Lecture 4: Discrete Phase Modeling (DPM) 15.0 Release
Advanced Combustion Training
Outline •
Solid and liquid fuels and modeling approaches
•
Discrete Phase Model (DPM) overview – – –
• • • •
Physical Processes and Coupling Injections/particle Injections/particle Types Incorporating turbulence
Evaporating liquid fuel droplets and spray modeling Solid particle combustion Best practices for DPM reactive flows Appendices – – – –
A: Examples B: Post-processing C: Atomizer Models D: Breakup and Coalescence models
Solid and Liquid Fuels •
Solid fuels –
•
Types of solid material used as fuel to produce energy
–
Consists of volatiles, char, moisture and ash
–
Examples: Coal, Biomass, Tires, Waste ……
Liquid fuels –
–
–
Hydrocarbons existing in the liquid form at room temperature Fumes (vapor) of liquid fuels are flammable instead of liquid itself Examples: Petroleum (gasoline, diesel, kerosene), CNG, biodiesel, ethanol, methanol ……
Modeling Approaches Discrete Phase Model (DPM) • •
Volume loading less than ~10 % Liquid droplets or solid particles tracked in Lagrangian reference frame
Multiphase Models • • •
Euler-Euler (E-E) model for gas-liquid flows Euler-Granular (E-G) model for gas-solid flows Volume of Fluids (VOF) model when gas-liquid interface needs to be captured
Dense DPM (DDPM) •
Lagrangian tracking with volume blockage considered in Eulerian reference frame
Discrete Element Method (DEM) •
Lagrangian Lagrangian tracking with particle collision using DEM
DPM for Solid or Liquid Fuels •
•
Liquid Fuels –
Internal combustion engines
–
Gas turbines
–
Liquid rocket engines
–
Oil fired boilers
–
Scrubbers, etc.
Solid Fuels –
Pulverized coal/biomass fired boilers
–
Entrained flow gasifiers
–
Flash calciners, etc.
Lagrangian Particle Tracking (DPM): Overview Continuous Phase Flow Field Calculation
Particle Trajectory Calculation
Update Continuous Phase Source Terms
Particle Trajectory Mass, Momentum and Heat Exchange
= ∅ ∅ =
•
Two way coupling: Continuous phase source term ( SDPM) updated
•
One way coupling: SDPM = 0
Particle Tracking •
Particle injection
•
Particle motion – –
•
Gives velocity and new location of particle
governs Δt governs
the accuracy and speed of calculation
Particle reaching boundaries – – –
Surface
Hollow Cone
Force balance Integration over time •
–
Single
Group
Outlet: escape Walls: trapped, reflect Incomplete
= = −∆ + =
+ = ∆
−∆
−∆
Heat and Mass Transfer •
Heat transfer
•
Mass transfer
= ∞ = = . .
–
Due to Type evaporation/boiling/devolatilization/heterogeneous-reactions evaporation/boiling/devolatilizatio n/heterogeneous-reactions Particle Heat and Mass Transfer Tr ansfer Mass-less Inert Droplet
Multi-component Multi-compo nent Combusting
No drag! Used for Residence Time Distribution Studies Inert Heating and Cooling Heating, Evaporation and Boiling Multi-component Multi-comp onent evaporation Heating, Devolatilizatio Devolatilization n and heterogeneous reaction
Particle Life Cycle •
The Entry State –
•
•
Properties updated to the values at the exit from the Previous Cell
The particle is tracked through the Current Cell based on Δt The Current State –
The Exit State (Entry State to next cell)
•
Particle reaches boundary
•
During it’s motion, particle can
–
Entry State
Properties are updated at every tracked position
•
–
Previous Cell
Exchange mass, momentum and heat with continuous phase Change composition
Injection State
Current Cell Current State
Exit State (Entry to next cell) Particle Reaching Boundary Boun dary
Particle Tracking Options •
•
•
Steady particle tracking with steady state solution Unsteady particle tracking with steady flow Unsteady particle tracking with unsteady flow –
–
Same particles and continuous phase time step size
Different particles and continuous phase time step size
Steady Particle Tracking with Steady Flow •
DPM calculation at each N th continuous phase iteration
•
Particles tracked from injection point till final state/fate
•
Tracking parameters
•
•
–
Max. number of steps and
–
Length scale or step length factor
N
Integration time step is calculated as –
If length scale is specified
–
If step length factor is specified
∆ = ∗ ∆ ∆ = ∅
Calculations for a given particle continue till it escapes from the domain/reaches other fates/max no of steps reached
t*
Estimated time required for particle to traverse the current cell
Unsteady Particle Tracking with Steady Flow •
•
DPM calculation at each N th continuous phase iteration Each particle is ADVANCED ADVANCED from from it's last position in the previous DPM calculation –
For specified particle time step size ( t p ) •
–
–
With the integration time step calculated from tracking parameters parameters
For J For J number number of time steps Along with Injection mass flow rate, this determines the mass of parcels that are introduced in the system.
N J
t p
Unsteady Particle Tracking with Unsteady Flow Different time step size for particles and continuouss phase continuou •
DPM calculation – –
•
At the beginning of each flow time step Also at N th continuous phase iteration within the same time step if N < < N per_time_step
During each DPM calculation –
Particles are ADVANCED ADVANCED from from their position in the previous flow time step •
• •
Till they move to their new positions at the end of current flow time step With specified particle time step size ( t p ) Therefore, number of DPM time steps in a flow time step = t flow / t p
N t p
Unsteady Particle Tracking with Unsteady Flow Different time step size for particles and continuouss phase continuou Particle injection at •
Particle Time Step –
–
•
Injecting particles at each particle time step size Integration time step is the specified particle time step
Fluid Flow Time Step –
–
Injecting particle in each flow time step Integration time step is the specified particle time step
Unsteady Particle Tracking with Unsteady Flow Same time step size for particles and continuouss phase continuou •
DPM calculation – –
•
At the beginning of each flow time step Also at N th continuous phase iteration within the same time step if N < < N per_time_step
During each DPM calculation –
Particles are ADVANCED ADVANCED from from their position in the previous flow time step •
•
•
Till they move to their new positions at the end of current flow time step With flow time step size ( t flow ) Therefore, number of DPM time steps in a flow time step = 1
N
DPM Calculation - Steady Flow Continuous phase calculation
Freeze the continuous phase flow field
Seed the particle at the current injection point Compute time step size based on local cell velocity
Integrate particle equation of motion
Seed the next particle
No
Yes
Yes End of particle list?
No Particle fate changes?
DPM Calculation - Unsteady Flow Continuous phase time step/iteration step/iteration calculation
Particle at its current location Compute time step size based on local cell velocity
Next particle at its current location
Integrate particle equation of motion
No Yes
Yes End of particle list?
No Particle changes fate?
Update the particle location
Source Calculations •
Effect of Under-Relaxation Factor (URF) –
DPM source terms calculated and updated at every particle DPM iteration/time step •
•
# of particle iterations required for achieving full source term increases with decrease in URF Must use URF of 1 if only one particle iteration is done in a time step –
•
Calculations may not be stable in some cases
Effect of update DPM Sources Every Flow Iteration –
Useful for unsteady calculations •
Particle source terms calculated every DPM iteration and updated every continuous phase iteration
=
Injections •
Injection panel provides initial information about –
•
Location, Velocity, Temperature, Start time, Diameter, Composition, Flow rate, Stop time
Several types of injection definitions available –
Direct specification of initial conditions •
–
Single, Group, Surface, Cone, etc.
Automated computation of initial conditions based on the injector geometry •
Atomizer Models
•
Specifically to characterize liquid sprays
•
More details in the Appendix
Single Group Cone
Surface
Turbulent Dispersion Models •
•
•
When particles enter a turbulent eddy, they try to follow it for the time they are crossing the eddy This effect leads to lateral dispersion which has to be considered in modeling Two approaches are available –
Discrete random walk model (Stochastic Tracking)
–
Particle cloud model (Cloud Tracking)
Stochastic vs. vs. Cloud Tracking •
Stochastic tracking –
–
–
•
Accounts for the effect of turbulence on particle dispersion. Sufficient number of tries (possible trajectories) required for smooth distribution of the source terms Recommended for use in complex geometry
Cloud tracking –
–
–
Local variations in flow properties (e.g. temperature) get averaged out inside the particle cloud Smooth distributions of particle concentrations and coupling source terms
Each diameter size requires its own cloud trajectory calculation
Evaporating Liquid Fuel Droplets 15.0 Release
Advanced Combustion Training
Modeling Modeling Physical Processes Vapor reacting in gas phase ph ase Fuel evaporation and boiling
•
Droplet combustion steps –
Inert heating •
–
Evaporation •
–
T p < T Evaporation T boil < T < T p < T Evaporation
Boiling • •
T p = T boil M p > 0
T e r boil e u s t a a r h e T evap P p s m a e G T T inj
Boiling Evaporation Inert heating Particle residence time
Evaporating Particle Models •
Diffusion Controlled (Default)
= , ,∞
, = ; ,∞ = ∞ = , = . . . . –
•
For low evaporation rates
Convection/Diffusion Controlled
= ∞ = , ,,∞
–
•
For higher evaporation rates
Requires accurate specification of saturation pressure and diffusion coefficients
Evaporating Particle Models (cont…) •
Boiling
•
= , . , −
Many sub models are available in the DPM panel –
Temperature dependent latent heat option
–
Pressure dependent boiling
–
Breakup of droplets
Spray Modeling •
Atomizer Model – –
•
Injection Types – – –
•
Plain-orifice atomizer Pressure-swirl atomizer
Solid Cone Hollow Cone Special Spray Shapes
Spray
Droplet Breakup Models – – –
–
Taylor Analogy Breakup (TAB) Wave Kelvin-Helmholtz Kelvin-Helmholtz waves driven by aerodynamic forces with Rayleigh-Taylor (KHRT) Stochastic Secondary Droplet (SSD)
Penetration Penetration length
Spray Modeling (cont…) Additional models •
Droplet collision and coalescence
•
Dynamic drag law
•
Rosin-Rammler particle distribution
•
Time varying injection velocity
•
Wall-film model
•
Turbulence dispersion of particles
PW6000
Solid Particle Combustion 15.0 Release
Advanced Combustion Training
Solid Fuel Combustion Water vapor Drying Moisture Residuals
Ash
Volatiles
Devolatilization/ Devolatiliz ation/ Pyrolysis H2, CH4, CO, CO2, H2O, Tar...
Char Gasification/Combustion
•
Applications –
Furnaces, Boilers, Incinerators (waste-to-heat), Gasifiers (production of syngas)
Modeling Physical Processes •
Drying
Particle combustion steps –
Inert heating •
–
Volatiles
Ash
Devolatilization
Char
M p > (M (M0 - Mmoisture)
Devolatilization •
–
Sensible Heating
T p < T Evaporation
Drying (Moisture release) •
–
Moisture
M p > (M0 - Mmoisture - Mvol )
Combustion •
M p > (M0 - Mmoisture - Mvol - Mcomb)
– Inert heating
Combustion
T exit e r u t aT r e devol pT m boil eT T evap
T inj
Inert heating Combustion Devolatilization Inert heating Boiling Evaporation Inert heating
Mass Transfer Laws •
Evaporation and boiling of moisture –
•
•
Same as droplet evaporation and boiling
Devolatilization –
Constant rate model (default)
–
Single kinetic rate model
–
Two competing rates model (Kobayashi model)
–
CPD (Chemical Percolation Devolatilization) Devolatilization) model
Char combustion –
Diffusion-limited rate model (default)
–
Kinetics/diffusion-limited rate model
–
Intrinsic model
–
CBK (Carbon Burnout Kinetic) model (beta)
–
Multiple surface reactions model
Model Set-up Species transport model • • • • •
Switch on turbulence model Switch on species transport model Enable volumetric reaction Select FR/ED or ED model Set up solid fuel properties using coal calculator –
•
Mixture material would be set up automatically
Set up boundary conditions
Non-premixed model •
• •
Can also be used for modeling solid combustion Set up using coal calculator One or two mixture fraction option
Injection Set-up • • •
•
•
Set up the injection type Select particle type as Combusting Particle material name would be set as that specified in the coal panel, automatically* automatically * Set devolatilizing, oxidizing and product species Switch ON Wet combustion model – – –
•
Liquid fraction would be set automatically* automatically * Select H 2O as evaporating species Droplet material would be added in the materials panel
Set up point properties and turbulent turbu lent dispersion model *Assuming material set up is done using coal calculator
Best Practices 15.0 Release
Advanced Combustion Training
Fuel Injections •
•
•
Cone injection for liquid fuel with enough number of streams to define the spray Surface injection with Rosin Rammler distribution for solids (coal, biomass, etc.) Fuel using an external file (File injection)
(( x y z u v w diameter temperature mass-flow) name )
Checklist •
Evaporating particle properties –
Evaporation temperature temperature for droplets is slightly higher than the particle injection temperature
–
Make sure that the following properties are properly prescribed •
•
Saturation vapor pressure, Binary Diffusivity, Latent Heat, Boiling Point, Specific heat
Combusting particle properties –
–
–
Devolatilization temperature temperature for combusting particle is set higher than boiling temperature of droplet material Volatile and char fraction are specified on dry basis If char is oxidized to CO, burnout stoichiometry ratio and heat of reaction for burnout are modified accordingly •
Default values are for char oxidizing to CO 2
–
Wet combustion liquid fraction is on volume basis
–
For the multiple char reaction model, the solid species mass fractions are defined in the
Some Tips & Tricks •
Solution Controls –
Default Under Relaxation Factors (URFs) •
Fine for simple cases
•
Too aggressive for complex cases –
–
Solution can become unstable
Effect of under relaxation is highly non-linear •
Under-relax density when using the mixture-fraction PDF model (~0.7)
•
Under-relax velocity for high buoyancy flows
•
Under-relax species, energy to start up the solution (~0.9) –
Once solution is stable, attempt to increase species, energy, mixture and r adiation URF’s to 1
Some Tips & Tricks (cont…) For better convergence in steady state analysis •
Start with non-reacting flow without radiation (first order solution) –
• • • •
Patch higher temperature (~1500-2000K) in the flame region Do 1 iteration with continuous phase iteration per DPM iteration set to 1 Set required required DPM iteration frequency (25 or more) Run reacting flow calculation with lower species and energy with underrelaxation factors (URF) ~ 0.9 –
• • •
Gradually ramp up these URFs to 1
Reduce the DPM URF for non-converging simulations (~ 0.1 or lower) Include radiation (DO radiation model is recommended) Include particle-radiation interactions – –
•
Disabled reactions, radiation equations and fluid-particle interaction
Coupled heat and mass solution option May need to lower energy URF
Solve until mass/energy balance is obtained and solution monitors stabilize
Some Tips & Tricks (cont…) Some general notes on convergence •
Often the problem in converging a combustion simulation is related to the high source term generated in certain cells –
Distribute these sources more evenly •
•
•
•
• • • • •
Increase the number of DPM stochastic tries Note that this will increase the CPU time Increase the number of gas phase iterations per DPM iteration
Residuals should be less than 10 -3 except for Energy, radiation and mixture fraction, which should be less than 10 -6 The mass and energy flux reports must balance Monitor variables of interest (e.g. mean temperature at the outlet) Solution is stable and not changing if the case is run further Ensure contour plots of field variables are smooth, realistic and steady Ash tracking may increase the DPM tracking time –
Can be removed via a UDF
Node Based Averaging •
Volume fraction standard average
Node based averaging of DPM source terms and DDPM volume fraction – Standard averaging dumps all volume fraction into
0.013
one cell
– Node based averaging distributes volume fraction
over several cells by collecting data on mesh nodes
– Several methods available – Strongly reduces grid dependency – Improves convergence behavior for steady
0.0
simulations
– Allows for larger time steps in transient simulations – Requires more memory
Volume fraction
Source Term Linearization •
Robust source term linearization for momentum, energy, and species with respect to cell variable
,∅ = ,∅
•
Can be combined with Node Based Averaging for simulations without mass transfer
Summary •
Solid and liquid fuels and modeling approaches
•
Discrete Phase Model (DPM) overview
•
Evaporating liquid fuel droplets and spray modeling
•
Solid particle combustion combustion
•
Best practices for DPM reactive flows
•
Appendices –
A: Examples
–
B: Post-processing
–
C: Atomizer Models
–
D: Breakup and Coalescence models
Appendix - A: Examples 15.0 Release
Advanced Combustion Training
Example-1: Spray in a Port-Injection Engine • •
Fluent dynamic mesh is used to model the moving valve DPM and spray model is used in conjunction with the dynamic mesh model
Spray Images
Wall Film Images
Wall Film Images
Example-2: Spray in a Diesel Engine •
A Caterpillar engine is used to demonstrate the spray in a directinjection diesel engine –
•
•
•
A 60 degree sector is used due to the symmetric geometry and injections injections
Fluent dynamic mesh is used to model the moving piston DPM and spray model is used in conjunction with the dynamic mesh model Particle and vapor fraction are plotted together
Case Study 2: Spray Images
Example-3: Spray Modeling in a Diesel injection •
Injector: Proprietary – – – –
•
Spray chamber: – – –
•
Seven holes Injection pressure = 1600 bar Orifice diameter = 0.167 mm Injection profile is given
air inlet (T = 710 K, p = 5 MPa)
quartz glass window
pressure chamber common-rail injector
incident beams liner
100 mm
outlet
Air flow velocity = 0.05 m/s Air temperature = 710 K Air pressure = 50 bar
Fuel: EN 590 summer diesel fuel
SAE 2006-01-0241, Adjustment and Verification of Model Parameters for Diesel Injection CFD Simulation –
Prof. Dr. Winfried Waidmann, Fachhochschule Aalen, Aalen, Germany
–
Dr. Andreas Boemer, DEUTZ DEUTZ AG, Köln, Germany
Modeling Setup by Authors Models
Parameters
Comments
Solid cone injection
10 degree cone half angle
Primary break-up, value metered from the shadowgraphs
KH-RT breakup model
B0 = 0.61, B1 = 18, C3 = 2.5, c = 30
Secondary break-up
Droplet collision
Default
Necessary in combination with the secondary break-up model
Initial droplet diameter
0.167 mm
Identical to nozzle diameter
Fuel injection temperature
330 K
50 K below measured nozzle temperature
Aerodynamic drag
Dynamic drag coefficient
Includes droplet deforming due to aerodynamic forces
Injection velocity
Variable, max. 430 m/s
Calculated from measured time dependent mass flux (Figure 2)
Turbulent droplet dispersion
Default
Turbulent tracking of the droplets
Number of injected particle streams
500 parcels per time step
Distributes the discrete phase source terms onto the flow
Time stepping
50 ms
Corresponds to 0.5 degree of crank angle
Turbulence
Standard k, e-model
Turbulence model not varied
Fuel
N-Heptane
To represent the diesel fuel
Modeling Setup (Modifications) Models
Parameters
Comments
Solid cone injection
10 degree cone half angle
Primary break-up, value metered from the shadowgraphs
KH-RT breakup model
B0 = 0.61, B1 = 18, C3 = 2.5, c = 30
Secondary break-up
Droplet collision
Default
Necessary in combination with the secondary break-up model
Initial droplet diameter
Sqrt(C_D) * 0.167 mm
The discharge coefficient needs to be included
Fuel injection temperature
330 K
50 K below measured nozzle temperature
Aerodynamic drag
Dynamic drag coefficient
Includes droplet deforming due to aerodynamic forces
Injection velocity
430 / (C_D * Anozzle * Rholiq)
The discharge coefficient needs to be included
Turbulent droplet dispersion
Default
Turbulent tracking of the droplets
Number of injected particle streams
500 parcels per time step
Distributes the discrete phase source terms onto the flow
Time stepping
50 ms
Corresponds to 0.5 degree of crank angle
Turbulence
Standard k, e-model
Turbulence model not varied
Fuel
C12H26
A better representation for spray modelling
Results: Shape of the Spray Experimental
Simulation
Results: Penetration Length
Results: Drop Size Distribution
Measuring planes
Example-4: 2550 TPD Coal Gasifier •
Two stage, up flow, prototype entrained flow gasifier
•
Operating pressure
2.84 MPa
Proximate Analysis
Post processing surface
Ultimate Analysis (DAF)
Volatiles
30.84 %
Carbon
79.22 %
Fixed Carbon
42.85 %
Hydrogen
5.55 %
Ash
11.23 %
Oxygen
9.7 %
Moisture
15.28 %
Nitrogen
1.65 %
HHV, HHV, J/kg (As received)
2.476e+07
Sulfur
3.38 %
Coal, water and oxygen inlets Oxygen + Nitrogen Oxygen mass fraction
2 X 11.44 kg/s, 440K 0.944
Fuel (Combustible Discrete Phase)
2 X 10.93 kg/s, 450K
Water (Evaporating Discrete Phase)
2 X 4.53 kg/s, 450K
Coal, water inlet Fuel (Combustible Discrete Phase)
6.17 kg/s, 450K
Water (Evaporating Discrete Phase)
2.56 kg/s, 450K
Models • • •
Turbulence : Standard k- ɛ model Gas Phase: Eulerian Solid phase: Lagrangian –
Moisture vaporization •
–
Coal Devolatization •
–
•
Two-competing rates model
Char oxidation and gasification reactions •
•
Convection/Diffusion Controlled Model
Multiple particle surface reaction model
Radiation: Discrete Ordinate Reaction: Eddy dissipation/finite rate model – –
9 gas phase reactions 4 particle surface reactions
Results: Contours
Temperature (K)
Velocity (m/s)
Syngas Composition at Outlet
Appendix - B: Post-processing of Particle Variables 15.0 Release
Advanced Combustion Training
Time Statistics of Particle Variables •
Ability to post process DPM variables –
Mean and RMS values for transient simulations
Time Statistics of Particle Variables •
Data sampling for Time Statistics of DPM post processing variables
Time Statistics of Particle Variables •
Accum Provides accumulated values within a cell n p
accum
t r esidence
p
time steps p i n cell
•
Mean
•
Accum results can be used to assess statistical errors
t r esidence p
ti m e steps p in ce cell
n p ti m e steps p in cell cell
RMS
t flow sol ver ver
Distributes contribution of a parcel over all cells crossed within a time step
Provides mean averages n p
•
•
Averages over all particle events in the cell during sampling time for statistics
t flow solver t r esidence t flow sol ver ver
Provides RMS values
n p time steps p in cell
t r esidence t flow solver n p
2 p
t r esidence t
2
Appendix - C: Atomizer Models 15.0 Release
Advanced Combustion Training
Plain-Orifice Atomizer •
Pipe with a round hole
•
Three regimes
•
–
Single phase
–
Cavitating
–
Flipped
Liquid Jet
Orifice Walls
Downstream Gas
Inputs –
Atomizer location
–
Axis (3D)
–
Mass flow rate
–
Start and stop times
–
Vapor pressure
–
Inner diameter
–
Orifice length
–
Inlet corner radius of curvature
–
Spray angle Constant A
–
Azimuthal start and stop angles (3D)
Decreasing cavitation parameter
Vapor
K
Liquid Jet Vapor
Orifice Walls
Downstream Gas
Liquid Jet
Orifice Walls
Downstream Gas
p 1
p v
p 1
p 2
Pressure Swirl Atomizer •
•
Implemented Implemented Linearized L inearized Instability Sheet Atomization (LISA) model of Schmidt et al. (1999) Assumes that KH waves break the sheet up into ligaments which then break up into droplets due to varicose instability
Lb h dL d0
h0
User Inputs –
Atomizer location
–
Axis (3D)
–
Mass flow rate
–
Start and stop times
–
Inner diameter
–
Spray half angle
–
Upstream pressure
–
Sheet constant
–
Ligament constant
–
Azimuthal start and
–
Stop angles (3D)
Air-Blast Atomizer •
•
Additional air is directed through the nozzle, leading to smaller droplet diameters Modeled as a variation of pressure-swirl atomizer
User Inputs: – – – – –
Gas Flow
Initial Angle
Inner Diameter
Liquid Flow
Outer Diameter
– – –
– – –
•
Note: Gas flow is NOT setup for you automatically
–
Atomizer location Axis (3D) Mass flow rate Start and stop times Inner diameter Outer diameter Spray half angle Maximum relative velocity between central air and sheet Sheet constant Ligament constant Azimuthal start and stop Angles (3D)
Flat-Fan Atomizer •
•
Liquid enters as a flat sheet
Sheet breakup is taken from pressureswirl atomizer
Normal vector 2
Virtual origin
Center point
User Inputs: –
Atomizer location
–
Axis (3D)
–
Normal (3D)
–
Mass flow rate
–
Start and stop times
–
Spray half angle
–
Orifice width
–
Flat fan sheet constant
Effervescent Atomizer •
Super-heated or very hot liquid is discharged
•
User Inputs: – –
•
•
Liquid is evaporating rapidly when leaving nozzle
– – –
A dense liquid core surrounded by a shroud of smaller droplets u
– –
•
m
•
C ct A
l
d m ax
–
d C ct 2
d 0
d e m ax
Atomizer location Axis (3D) Mass flow rate Start and stop times Inner diameter Vapor pressure Mixture quality Mass fraction of superheated Injected liquid that vaporizes Saturation temperature Dispersion constant Maximum Half Angle Azimuthal start and stop angles (3D)
S
– – –
Appendix - D: Breakup and Coalescence models 15.0 Release
Advanced Combustion Training
Secondary Spray Models •
•
Several advanced secondary spray models are available: –
Collision and Coalescence Model (O’Rourke)
–
Taylor Analogy Breakup (TAB) Model
–
Kelvin-Helmholtz Kelvin-Helmholtz (Wave) Breakup Model
–
KHRT Model
–
SSD Model
Dynamic Drag Model for Distorting Drops –
•
Since droplets do deform, it is important to use the right drag law
These models are fully compatible with the primary atomization models
Collision and Coalescence Model •
•
•
Particles move around and may collide with each other oth er The mean expected number of collisions between one drop in a parcel 1 with all droplets in parcel 2 is calculated from (O’Rourke, 1981) The probability distribution for the number of collisions of a drop in parcel 1 with all the drops in parcel 2 is Poisson Distribution
r 2 r 1
Collision and Coalescence Model (Cont…) •
What happens after collision? –
•
•
Droplets may bounce or coalesce
Head-on collision leads to coalescence Oblique collisions tend to bouncing depending on the Weber number and a critical offset
r 2 b > bcrit => bouncing •
The properties of the coalesced drops are determined from conservation laws while momentum conservation determines the velocity of grazing droplets –
•
r 1
Model is applicable only for We < 100
Only one collision per time step assumed
2
W e
u d p
p
Taylor Analogy Breakup (TAB) Model •
Raleigh-Taylor’s analogy between an oscillating, distorting droplet and a spring mass system (O’Rourke, 1981): –
Surface tension
–
Drag
–
Droplet viscosity
y •
External force C F C b
g l
u
2 2
r
Damping force C k 3
l r
y
C d l 2
l r
y
Droplet breaks up if distortion exceeds some level, then, energy balance balanc e is used to determine child drop size –
•
Spring restoring force
Number of drops from mass conservation
Child droplets have a velocity component normal to the parent p arent drop velocity
TAB Model (Cont…) •
•
•
After breakup, the number of DPM parcels remains constant, number of particles in a parcel increases and diameter decreases
Valid for low Weber number sprays (We<100) Validation done by comparing to the spray bomb experiments of Hiroyasu
10
8
] m c [ n o i t a r t e n e P
6
0.1MPa 1.1MPa 3MPa 5MPa TAB 0.1MP 0.1MPa TAB 1.1MP 1.1MPa TAB 3.0MP 3.0MPa TAB 5.0MP 5.0MPa
4
2
0 0
1
2
3
4
5
6
Wave Breakup Model •
•
•
Aerodynamic shear causes waves on droplet, unstable Kelvin-Helmholtz Kelvin-Helmholtz waves grow and small droplets stripped off Reitz (1987) derived from a jet stability analysis the maximum growth rate and corresponding wavelength The size of the child droplets is proportional to the fastest growing wavelength
Wave Model (Cont…) •
When a prescribed mass of droplets has been shed, a new particle forms
•
Applicable for high Weber number sprays
•
Validation done by comparing to experimental spray bomb data 10
8 ] m c [ n o i t a r t e n e P
6
0.1MPa 1.1MPa
4
3MPa 5MPa Wave 0.1 MPa
2
Wave 1.1 MPa Wave 3.0 MPa Wave 5.0 MPa
0 0
1
2
3
Time[ms]
4
5
Stochastic Secondary Droplet (SSD) •
SSD breakup methodology provides a statistically realistic model for simulating high Weber number sprays under diesel conditions –
–
–
–
Parameters for the size distribution are based on local conditions Liquid injected into the domain is represented by blobs with a known size (set by b y the user) The breakup model predicts the time at which breakup occurs, the number and properties of the new drops Drops larger than a critical radius, r c , are subject to breakup:
r c –
Wecr l 2
g u rel
The breakup time is defined as:
t bu
B
l
r
g
urel
Reference: –
Apte, et.al., “LES of atomizing spray with stochastic modeling of secondary breakup”, IJMF 29, 2003, pp 1503 -1522
Stochastic Secondary Droplet (SSD)
r c
t bu
W e cr
l 2 g r el
u
r
l
B g
u r el
Average NP for daughter parcels
