeneration. Typical Value: 10 (-) 5.1.3.8.2.6. User Defined Reactions (Without Archive) This is an interface to load a custom kinetic from a custom kernel. User-defined reaction mechanisms can be set by linking a user-routine. In this case the user can supply his user-routine with parameters set in the GUI. The two columns are: • The left column is designated for comments (BOOST interprets each entry as character) • The right column is used to specify input values (integer, double and character). It is the user's responsibility to interpret these values in the correct way in his user-routine. 5.1.3.8.2.7. User Defined Reactions This is an interface to load custom kinetic models developed using the AVL User Coding Interface (AUCI). Loading and maintaining an AUCI Catalytic Reaction Mechanism In general an arbitrary number of AUCI Catalytic Reaction Mechanism models can be loaded. In order to add or delete an AUCI model click Insert and Remove repsectively next to the table. An AUCI model ("Archive") is stored in an ucp and uca file respectively, and the existing predefined kinetic models are available as ucp files in the installation. An already loaded Archive can be enabled or disabled in the simulation by selecting Yes and No respectively in the first column of the table. The buttons below the table provide the following functions:
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5. BOOST Aftertreatment Button
Description
Select Archive
Opens a filebrowser to select an ucp or uca file.
Reload Archive
Reload the Archive from the selected row. In order to reset the Model Parameters with the default values from the AUCI model click "No" in the pop-up box "Keep current parameter values?".
Edit Archive
Launches AUCI Catalytic Reaction Mechanism graphical user interface (GUI). If a row has been selected in the table the AUCI model will be opened in that GUI.
Model Parameters
Interface to access the public model parameters from the selected Archive. In the pop-up window these parameters can be modified and global/local parameters can be assigned to them for access in the Parameter or Case Explorer.
Designing an AUCI Catalytic Reaction Mechanism AUCI is a graphical user interface that supports designing custom kinetic models for catalysts and filters as well as custom transfer models for heat and mass transfer as well as pore diffusion. Please, refer to the related AUCI documentation for more details on using AUCI. 5.1.3.8.2.8. Map Based Conversion This model comprises different input of conversion maps, where the user can specify the conversion of selected species depending on several conditions like massflow, substrate temperature and further more. Species conversion maps can be added or removed by clicking the right mouse button on the tree node Map Based Conversion. Conversion Definition The following input data has to be specified: Typical Values and Ranges Species
Enter the name of a General Species whose conversion is specified for. If the species is not contained in the Gas Composition then the Conversion map is ignored.
Conversion
Select the conversion specification Constant: Enter a constant conversion value. Table: Specify the conversion as a function of one of the conversion dependencies. Map: Specify the conversion as a function of two of the conversion dependencies. If Constant is selected, enter a value for constant species conversion.
Table for Conversion of The following input data has to be specified:
218
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5. BOOST Aftertreatment Typical Values and Ranges Conversion Dependency
The following Conversion Dependencies are available: • Inlet Gas Temperature • Mean Solid Temperature • Inlet Massflow • Inlet Excess Oxygen Ratio • Inlet GHSV
Conversion Table
Specify the conversion as a function of the selected Conversion Dependency.
Map for Conversion of The following input data has to be specified: Typical Values and Ranges Conversion Dependency 1 and Conversion Dependency 2
The following Conversion Dependencies are available: • Inlet Gas Temperature • Mean Solid Temperature • Inlet Massflow • Inlet Excess Oxygen Ratio • Inlet GHSV
Conversion Map
Specify the conversion as a function of the selected Conversion Dependency 1 and Conversion Dependency 2.
5.1.3.8.3. Transport Model At "My_Transport" different pore diffusion models can be selected. The transport model for the active washcoat layer model determines the calculation of the diffusion coefficient Dk,eff for every species of the pore diffusion model (see section Transport Models
page [21]
).
Note: For specification of the transport model the Washcoat Layer (WCL) Model must be active. The transport model has to be specified for each washcoat layer separately. The following models are available: 5.1.3.8.3.1. Constant Pore Diffusion For this model constant diffusion coefficients are applied. If Constant Pore Diffusion is selected, the following input data has to be specified: Typical Values and Ranges Diffusion Coefficients
Determines the effective diffusion coefficient Dk,eff of every species in the washcoat layer.
FIRE BOOST Aftertreatment
10
-14
-5
2
-10 (m /s)
219
5. BOOST Aftertreatment 5.1.3.8.3.2. Effective Pore Diffusion The effective diffusion coefficient is calculated with the free gas flow diffusion coefficient adapted with the washcoat layer porosity and tortuosity. A scaling factor allows linear variation of the calculated value for every species. If Effective Pore Diffusion is selected, the following input data has to be specified: Typical Values and Ranges Tortuosity
Determines the tortuosity layer.
Diffusion Scaling Factors
Determines the scaling factors multiplied to the calculated effective diffusion coefficient Dk,eff of every species in the washcoat layer.
wcl
of the washcoat
1-5 (-) 0-100 (-)
5.1.3.8.3.3. Random Pore Diffusion This model assumes that the washcoat features two distinct characteristic pore size diameters, called macro- and micro-pores. The two macro and micro pore diffusion coefficients are combined applying probabilistic and geometrical considerations. If Random Pore Diffusion is selected, the following input data has to be specified: Typical Values and Ranges Macropore Porosity
Determines the porosity (= gas void fraction) of the macro pores.
0-1 (-)
Micropore Porosity
The value of the micropore porosity is not entered, but calculated out of the above macropore porosity and the washcoat layer page [196] porosity specified at My_Layer according to .
0-1 (-)
Macropore Diameter
Determines the mean diameter of the macro pores.
10 -10 (m)
Micropore Diameter
Determines the mean diameter of the micro pores.
10 -10 (m)
Diffusion Scaling Factors
Determines the scaling factors multiplied to the calculated effective diffusion coefficient Dk,eff of every species in the washcoat layer.
0-100 (-)
-8
-4
-9
-5
5.1.3.8.3.4. Parallel Pore Diffusion The model combines the transport effects of the pure gas phase and Knudsen diffusion assuming both transport effects are taking place in parallel. If Parallel Pore Diffusion is selected, the following input data has to be specified: Typical Values and Ranges
220
Tortuosity
Determines the tortuosity layer.
Pore Diameter
Determines the mean pore diameter of washcoat layer.
wcl
of the washcoat
FIRE BOOST Aftertreatment
1-5 (-) -9
-3
10 -10 (m)
5. BOOST Aftertreatment Diffusion Scaling Factors
Determines the scaling factors multiplied to the calculated effective diffusion coefficient Dk,eff of every species in the washcoat layer.
0-100 (-)
5.1.3.8.3.5. User Defined Pore Diffusion This is an interface to load pore diffusion models designed using AUCI Transfer Models. Details on the usage of AUCI can be found in the related documentation. If User Defined Pore Diffusion is selected, the following input data can be specified: Typical Values and Ranges User Coding Archive
Path and filename of the AUCI Transfer Model. Click on Select Archive to choose an exsting AUCI model. Click on Edit Archive to open AUCI Transfer Model and design a user defined pore diffusion models.
ucp or uca file
5.1.3.8.4. Washcoat Properties from AUCI Custom Models In order to respect proprietary information, washcoat properties may also be provided by a custom model. Note: Details on the handling of washcoat properties before the BOOST v2014.1 release can be found in the FAQ section of the BOOST Aftertreatment Application Examples Guide. Loading a washcoat property from an AUCI custom model For some of the washcoat properties it is possible to load the respective property's value from an AUCI custom model instead of entering the value directly in the component's mask in the BOOST GUI; the related selection and input looks for example like that: Figure 57. Example: Washcoat Layer Thickness Value provided via BOOST GUI.
The washcoat property – in the above example the washcoat layer thickness – can be either: 1. typed in directly in the BOOST GUI, 2. loaded from the indicated AUCI Catalytic Reaction Mechanism, 3. loaded from an AUCI Transfer Model. In the latter two cases only AUCI models loaded in the same washcoat layer can be referred to. In the below example, the second option, i.e. From AUCI Catalytic Reaction Mechanism has been chosen as source for the washcoat layer thickness and the index of the AUCI model is 1: Figure 58. Example: Washcoat Layer Thickness Value loaded from an AUCI Catalytic Reaction Mechan
Hence, the custom kinetic model number 1 at the related subnode My_Reaction to be considered:
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page [197]
is going
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5. BOOST Aftertreatment
Note: Only if washcoat properties are provided with the AUCI Catalytic Reaction Mechanism the input will actually be taken from the custom model. Detailed information on how to specify washcoat properties in AUCI can be found in the related AVL User Coding Interface documentation.
In the next example, the washcoat layer thickness is taken From AUCI Transfer Model: Figure 59. Example: Washcoat Layer Thickness Value loaded from an AUCI Transfer Model (Pore Diffu
page [219]
This requires that the Transport Model at the related subnode My_Transport is set to User Defined Pore Diffusion and that an AUCI model comprising a pore diffusion model is loaded:
Note: ucp as well as uca files can be loaded as AUCI models. Affected simulation variables The different washcoat layer properties are used in the different parts of the entire washcoat and kinetic modeling. The below table gives an overview on what is actually used when.
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Simulation Submodel
Required Washcoat Property
Surface Reaction Model
Washcoat Layer Model
Flow
WCL Thickness
As indicated in BOOST GUI.(*)
As indicated in BOOST GUI.(*)
Solid Enthalpy Balance
WCL Bulk Density
Washcoat Property not required
As indicated in BOOST GUI.(*)
Species Balance in the Reaction Layer
WCL Porosity, WCL Thickness
Washcoat Property not required
As indicated in BOOST GUI.(*)
Transport Model in the WCL
WCL Porosity
-
As indicated in BOOST GUI.(*)
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5. BOOST Aftertreatment Simulation Submodel
Required Washcoat Property
Surface Reaction Model
Washcoat Layer Model
Reaction Rate Evaluation (**)
WCL Bulk Density
The value included in the AUCI model is considered.
As indicated in BOOST GUI.(*)
(*): This can be the BOOST GUI input or the value included in the indicated AUCI model. (**): Affects the conversion from unit group "Washcoat Mass Based" only. 5.1.3.9. Homogenous Gas Phase Reactions Within a catalyst homogenous gas phase reactions can be taken into account. If activated, a chemistry set has to be referred through its key. 5.1.3.10. Result Specification Typical Values and Ranges Spatial Position
The following options are available: • Use Grid: All results are written at all the points of the computational grid. • Set Grid: All results are written at a user-defined equally spaced grid. • Use 5 Points: All results are written at an equally spaced grid of five points in both axial and radial (for the case of 2D simulations) direction. • User Defined: All results are written at user-defined dimensionless coordinates in axial and radial (for the case of 2D simulations) direction.
Axial Output Points
Determines the number of equally spaced axial positions in the element at which all transient simulation results are written.
5-30 (-)
Radial Output Points
Determines the number of equally spaced radial positions in the element at which all transient simulation results are written. In the case of 1D simulation this value is set to 1. In the case of 2D simulation all the results are given on a mesh of (Axial Output Points x Radial Output Points).
5-30 (-)
User Defined Axial, Radial
Determines dimensionless coordinates at which all transient simulation results are written. In 1D simulations the radial coordinate is set to 0.
(0-1, 0-1) (-)
Type of Results
The following options are available: • Reduced: A reduced set of mean and outlet values is written. • Standard: A standard set of results (temperatures, pressures, conversions,...) is written. • Standard, Properties:
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5. BOOST Aftertreatment The standard set of results is extended by properties such as heat capacities, conductivities, transfer coefficients. • Standard, Fluxes: The standard set of results is extended by mass and heat fluxes. • Standard, Sources: The standard set of results is extended by sources from the individual chemical reactions. • All: All results, the standard set, properties, fluxes and sources are written. General information on how to use the BOOST post-processor and how to graphically display all the simulation results is available in the BOOST Users Guide and the GUI Users Guide.
5.1.4. Particulate Filter For the simulation of particulate filters, the same input procedure is required as described for the page [181] page [187] catalytic converter (see Section Run Information to Section Catalyst ). This means that run information, definitions of the gas and also solid species and boundary conditions have to be supplied by the user. The specification of the particulate filter itself also follows the input page [187] concept of the catalytic converter presented in Section Catalyst . Thus, in the following section, only filter specific input data is explained. 5.1.4.1. General Two different approaches are available to apply chemical reactions within Particulate Filters. If the Chemical Reactions toggle switch is activated, the user has access to several predefined page regeneration and catalytic reaction models which are described in Chemical Reactions [151] . By activating the Chemical Reactions with Archive toggle switch user-defined reaction mechanisms developed by using the AVL User Coding Interface can be applied. If the No Chemical Reactions toggle switch is activated, no chemical reactions can be modeled and default values will be considered for the numerical and physical properties for the singlechannel converter model as well as the filter flow model. Select to Couple to upstream element to thermally couple the particulate filter to an upstream page [75] element via wall heat conduction (see Thermal Coupling for details). When Consider Air Gap between the Substrates is deselected, thermal coupling to an upstream element's substrate (e.g. another particulate filter or a catalyst) is active. Select it to suppress this thermal coupling (notice that this is only relevant Couple to upstream element is selected. See Thermal page [76] Coupling (Substrates) for details). 5.1.4.2. Type Specification 5.1.4.2.1. Channel Structure This section summarizes the different channel geometries which can be chosen for the Filter Substrate. 5.1.4.2.1.1. Square Cell + Asymmetrical Cell PF Click on Square + Asymmetrical Cell PF to obtain the parameter specification of the square cell PF. Typical Values and Ranges Cell density (CPSI) Determines the type of monolith: Number of channels 2 per in . 224
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100-900 (1/in )
5. BOOST Aftertreatment Wall thickness
Determines the thickness of the monolith's walls = Wall.
0.006-0.015 (in)
Enable Enables the calculation for asymmetrical channel Asymmetrical diameters. Channel Diameters
Off (default)
Ratio of Channel Diameters
1-1.4 (-)
Determines the ratio of the channel diameters (d1/d2, page [144] see Fig. 46 ).
5.1.4.2.1.2. Simplified Square Cell PF Click on Simplified Square Cell PF to obtain the parameter specification of the square cell PF with equal inlet and outlet channel diameter. The simplified square cell PF corresponds to a Square + Asymmetrical Cell PF with diameter ratio of 1. Typical Values and Ranges Open frontal area (OFA)
Determines the open frontal area (= fluid volume fraction) of monolith ( g).
0.5-0.75 (-)
Hydraulic diameter
Determines the hydraulic diameter of the monolith (d). 0.001-0.005 (m)
5.1.4.2.1.3. Hexahex Click on Hexahex to obtain the following parameter specification. Typical Values and Ranges 2
Cell density (CPSI) Determines the total number of inlet and outlet 2 channels per in .
200-500 (1/in )
Wall thickness
Determines the thickness of the monolith's walls = Wall.
0.004-0.015 (in)
Inlet Channel Side Ratio (a/b)
Determines the ratio between the side lengths a and b of the hexagonal inlet channel.
0.666 (-) (default)
Perimeter Efficiency (a)
Since the side length a is located adjacent to another inlet channel wall of side length a, it is expected that there is reduced filtration along this wall. The Perimeter Efficiency determines the fraction of the side length used for filtration and is in the range between 0. and 1. 1. soot deposition along the entire wall 0. no soot deposition along this wall
0.0-1.0 (-)
5.1.4.2.1.4. Hex3 Click on Hex3 to obtain the following parameter specification. Typical Values and Ranges 2
Cell density (CPSI) Determines the total number of inlet and outlet 2 channels per in .
200-500 (1/in )
Wall thickness
0.004-0.015 (in)
Determines the thickness of the monolith's walls = Wall.
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5. BOOST Aftertreatment Inlet Channel Side Ratio (a/b)
Determines the ratio between the side lengths a and b of the hexagonal inlet channel.
0.81 (-) (default)
Perimeter Efficiency (a)
Since the side length a is located adjacent to another inlet channel wall of side length a, it is expected that there is reduced filtration along this wall. The Perimeter Efficiency determines the fraction of the side length used for filtration and is in the range between 0. and 1. 1. soot deposition along the entire wall 0. no soot deposition along this wall
0.0-1.0 (-)
5.1.4.2.1.5. General Cell PF Click on General Cell PF to obtain the parameter specification of any arbitrary inlet channel geometry which can be reproduced by multiple reflection of the general symmetry element (GSE). Note, the GSE is the geometrical base of the PF inlet channel geometries in BOOST/ FIRE since it determines the formation and structure of the soot and ash layer. The Unity Cell represents the smallest repetitive element for reflection to represent the PF geometry consisting of inlet and outlet channels. Typical Values and Ranges 100-900 (1/in )
Nr of Inlet Determines the number of inlet channels per unity Channels per Unity cell. Cell
1-3 (-)
Nr of Outlet Determines the number of outlet channels per unity Channels per Unity cell. Cell
1 (-)
Nr of GSEs per Inlet Channel
Determines the number of general symmetry elements per single inlet channel.
1-12 (-)
Wall thickness
Determines the thickness of the monolith's walls = wall.
0.004-0.015 (-)
Center Corner Determines the sum of the angles Angle (alpha+beta) general symmetry element.
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2
Cell density (CPSI) Determines the total number of inlet and outlet 2 channels per in .
and
of the
45-90 (deg)
Right Corner Angle (gamma)
Determines the angle
of the GSE.
45-90 (deg)
Left Corner Angle (phi)
Determines the angle
of the GSE.
45-90 (deg)
Side length (l1)
Determines the length of the first side along the channel wall of the GSE.
0.1-1 (mm)
Side length (l2)
Determines the length of the second side along the channel wall of the GSE.
0.1-1 (mm)
Filtration Efficiency at l1
The Filtration Efficiency determines the faction of the side length l1 used for filtration and is in the range between 0. and 1. 1. soot deposition along the entire wall 0. no soot deposition along this wall.
0-1 (-)
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5. BOOST Aftertreatment Filtration Efficiency at l2
The Filtration Efficiency determines the fraction of 0-1 (-) the side length l2 used for filtration and is in the range between 0. and 1. 1. soot deposition along the entire wall 0. no soot deposition along this wall.
Channel Shape Factor
Determines the difference of the pressure drop due to the gas flow in the channels between the present channel and a channel of circular shape. The shape factor is 0.89 for squared channels 0.95 for hexagonal channels 0.98 for octagonal channels, and 1.0 for channels with circular cross-section.
Outlet Channel Perimeter
Determines the perimeter of the single outlet channel. 1-10 (mm)
Outlet Channel Cross Section
Determines the cross-section of the single outlet channel.
0.5-1 (-)
2
0.5-5 (mm )
5.1.4.2.2. Filter Type At this page information about the position of the Channel Plugs has to be given. Two Filter Types with different Channel Plugging are available: Activate Wall Flow Filter to chose the standard Particulate Filter plugged at the front (outlet channels) and at the rear (inlet channels). Activate Partial Wall Flow Filter to chose a Particulate Filter plugged only at the front (i.e. with page [57] removed inlet channel plugs) . For more info see Modelling a Partial Wall Flow Filter . 5.1.4.3. Soot and Filter Properties Select Soot and Filter Properties in the parameter tree to access the following input fields. The soot and filter properties comprise thermodynamic data of the soot and fluid mechanic information of the soot and the filter. Additionally a particle mass can be specified that is used as initial condition for all soot mass balances. 5.1.4.3.1. Soot Layer Properties Typical Values and Ranges 3
Layer Packing Density
Determines the packing density of the soot.
5-30 (kg/m )
Migration Constant
Determines the impact of soot migration due to a convective transport.
1E-15-1E-5 (-)
5.1.4.3.2. Pressure Drop Typical Values and Ranges 2
Wall Permeability
Determines the permeability of the filter wall.
1E-15-1E-12 (m )
Soot Permeability
Determines the permeability of the soot bed. This property may be specified as one of: • Constant • Table (dependent on temperature or wall velocity)
1E-16-1E-13 (m )
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5. BOOST Aftertreatment • Map (dependent on both, temperature and wall velocity) • Formula (see. Soot Permeability page [50]) Enable Depth Filtration
Enables the application of a depth filtration layer in addition to a cake filtration layer
Off (default)
Sublayer Thickness
Determines the thickness of the depth flirtation layer.
10-100 (micron)
Depth Filtration Threshold
Determines the maximum soot loading that can be deposited within the depth filtration layer
0-3 (g/l)
Depth Filtration Permeability
Determines the permeability of the soot depth filtration layer
1E-16-1E-13 (m )
Inlet Loss Coefficient
Friction factor for pressure losses at the inlet.
0.5-10 (-)
Outlet Loss Coefficient
Friction factor for pressure losses at the outlet.
0.5-10 (-)
Consider Inlet/ Outlet Plugs
Enables the specification of inlet and outlet plugs closing the inlet and outlet channel at one site.
Off (default)
Length of PF Inlet- Determines the length of the inlet and outlet plugs. Outlet Plugs
2
0-20 (mm)
5.1.4.3.3. Filter Efficiency Typical Values and Ranges Soot Deposition Ratio
Determines the ratio between inlet soot mass and soot mass trapped in the Particulate Filter
0-1 (-)
5.1.4.3.4. Soot Mass Initialization Typical Values and Ranges 3
Soot Mass
Determines the Initial Soot Mass per Filter Volume. This property may be defined as • constant • table (dependent on the filter length)
5-30 (kg/m )
Max. fraction going to depth layer
The initial soot loading is partitioned proportionally between the depth and the cake layer, where 1.0 means all soot goes to the depth layer while 0.0 means all soot goes to the cake layer. Once the page [149] depth filtration threshold is reached, the remaining soot goes to the cake layer.
0-1(-)
5.1.4.4. Ash Properties Select Ash Properties in the parameter tree to access the following input fields. Typical Values and Ranges Enable Ash Model 228
If On/Off is selected, the ash model is activated.
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Off (default)
5. BOOST Aftertreatment 3
Ash Packing Density
Determines the packing density of the ash layer.
100-500 (kg/m )
Ash Permeability
Determines the permeability of the ash layer.
1E-15-1E-13 (m )
Specify Ash Plug Fraction
Enables the distribution of the ash mass into a Layer and a Plug fraction
Off (default)
2
Ash Layer/Plug Determines the ratio of ash that is stored in the Distribution Factor ash layer to ash stored in the ash plug. A factor of 1 means all the ash is stored in the layer. A factor of 0 means all the ash is stored in the ash plug. If the ash loading is not specified as constant value but as function of the filter length, the shape of the axial profile is kept but scaled down by the ashdistribution factor.
(0-1) (-)
Ash Mass
0-100 (g/l)
Determines the initial ash loading in the filter. This property can be specified as a constant value, as a function of the filter length or as a formula. Click on
to define table or formula data.
5.1.4.5. Chemical Reactions BOOST has four different pre-defined reaction models for the simulation of soot regeneration. The reaction model can be applied to two different reaction zones, an upper and a catalytic sub-layer. For both layers one and the same reaction approach is applied, where the user has access to all reaction parameters. The reaction scheme in the sub layer can only be activated if the Depth Filtration Model is also enabled. The parameters can be defined separately for each reaction layer. Additionally the user can specify an arbitrary number of coating zones which are applied to all catalytically supported reactions (depth filtration layer, filter wall and outlet channel). Each kinetic parameter of a chosen catalytically supported reaction can be individually specified for each Coating Zone. Together with the O2-thermal and O2-fuel-additive Soot Regeneration Mode the Oxygen diffusion into the soot layer can be considered. Therefore a lumped diffusion coefficient has to be specified. In the catalytic wall layer, a pre-defined reaction model is available with full access to all reaction parameters. Furthermore there is the possibility for the user to define a kinetic model with an page [132] arbitrary number of catalytic reactions (see section Stoichiometry Specification and section page [133] Kinetic Parameters Specification ). Note that all reaction parameters were chosen for one type of regeneration simulation. For other filter applications these reaction parameters may change and therefore have to be supplied by the user. Enable O2 Diffusion into Soot Layer Lumped DiffusionCoefficient
On /Off -6
-5
2
Coefficient for the concentration gradient driven O2 10 -10 (m /s) diffusion from the inlet channel into the soot layer.
Soot Regeneration Mode None
No reactions are taken into account. In this case sub-layer reactions cannot be specified.
O2-thermal
A reaction mechanism (see Section Filter Regeneration with Oxygen [90] ) consisting of two reactions is applied. Soot is oxidized depending on the temperature range either to CO or to CO2.
page
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5. BOOST Aftertreatment O2-fuel-additive
The same reaction mechanism as given by O2-thermal is set up.
O2-NO2
In addition to the reaction mechanism of O2-thermal, a soot oxidation reaction in presence of NO2 can be used and specified. Details of this NO2 reaction are explained in Section Filter Regeneration with Oxygen page [91] and Nitric Dioxide .
O2-NO2-NO2catalytic
In addition to the reaction mechanism of O2-NO2 the reversible oxidation of NO to NO2 is taken into account. As explained in Section page [92] Filter CSF Catalytic Reactions , this reaction is catalytically supported and takes place in the sub-layer that can be specified. In the upper layer the reaction can be switched off by setting the appropriate reaction constants.
User Defined
This enables the possibility to supply user-defined soot regeneration models. The specification of these models is described in section page [132] Stoichiometry Specification and section Kinetic Parameters page [133] Specification .
PF Zone Coating Table
An arbitrary number of Coating Zones can be inserted for which dimensionless section lengths have to be defined. The sum of all section lengths has to be one.
Regeneration Mode Sublayer Toggle switch
This enables or disables the application of soot sub-layer reactions. The switch only can be activated if the Depth Filtration Model is also enabled.
Catalytic Wall Reactions None
No catalytic wall reactions are taken into account.
CO-HC-NOConversion
A pre-defined reaction mechanism for the catalytically supported conversion of CO, C3H6, C3H8 and NO is enabled.
Selective Catalytic Reduction
A predefined reaction mechanism for the catalytically supported SCR reactions is enabled.
User Defined
This enables the possibility to supply user-defined wall reaction models. The specification of these models is described in section Stoichiometry page [132] page [133] Specification and section Kinetic Parameters Specification .
Fraction of Catalytic Wall Height
Determines a fraction of the entire wall height that is catalytically active. A fraction of 1 comprises the entire wall height.
0-1 (-)
Catalytic Reactions Outlet Channel Enable Outlet Channel Reactions Mass Transfer Scaling Factor
This specifies a factor for the linear scaling of the mass transfer from the outlet channel bulk to the catalytic filter wall.
On/Off
Note: The activation of Regeneration Mode Sublayer is only possible if depth filtration is activated (Enable Depth Filtration at Soot and Filter Properties). 230
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
kf
Determines a frequency factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
qf
Determines an exponential factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
Ef
Determines an activation energy in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
K
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
kf
Determines a frequency factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
qf
Determines an exponential factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user
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5. BOOST Aftertreatment can choose the table option to specify individual values for each coating section. Ef
O2 - NO2
Determines an activation energy in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
O2 K1
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E1
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
kf
Determines a frequency factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
qf
Determines an exponential factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
Ef
Determines an activation energy in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
NO2
232
K3
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E3
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E1
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
kf
Determines a frequency factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
qf
Determines an exponential factor in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
Ef
Determines an activation energy in the CO/CO2 shift reaction (see Section Filter Regeneration with page [90] Oxygen ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
NO2 K3-K4
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
E3-E4
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
NO2- Catalytic K5
Determines a frequency factor used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table
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5. BOOST Aftertreatment option to specify individual values for each coating section. E5
Determines an activation energy used in the predefined regeneration mechanism (see Section page [92] Filter CSF Catalytic Reactions ). In the catalytic sublayer the user can choose the table option to specify individual values for each coating section.
5.1.4.5.2. Catalytic Wall Reactions The different reactions can be enabled/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters. The string "all" means that a certain reaction is activated in all PF Coating Sections, but it is also possible to replace "all" with specific coating section numbers separated by commas (e.g. "1,3,4"). 5.1.4.5.2.1. CO, HC and NO Oxidation R1: CO Oxidation
R2: C3H6 Oxidation
R3: C3H8 Oxidation
234
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
K1 - K5
Determine the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section.
E1 - E5
Determine the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion
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5. BOOST Aftertreatment mechanism (see Section Filter CSF Catalytic page [92] Reactions ). The user can choose the table option to specify individual values for each coating section. R4: NO Oxidation
K
Determines the frequency factor used in the pre-defined reversible power-law conversion mechanism (see Section TWC Catalyst Reactions page [78] ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined reversible power-law conversion mechanism (see Section TWC Catalyst Reactions page [78] ). The user can choose the table option to specify individual values for each coating section.
Determines the maximum amount of ammonia that can be stored at the solid surface site (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
Initial Surface Coverage Fraction of NH3
Determines the coverage fraction of NH3 at the solid surface. This property can be specified as constant value or as function of the catalyst length. The user can choose the table option to specify individual values for each coating section. Typical Values & Ranges: 0-1[-]
Coverage Determines a surface coverage dependency in Dependency the pre-defined ad-/desorption mechanisms (see (epsilon) Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section. Typical Values & Ranges: 0-1[-] Max Surface Coverage Fraction of NH3
Determines the maximum surface coverage fraction of NH3 at the solid surface. This property can be specified as constant value or as function of temperature. The user can choose the table option to specify individual values for each coating section.
NH3 Surface Coverage Fraction Dependency m
Determines the adsorption rate dependence of the NH3 surface coverage fraction. The user can choose the table option to specify individual values for each coating section.
K1 - K2
Determine frequency factors used in the predefined ad/desorption mechanisms (see Section HSO-SCR Catalyst Reactions, Transient Approach
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5. BOOST Aftertreatment page [83]
). The user can choose the table option to specify individual values for each coating section.
R3: NO Reduction
R4: NOx Reduction
R5: NO2 Reduction
236
E1 - E2
Determine the activation temperatures used in the pre-defined ad-/desorption mechanisms (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
Critical Surface Coverage
Determines a tuning factor that slows down the reaction rate above a critical surface coverage (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
K
Determines the frequency factor used in the predefined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
Critical Surface Coverage
Determines a tuning factor that slows down the reaction rate above a critical surface coverage (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
K
Determines the frequency factor used in the predefined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
Critical Surface Coverage
Determines a tuning factor that slows down the reaction rate above a critical surface coverage (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table
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5. BOOST Aftertreatment option to specify individual values for each coating section.
R6: NH3 Oxidation (Transient Approach)
K
Determines the frequency factor used in the predefined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
K
Determines the frequency factor used in the pre-defined transient oxidation mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient oxidation (see Section HSOpage SCR Catalyst Reactions, Transient Approach [83] ). The user can choose the table option to specify individual values for each coating section.
R7: NH3 Oxidation K (Steady-State Approach)
Determines the frequency factor used in the predefined power-law oxidation mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-power-law transient oxidation (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
R8: NO Oxidation
Rate Approach 1 K
Determines the frequency factor used in the pre-defined transient and reversible power-law conversion mechanism (see Section HSO-SCR page [83] Catalyst Reactions, Transient Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined transient and reversible power-law conversion mechanism (see Section HSO-SCR page [83] Catalyst Reactions, Transient Approach ).
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5. BOOST Aftertreatment The user can choose the table option to specify individual values for each coating section. A
Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism see Section HSO-SCR Catalyst page [83] Reactions, Transient Approach ). The user can choose the table option to specify individual values for each coating section.
Rate Approach 2
R9: NO2 Formation
K, KR
Determine the frequency factors used in the pre-defined transient and reversible power-law conversion mechanism, respectively (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
E, ER
Determine the activation temperatures used in the pre-defined transient and reversible power-law conversion mechanism, respectively (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
A, AR
Determine the temperature dependencies used in the pre-defined transient and reversible power-law conversion mechanism, respectively (see Section HSO-SCR Catalyst Reactions, Transient Approach page [83] ). The user can choose the table option to specify individual values for each coating section.
m
Modifies the NH3 dependency. The user can choose the table option to specify individual values for each coating section.
K
Determines the frequency factor used in the predefined power-law conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
E
Determines the activation temperature used in the pre-defined power-law conversion mechanism (see Section HSO-SCR Catalyst Reactions, Transient page [83] Approach ). The user can choose the table option to specify individual values for each coating section.
5.1.4.5.2.3. Catalytic Outlet Channel Reactions page [156] The same reaction set as defined in the Catalytic Wall Reactions Model is selected. Sub-pages for the detailed specification of the reaction parameters appear. The user can choose the table option to specify individual values for each coating section.
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5. BOOST Aftertreatment 5.1.4.6. Chemical Reactions with Archive The user has the possibility to specify an arbitrary number of different particulate filter coating zones with specific dimensionless zone lengths. For each inserted Zone Soot Regeneration and Catalytic Gas Reaction mechanisms, developed by using the AVL User Coding Interface, have to be applied separately. Typical Values and Ranges Zone Name
User-given name for each PF Coating Zone
Zone_1 (default)
Zone length
Determines the dimensionless length for every PF Coating Zone. The sum over all zone lengths must be 1.0. The dimensioned zone length is determined by multiplication with the Length of Monolith.
0-1(-)
Regeneration
User-given name of the Regeneration model for each Coating Zone.
My_Regeneration1 (default)
Catalytic Gas Reactions
User-given name of the Catalytic Gas Reaction model for each Coating Zone.
My_Cat_Reaction1 (default)
5.1.4.6.1. Soot Regeneration Reactions An arbitrary number of different soot regeneration reaction models can be applied to two different reaction zones, a soot cake and a catalytic sub-layer (depth filtration layer). The reaction schemes in the sub-layer can only be activated if the Depth Filtration Model is also enabled. Note: The activation of Regeneration Mode Sublayer is only possible if depth filtration is activated (Enable Depth Filtration at Soot and Filter Properties). The soot regeneration reaction mechanisms can be developed using the AVL User Coding Interface. The result is a shared object (.so)/dynamic link library (DLL) that is linked to FIRE/ BOOST during run-time. The .so(s)/DLL(s) and public model parameters are stored in an .ucp and .uca file respectively, that needs to be specified in the file browser dialog for an inserted model by clicking Select Archive. After the .ucp/.uca file has been selected the public model parameters (e.g. kinetic parameters, reaction switches, ...) are loaded and can be edited by clicking Model Parameters. Clicking Reload Archive reloads the Archive from the selected row. In order to reset the Model Parameters with the default values from the AUCI model click "No" in the pop-up box "Keep current parameter values?". In order to create a soot regeneration reaction mechanism in the first place, the AVL User Coding Interface can be launched by clicking the button Edit Archive. 5.1.4.6.2. Catalytic Gas Reactions An arbitrary number of different catalytic gas reaction models can be applied to each particulate filter coating zone. The catalytic gas reaction mechanisms can be developed using the AVL User Coding Interface. The result is a shared object (.so)/dynamic link library (DLL) that is linked to FIRE/BOOST during run-time. The .so(s)/DLL(s) and public model parameters are stored in an .ucp and .uca file respectively, that needs to be specified in the file browser dialog for an inserted model by clicking Select Archive. After the .ucp/.uca file has been selected the public model parameters (e.g. kinetic parameters, reaction switches, ...) are loaded and can be edited separately for inlet channels, wall and outlet channels by clicking Wall, Inlet or Outlet Channel Model Parameters. Clicking Reload Archive reloads the Archive from the selected row. In order to reset the Model Parameters with the default values from the AUCI model click "No" in the pop-up box "Keep current parameter values?". In order to create a catalytic gas
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5. BOOST Aftertreatment reaction mechanism in the first place, the AVL User Coding Interface can be launched by clicking the button Edit Archive. Wall Reactions Enable Wall Reactions
On /Off
Catalytic Wall Fraction
0-1 (-)
Determines a fraction of the entire wall height that is catalytically active. A fraction of 1 comprises the entire wall height.
Inlet and Outlet Channel Reactions Enable Inlet Channel Reactions
On/Off
Mass Transfer Scaling Factor
1
This specifies a factor for the linear scaling of the mass transfer from the inlet channel bulk to the catalytic filter wall.
Enable Outlet Channel Reactions
On/Off
Mass Transfer Scaling Factor
1
This specifies a factor for the linear scaling of the mass transfer from the Outlet channel bulk to the catalytic filter wall.
Enable User Defined Mass Transfer Model
On/Off
User Coding Mass Transfer Model
A user Coding Mass Transfer Model needs to be specified by clicking Select Archive. In order to create a mass transfer mechanism in the first place, the AVL User Coding Interface can be launched by clicking the button Edit Archive.
Empty (default)
Effective Catalyst Loading
This specifies a factor for the linear scaling of the 1 reaction rates of the catalytic conversion reactions.
5.1.5. Aftertreatment Pipe For the simulation of pipes, a similar input procedure is required as described for the catalytic page [181] page [187] converter (see Section Run Information to Section Catalyst ). This means that run information, definitions of the gas and also solid species and boundary conditions have to be supplied by the user. The specification of the pipe itself also follows the input concept of the page [187] catalytic converter presented in Section Catalyst . 5.1.5.1. General Typical Values and Ranges
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Pipe Length
Determines the length of the pipe.
10-3000 (mm)
Number of Grid points
Determines the numerical discretization of the pipe.
5-50 (-)
Diameter
Determines the inner diameter of the pipe. This value can be set as constant or as function of pipe length.
10-300 (mm)
Bend Pipe
Enables the input of a pipe bending radius
Bending Radius
Determines the bending radius of the pipe. This value can be set as constant or as function of pipe length.
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5. BOOST Aftertreatment Laminar Friction Coeff
Determines a friction coefficient in the regime of 10-300 (-) laminar flow. This value can be set as constant or as function of pipe length.
Turbulent Friction
Switch to decide how the turbulent friction is specified. Either via a turbulent friction coefficient or a surface roughness
Friction Coefficient
Determines a friction coefficient in the regime of turbulent flow. This value can be set as constant or as function of pipe length.
Surface Roughness
Determines the surface roughness of the inner side 0.05-1 (mm) of the pipe wall. This value can be set as constant or as function of pipe length.
Friction Multiplyer
Determines a multiplier applied to the friction coefficient evaluated for the given surface roughness.
Gas-Wall Heat Transfer
Determines a heat transfer law applied for the heat exchange between the gas phase and the solid pipe wall
Heat Transfer Coefficient
Determines a constant heat transfer coefficient for the heat exchange between the gas phase and the solid pipe wall
10-500 (W/(m ·K))
Heat Transfer Factor
Determines a scaling factor that is applied to the chosen heat transfer model. This value can be set as constant or as function of pipe length.
0.1-10 (-)
Wall Temperature
Determines an initial wall temperature. This value can be set as constant or as function of pipe length.
273-1000 (K)
Variable Wall Temperature
Enables the transient simulation of the pipe wall. If not enabled, a constant pipe wall temperature is used in the model.
Chemistry
Within a pipe, homogeneous gas phase reactions can be taken into account. If activated, a chemistry set has to be referred through its key.
Couple to upstream element
Select to couple the pipe to an upstream element page via wall heat conduction (see Thermal Coupling [75] for details).
0.019 (-)
0.1-10 (-)
2
5.1.5.2. Variable Wall Temperature Typical Values and Ranges Solid Material Table
Add a solid wall layer by clicking on Insert.
Solid Material
Determines a solid material for a given wall layer. Click in the input field and select a material from the selection field. The properties of the solid material can be specified in the pull-down menu . The first line in the table
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5. BOOST Aftertreatment represents the innermost wall layer and the last line the outermost wall layer. Layer Thickness
Determines the thickness of each individual wall layer.
No. of Grid Points
Determines the numerical discretization of each wall 3-10(-) layer in radial direction.
Ambient Temperature
Determines the temperature of the ambient. This value is constant or a function of simulation time.
Radiation Sink Temperature
Determines the temperature used for the evaluation 273-1000 (K) of radiative heat transfer. This value is a constant or a function of simulation time.
Convection Model
Enables the application of a convection model for the external heat transfer from the pipe surface to the ambient.
Convection Coefficient
Enables the application of a convection coefficient for the external heat transfer from the pipe surface to the ambient.
Coolant
Determines a fluid which is assumed to flow around the pipe. Fluid properties of air and water are available.
Characteristic Determines the velocity of the coolant flowing Velocity of Coolant around the pipe. A cross-flow regime is assumed. Convection Coefficient
0.1-30 (mm)
273-1000 (K)
0.1-30(m/s) 2
Determines a convective heat transfer coefficient for 7-100 (W/(m ·K)) the external heat transfer. This value is constant or a function of simulation time.
5.1.5.3. Result Specification The following options are available: • Use Grid: All results are written at all the points of the computational grid. • Set Grid: All results are written at a user-defined equally spaced grid. • Use 5 Points: All results are written at an equally spaced grid of five points in both axial and radial (for the case of 2D simulations) direction. • User Defined: All results are written at the user-defined dimensionless coordinates in axial and radial (for the case of 2D simulations) direction. The following input data can be specified: Typical Values and Ranges
242
Axial Output Points
Determines the number of equally spaced axial positions in the element at which all transient simulation results are written.
5-30 (-)
Radial Output Points
Determines the number of equally spaced radial positions in the element at which all transient simulation results are written. For a 1D simulation this value is set to 1. For a 2D simulation, all the
5-30 (-)
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5. BOOST Aftertreatment results are given on a mesh of (Axial Output Points x Radial Output Points). User Defined Axial, Radial
Determines dimensionless coordinates at which all transient simulation results are written. In 1D simulations, the radial coordinate is set to 0.
(0-1, 0-1) (-)
The Type of Results of all the transient results can be specified by the user as follows. • Reduced: A reduced set of mean and outlet values is written. • Standard: A standard set of results (temperatures, pressures, conversions, …) is written. • Standard, Properties: The standard set of results is extended by properties such as heat capacities, conductivities, transfer coefficients. • Standard, Fluxes: The standard set of results is extended by mass and heat fluxes. • Standard, Sources: The standard set of results is extended by sources from the individual chemical reactions. • All: All results, the standard set, properties, fluxes and sources are written. General information on how to use the BOOST post-processor and how to graphically display all the simulation results is available in the BOOST Users Guide and the IMPRESS Chart Users Guide.
5.1.6. Aftertreatment Injector The Aftertreatment Injector ( ) offers the possibility to introduce mass into the exhaust aftertreatment line downstream of the inlet boundary at a certain user-defined position. Injection of gases and liquids is possible. 5.1.6.1. General Specify the state of aggregation of the injected fluid: choose between gaseous and liquid. In case of liquid, the partitioning of the total injected mass between the various phases (gas phase, droplet, and wallfilm) may be set. Typical Values and Ranges General Injection Mass Flow
Determines the injected mass flow. This value can be set as constant or as a function of time.
Injection Temperature
Determines the temperature of the injected mass.
Injected fluid specification
Choose between gaseous and liquid.
Liquid Injected Fluid phase partitioning Note: All of the settings in this block are only relevant/enabled when liquid is chosen at the Injected fluid specification radio button group above. Injected fluid
Choose between • 1. to Gas Phase only (instantaneous decomp./evap)
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5. BOOST Aftertreatment • 2. to Liquid Phase only • 3. partition among Gas/Liquid Phases Choosing cases 2 and 3 invokes a Liquid Phase. For case 3, the Fraction of Injected Fluid to Gas Phase may be chosen. This determines the part of the total injected mass going to the Gas Phase, while the rest of the mass goes to the Liquid Phase. Liquid Phase
Choose between • 4. Droplets only • 5. Wallfilm only • 6. partition among Droplets/Wallfilm Choosing cases 5 and 6 enables the Wallfilm. For case 6, the Fraction of Liquid Phase to Wallfilm may be entered. This determines the portion of the liquid phase mass that goes to the Wallfilm; the rest of the mass is transported as a separate droplet phase (see Liquid Species page [75] Transport ).
Partitioning summary
This read-only block gives an overview about the fractions of the total injected mass which go to the gas phase, the droplet phase, and the wallfilm phase, respectively.
Liquid Injected Fluid Phase Partitioning The following scheme illustrates the possibilities of partitioning an injected liquid among the various phases:
The decisions how to partition the injected mass are done via the radio buttons 1-6. Radio buttons 1-3 decide the first level (gas vs. liquid phase), while buttons 4-6 decide the second level (wallfilm vs. droplets). 5.1.6.2. Gaseous Injected Fluid Specify the composition of the gaseous injected fluid. Select the species fraction unit from the pull-down menu Unit of Species; possible options are 'Mass Fraction (kg/kg)' and 'Mole Fraction (mol/mol)'. Add/remove species with Insert/Remove. Click on a Species input field to open a list of possible species that have been specified previously in Simulation | Control | Aftertreatment Analysis in the Gas Composition table. Enter a mass fraction; possible values are 0-1 (-). The total sum of mass fractions has to be 1, the font color will be red when this criterion is not fulfilled; it can be corrected by choosing a row and clicking Correct; the correction will be applied to the selected row. Load and store tables by clicking the corresponding buttons. 244
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5. BOOST Aftertreatment 5.1.6.3. Liquid Injected Fluid Specify the composition of the liquid injected fluid. Add/remove liquids with Insert Liquid/Remove Liquid. Click on a Liquid input field to open a list of possible liquids that have been specified beforehand in Model | Liquid Materials. Enter a mass fraction; possible values are 0-1 (-). Note: The total sum of mass fractions has to be 1. For each of the liquids in the table, a new sub page [n] Composition of is available. On each of these pages, there are two input tables in which you may enter: 1. the gas species the liquid is mapped to upon decomposition/evaporation (e.g. WATER may evaporate to H2O, or UREA may decompose into HNCO and NH3). 2. possible liquid sub-species the liquid may consist of (e.g. ADBLUE may be mapped onto the liquid species UREA and WATER) page [243] The tables are active (and need input) depending on the settings done on the General page. Table 1 is inactive when radio button 4 is selected, Table 2 is inactive when radio button 1 is selected. 5.1.6.3.1. Composition of Injected Liquid For each specified liquid at the Liquid Injected Fluid Window a 'Composition of Injected Liquid' page will be enabled. Here, specify the stoichiometric composition of the liquid, i.e. onto which gas species the liquid will be mapped. The procedure works the same as for the 'Gaseous Injected Fluid'. The only difference is that mass fractions can be negative too, which refers to consumption of a certain gas species; still, the total sum of mass fractions has to be 1. Below that table, some examples of how to map a liquid onto gas species are displayed. 5.1.6.4. Wallfilm Modeling This is activated if Liquid is specified as the injected fluid. Select Enable Wallfilm Modeling to access the options. Typical Values and Ranges Wallfilm Thickness
Determines the thickness of the wallfilm.
Fraction of Liquid to Wallfilm
Determines the fraction of liquid mass directly stored in the wallfilm after injection.
Evaporation Rate Multiplier
Determines a multiplier for the evaporation rate.
5.1.6.5. Result Specification The following options are available: • Use Grid: All results are written at all the points of the computational grid. • Set Grid: All results are written at a user-defined equally spaced grid. • Use 5 Points: All results are written at an equally spaced grid of five points in both axial and radial (for the case of 2D simulations) direction. • User Defined: All results are written at the user defined dimensionless coordinates in axial and radial (for the case of 2D simulations) direction. The following input data can be specified:
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5. BOOST Aftertreatment Typical Values and Ranges Axial Output Points
Determines the number of equally spaced axial positions in the element at which all transient simulation results are written.
5-30 (-)
Radial Output Points
Determines the number of equally spaced radial 5-30 (-) positions in the element at which all transient simulation results are written. For a 1D simulation, this value is set to 1. For a 2D simulation, all the results are given on a mesh of (Axial Output Points x Radial Output Points).
User Defined Axial, Radial
Determines dimensionless coordinates at which all transient simulation results are written. In 1D simulations, the radial coordinate is set to 0.
(0-1, 0-1) (-)
The Type of Results of all the transient results can be specified by the user as follows. • Reduced: A reduced set of mean and outlet values is written. • Standard: A standard set of results (temperatures, pressures, conversions, …) is written. • Standard, Properties: The standard set of results is extended by properties such as heat capacities, conductivities, transfer coefficients. • Standard, Fluxes: The standard set of results is extended by mass and heat fluxes. • Standard, Sources: The standard set of results is extended by sources from the individual chemical reactions. • All: All results, the standard set, properties, fluxes and sources are written. General information on how to use the BOOST post-processor and how to graphically display all the simulation results is available in the BOOST Users Guide and the IMPRESS Chart Users Guide.
5.1.7. Control Elements 5.1.7.1. Temperature Sensor The Temperature Sensor component can be used to sense gas temperatures from different components (Aftertreatment Pipe, Catalyst, Particulate Filter). For the simulation of the temperature sensor model, the below input is required and described. page [73] Details of the physical model are explained in section Temperature Sensor Model . General Typical Values and Ranges
246
Length
Determines the length of the thermocouple.
5-100 (mm)
Diameter
Determines the diameter of the thermocouple.
0.1-1 (mm)
Number of grid points
Determines the numerical discretization of the thermocouple with respect to spatial dimension x.
5-50 (-)
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5. BOOST Aftertreatment Heat Radiation
Determines whether heat radiation between the thermocouple and the wall is considered in the calculation of the thermocouple temperature.
Initial Temperature Determines the initial temperature of the thermocouple. Material
Determines a solid material for the thermocouple. Click in the input field and select a material from the selection field. The properties of the solid material can be specified in the pull-down menu .
Sampling Rate
Determines a sampling rate with which the thermocouple signal is sampled.
273-1000 (K)
1 - 1000 (Hz)
Sensor Channels Variable
Specify a name for the sensor channel.
Element
Select an element to with which the Temperature Sensor shall be connected.
Sensor Channel
Select a sensor channel out of the list of available sensor channels of the connected element. Note: The Temperature Sensor can process only gas temperatures. Therefore select only those sensor channels which refer to a gas temperature. The BOOST calculation kernel will stop with an appropriate error message if a sensor channel other than a gas temperature has been selected.
Output Channels Tip: For every sensor channel in the Temperature Sensor element a corresponding output channel will be generated that can be sensed by another Control Element, for example when considering the Temperature Sensor in a control unit. 5.1.7.2. Formula Interpreter The Formula Interpreter Element ( ) can be used to 1. sense values (i.e. maximum temperatures, conversion rates, …) from different components (Catalyst, Particulate Filter, Pipe, Aftertreatment Injector) 2. perform calculations with these values (C-code that is interpreted by BOOST and executed after each calculation step (the time step is taken from the input field 'Result Output Interval' on the page the Global | Aftertreatment Analysis) 3. actuate values (mass flow, temperature, …) at different components (Aftertreatment Boundary) For a detailed description on how to handle the Formula Interpreter Element please refer to section 4.16.6 of the BOOST Users Guide. BOOST Aftertreatment offers the following pre-defined function to be used in the Formula Interpreter: • bst_terminate_atm() is terminating the current simulation run.
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5. BOOST Aftertreatment Figure 60. Formula Interpreter - Formula Specification
5.1.7.3. Engine Interface For a detailed description of how to handle the Engine Interface Element ( section 4.16.4 of the BOOST Users Guide.
) please refer to
5.1.7.4. PID Controller For a detailed description of how to handle the PID Controller Element ( section 4.16.5 of the BOOST Users Guide.
) please refer to
5.1.7.5. Monitor The Monitor Element ( ) can be used to sense values (i.e. maximum temperatures, conversion rates, …) from different components (Catalyst, Particulate Filter, Pipe, Formula Interpreter). The monitored values are shown in the Online Monitor (accessed from the Simulation Status dialog, Monitor button) and in an individual section of the results-tree in IMPRESS Chart. For a detailed description on how to handle the Monitor Element please refer to section 4.16.7 of the BOOST Users Guide. Figure 61. Monitor - Sensor Specification
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5. BOOST Aftertreatment 5.1.8. Solid Materials An arbitrary list of solid materials can be specified on the input page 'Solid Material'. The page can be accessed from the pull-down menu item 'Model'. By right-clicking on the entry 'Material' in the tree at the left side of the page, new material pages can be added. Currently the properties of steel and air are supplied with default values. Typical Values and Ranges Material Name
Determines a name for the material. Via this name the material properties can be accessed from the page 'Pipe-Variable Wall Temperature'.
Density
Determines the density of the material.
1-6000 (kg/m )
Thermal Conductivity
Determines the thermal conductivity of the material. This value can be set constant or as function of temperature.
0.01-50 (W/(m·K))
Specific Heat
Determines the specific heat of the material. This value can be set constant or as function of temperature.
500-2000 (J/ (kg·K))
Opaque
Enable the input of emissivities of the inner and outer surface of opaque (non-transparent) materials.
Emissivity inner
Determines an emissivity at the inner surface of an opaque material.
0-1 (-)
Emissivity outer
Determines an emissivity at the outer surface of an opaque material.
0-1 (-)
3
5.1.9. Liquid Materials An arbitrary list of liquid materials can be specified under Model | Liquid Materials. To add a new material, right-click on Material in the tree and select Material : Add from the sub-menu. Currently, properties of the following liquid materials are supplied with default values: Water, UREA, AdBlue and Diesel. Note that UREA is not treated as a liquid by BOOST, but dummy values (e.g. from water) have to be specified for all properties except 'Molar Weight'. Typical Values and Ranges Material Name
Determines a name for the material. Via this name the material properties can be accessed from Aftertreatment Injector - Liquid Injected Fluid.
Molar Weight
Determines the molar weight of the liquid.
Liquid Density
Determines the density of the liquid. This value can be set constant or as a function of temperature.
Specific Heat
Determines the specific heat of the liquid. This value can be set constant or as a function of temperature.
Thermal Conductivity
Determines the thermal conductivity of the liquid. This value can be set constant or as a function of temperature.
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5. BOOST Aftertreatment Heat of Evaporation
Determines the heat of evaporation of the liquid. This value can be set constant or as a function of temperature.
Vapor Pressure
Determines the vapor pressure of the liquid. This value can be set constant or as a function of temperature.
5.1.10. Homogenous Gas Phase Reactions - Input data The Homogenous Gas Phase Reactions chemistry interpreter needs a text based chemistry input file with an arbitrary name, where the stoichiometries of the reactions, the kinetic Parameters (A, b and E) and – optionally – auxiliary data are defined. The reaction specification part begins with 'REACTIONS' and ends with 'END'. The number of blanks or empty lines between specification blocks/lines is arbitrary. Comment lines beginning with '!' are allowed. Example for such a chemistry input file:
REACTIONS 2O+M<=>O2+M 1.200E+17 -1.000 .00 H2/2.40/ H2O/15.40/ CH4/2.00/ CO/1.75/ CO2/3.60/ C2H6/3.00/ AR/ .83/ O+H+M<=>OH+M 5.000E+17 -1.000 .00 H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ AR/ .70/ O+H2<=>H+OH 3.870E+04 2.700 6260.00 END The chemistry interpreter reads this input file during the preprocessing and creates an Info file ('input_file_name'_out.dat in the input file directory) with the specified chemistry. Currently about 95% of the auxiliary-keywords known by the CHEMKIN-II Version 4.9, April 1994, DOUBLE PRECISION are considered by the interpreter. Therefore it is capable of reading and interpreting the corresponding chem.inp files.
5.1.11. Input Data Checklist: Catalytic Converter and Particulate Filter The purpose of the following checklist is to give a brief overview of which input data has to be supplied and specified by the user in order to run BOOST aftertreatment simulations. CAT/PF Start Time Global Information End Time
CAT/PF Inlet/Outlet Conditions
Determines the beginning of the simulation, i.e. the start time of the integration Determines the end of the simulation, i.e. the end time of the integration
Gas Composition
Determines the number and type of gas species transported through the system
Solid Species
Determines the number and type of solid components transported by the gas flux
Inlet Mass Flux
Determines the mass entering the aftertreatment element
Inlet Gas Temperature
Determines the temperature of the gas flux entering the aftertreatment element.
Inlet Gas Fractions Determines the mass (or mole) fractions of all the gas species defined Inlet Solid Mass Fractions 250
Determines the mass flux of the solid species as a fraction of the gas mass flux
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CAT/PF Monolith Geometry
CAT/PF Friction
CAT/PF Solid Properties
CAT/PF Radial Heat Loss Conditions
Outlet Pressure
Determines the pressure at the outlet of the aftertreatment element
Monolith Volume
Determines the volume of the monolith comprising both, the volume of the gas phase and the volume of the solid substrate
Monolith Length
Determines the length of the monolith
Cell density (CPSI)
Determines the cell structure using the number of 2 channels per in
Wall thickness
Determines the thickness of the monolith's walls
Washcoat thickness
Determines the thickness of the washcoat
Friction Coefficient Determines a friction coefficient in the case of turbulent flow Friction Multiplier
Determines a dimensionless factor that considers the influence of the channel shape in the case of laminar flow
Density
Determines the density of the monolith material
Thermal Conductivity
Determines the thermal conductivity of the monolith material
Specific Heat
Determines the specific heat of the monolith material
External Heat Transfer Coefficient
Determines the heat transfer between the shell and the environment
Thickness, Shell, Insulation Mat
Determines the thickness of the shell
Thermal Determines the thermal conductivity of the shell Conductivity, Shell, Insulation Mat
CAT Reactions
PF Physical Properties
Environment Temperature
Determines the temperature of the environment
Conversion Reactions
Determines the application of conversion model. Predefined reaction models can be chosen and adapted.
Surface Storage
Determines the application of surface storage mechanisms. Pre-defined reactions can be chosen and adapted by the user.
Density, Soot
Determines the packing density of the soot
Migration Constant Determines the impact of soot migration due to convective transport Wall Permeability
Determines the permeability of the filter wall
Soot Permeability
Determines the permeability of the soot bed
Soot Mass
Determines a volume specific soot mass that is used as initial conditions for all soot balances
FIRE BOOST Aftertreatment
251
5. BOOST Aftertreatment PF Reactions
Regeneration Modes
Determines the application of pre-defined regeneration modes. It can be chosen between bare-trap, fuel additive, NO2 and catalytically supported NO2 regeneration.
5.1.12. Best Practice In general, speed-up and stability of simulations are antagonists. Speed-up is often reached through model reduction and simplification, while at the same time stability is lost when the resulting model is not capable anymore to handle the applied boundary conditions and transience resulting from model physics and chemistry. Both aspects – the simulation time and the model stability – are influenced by the simulation model set-up on the one hand and the solver settings on the other hand. In the below sections selected model and solver input is presented, that definitely influences speed-up and stability. 5.1.12.1. Simulation Model Set-up In order to ensure fast and at the same time stable simulations there are certain things to be considered during set-up of the BOOST Aftertreatment simulation model that are comprised in this section. The sections for the input data regarding the Aftertreatment components offer typical values and ranges for most of the input data. Dependent on the actual simulation model some inputs need to get special attention and are to be chosen thoroughly. General Remarks • A smaller number of grid points speeds up the simulation, whereas increasing the number of grid points leads to higher stability. • For multi-component systems, i.e. simulation models with more than one exhaust aftertreatment component, the most stable flow solution has been detected for homogeneous axial discretization cell length. This means that the mean axial discretization cell lengths of all components have the same order of magnitude. The reason is of numerical nature: the BOOST Aftertreatment solver makes use of matrix inversion techniques. The subject matrix is the so called Jacobian, which is the first derivative of the system state with respect to the system solution state (temperature, pressure, species concentrations). As the single components are discretized in axial direction, the system state comprises all the states of the different axial discretization cells, and eventually the Jacobian contains entries for each axial discretization cell and their numerical relationship. The latter one simply reflects the physical processes between two axial discretization cells. As a matter of fact, the geometrical information of the system is also considered in the calculation of the Jacobian. Strongly inhomogeneous discretization now can lead to an illconditioned Jacobian, especially when the system is experiencing high transience and stiff kinetics. Such an ill-conditioned system is hard to solve, if at all. In contrast to that more or less homogeneous axial discretization improves the Jacobians conditioning and therefore stabilizes the entire simulation. As a side effect, the computation time is decreased as well, because the solver is not forced to do so many steps in order to converge. • If transient inlet/outlet boundary conditions are applied that result from experimental data, it if very useful to pre-process these data before loading them in the BOOST Aftertreatment model. Usually experimental data show “noise” which superposes the main effect, for example a temperature rise. This noise can be eliminated by applying the running average method to the experimental data. • It is also very helpful to specify the initial solid temperatures of the various components as the inlet gas temperature at simulation start time. Of course, this is obsolete if this heat-up/ cool-down is really intended to be modeled. Catalyst • In order to decrease computation time, it is always helpful to decrease the number of grid points. Anyhow due to experience a number of 10 to 15 works best in most of the cases. For non-reactive catalysts this number can even by decreased. If instability is detected it should be increased, especially when for example nearly all of the conversion occurs at the catalyst 252
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment front and/or when the reaction mechanism also contains surface storage reactions which lead to higher transience in the conversion behavior it is good to increase the number of grid points and choose a grid shape factor smaller 1.0 (for example 0.8). • The presented pre-defined reaction mechanisms with their default parametrization have been validated for specific washcoats as presented in the mentioned references. Particulate Filter (PF) • If the PF element is used as a simple pressure drop element only the number of grid points that typically leads to stable simulation is around 20-25. As soon as kinetics is enabled in the PF the number of grid points should be increased and experience shows that 50 is a good value. A larger number than 80 is known to be unsuitable due to very high computational effort and increasing instability resulting in multi-component systems from inhomogenous axial discretization lengths leading to an ill conditioned Jacobian matrix. • A grid shape factor of 1.0 has been experienced as to give the most stable solution. 5.1.12.2. Aftertreatment Solver Settings There are several possibilities to influence the solver performance. The below section summarizes recommendations how some solver characteristics can be set in order to decrease simulation time and increase stability. General Remarks • The smaller the time step the slower the simulation due to more post-processing calls (i.e. calculation and storage of results), whereas a larger time step can lead to instabilities, especially when a. the kinetics is very stiff, b. highly transient inlet conditions challenge the PF flow solver. • For very stiff problems the solver option “Enable High-Robustness Option” at Simulation | Control | Aftertreatment Analysis might lead to more stability. The main problems targeted with that option are a. “Freezing”: the solver seems to do nothing, but actually the solver is using very small time steps, that are far below the provided User time step (Simulation | Control | Aftertreatment Analysis) or DLL time step (set in external application SimuLink, NI Veristand, ...), b. Convergence Failure: the solver diverged, for example due to very stiff system. Note: An ill-conditioned Jacobian cannot be solved easier using the “HighRobustness” option. c. The applied solver tolerances of the BOOST Aftertreatment solution variables (temperature, pressure, species concentrations) have been chosen with high care. If for whatsoever reason the tolerances need to be adjusted, this can be done at Simulation | Control | Aftertreatment Analysis | Solver Options. The pre-defined tolerances are divided by the entered value; therefore values smaller 1.0 lead to more loose tolerances, whereas values larger 1.0 lead to stricter tolerances. User Defined Parameter The below table summarizes User Defined Parameters that allow additionally to the GUI input to influence the solver configuration and adjust other component parameter. The User Defined Parameters are grouped by component. Parameter Key
Value
Description
ATM Solver ATM_DISABLE_NAN_CHECK YES / NO
FIRE BOOST Aftertreatment
After each successful solver time step the solution vector is checked for NaN. In order 253
5. BOOST Aftertreatment Parameter Key
Value
Description save computation time this check might be disabled.
ATM_SET_NR_FAILSKIP
number
Change the number of allowed solver failure. Some failure are repairable, that’s why a number > 1 is suggested. Default is 20.
ATM_SOLVER_DFLT_OPT
ON / OFF
With BOOST v2009.1 enhancements in the solver performance have been introduced that led to significant speed-up. However in some cases lower stability might occur. By enabling the solver configuration (ON) before v2009.1 the simulation time will be in general significantly slower, but might be more stable on the other side.
ATM_DLL_SOLVER_OSETTINGS YES / NO
With BOOST v2011.1 enhancements in the solver performance regarding DLL applications have been introduced that led to significant speed-up. However in some cases lower stability might occur. By enabling the solver configuration (YES) before v2011.1 the simulation time will be in general slower, but might be more stable on the other side.
ATM_CONG_TOLFACTOR* >1.0: stricter <1.0: looser
Change the tolerance applied to the continuity equation in element .
ATM_UPDATE_THERMDAT
FCN / TIMELOOP
Update thermal properties in each solver time step or in User defined time step only. In order to gain speed-up choose TIMELOOP.
ATM_UPDATE_TRANDAT
FCN / TIMELOOP
Update transport properties in each solver time step or in User defined time step only. In order to gain speed-up choose TIMELOOP.
ATM_UPDATE_DIMLESS_NUMBERS FCN / TIMELOOP
254
Update dimensionless numbers (i.e. Re, Pr, Nu, …) in each solver time step or in
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment Parameter Key
Value
Description User defined time step only. In order to gain speed-up choose TIMELOOP.
ATM_UPDATE_SOLID_PRPS FCN / TIMELOOP
Update substrate properties in each solver time step or in User defined time step only. In order to gain speed-up choose TIMELOOP.
ATM_MIMIC_DLLMODE
Using this User Defined Parameter in a BOOST standalone run the conditions and solver configuration that are present in DLL applications are emulated. The goal is to speed-up and/ or stabilize the simulation model before running it in the real DLL application, because the model can be adjusted in a more convenient way. Within that emulation the User can adjust the model according to the recommendations described above. The following modes are available: • mode = 0: off; standalone BOOST AT simulation • mode = 1: S-Function • mode = 2: NI Veristand • mode = 3: CRUISE link
mode
Note: As the DLL application is emulated only with respect to solver settings, boundary conditions and/ or actuation of any parts of the model need to be defined within the BOOST model via Aftertreatment Boundary and with help for example of the Formula Interpreter element. ATM_SOLVER_MAX_STEPSIZEtimestep
FIRE BOOST Aftertreatment
Change the maximum timestep (seconds) applied solver time step to a fixed 255
5. BOOST Aftertreatment Parameter Key
Value
Description value. The time step to be taken by the solver is estimated internally in two different steps. In the first one the maximum possible time step is determined by analyzing the event horizon, in the second one the current time step is set based on the history of integration and limited by the maximum solver time step. The maximum solver time step is in general variable in pure simulations and shouldn’t be adjusted if not for strong reasons. In case of DLL applications the maximum time step cannot be estimated due to missing information about the event horizon. Therefore it might be helpful in such cases to limitate the maximum solver time step.
Catalyst ATM_CAT_HOMREAC_ENERSPLIT 0.0 <= x <= 1.0
When simulating homogeneous gas phase reactions in the catalyst solver stability is increased by adding a certain fraction x of enthalpy rate to the solid phase.
Change the number of iterations for the soot balance in the PF Flow Solver.
ATM_DPF_MOMENTUM_CORR_FAC 0.0 <= factor <= 1.0
Change the factor to scale the momentum correction in the inlet channel momentum balance equation in the PF Flow solver. A value of 0.0 means the correction is disabled.
Aftertreatment Pipe ATM_PIP_GRIDSHAPE*value
256
Specify the value of the grid shape factor of Pipe . Compare definition of grid
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment Parameter Key
Value
Description shape factor in Catalyst element for reference.
ATM_PIPE_SET_ITERATIONS number
Change the number of iterations used in solving the multi-layered wall model (“Variable Wall Temperature”).
Aftertreatment Injector ATM_INJ_NRDIFFCELLS* number
Change the number of axial discretization cells in the diffusion zone of Injector .
ATM_INJ_NRINJCELLS*number
Change the number of axial discretization cells in the injection zone of Injector .
ATM_INJ_PIPELENGTH* length
Set the axial length of the pipe representing the Injector .
ATM_INJ_COPYDSPIPE* YES / NO
Enable / disable copying the properties of an attached downstream pipe to the pipe representing the Injector . Note: the diameter is assumed to be constant and is equal to the pipe diameter at inlet.
Aftertreatment Boundary ATM_REFINED_BND
number
ATM_SOAK_DETECTORLIMIT value
Apply refined and equidistant boundary tables. The provided number is the number of table points. Soak phases in transient inlet conditions are handled in a special way. The solver assumes a minimum massflow below which soak is assumed. The value of this minimum massflow (kg/s) can be changed; the default value is 1.0E-07 kg/s.
CRUISE - BOOST Aftertreatment - Link ATM_BAC_ENABLE_ARBMODEL YES / NO
FIRE BOOST Aftertreatment
The CRUISE - BOOST AT link allows mainly two types of aftertreatment models: a single catalyst (oxidation catalyst) or a single PF. Using this User Defined Parameter 257
5. BOOST Aftertreatment Parameter Key
Value
Description it is possible to run arbitrary BOOST Aftertreatment models in CRUISE.
5.2. Databus Channels The aftertreatment components offer different sensor and actuator channels to be accessed by the control elements. These databus channels are presented in this section.
Engine lambda at inlet. A definition of lambda according to page [95] Brinkmeier [10 ] is assumed; page [98] cf. also Eq.320 .
Gas Species Fraction
Gas Species Fraction
-
Fraction of the inlet mass flux allotted for gas species .
-
Fraction of the inlet mass flux allotted for solid species (C(S)).
Unit
Description
Solid Species Fraction Solid Species Fraction
-
Fraction of the mass flux allotted for solid species (C(S)).
Lambda ICVT
-
-
Engine lambda at outlet page according to Brinkmeier [10 [95] page [98] ]; cf. also Eq.320 .
Actuator Channel
Submenu
Unit
Description
Pressure
-
Pa
Absolute pressure at the outlet.
Temperature
-
K
Temperature at the outlet (Adiabatic Backflow: off).
Massflow
-
kg/s
Total outlet mass flux (Adiabatic Backflow: off).
Gas Species Fraction
Gas Species Fraction
-
Fraction of the outlet mass flux allotted for gas species (Adiabatic Backflow: off).
Solid Species Fraction Solid Species Fraction
Outlet Boundary Databus Channels: Sensor Channel
258
Submenu
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment Solid Species Fraction Solid Species Fraction
-
Fraction of the outlet mass flux allotted for solid species (C(S)) (Adiabatic Backflow: off).
5.2.2. Catalyst Databus Channels Sensor Channel
Submenu
Unit
Description
Mean Temperature
-
s
Mean substrate temperature of the element at each time point.
Max Temperature
-
K
Highest substrate temperature in the entire element at each time point.
Min Temperature
-
K
Lowest substrate temperature in the entire element at each time point.
Max Temperature Gradient -
K
Maximum spatial temperature gradient in the whole converter at each time point, i.e. the maximum temperature difference between adjacent grid cells divided by the first cell's length.
Outlet Massflow
Flow
kg/s
Total gas mass emerging at the outlet per time unit.
Outlet Temperature
-
K
Gas temperature at the outlet.
Overall Pressure Drop
Flow
Pa
Difference between absolute pressure at element's inlet and outlet.
Outlet Gas Species Mole Fraction
Outlet Gas Species Mole Fraction
Molar fraction of the respective gas species .
-
Molar fraction of gas species at axial point , where x is one of five measuring points whose axial positions are: 0.0, 0.25, 0.5, 0.75 and 1.0, respectively.
Gas Species Mole Fraction Gas Species Mole Pnt Fraction
Outlet Gas Species Mass Fraction
Outlet Gas Species Mass Fraction
Overall Gas Species Conversion
Overall Gas Species Conversion
%
Overall conversion of gas species .
Cumulative Outlet Species Massflow
Cumulative Outlet Species Massflow
kg
Integrated result of the outlet mass flux of species summarized from the beginning
FIRE BOOST Aftertreatment
Mass fraction of gas species at the outlet.
259
5. BOOST Aftertreatment of the simulation up to the current time point:
260
Mean GHSV
Flow
1/s
Volume flux of the gas divided by the entire volume of the element.
Inlet Pressure
-
Pa
Absolute pressure at the inlet.
Gas Temperature Pnt
Gas Temperature (5 Points)
K
Temperature of the gas at axial point x, where x is one of five measuring points evenly distributed over the element's length (axial positions: 0.0, 0.25, 0.5, 0.75, 1.0).
Solid Temperature Pnt
Solid Temperature (5 Points)
K
Temperature of the solid at axial point x, where x is one of five measuring points evenly distributed over the element's length (axial positions: 0.0, 0.25, 0.5, 0.75, 1.0).
Outer Wall Temperature Pnt
Outer Wall Temperature (5 Points)
K
Temperature of the outermost layer (Variable Wall Temperature Model) of the wall at axial point x, where x is one of five measuring points evenly distributed over the element's length (axial positions: 0.0, 0.25, 0.5, 0.75, 1.0).
Inlet Gas Phase Heat Capacity
Inlet Gas Properties
J/(kg·K)
Heat capacity of the gas at the inlet.
Inlet Gas Phase Enthalpy
Inlet Gas Properties
J/kg
Enthalpy of the gas phase at the inlet.
Inlet Gas Phase Molar Mass
Inlet Gas Properties
kg/kmol
Molar mass of the gas phase at the inlet.
Inlet Gas Phase Density
Inlet Gas Properties
kg/m
Density of the gas phase at the inlet.
Outlet Gas Phase Heat Capacity
Outlet Gas Properties
J/(kg·K)
Heat capacity of the gas at the outlet.
Outlet Gas Phase Enthalpy
Outlet Gas Properties
J/kg
Enthalpy of the gas phase at the outlet.
Outlet Gas Phase Molar Mass
Outlet Gas Properties
kg/kmol
Molar mass of the gas phase at the outlet.
Outlet Gas Phase Density
Outlet Gas Properties
kg/m
3
3
Density of the gas phase at the outlet.
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment Mean Surface Fraction Ce2O3(S)
Mean Surface Fraction
-
Overall fraction of catalytic surface covered by species Ce2O3(S) (Pre-defined TWC model, Reactions 10-13).
Mean Surface Fraction CeO2(S)
Mean Surface Fraction
-
Overall fraction of catalytic surface covered by species CeO2(S) (Pre-defined TWC model, Reactions 10-13).
Mean Surface Fraction Rh(S)
Mean Surface Fraction
-
Overall fraction of catalytic surface covered by species Rh(S) (Pre-defined TWC model, Reactions 14-19).
Mean Surface Fraction RhO(S)
Mean Surface Fraction
-
Overall fraction of catalytic surface covered by species RhO(S) (Pre-defined TWC model, Reactions 14-19).
Mean Surface Fraction BaCO3(S)
Mean Surface Fraction
-
Overall fraction of catalytic surface covered by species BaCO3(S) (Pre-defined TWC model, Reactions 20 & 21).
Mean Surface Fraction Ba(NO3)2(S)
Mean Surface Fraction
-
Overall fraction of catalytic surface covered by species Ba(NO3)2(S) (Pre-defined TWC model, Reactions 20 & 21).
Mean Surface Fraction Me(S)
Mean Surface Fraction
-
Overall fraction of catalytic surface covered by species Me(S) (Pre-defined SCR Transient model, Reactions 2 & 3).
Mean Surface Fraction Me-NH3(S)
Mean Surface Fraction
-
Overall fraction of catalytic surface covered by species Me-NH3(S) (Pre-defined SCR Transient model, Reactions 2 & 3).
Mean Reaction Rate
Mean Reaction Rate
kmol/ 3 (m ·s)
Mean rate of reaction of Pre-defined SCR Transient model, with enabled reaction number (x=1-10, rate per total catalyst volume).
Surface Fraction MeNH3(S) Pnt
Surface Fraction (5 points)
Fraction of catalytic surface covered by species Me-NH3(S) in one of five equal-sized adjacent regions (Pre-defined SCR Transient model, Reactions 2 & 3).
Mean Surface Fraction User
Mean Surface Fraction
Overall fraction of catalytic surface covered by the th surface species, where x=1-10. Surface species are numbered
-
FIRE BOOST Aftertreatment
261
5. BOOST Aftertreatment continuously for all user mechanisms in order of their appearance (AUCI or Fortran user coding).
262
Surface Fraction User Pnt
Surface Fraction (5 points)
Fraction of catalytic surface covered by the th surface species, where x=1-6, in one of five () equal-sized adjacent regions. Surface species are numbered continuously for all user mechanisms in order of their appearance (AUCI or Fortran user coding).
Inlet NH3/NOx ratio
-
-
Provides the ratio of NH3 mole fraction to NOx mole fraction (= NO + NO2) at the Catalyst inlet. If neither NH3 nor NO and NO2 are present in the gas phase the sensor channel value is zero.
Inlet NO2/NOx ratio
-
-
Provides the ratio of NO2 mole fraction to NOx mole fraction (= NO + NO2) at the Catalyst inlet. If neither NO2 nor NO are present in the gas phase the sensor channel value is zero.
Actuator Channel
Submenu
Unit
Description
Wall Heat Source All
-
W
Allows to introduce heat into the wall over the whole aftertreatment element's length.
Wall Heat Source Zone Wall Heat Source By Zone
W
Allows to introduces heat into the wall into zone x, where x=1-5 corresponds to five adjacent zones one fifth of the total length, each.
Ambient Wall Temperature -
K
Sets the ambient temperature.
Ambient Velocity
m/s
Sets the velocity of the ambient gas.
General Catalytic Reaction Rate Multiplier
-
Sets a dimensionless factor by which all catalytic reaction rates are multiplied.
Conversion Of Species
-
Actuates the conversion of the indicated species "X" in a map-based conversion catalyst. Precondition for the usage of this actuator channel is an already generated conversion map for that species in the catalyst element; here any input will be overruled, if the actuator channel
-
Conversion Of Species
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment for that particular species is connected to the catalyst. Any actuator channel value will be cut to the range (0,1). Using the available control elements (e.g. Engine Interface, Formula Interpreter, Matlab DLL, ...) arbitrary conversion maps can be defined in addition to the available conversion maps at the catalyst element.
Mean substrate temperature of the element at each time point.
Max Temperature
-
K
Highest substrate temperature in the entire element at each time point.
Min Temperature
-
K
Lowest substrate temperature in the entire element at each time point.
Max Temperature Gradient -
K
Maximum spatial temperature gradient in the whole converter at each time point, i.e. the maximum temperature difference between adjacent grid cells divided by the first cell's length.
Outlet Massflow
Flow
kg/s
Total gas mass emerging at the outlet per time unit.
Outlet Temperature
-
K
Gas temperature at the outlet.
Overall Pressure Drop
Flow
Pa
Difference between absolute pressure at element's inlet and outlet.
Outlet Gas Species Mole Fraction
Outlet Gas Species Mole Fraction
Molar fraction of the respective gas species .
Mean GHSV
Flow
1/s
Volume flux of the gas divided by the entire volume of the element.
Inlet Pressure
-
Pa
Absolute pressure at the inlet.
Soot Mass
-
kg
Total soot mass in the particulate filter.
Inlet Soot Massflow
-
kg/s
Soot mass entering the particulate filter per time unit.
Gas Temperature Pnt
Gas Temperature (5 Points)
K
Temperature of the gas at axial point x, where x is one of
FIRE BOOST Aftertreatment
263
5. BOOST Aftertreatment five measuring points evenly distributed over the element's length (axial positions: 0.0, 0.25, 0.5, 0.75, 1.0).
264
Solid Temperature Pnt
Solid Temperature (5 Points)
K
Temperature of the solid at axial point x, where x is one of five measuring points evenly distributed over the element's length (axial positions: 0.0, 0.25, 0.5, 0.75, 1.0).
Outer Wall Temperature Pnt
Outer Wall Temperature (5 Points)
K
Temperature of the outermost layer (Variable Wall Temperature Model) of the wall at axial point x, where x is one of five measuring points evenly distributed over the element's length (axial positions: 0.0, 0.25, 0.5, 0.75, 1.0).
Inlet Gas Phase Heat Capacity
Inlet Gas Properties
J/(kg·K)
Heat capacity of the gas at the inlet.
Inlet Gas Phase Enthalpy
Inlet Gas Properties
J/kg
Enthalpy of the gas phase at the inlet.
Inlet Gas Phase Molar Mass
Inlet Gas Properties
kg/kmol
Molar mass of the gas phase at the inlet.
Inlet Gas Phase Density
Inlet Gas Properties
kg/m
Density of the gas phase at the inlet.
Outlet Gas Phase Heat Capacity
Outlet Gas Properties
J/(kg·K)
Heat capacity of the gas at the outlet.
Outlet Gas Phase Enthalpy
Outlet Gas Properties
J/kg
Enthalpy of the gas phase at the outlet.
Outlet Gas Phase Molar Mass
Outlet Gas Properties
kg/kmol
Molar mass of the gas phase at the outlet.
Outlet Gas Phase Density
Outlet Gas Properties
kg/m
Density of the gas phase at the outlet.
Actuator Channel
Submenu
Unit
Description
Wall Heat Source All
-
W
Allows to introduce heat into the wall over the whole aftertreatment element's length.
Wall Heat Source Zone Wall Heat Source By Zone
W
Allows to introduces heat into the wall into zone x, where x=1-5 corresponds to five adjacent zones one fifth of the total length, each.
Ambient Wall Temperature -
K
Sets the ambient temperature.
Ambient Velocity
m/s
Sets the velocity of the ambient gas.
-
3
3
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment General Catalytic Reaction Rate Multiplier
-
Sets a dimensionless factor by which all catalytic reaction rates are multiplied.
Mean substrate temperature of the element at each time point.
Max Temperature
-
K
Highest substrate temperature in the entire element at each time point.
Min Temperature
-
K
Lowest substrate temperature in the entire element at each time point.
Outlet Massflow
Flow
kg/s
Total gas mass emerging at the outlet per time unit.
Gas Temperature Pnt
Gas Temperature (5 Points)
K
Temperature of the gas at axial point x, where x is one of five measuring points evenly distributed over the element's length (axial positions: 0.0, 0.25, 0.5, 0.75, 1.0).
Outer Wall Temperature Pnt
Outer Wall Temperature (5 Points)
K
Temperature of the outermost layer (Variable Wall Temperature Model) of the wall at axial point x, where x is one of five measuring points evenly distributed over the element's length (axial positions: 0.0, 0.25, 0.5, 0.75, 1.0).
Inlet Gas Phase Heat Capacity
Inlet Gas Properties
J/(kg·K)
Heat capacity of the gas at the inlet.
Inlet Gas Phase Enthalpy
Inlet Gas Properties
J/kg
Enthalpy of the gas phase at the inlet.
Inlet Gas Phase Molar Mass
Inlet Gas Properties
kg/kmol
Molar mass of the gas phase at the inlet.
Inlet Gas Phase Density
Inlet Gas Properties
kg/m
Density of the gas phase at the inlet.
Outlet Gas Phase Heat Capacity
Outlet Gas Properties
J/(kg·K)
Heat capacity of the gas at the outlet.
Outlet Gas Phase Enthalpy
Outlet Gas Properties
J/kg
Enthalpy of the gas phase at the outlet.
Outlet Gas Phase Molar Mass
Outlet Gas Properties
kg/kmol
Molar mass of the gas phase at the outlet.
Outlet Gas Phase Density
Outlet Gas Properties
kg/m
3
FIRE BOOST Aftertreatment
3
Density of the gas phase at the outlet. 265
5. BOOST Aftertreatment Inlet Reynolds Number
-
-
Reynolds number at the inlet.
Actuator Channel
Submenu
Unit
Description
Wall Heat Source All
-
W
Allows to introduce heat into the wall over the whole aftertreatment element's length.
Wall Heat Source Zone Wall Heat Source By Zone
W
Allows to introduces heat into the wall into zone x, where x=1-5 corresponds to five adjacent zones one fifth of the total length, each.
Gas Heat Source All
W
Allows to introduce heat directly into the gas over the whole aftertreatment element's length.
Gas Heat Source Zone Gas Heat Source By Zone
W
Allows to introduces heat directly into the gas into zone x, where x=1-5 corresponds to five adjacent zones one fifth of the total length, each.
Ambient Wall Temperature -
K
Sets the ambient temperature.
Ambient Velocity
-
m/s
Sets the velocity of the ambient gas.
Inlet Friction Multiplier
-
-
Dimensionless factor to influence the Darcy factor at the inlet (e.g. to simulate a certain surface roughness).
-
5.2.5. Aftertreatment Injector Databus Channels
266
Sensor Channel
Submenu
Unit
Description
Inj. Massflow
-
kg/s
Total injected mass per time unit.
Inlet Gas Phase Heat Capacity
Inlet Gas Properties
J/(kg·K)
Heat capacity of the gas at the inlet.
Inlet Gas Phase Enthalpy
Inlet Gas Properties
J/kg
Enthalpy of the gas phase at the inlet.
Inlet Gas Phase Molar Mass
Inlet Gas Properties
kg/kmol
Molar mass of the gas phase at the inlet.
Inlet Gas Phase Density
Inlet Gas Properties
kg/m
Density of the gas phase at the inlet.
Outlet Gas Phase Heat Capacity
Outlet Gas Properties
J/(kg·K)
Heat capacity of the gas at the outlet.
Outlet Gas Phase Enthalpy
Outlet Gas Properties
J/kg
Enthalpy of the gas phase at the outlet.
Outlet Gas Phase Molar Mass
Outlet Gas Properties
kg/kmol
Molar mass of the gas phase at the outlet.
3
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment 3
Outlet Gas Phase Density
Outlet Gas Properties
kg/m
Density of the gas phase at the outlet.
Actuator Channel
Submenu
Unit
Description
Inj. Massflow
-
kg/s
Total injected mass per time unit.
5.2.6. Solver Databus Channels For the Aftertreatment Solver the following sensor and actuator channels are available. In order to connect one of the databus channels select "Global" as Element in the related input pages of the Control elements. Sensor Channel
Unit
Description
Time
s
Provides the current simulation time.
Realtime Factor
-
Provides the current realtime factor of the simulation.
Actuator Channel
Unit
Description
Operation Control
-
Send information about current engine state: 'Engine On' set value to 1. 'Engine Off' set value to 0.
page [300]
5.3. Simulation Results In this section the available simulation results of the individual components are described.
5.3.1. Catalyst Results All data from the aftertreatment analysis simulations are given as transient values. The availability of the results listed below is directed by the "Type of Results" setting on the element's Results Specification page. There are three main results levels standing for an increasing number of results: Reduced, Standard and All. • The results grouped under "Reduced (Mean and Outlet values)" are a minimal set of results, thus, all of the levels higher than "Reduced" include the reduced results. • Results not marked as Reduced are generally axially resolved, i.e. they refer to local values associated with a given output cell/spatial position. The spatial position is part of the folder name and the curve name. • Each of the special results groups "Standard, Properties", "Standard, Fluxes" and "Standard, Sources" comprises the Standard results augmented by an extra set of results marked as Property, Flux and Source, respectively, in the Availability column. • The results type "All" comprises all of the applicable results in the table (i.e. also properties, fluxes and sources). Results marked as Extended in the Availability column are only shown when this results type ("All") was selected (i.e. they are not in any of the other results subsets). Result Name
Unit
Description/Definition
Availability
Maximum Temperature
K
Highest substrate temperature in the entire element at each time point.
Reduced
Minimum Temperature
K
Lowest substrate temperature in the Reduced entire element at each time point.
FIRE BOOST Aftertreatment
267
5. BOOST Aftertreatment Mean Temperature
K
Mean substrate temperature of the element at each time point. This is the mean substrate temperature at each time point, calculated by summing up the substrate temperature in each cell weighted by its share of the total converter volume.
Reduced
Maximum Temperature Gradient
K/m
Maximum spatial temperature gradient in the whole converter at each time point, i.e. the maximum temperature difference between adjacent grid cells divided by the first cell's length.
Reduced
Position of Maximum Gradient
-
Relative location of the Maximum Temperature Gradient in the catalyst (i.e. the midpoint of the cell exhibiting that gradient).
Reduced
Mean GHSV (Gas Hourly Space Velocity)
Hz
Volume flux of the gas divided by the entire volume of the element:
Reduced
The Mean GHSV is the sum of the individual cells' GHSVs weighted by each cell's volume, at each time point. It is a measure of how often the gas volume of the converter is replaced per time unit.
268
Mean GHSV at Norm Conditions
Hz
The Mean GHSV (see above), but Reduced evaluated at a temperature of 273 K and a pressure of 1.013 bar.
Inlet Redox Ratio
-
Inlet RR is the amount of oxygen Reduced required for full oxidation of carbon and hydrogen divided by the amount oxygen available in the gas-phase. page [98] Refer to Eq.318 .
Inlet Excess Oxygen Ratio
-
is the amount of oxygen available in the gas-phase divided by the amount of oxygen required for full oxidation of carbon and hydrogen. page [98] Refer to Eq.319 .
FIRE BOOST Aftertreatment
Reduced
5. BOOST Aftertreatment Inlet Engine Lambda
-
Evaluated according to Brinkmeier page [95] [10 ], where a fuel CHx ratio of x=1.814 is assumed and the mole fraction of oxygen in air is assumed to be 0.2095. page [98] Refer to Eq.320 .
Reduced
Converter Pressure Drop
Pa
Difference between absolute pressure at element's inlet and outlet.
Reduced
Ambient Temperature
K
Temperature of the ambient gas around the element.
Reduced
Radiation Sink Temperature
K
Temperature of the radiation sink around the element (Variable Wall Temperature Model).
Reduced
Cumulative Inlet Heat Flow
J
Integrated result of the inlet heat Reduced flow summarized from the beginning of the simulation up to the current time point.
Cumulative Outlet Heat Flow
J
Integrated result of the outlet heat Reduced flow summarized from the beginning of the simulation up to the current time point.
Mean Continuity Source
kg/(m ·s)
Mean Energy Source
3
Mean value of all gas phase mass sources throughout the converter at each time point.
Source
W/m
Mean value of all gas phase energy sources due to chemical reactions throughout the converter at each time point.
Source
Overall Conversion
%
The overall conversion C of the Reduced species i is derived from its inlet and outlet mass fractions at each time step of the calculation:
Overall Conversion molebased
%
The mole-based conversion is the Reduced overall conversion discussed above evaluated with mole fractions, rather than mass fractions.
Cumulative Mass Flux In
kg
Integrated result of the inlet Reduced species fluxes summarized from the beginning of the simulation up to the current time point:
3
FIRE BOOST Aftertreatment
269
5. BOOST Aftertreatment
270
Cumulative Mass Flux Out
kg
Integrated result of the outlet Reduced species fluxes summarized from the beginning of the simulation up to the current time point:
Gas Wall Heat Flow
W
Mean heat transfer from the gas to the wall throughout the element at each time point.
Cumulative Gas Wall Heat Flow
J
Integration of the result above, Reduced from the beginning of the simulation up to the current time point. This resembles the energy transferred from the gas to the wall.
Overall Wall-Amb Heat Flow
W
Heat flow from the wall to the Reduced ambient summed-up over the entire element outer surface and considering convective and radiation heat losses.
Convec Wall-Amb Heat Flow
W
Convective heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Reduced
Radiat Wall-Amb Heat Flow
W
Radiation heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Reduced
Overall Cumulative Wall-Amb Heat Flow
J
Cumulated heat flow from the wall Reduced to the ambient summed-up over the entire element's outer surface and considering convective and radiation heat losses.
Reduced
Convec Cumulative Wall-Amb J Heat Flow
Cumulated convective heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Reduced
Radiat Cumulative Wall-Amb Heat Flow
Cumulated radiation heat flow from the wall to the ambient summedup over the entire element's outer
External heat source added to the element's solid substrate summedup over the entire substrate volume.
Wall-Ambient Heat Trans Coeff
W/(m ·K)
Heat transfer coefficient of the wall- Reduced ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Overall
-
Ratio of overall convective heat transfer to conductive heat transfer of the wall-to-ambient heat transfer.
Reduced
Prandtl
-
Dynamic viscosity multiplied with heat capacity divided by heat conductivity of the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Grashof
-
Ratio of the buoyancy force to the viscous force acting on the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Reynolds
-
Fluid velocity multiplied with characteristic length divided by kinematic fluid viscosity of the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Nusselt Free Convection
-
Ratio of free convective heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Reduced
2
Reduced
Nusselt Laminar Forced Conv -
Ratio of laminar forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Turbulent Forced Conv
-
Ratio of turbulent forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Forced Convection
-
Ratio of overall forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Overall Surface Density
mol/m
2
Amount of moles per surface unit that can be stored at a specific surface site. (Pre-defined or AUCI reaction models having
FIRE BOOST Aftertreatment
Reduced
271
5. BOOST Aftertreatment surface sites; for the latter case, result "Storage site densities" must be enabled under "Model Encapsulation")
272
Overall Surface Fraction
-
Mean fraction that a given surface species covers of a given surface site. (Pre-defined or AUCI reaction models having surface sites; for the latter case, result "Storage site species fractions" must be enabled under "Model Encapsulation")
Reduced
Overall Surface Loading
kg
Total mass of a given surface species in a converter. (Predefined or AUCI reaction models having surface sites; for the latter case, result "Storage site species loadings" must be enabled under "Model Encapsulation")
Reduced
Mean Species Source
kg/(m ·s)
Local species reaction rates are summarized over all reactions and converted from moles to mass. Mean value of all local sources throughout the converter at each time point.
Source
Mean Reaction Rate
kmol/ 3 (m ·s)
Mean value of all local rates of a certain reaction throughout the converter at each time point.
Source
Gas Temperature
K
Temperature of the gas phase.
Standard
Solid Temperature
K
Axially resolved temperature of the solid substrate.
Standard
Wall Temperature
K
Axially resolved temperature of each wall layer (i.e. radial grid point of the wall). (Variable Wall Temperature model)
Standard
Velocity
m/s
Interstitial velocity inside the Standard channels of the catalyst. In case of a particulate filter the velocity inside the channels of the surrogate catalyst (monolith with removed plugs).
Pressure
Pa
Absolute pressure at each axial output point.
Standard
Mass Fraction
kg/kg
Gas species mass fractions at each axial output point.
Standard
Mole Fraction
mol/mol
Gas species molar fractions at each axial output point.
Standard
Redox Ratio
-
See Inlet Redox Ratio
3
page [
FIRE BOOST Aftertreatment
]
.
Standard
5. BOOST Aftertreatment Excess Oxygen Ratio
-
See Inlet Excess Oxygen Ratio ] .
page
Standard
[
page [
]
Engine Lambda
-
See Inlet Engine Lambda
Surface Fraction
-
Fraction of a given surface site Standard which is occupied by a given surface species, at each axial output point.
Surface Loading
kg/m
Mass Density
.
Standard
3
Mass of a given surface species per Standard total converter volume at each axial output point (mass based density).
kg/m
3
Mass based density of the gas mixture.
Property
Molar Mass
kg/kmol
Average molar Mass of the gas mixture.
Property
Molar Concentration
kmol/m
Mole based density of the gas mixture.
Property
Heat Capacity
J/(kg·K)
Heat capacity of the gas phase.
Property
Enthalpy
kJ/kg
Enthalpy of the gas phase.
Property
Conductivity
W/(m·K)
Thermal conductivity of the gas phase.
Property
Viscosity
Pa·s
Viscosity of the gas phase.
Property
Inner Heat Transfer Coeff
W/(m ·K)
Heat transfer coefficient between gas phase and solid substrate.
Property
Mass Transfer Coeff
m/s
Mass transfer coefficient between gas bulk phase and substrate surface.
Property
Reynolds (Re)
-
Gas velocity multiplied with hydraulic diameter divided by kin. gas viscosity (ratio of inertial to viscous forces).
Property
Prandtl (Pr)
-
Dyn. gas viscosity multiplied with gas heat capacity divided by gas heat conductivity (ratio of momentum diffusivity to thermal diffusivity).
Property
Schmidt (Sc)
-
Kin. gas species viscosity divided by gas species diffusion coefficient (ratio of momentum diffusivity to mass diffusivity).
Property
Nusselt (Nu)
-
Gas heat transfer coefficient multiplied with characteristic length divided by gas heat conductivity (ratio of convective to conductive heat transfer).
Property
Sherwood (Sh)
-
Gas species mass transfer coefficient multiplied with
Property
2
3
FIRE BOOST Aftertreatment
273
5. BOOST Aftertreatment characteristic length divided by gas species diffusion coefficient (ratio of convective to diffusive mass transfer). Peclet Heat Transfer
-
Peclet number for thermal diffusion (Re·Pr).
Property
Peclet Mass Transfer
-
Peclet number for mass diffusion (Re·Sc).
Property
External Heat Source
W
Energy input coming from an external heat source, axially resolved.
Property
GHSV
Hz
See Mean GHSV
Mass Flux
kg/s
Gas phase mass flux.
Flux
Species Mass Flux
kg/s
Mass flux of the individual gas phase species.
Flux
Energy Flux
W
Enthalpy flux of the gas phase.
Flux
Species Energy Flux
W
Individual gas species enthalpy flux. Flux
Reaction Rate
kmol/ 3 (m ·s)
Rates of individual chemical reactions (per total converter volume).
Source
Rate Continuity
kg/(m ·s)
Continuity source due to chemical reactions (per total converter volume).
Source
Rate Energy
J/(m ·s)
Rate Species
kg/(m ·s)
Molar Concentration
kmol/m
Mass Density
Mole Fraction
3
3
3
page [
]
.
Energy source due to chemical Source reactions, i.e. rate of heat produced/ consumed by the sum of all chemical reactions (per total converter volume). Consumption/production rates of individual gas species due to chemical reactions (per total converter volume).
Source
Molar concentration (= molar density) of individual gas species in the washcoat layer. (subfolder Washcoat Layer)
Extended
kg/m
Mass density of individual gas species in the washcoat layer. (subfolder Washcoat Layer)
Extended
-
Molar fraction of individual gas species in the washcoat wayer (per total number of moles in the layer). (subfolder Washcoat Layer)
Extended
3
3
5.3.2. Particulate Filter Results All data from the aftertreatment analysis simulations are given as transient values. 274
Flux
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment The availability of the results listed below is directed by the "Type of Results" setting on the element's Results Specification page. There are three main results levels standing for an increasing number of results: Reduced, Standard and All. • The results grouped under "Reduced (Mean and Outlet values)" are a minimal set of results, thus, all of the levels higher than "Reduced" include the reduced results. • Results not marked as Reduced are generally axially resolved, i.e. they refer to local values associated with a given output cell/spatial position. The spatial position is part of the folder name and the curve name. • Each of the special results groups "Standard, Properties", "Standard, Fluxes" and "Standard, Sources" comprises the Standard results augmented by an extra set of results marked as Property, Flux and Source, respectively, in the Availability column. • The results type "All" comprises all of the applicable results in the table (i.e. also properties, fluxes and sources). Results marked as Extended in the Availability column are only shown when this results type ("All") was selected (i.e. they are not in any of the other results subsets). Result Name
Unit
Description/Definition
Availability
Maximum Temperature
K
Highest substrate temperature in the entire element at each time point.
Reduced
Minimum Temperature
K
Lowest substrate temperature in the Reduced entire element at each time point.
Mean Temperature
K
Mean substrate temperature of the element at each time point. This is the mean substrate temperature at each time point, calculated by summing up the substrate temperature in each cell weighted by its share of the total converter volume.
Reduced
Maximum Temperature Gradient
K/m
Maximum spatial temperature gradient in the whole converter at each time point, i.e. the maximum temperature difference between adjacent grid cells divided by the first cell's length.
Reduced
Position of Maximum Gradient
-
Relative location of the Maximum Temperature Gradient in the catalyst (i.e. the midpoint of the cell exhibiting that gradient).
Reduced
Mean GHSV (Gas Hourly Space Velocity)
Hz
Volume flux of the gas divided by the entire volume of the element:
Reduced
FIRE BOOST Aftertreatment
275
5. BOOST Aftertreatment The Mean GHSV is the sum of the individual cells' GHSVs weighted by each cell's volume, at each time point. It is a measure of how often the gas volume of the converter is replaced per time unit.
276
Mean GHSV at Norm Conditions
Hz
The Mean GHSV (see above), but Reduced evaluated at a temperature of 273 K and a pressure of 1.013 bar.
Inlet Redox Ratio
-
Inlet RR is the amount of oxygen Reduced required for full oxidation of carbon and hydrogen divided by the amount oxygen available in the gas-phase. page [98] Refer to Eq.318 .
Inlet Excess Oxygen Ratio
-
is the amount of oxygen available in the gas-phase divided by the amount of oxygen required for full oxidation of carbon and hydrogen. page [98] Refer to Eq.319 .
Reduced
Inlet Engine Lambda
-
Evaluated according to Brinkmeier page [95] [10 ], where a fuel CHx ratio of x=1.814 is assumed and the mole fraction of oxygen in air is assumed to be 0.2095. page [98] Refer to Eq.320 .
Reduced
Converter Pressure Drop
Pa
Difference between absolute pressure at element's inlet and outlet.
Reduced
Ambient Temperature
K
Temperature of the ambient gas around the element.
Reduced
Radiation Sink Temperature
K
Temperature of the radiation sink around the element (Variable Wall Temperature Model).
Reduced
Inlet Pressure Drop
Pa
Inlet pressure drop of the PF due to contraction of the flow. Refer to page [48] Filter Flow Model .
Reduced
Outlet Pressure Drop
Pa
Outlet pressure drop of the PF due to expansion of the flow. Refer to page [48] Filter Flow Model .
Reduced
Inlet Plug Pressure Drop
Pa
Pressure drop contribution of the flow along the inlet plug. Refer to page [48] Filter Flow Model .
Reduced
Outlet Plug Pressure Drop
Pa
Pressure drop contribution of the flow along the outlet plug. Refer to page [48] Filter Flow Model .
Reduced
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment Wall Pressure Drop
Pa
Mean value of the pressure drop of Reduced the filter wall over the effective filter page length. Refer to Filter Flow Model [48] .
Soot Depth Pressure Drop
Pa
Mean value of the soot depth layer Reduced pressure drop over the effective filter page length. Refer to Filter Flow Model [48] .
Soot Cake Pressure Drop
Pa
Mean value of the soot cake layer Reduced pressure drop over the effective filter page length. Refer to Filter Flow Model [48] .
Ash Cake Pressure Drop
Pa
Mean value of the ash cake layer Reduced pressure drop over the effective filter page length. Refer to Filter Flow Model [48] .
Inlet Channel Pressure Drop
Pa
Mean value of the inlet channel Reduced pressure drop over the effective filter page length. Refer to Filter Flow Model [48] .
Outlet Channel Pressure Drop
Pa
Mean value of the outlet channel Reduced pressure drop over the effective filter page length. Refer to Filter Flow Model [48] .
Overall Pressure Drop
Pa
Overall Pressure Drop of the Converter.
Overall Soot Mass
kg/m
Overall soot mass given as a Reduced volume specific value, where the overall volume of the filter is used as reference.
Overall Soot Mass (abs)
kg
Overall soot mass given as absolute Reduced value.
Overall Soot Mass (Cake)
kg/m
Overall Cake layer soot mass given as a volume specific value, where the overall volume of the filter is used as reference.
Reduced
Overall Soot Mass (Cake) (abs)
kg
Overall Cake layer soot mass given as absolute value.
Reduced
Overall Soot Mass (Depth)
kg/m
Overall Depth layer soot mass given Reduced as a volume specific value, where the overall volume of the filter is used as reference.
Overall Soot Mass (Depth) (abs)
kg
Overall Depth layer soot mass given Reduced as absolute value.
Overall Ash Mass (Cake)
kg/m
3
3
3
3
Reduced
Overall ash mass given as a volume Reduced specific value, where the overall
FIRE BOOST Aftertreatment
277
5. BOOST Aftertreatment volume of the filter is used as reference.
278
Inlet Soot Massflux
kg/s
Inlet Soot Loading
3
Absolute soot mass flux at the converter inlet.
Reduced
kg soot per kg inlet gas.
Reduced
Mean value of all gas phase mass sources throughout the converter at each time point.
Source
Source
Mean Continuity Source
kg/(m ·s)
Mean Energy Source
W/m
Mean value of all gas phase energy sources due to chemical reactions throughout the converter at each time point.
Overall Conversion
%
The overall conversion C of the Reduced species i is derived from its inlet and outlet mass fractions at each time step of the calculation:
Overall Conversion molebased
%
The mole-based conversion is the Reduced overall conversion discussed above evaluated with mole fractions, rather than mass fractions.
Cumulative Mass Flux In
kg
Integrated result of the inlet Reduced species fluxes summarized from the beginning of the simulation up to the current time point:
Cumulative Mass Flux Out
kg
Integrated result of the outlet Reduced species fluxes summarized from the beginning of the simulation up to the current time point:
Overall Wall-Amb Heat Flow
W
Heat flow from the wall to the Reduced ambient summed-up over the entire element outer surface and considering convective and radiation heat losses.
3
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment Convec Wall-Amb Heat Flow
W
Convective heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Reduced
Radiat Wall-Amb Heat Flow
W
Radiation heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Reduced
Overall Cumulative Wall-Amb Heat Flow
J
Cumulated heat flow from the wall Reduced to the ambient summed-up over the entire element's outer surface and considering convective and radiation heat losses.
Convec Cumulative Wall-Amb J Heat Flow
Cumulated convective heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Radiat Cumulative Wall-Amb Heat Flow
J
Cumulated radiation heat flow from Reduced the wall to the ambient summedup over the entire element's outer surface. (Variable Wall Temperature Model)
Overall External Heat Source
W
External heat source added to the element's solid substrate summedup over the entire substrate volume.
Wall-Ambient Heat Trans Coeff
W/(m ·K)
Heat transfer coefficient of the wall- Reduced ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Overall
-
Ratio of overall convective heat transfer to conductive heat transfer of the wall-to-ambient heat transfer.
Reduced
Prandtl
-
Dynamic viscosity multiplied with heat capacity divided by heat conductivity of the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Grashof
-
Ratio of the buoyancy force to the viscous force acting on the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Reynolds
-
Fluid velocity multiplied with characteristic length divided by kinematic fluid viscosity of the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
2
FIRE BOOST Aftertreatment
Reduced
Reduced
279
5. BOOST Aftertreatment Nusselt Free Convection
280
-
Ratio of free convective heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Reduced
Nusselt Laminar Forced Conv -
Ratio of laminar forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Turbulent Forced Conv
-
Ratio of turbulent forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Forced Convection
-
Ratio of overall forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Overall Surface Fraction
-
Mean fraction that a given surface species covers of a given surface site. (Pre-defined or AUCI reaction models having surface sites; for the latter case, result "Storage site species fractions" must be enabled under "Model Encapsulation")
Reduced
Overall Surface Loading
kg
Total mass of a given surface species in a converter. (Predefined or AUCI reaction models having surface sites; for the latter case, result "Storage site species loadings" must be enabled under "Model Encapsulation")
Reduced
Mean Species Source
kg/(m ·s)
Local species reaction rates are summarized over all reactions and converted from moles to mass. Mean value of all local sources throughout the converter at each time point.
Source
Mean Reaction Rate
kmol/ 3 (m ·s)
Mean value of all rates of a certain Source reaction throughout the converter at each time point.
Gas Temperature
K
Temperature of the gas phase.
Standard
Solid Temperature
K
Axially resolved temperature of the solid substrate.
Standard
Wall Temperature
K
Axially resolved temperature of each wall layer (i.e. radial grid point of the wall). (Variable Wall Temperature model)
Standard
3
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment Velocity
m/s
Interstitial velocity inside the Standard channels of the catalyst. In case of a particulate filter the velocity inside the channels of the surrogate catalyst (monolith with removed plugs).
Pressure
Pa
Absolute pressure at each axial output point.
Standard
Mass Fraction
kg/kg
Gas species mass fractions at each axial output point.
Standard
Mole Fraction
mol/mol
Gas species molar fractions at each axial output point.
Standard
Redox Ratio
-
See Inlet Redox Ratio
Excess Oxygen Ratio
-
See Inlet Excess Oxygen Ratio [ ] .
Engine Lambda
-
See Inlet Engine Lambda
Soot Mass
kg/m
Soot mass given as a volume specific value, where the overall volume of the filter is used as reference.
Standard
Soot Mass (abs)
kg
Soot mass given as absolute value.
Standard
3
3
page [
]
Standard
. page
page [
]
.
Standard Standard
Soot Mass (Cake)
kg/m
Cake layer soot mass given as a Standard volume specific value, where the overall volume of the filter is used as reference.
Soot Mass (Cake)(abs)
kg
Cake layer soot mass given as absolute value.
Soot Mass (Depth)
kg/m
Depth layer soot mass given as a Standard volume specific value, where the overall volume of the filter is used as reference.
Soot Mass (Depth)(abs)
kg
Depth layer soot mass given as absolute value.
Standard
Ash Mass (Cake)
kg/m
Ash mass given as a volume specific value, where the overall volume of the filter is used as reference.
Standard
Soot Height (Cake)
m
Height of soot cake layer.
Standard
Soot Height (Depth)
m
Height of soot depth layer.
Standard
Ash Height (Cake)
m
Height of ash cake layer.
Standard
Inlet Channel Pressure
Pa
Absolute pressure in the Inlet channel.
Standard
Outlet Channel Pressure
Pa
Absolute pressure in the outlet channel
Standard
3
3
FIRE BOOST Aftertreatment
Standard
281
5. BOOST Aftertreatment
282
3
Gas density inside the inlet channel. Standard
kg/m
3
Gas density inside the outlet channel.
Standard
Inlet Channel Velocity
m/s
Interstitial velocity inside the filter inlet channel.
Standard
Outlet Channel Velocity
m/s
Interstitial velocity inside the filter outlet channel.
Standard
Wall Velocity
-
Wall velocity at each axial output point divided by the mean wall velocity.
Standard
Wall Velocity 1
m/s
Velocity of the gas entering the soot cake.
Standard
Wall Velocity 2
m/s
Velocity of the gas entering the filter wall.
Standard
Wall Mass Flow 1
kg/s
Wall mass flow in the inlet channel (neglecting chemical reactions)
Standard
Wall Mass Flow 2
kg/s
Wall mass flow in the outlet channel (neglecting chemical reactions)
Standard
Surface Fraction
-
Fraction of a given surface site Standard which is occupied by a given surface species, at each axial output point.
Surface Loading
kg/m
Mass Density
Inlet Channel Density
kg/m
Outlet Channel Density
3
Mass of a given surface species per Standard total converter volume at each axial output point (mass based density).
kg/m
3
Mass based density of the gas mixture.
Property
Molar Mass
kg/kmol
Average molar Mass of the gas mixture.
Property
Molar Concentration
kmol/m
Mole based density of the gas mixture.
Property
Heat Capacity
J/(kg·K)
Heat capacity of the gas phase.
Property
Enthalpy
kJ/kg
Enthalpy of the gas phase.
Property
Conductivity
W/(m·K)
Thermal conductivity of the gas phase.
Property
Viscosity
Pa·s
Viscosity of the gas phase.
Property
Inner Heat Transfer Coeff
W/(m ·K)
Heat transfer coefficient between gas phase and solid substrate.
Property
Mass Transfer Coeff
m/s
Mass transfer coefficient between gas bulk phase and substrate surface.
Property
Reynolds (Re)
-
Gas velocity multiplied with hydraulic diameter divided by kin.
Property
2
3
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment gas viscosity (ratio of inertial to viscous forces). Prandtl (Pr)
-
Dyn. gas viscosity multiplied with gas heat capacity divided by gas heat conductivity (ratio of momentum diffusivity to thermal diffusivity).
Property
Schmidt (Sc)
-
Kin. gas species viscosity divided by gas species diffusion coefficient (ratio of momentum diffusivity to mass diffusivity).
Property
Nusselt (Nu)
-
Gas heat transfer coefficient multiplied with characteristic length divided by gas heat conductivity (ratio of convective to conductive heat transfer).
Property
Sherwood (Sh)
-
Gas species mass transfer coefficient multiplied with characteristic length divided by gas species diffusion coefficient (ratio of convective to diffusive mass transfer).
Property
Peclet Heat Transfer
-
Peclet number for thermal diffusion (Re·Pr).
Property
Peclet Mass Transfer
-
Peclet number for mass diffusion (Re·Sc).
Property
External Heat Source
W
Energy input coming from an external heat source, axially resolved.
Property
GHSV
Hz
See Mean GHSV
Mass Flux
kg/s
Gas phase mass flux.
Flux
Species Mass Flux
kg/s
Mass flux of the individual gas phase species.
Flux
Energy Flux
W
Enthalpy flux of the gas phase.
Flux
Species Energy Flux
W
Individual gas species enthalpy flux. Flux
Reaction Rate
kmol/ 3 (m ·s)
Rates of individual chemical reactions (per total converter volume).
Source
Rate Continuity
kg/(m ·s)
Continuity source due to chemical reactions (per total converter volume).
Source
Rate Energy
J/(m ·s)
3
3
page [
]
.
Flux
Energy source due to chemical Source reactions, i.e. rate of heat produced/ consumed by the sum of all chemical reactions (per total converter volume).
FIRE BOOST Aftertreatment
283
5. BOOST Aftertreatment Rate Species
3
kg/(m ·s)
Consumption/production rates of individual gas species due to chemical reactions (per total converter volume).
Source
5.3.3. Aftertreatment Pipe Results All data from the aftertreatment analysis simulations are given as transient values. The availability of the results listed below is directed by the "Type of Results" setting on the element's Results Specification page. There are three main results levels standing for an increasing number of results: Reduced, Standard and All. • The results grouped under "Reduced (Mean and Outlet values)" are a minimal set of results, thus, all of the levels higher than "Reduced" include the reduced results. • Results not marked as Reduced are generally axially resolved, i.e. they refer to local values associated with a given output cell/spatial position. The spatial position is part of the folder name and the curve name. • Each of the special results groups "Standard, Properties", "Standard, Fluxes" and "Standard, Sources" comprises the Standard results augmented by an extra set of results marked as Property, Flux and Source, respectively, in the Availability column. • The results type "All" comprises all of the applicable results in the table (i.e. also properties, fluxes and sources). Results marked as Extended in the Availability column are only shown when this results type ("All") was selected (i.e. they are not in any of the other results subsets). Result Name
Unit
Description/Definition
Availability
Maximum Temperature
K
Highest substrate temperature in the entire element at each time point.
Reduced
Minimum Temperature
K
Lowest substrate temperature in the Reduced entire element at each time point.
Mean Temperature
K
Mean substrate temperature of the element at each time point. This is the mean substrate temperature at each time point, calculated by summing up the substrate temperature in each cell weighted by its share of the total converter volume.
Reduced
Mean GHSV (Gas Hourly Space Velocity)
Hz
Volume flux of the gas divided by the entire volume of the element:
Reduced
The Mean GHSV is the sum of the individual cells' GHSVs weighted by each cell's volume, at each time point. It is a measure of how often 284
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment the gas volume of the converter is replaced per time unit. Mean GHSV at Norm Conditions
Hz
The Mean GHSV (see above), but Reduced evaluated at a temperature of 273 K and a pressure of 1.013 bar.
Inlet Redox Ratio
-
Inlet RR is the amount of oxygen Reduced required for full oxidation of carbon and hydrogen divided by the amount oxygen available in the gas-phase. page [98] Refer to Eq.318 .
Inlet Excess Oxygen Ratio
-
is the amount of oxygen available in the gas-phase divided by the amount of oxygen required for full oxidation of carbon and hydrogen. page [98] Refer to Eq.319 .
Reduced
Inlet Engine Lambda
-
Evaluated according to Brinkmeier page [95] [10 ], where a fuel CHx ratio of x=1.814 is assumed and the mole fraction of oxygen in air is assumed to be 0.2095. page [98] Refer to Eq.320 .
Reduced
Converter Pressure Drop
Pa
Difference between absolute pressure at element's inlet and outlet.
Reduced
Ambient Temperature
K
Temperature of the ambient gas around the element.
Reduced
Radiation Sink Temperature
K
Temperature of the radiation sink around the element (Variable Wall Temperature Model).
Reduced
Cumulative Inlet Heat Flow
J
Integrated result of the inlet heat Reduced flow summarized from the beginning of the simulation up to the current time point.
Cumulative Outlet Heat Flow
J
Integrated result of the outlet heat Reduced flow summarized from the beginning of the simulation up to the current time point.
Mean Continuity Source
kg/(m ·s)
Mean Energy Source
W/m
Mean value of all gas phase energy Source sources due to chemical reactions throughout the element at each time point.
Cumulative Mass Flux In
kg
Integrated result of the inlet Reduced species fluxes summarized from the
3
3
Mean value of all gas phase mass sources throughout the element at each time point.
FIRE BOOST Aftertreatment
Source
285
5. BOOST Aftertreatment beginning of the simulation up to the current time point:
286
Cumulative Mass Flux Out
kg
Integrated result of the outlet Reduced species fluxes summarized from the beginning of the simulation up to the current time point:
Overall Friction Coefficient
-
Total friction (weighted sum of Turbulent and Laminar Friction Coefficients).
Reduced
Turbulent Friction Coefficient
-
Turbulent Friction Coefficient.
Reduced
Laminar Friction Coefficient
-
Laminar Friction Coefficient.
Reduced
Reynolds
-
Reynolds number
Reduced
Gas Wall Heat Flow
W
Mean heat transfer from the gas to the wall throughout the element at each time point.
Reduced
Cumulative Gas Wall Heat Flow
J
Integration of the result above, Reduced from the beginning of the simulation up to the current time point. This resembles the energy transferred from the gas to the wall.
Gas-Wall Heat Transfer Coeff W/(m²·K)
Mean heat transfer coefficient.
Reduced
Nusselt
-
Nusselt number, ratio of convective to conductive heat transfer.
Reduced
Overall Wall-Amb Heat Flow
W
Heat flow from the wall to the Reduced ambient summed-up over the entire element outer surface and considering convective and radiation heat losses.
Convec Wall-Amb Heat Flow
W
Convective heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Reduced
Radiat Wall-Amb Heat Flow
W
Radiation heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Cumulated heat flow from the wall Reduced to the ambient summed-up over the entire element's outer surface and considering convective and radiation heat losses.
Convec Cumulative Wall-Amb J Heat Flow
Cumulated convective heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Radiat Cumulative Wall-Amb Heat Flow
J
Cumulated radiation heat flow from Reduced the wall to the ambient summedup over the entire element's outer surface. (Variable Wall Temperature Model)
Overall External Heat Source
W
External heat source added to the element's solid substrate summedup over the entire substrate volume.
Wall-Ambient Heat Trans Coeff
W/(m ·K)
Heat transfer coefficient of the wall- Reduced ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Overall
-
Ratio of overall convective heat transfer to conductive heat transfer of the wall-to-ambient heat transfer.
Reduced
Prandtl
-
Dynamic viscosity multiplied with heat capacity divided by heat conductivity of the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Grashof
-
Ratio of the buoyancy force to the viscous force acting on the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Reynolds
-
Fluid velocity multiplied with characteristic length divided by kinematic fluid viscosity of the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Nusselt Free Convection
-
Ratio of free convective heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Reduced
2
Nusselt Laminar Forced Conv -
Reduced
Reduced
Ratio of laminar forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Ratio of turbulent forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Forced Convection
-
Ratio of overall forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Gas Temperature
K
Temperature of the gas phase.
Standard
Solid Temperature
K
Axially resolved temperature of the solid substrate.
Standard
Wall Temperature
K
Axially resolved temperature of each wall layer (i.e. radial grid point of the wall). (Variable Wall Temperature model)
Standard
Velocity
m/s
Interstitial velocity inside the Standard channels of the catalyst. In case of a particulate filter the velocity inside the channels of the surrogate catalyst (monolith with removed plugs).
Pressure
Pa
Absolute pressure at each axial output point.
Standard
Mass Fraction
kg/kg
Gas species mass fractions at each axial output point.
Standard
Mole Fraction
mol/mol
Gas species molar fractions at each axial output point.
Standard
Redox Ratio
-
See Inlet Redox Ratio
Excess Oxygen Ratio
-
page [
]
Standard
.
See Inlet Excess Oxygen Ratio ] .
page
Standard
[
288
page [
]
Engine Lambda
-
Mass Density
kg/m
Mass based density of the gas mixture.
Property
Molar Mass
kg/kmol
Average molar Mass of the gas mixture.
Property
Molar Concentration
kmol/m
Mole based density of the gas mixture.
Property
Heat Capacity
J/(kg·K)
Heat capacity of the gas phase.
Property
Enthalpy
kJ/kg
Enthalpy of the gas phase.
Property
Conductivity
W/(m·K)
Thermal conductivity of the gas phase.
Property
Viscosity
Pa·s
Viscosity of the gas phase.
Property
See Inlet Engine Lambda 3
3
FIRE BOOST Aftertreatment
.
Standard
5. BOOST Aftertreatment 2
Inner Heat Transfer Coeff
W/(m ·K)
Heat transfer coefficient between gas phase and solid substrate.
Property
Mass Transfer Coeff
m/s
Mass transfer coefficient between gas bulk phase and substrate surface.
Property
Reynolds (Re)
-
Gas velocity multiplied with hydraulic diameter divided by kin. gas viscosity (ratio of inertial to viscous forces).
Property
Prandtl (Pr)
-
Dyn. gas viscosity multiplied with gas heat capacity divided by gas heat conductivity (ratio of momentum diffusivity to thermal diffusivity).
Property
Schmidt (Sc)
-
Kin. gas species viscosity divided by gas species diffusion coefficient (ratio of momentum diffusivity to mass diffusivity).
Property
Nusselt (Nu)
-
Gas heat transfer coefficient multiplied with characteristic length divided by gas heat conductivity (ratio of convective to conductive heat transfer).
Property
Sherwood (Sh)
-
Gas species mass transfer coefficient multiplied with characteristic length divided by gas species diffusion coefficient (ratio of convective to diffusive mass transfer).
Property
Peclet Heat Transfer
-
Peclet number for thermal diffusion (Re·Pr).
Property
Peclet Mass Transfer
-
Peclet number for mass diffusion (Re·Sc).
Property
External Heat Source
W
Energy input coming from an external heat source, axially resolved.
Property
GHSV
Hz
See Mean GHSV
Mass Flux
kg/s
Gas phase mass flux.
Flux
Energy Flux
W
Enthalpy flux of the gas phase.
Flux
3
Hom. Reaction Rate Energy
J/(m ·s)
Hom. Reaction Rate Species
kg/(m ·s)
3
page [
]
.
Flux
Energy source due to chemical Source reactions, i.e. rate of heat produced/ consumed by the sum of all chemical reactions (per total converter volume). Consumption/production rates of individual gas species due
FIRE BOOST Aftertreatment
Source
289
5. BOOST Aftertreatment to chemical reactions (per total converter volume).
5.3.4. Aftertreatment Injector Results All data from the aftertreatment analysis simulations are given as transient values. The availability of the results listed below is directed by the "Type of Results" setting on the element's Results Specification page. There are three main results levels standing for an increasing number of results: Reduced, Standard and All. • The results grouped under "Reduced (Mean and Outlet values)" are a minimal set of results, thus, all of the levels higher than "Reduced" include the reduced results. • Results not marked as Reduced are generally axially resolved, i.e. they refer to local values associated with a given output cell/spatial position. The spatial position is part of the folder name and the curve name. • Each of the special results groups "Standard, Properties", "Standard, Fluxes" and "Standard, Sources" comprises the Standard results augmented by an extra set of results marked as Property, Flux and Source, respectively, in the Availability column. • The results type "All" comprises all of the applicable results in the table (i.e. also properties, fluxes and sources). Results marked as Extended in the Availability column are only shown when this results type ("All") was selected (i.e. they are not in any of the other results subsets). Result Name
Unit
Description/Definition
Availability
Maximum Temperature
K
Highest substrate temperature in the entire element at each time point.
Reduced
Minimum Temperature
K
Lowest substrate temperature in the Reduced entire element at each time point.
Mean Temperature
K
Mean substrate temperature of the element at each time point. This is the mean substrate temperature at each time point, calculated by summing up the substrate temperature in each cell weighted by its share of the total converter volume.
Reduced
Mean GHSV (Gas Hourly Space Velocity)
Hz
Volume flux of the gas divided by the entire volume of the element:
Reduced
The Mean GHSV is the sum of the individual cells' GHSVs weighted by each cell's volume, at each time point. It is a measure of how often the gas volume of the converter is replaced per time unit. 290
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment Mean GHSV at Norm Conditions
Hz
The Mean GHSV (see above), but Reduced evaluated at a temperature of 273 K and a pressure of 1.013 bar.
Inlet Redox Ratio
-
Inlet RR is the amount of oxygen Reduced required for full oxidation of carbon and hydrogen divided by the amount oxygen available in the gas-phase. page [98] Refer to Eq.318 .
Inlet Excess Oxygen Ratio
-
is the amount of oxygen available in the gas-phase divided by the amount of oxygen required for full oxidation of carbon and hydrogen. page [98] Refer to Eq.319 .
Reduced
Inlet Engine Lambda
-
Evaluated according to Brinkmeier page [95] [10 ], where a fuel CHx ratio of x=1.814 is assumed and the mole fraction of oxygen in air is assumed to be 0.2095. page [98] Refer to Eq.320 .
Reduced
Converter Pressure Drop
Pa
Difference between absolute pressure at element's inlet and outlet.
Reduced
Ambient Temperature
K
Temperature of the ambient gas around the element.
Reduced
Radiation Sink Temperature
K
Temperature of the radiation sink around the element (Variable Wall Temperature Model).
Reduced
Cumulative Inlet Heat Flow
J
Integrated result of the inlet heat Reduced flow summarized from the beginning of the simulation up to the current time point.
Cumulative Outlet Heat Flow
J
Integrated result of the outlet heat Reduced flow summarized from the beginning of the simulation up to the current time point.
Mean Continuity Source
kg/(m ·s)
Mean Energy Source
Cumulative Mass Flux In
3
Mean value of all gas phase mass sources throughout the converter at each time point.
Source
W/m
Mean value of all gas phase energy sources due to chemical reactions throughout the converter at each time point.
Source
kg
Integrated result of the inlet Reduced species fluxes summarized from the beginning of the simulation up to the current time point:
3
FIRE BOOST Aftertreatment
291
5. BOOST Aftertreatment
292
Cumulative Mass Flux Out
kg
Integrated result of the outlet Reduced species fluxes summarized from the beginning of the simulation up to the current time point:
Injection Mass Flux
kg/s
Total injected mass per time unit.
Reduced
Cumulative Injector Mass
kg
Accumulated total mass injected into the system over time.
Reduced
Mean Wallfilm Temperature
K
Mean temperature of the wall film. (Wallfilm model)
Reduced
Total Wallfilm Mass
kg
Total mass stored in the wall film. (Wallfilm model)
Reduced
Wallfilm Surface
m²
Total surface area of the wall film. (Wallfilm model)
Reduced
Wallfilm Volume
mm³
Total volume of the wall film. (Wallfilm model)
Reduced
Total Wallfilm Evaporation Mass Flux
kg/s
Mass evaporating from the wall film per time unit. (Wallfilm model)
Reduced
Overall Friction Coefficient
-
Total friction (weighted sum of Turbulent and Laminar Friction Coefficients).
Reduced
Turbulent Friction Coefficient
-
Turbulent Friction Coefficient.
Reduced
Laminar Friction Coefficient
-
Laminar Friction Coefficient.
Reduced
Reynolds
-
Reynolds number
Reduced
Gas Wall Heat Flow
W
Mean heat transfer from the gas to the wall throughout the element at each time point.
Reduced
Cumulative Gas Wall Heat Flow
J
Integration of the result above, Reduced from the beginning of the simulation up to the current time point. This resembles the energy transferred from the gas to the wall.
Gas-Wall Heat Transfer Coeff W/(m²·K)
Mean heat transfer coefficient.
Reduced
Nusselt
Nusselt number, ratio of convective to conductive heat transfer.
Heat flow from the wall to the Reduced ambient summed-up over the entire element outer surface and considering convective and radiation heat losses.
Convec Wall-Amb Heat Flow
W
Convective heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Reduced
Radiat Wall-Amb Heat Flow
W
Radiation heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Reduced
Overall Cumulative Wall-Amb Heat Flow
J
Cumulated heat flow from the wall Reduced to the ambient summed-up over the entire element's outer surface and considering convective and radiation heat losses.
Convec Cumulative Wall-Amb J Heat Flow
Cumulated convective heat flow from the wall to the ambient summed-up over the entire element's outer surface. (Variable Wall Temperature Model)
Radiat Cumulative Wall-Amb Heat Flow
J
Cumulated radiation heat flow from Reduced the wall to the ambient summedup over the entire element's outer surface. (Variable Wall Temperature Model)
Overall External Heat Source
W
External heat source added to the element's solid substrate summedup over the entire substrate volume.
Wall-Ambient Heat Trans Coeff
W/(m ·K)
Heat transfer coefficient of the wall- Reduced ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Overall
-
Ratio of overall convective heat transfer to conductive heat transfer of the wall-to-ambient heat transfer.
Reduced
Prandtl
-
Dynamic viscosity multiplied with heat capacity divided by heat conductivity of the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Grashof
-
Ratio of the buoyancy force to the viscous force acting on the ambient fluid surrounding the element. (Variable Wall Temperature Model)
Reduced
Reynolds
-
Fluid velocity multiplied with characteristic length divided
Reduced
2
FIRE BOOST Aftertreatment
Reduced
Reduced
293
5. BOOST Aftertreatment by kinematic fluid viscosity of the ambient fluid surrounding the element. (Variable Wall Temperature Model) Nusselt Free Convection
294
-
Ratio of free convective heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Reduced
Nusselt Laminar Forced Conv -
Ratio of laminar forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Turbulent Forced Conv
-
Ratio of turbulent forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Nusselt Forced Convection
-
Ratio of overall forced convective Reduced heat transfer to conductive heat transfer of the wall to ambient heat transfer. (Variable Wall Temperature Model)
Gas Temperature
K
Temperature of the gas phase.
Standard
Solid Temperature
K
Axially resolved temperature of the solid substrate.
Standard
Wall Temperature
K
Axially resolved temperature of each wall layer (i.e. radial grid point of the wall). (Variable Wall Temperature model)
Standard
Velocity
m/s
Interstitial velocity inside the Standard channels of the catalyst. In case of a particulate filter the velocity inside the channels of the surrogate catalyst (monolith with removed plugs).
Pressure
Pa
Absolute pressure at each axial output point.
Standard
Mass Fraction
kg/kg
Gas species mass fractions at each axial output point.
Standard
Mole Fraction
mol/mol
Gas species molar fractions at each axial output point.
Standard
Redox Ratio
-
See Inlet Redox Ratio
Excess Oxygen Ratio
-
See Inlet Excess Oxygen Ratio [ ] .
Engine Lambda
-
See Inlet Engine Lambda
page [
]
page [
FIRE BOOST Aftertreatment
Standard
. page
]
.
Standard Standard
5. BOOST Aftertreatment 3
Mass Density
kg/m
Mass based density of the gas mixture.
Property
Molar Mass
kg/kmol
Average molar Mass of the gas mixture.
Property
Molar Concentration
kmol/m
Mole based density of the gas mixture.
Property
Heat Capacity
J/(kg·K)
Heat capacity of the gas phase.
Property
Enthalpy
kJ/kg
Enthalpy of the gas phase.
Property
Conductivity
W/(m·K)
Thermal conductivity of the gas phase.
Property
Viscosity
Pa·s
Viscosity of the gas phase.
Property
Inner Heat Transfer Coeff
W/(m ·K)
Heat transfer coefficient between gas phase and solid substrate.
Property
Mass Transfer Coeff
m/s
Mass transfer coefficient between gas bulk phase and substrate surface.
Property
Reynolds (Re)
-
Gas velocity multiplied with hydraulic diameter divided by kin. gas viscosity (ratio of inertial to viscous forces).
Property
Prandtl (Pr)
-
Dyn. gas viscosity multiplied with gas heat capacity divided by gas heat conductivity (ratio of momentum diffusivity to thermal diffusivity).
Property
Schmidt (Sc)
-
Kin. gas species viscosity divided by gas species diffusion coefficient (ratio of momentum diffusivity to mass diffusivity).
Property
Nusselt (Nu)
-
Gas heat transfer coefficient multiplied with characteristic length divided by gas heat conductivity (ratio of convective to conductive heat transfer).
Property
Sherwood (Sh)
-
Gas species mass transfer coefficient multiplied with characteristic length divided by gas species diffusion coefficient (ratio of convective to diffusive mass transfer).
Property
Peclet Heat Transfer
-
Peclet number for thermal diffusion (Re·Pr).
Property
Peclet Mass Transfer
-
Peclet number for mass diffusion (Re·Sc).
Property
2
3
FIRE BOOST Aftertreatment
295
5. BOOST Aftertreatment External Heat Source
W
Energy input coming from an external heat source, axially resolved.
GHSV
Hz
See Mean GHSV
Mass Flux
kg/s
Gas phase mass flux.
Flux
Energy Flux
W
Enthalpy flux of the gas phase.
Flux
Hom. Reaction Rate Energy
J/(m ·s)
Hom. Reaction Rate Species
kg/(m ·s)
3
3
page [
]
.
Property
Flux
Energy source due to chemical Source reactions, i.e. rate of heat produced/ consumed by the sum of all chemical reactions (per total converter volume). Consumption/production rates of individual gas species due to chemical reactions (per total converter volume).
Source
5.3.5. Aftertreatment Boundary Results Inlet Boundary: Result Name
Unit
Description/Definition
Mass Flux
kg/s
Gas phase mass flux.
3
Volume Flow
m /s
Inlet gas phase volume flow if input is enabled at Inlet Aftertreatment Boundary.
Gas Temperature
K
Temperature of the gas phase.
Pressure
Pa
Absolute pressure at each axial output point.
Engine A/F Ratio
-
Inlet Engine Air/Fuel Ratio if input is enabled at Inlet Aftertreatment Boundary.
Engine Lambda
-
Inlet Engine Lambda if input of Engine A/ F Ratio is enabled at Inlet Aftertreatment Boundary.
Engine Lambda SAE-970514
-
Evaluated according to Silvis [80
Mass Fraction
kg/kg
Gas species mass fractions at the inlet.
Mole Fraction
kmol/kmol
Gas species mole fractions at the inlet.
Cumulative Mass Flux In
kg
Integrated result of the inlet species fluxes summarized from the beginning of the simulation up to the current time point:
Unit
Description/Definition
Outlet Boundary: Result Name 296
FIRE BOOST Aftertreatment
page [98]
].
5. BOOST Aftertreatment Mass Flux
kg/s
Gas phase mass flux.
Gas Temperature
K
Temperature of the gas phase.
Pressure
Pa
Absolute pressure at the outlet.
Engine Lambda
-
page
Evaluated according to Brinkmeier [10 ], where a fuel CHx ratio of x=1.814 is assumed and the mole fraction of oxygen in air is assumed to be 0.2095. page [98] Refer to Eq.320 .
[95]
Mass Fraction
kg/kg
Gas species mass fractions at the outlet.
Mole Fraction
kmol/kmol
Gas species mole fractions at the outlet.
Cumulative Mass Flux Out
kg
Integrated result of the outlet species fluxes summarized from the beginning of the simulation up to the current time point:
Overall Conversion
%
The overall conversion C of the species i is derived from its mass fractions at the inlet and the outlet boundary at each time step of the calculation:
5.3.6. Temperature Sensor Results All data from the aftertreatment analysis simulation are given as transient values. For each Sensor Channel selected at the Temperature Sensor a results folder is created which comprises the following standard results: Result
Unit
Description
Gas Temperature
K
Raw gas temperature from the connected element at the specified axial position. This temperature is the unaltered simulation result and input to the thermocouple calculation (cf. Temperature page [73] Sensor Model ).
Gas Velocity
m/s
Velocity of the gas at the axial position at which the gas temperature is measured.
Gas Density
kg/m
Density of the gas at the axial position at which the gas temperature is measured.
Gas Heat Capacity
J/(kg.K)
Heat capacity of the gas at the axial position at which the gas temperature is measured.
3
FIRE BOOST Aftertreatment
297
5. BOOST Aftertreatment Wall Temperature
K
Temperature of the pipe wall at the axial position at which the gas temperature is measured.
Substrate Temperature
K
Temperature of the monolith substrate at the axial position at which the gas temperature is measured.
Prandtl Number
-
Prandtl number at the axial position at which the gas temperature is measured.
Gas Heat Conductivity
W/(m.K)
Heat conductivity of the gas at the axial position at which the gas temperature is measured.
Gas Dynamic Viscosity
Pa.s
Dynamic viscosity of the gas at the axial position at which the gas temperature is measured.
Reynolds Number (Pipe Flow)
-
Reynolds number of the gas flowing through the pipe at the axial position at which the gas temperature is measured.
Reynolds Number (Channel Flow)
-
Reynolds number of the gas flowing through a converter channel at the axial position at which the gas temperature is measured.
Sensor Temperature
K
Measured gas temperature from the connected element at the specified axial position.
Solid Temperature (folder)
K
Temperature of the temperature sensor in each computational cell of the temperature sensor element.
Gas Velocity (folder)
m/s
Gas velocity along the temperature sensor axis considering the radial flow profile.
Gas Temperature (folder)
K
Gas temperature along the temperature sensor axis considering the radial flow profile.
Local Reynolds Number (folder)
-
Reynolds number of the gas flowing around the temperature sensor along the temperature sensor axis.
Local Nusselt Number (folder)
-
Nusselt number along the temperature sensor axis.
Heat Transfer Coefficient (folder)
W/(m .K)
2
Convective heat transfer coefficient along the temperature sensor axis.
5.3.7. Solver Results The Aftertreatment (ATM) Solver writes certain results related to its performance and stability. All data from the aftertreatment analysis simulation are given as transient values. The following standard results are available: Result
298
Unit
Description
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment Number of Jacobian Calculations
-
During the integration of the balance equation a Jacobian matrix is calculated. Depending on the changes the entire simulation model is experiencing during time integration a re-calculation of the Jacobian is required. The number of re-calculations is in general varying over the simulation time and it is also a measure for the computational effort. Typically there are a lot of Jacobian calculations in the very first time step, when the gas mass flow is evolving from initial condition zero to its value at the inlet boundary.
Number of Solver Steps
-
This is the number of steps the solver took for a time step.
Required CPU Time per Time Step
s
For each time step the time required by the CPU to solve the integration of the simulation model for that time step is measured.
Solver Time Step Size
s
The solver can vary the time step of the integration depending on certain conditions, like for example stiffness of the simulation model. This time step is independent of the Time Step Size entered by the User in the Simulation Control. The size of the solver time step is a measure for the changes the simulation model is experiencing: the smaller the time step the bigger the changes and vice versa.
Maximum Solver Time Step Size
s
The solver time step control is equipped with a time step limitation. It forces the solver not to exceed the maximum solver time step size.
Engine On(1)/Off(0)
-
The solver detects out of the inlet boundary conditions or when steered via related actuator channel whether engine is running (On, value 1) or whether it is shut-off (Off, value 0).
FIRE BOOST Aftertreatment
299
5. BOOST Aftertreatment Local Error in Time Step
-
Determines the size of the relative error the solver made in the last time step.
User Time Step Size
s
This is the time step size entered by the User in the Simulation Control.
Realtime Factor
-
This is the ratio of the CPU time required for the current time step to the current time step size. Values smaller 1.0 indicate that the simulation is faster than the (physical) realtime, whereas values larger 1.0 mean that the simulation is slower than realtime.
Inlet Boundary Condition This folder comprises the time derivatives of the inlet boundary conditions. Steep gradients usually require more computational Gradients effort and therefore more CPU time. Beyond that they are numerically challenging and can lead to convergence failures.
Workload Distribution
300
Gas Temperature Gradient
K/s
Time derivative of the inlet gas temperature.
Mass Flux Gradient
kg/s
Time derivative of the inlet gas mass flux.
Mass Fraction Gradient Gas Species
1/s
Time derivative of the inlet gas mass fraction of Gas Species.
-
This folder comprises the relative workload distribution of each element (Catalyst, Particulate Filter, ...) in the simulation run. The workload distribution is calculated as the CPU time spent on the element specific functions divided by the total CPU time spent on all element. The element specific functions considered are related to preprocessing (which reflects a none-zero workload distribution at time equals zero), time integration and postprocessing (i.e. result preparation).
2
FIRE BOOST Aftertreatment
5. BOOST Aftertreatment
5.4. Simulation Messages This section summarizes messages from the BOOST Aftertreatment simulation and provides hints for errors handling.
5.4.1. Message Analysis MESSAGES: Displaying messages after the calculation process allows the user to check for information, warnings and errors generated by the solver. Select Simulation | Show Messages to open the Message Browser as shown in the following window: Figure 62. Message Analysis Window
From the Sorted by pull down menu, select Message Type, Message ID, Element Name or Position for the desired display. Select the respective values in the Start from and End at pull down menus to display messages occurring within a certain crank angle interval. The global information is shown and more detailed information can be shown by clicking with the mouse. Click the expand button + to show the detailed information in the folder. In a steady-state engine simulation it is strongly recommended to check the messages from the main calculation program displayed during the last calculated cycle. If major irregularities have occurred, it is essential to check whether the calculation results are plausible. 5.4.1.1. Message Description Messages generated by the BOOST solver consist of a message header followed by text giving more detailed information. The format and components of the message header are described as follows: DEGCRA or in case of simulation task "Aftertreatment Analysis"
