Compressors

Flow through Centrifugal & Axial Flow Compressors NITISH BHUSHAN ‐ IIT DELHI Tutor – Tutor – Prof S. Prof S. Sarkar

Outline of the Presentation 

Compressors   

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Centrifugal Compressors   

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Configuration Working Blade Types

Axial Flow Compressors 

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What is a Compressor? Why increase a Fluid’s Pressure? Classification

Configuration Basic Operation

Efficiency Centrifugal Compressor Performance Curve FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Outline of the Presentation   

Centrifugal Compressors – Compressors – Analysis Axial Flow Compressors – Compressors – Analysis Sizing Parameters  

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Losses in Compressors Centrifugal compressors vs. Axial Flow Compressors  

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Centrifugal Compressors Axial Flow Compressors

Advantages of Axial of Axial Flow Compressors Advantages of Centrifugal of Centrifugal Compressors

Summary References Acknowledgements FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Comp Compres ressor sors s - Wh What at is is a comp compres ressor sor? ? 

Machine to raise pressure of a of a fluid

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Uses several energy transformations

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1.

Input energy converted to rotating mechanical energy

2.

Rotating impeller increases fluid’s kinetic energy (velocity)

3.

Decrease in kinetic energy due to flow area expansion & increase in pressure energy

Energy inputs: electricity, high pressure steam, fuel oil, compressed air, etc.

FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Compressors – Why increase a Fluid’s Pressure? 1.

Static Elevation –

2.

3.

Friction –

Fluid moving through piping system experiences frictional losses

–

Pressure increased to overcome these losses

Pressure –

4.

Ex: from one floor of a of a building to a higher floor

Pressure increased for process reasons. Ex: to move fluid into pressurized vessel

Velocity –

Velocity leaving compressor higher than entering velocity FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Compressors - Classification A. Principle of Energy Addition 1.

2.

Kinetic –

Energy continuously added to increase velocity

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Pressure increased with reduction in velocity

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Most important part : CENTRIFUGAL COMPRESSORS

Positive Displacement –

Energy addition is periodic (not continuous)

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Direct application of force to fluid

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Causes an increase in pressure to required value FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Compressors -Classification B.

How Energy Addition is Accomplished

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Second level of classification Kinetic : Centrifugal pumps, regenerative turbines & special compressors PD: Reciprocating & Rotary compressors

• •

C. Geometry Used • • •

Third level of classification Centrifugal: Support of impeller, rotor orientation, pump bearing system, no. of stages Positive Displacement: many types of rotary & reciprocating pumps, each with a unique geometry FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal Compressor 

A centrifugal compressor is a radial flow rotodynamic fluid machine that uses mostly air as the working fluid and utilizes the mechanical energy imparted to the machine from outside to increase the total internal energy of the fluid mainly in the form of increased static pressure head. It is best suited to small units of comparatively low pressure ratio where overall diameter is not a restricting criterion.


Centrifugal Compressors Configuration A. Impeller: imparts high velocity to the fluid • The impeller inlet is called the inducer or ‘eye’ • The impeller has seals relative to a back plate • The impeller outlet is called the exducer • The impeller vanes at exducer may be radial or

backswept • Free vortex flow until leading edge of diffuser vanes • Flow has high degree of swirl (50o) – axial straightener

vanes


Centrifugal Compressors Configuration Schematic views of a centrifugal compressor

Rotating Impeller

Single Sided Impeller

Double Sided Impeller


Centrifugal Pumps - Configuration B. Casing I.

II.

Volute Casing: Single cutwater where flow is separated. Flow moving around volute casing produces net radial force that must be carried by shaft & radial bearing system. Double or twin compressor volutes produce near radial symmetry & balance the hydraulic radial loads on pump shaft Diffuser Casing: More complex casing arrangement consisting of multiple flow paths. Liquid enters the nearest flow channel in the casing. Multiple cutwaters are there, evenly spaced around the impeller.


• Advantage of Diffuser casing : Results in near balancing of

radial forces, thus eliminating the need for heavy‐duty radial bearing system. Thus, the radial bearing load is MINIMIZED • Disadvantage of Diffuser casing: Diffuser casing has generally more complex parts than volute casing. Thus, depending on the size of the compressor, economics often do not justify use of diffuser casing FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal Compressors - Working • Impeller rotating with shaft & casing that encloses

impeller • Fluid forced into inlet by upstream pressure • Fluid moves to discharge side as impeller rotates • This creates a void or reduced pressure at impeller

inlet • Pressure at compressor casing inlet forces

additional fluid into impeller to fill the void


Centrifugal Compressors- Working 

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After reaching impeller, fluid entering moves along impeller vanes, increasing in velocity as it progresses Fluid at impeller outlet tip is at Max. Velocity Fluid enters casing where expansion of cross sectional area occurs

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Diffusion process occurs – fluid’s velocity decreases

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Pressure of fluid increases (Bernoulli’s equation)


VELOCITY & PRESSURE LEVELS OF FLUID IN A CENTRIFUGAL PUMP

PRESSURE

PRESSURE OUTLET TIP OF IMPELLER VANE INLET TIP OF IMPELLER VANE

VELOCITY

VELOCITY

SUCTION

FLOW PATH

DISCHARGE


Centrifugal Compressors - Blade Types There are three impeller vane types defined according to the exit blade angles (Discharge Vane Angles) 

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Impellers with exit blade angle equal to 90 degrees are radial vanes Impellers with exit blade angle less than 90 degrees are backward‐curved or backward swept Vanes with exit blade angle greater than 90 degrees are known as forward swept vanes The forward‐curved blade has the highest theoretical head. Radial vanes represent a compromise between max pressure ratio, max efficiency & size FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal Compressors - Blade Types FORWARD CURVED

RADIAL

HEAD

BACKWARD CURVED

FLOW RATE


Axial Flow Compressors 

Axial compressors are rotating, aerofoil based compressors in which the working fluid principally flows parallel to the axis of rotation. This is in contrast with centrifugal, axi‐centrifugal and mixed‐flow compressors where the air may enter axially but will have a significant radial component on exit.


Axial Flow Compressors • Axial flow compressor is capable of higher pressure • • • • •

ratio on a single shaft. The energy transfer in a single stage is very limited (stage pressure ratio of about 1.2) But ease of combining axial flow stages leads to pressure ratios of upto 6/1 or even higher Thus axial flow compressor is considered as consisting of many stages Single stage is considered as a fan For most aircraft & industrial gas turbine, axial flow compressor is used in preference to radial flow type FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Axial Flow Compressors- Configuration • One stage comprises a row of rotor blades followed

by row of stator vanes • A no. of such stages with rotors on a common shaft

form the compressor • Often a row of Outlet Guide Vanes (OGVs) are

required downstream to carry structural load • Variable Inlet Guide Vanes may be employed • These are a row of stator vanes whose angle may be

changed to improve off ‐design operation


Axial Flow Compressors– Basic Operation • Working fluid initially accelerated by rotor blades, then

decelerated in stator blades where kinetic energy transferred in rotor is converted to static pressure • Many stages necessary for required overall pressure ratio • Flow always subject to adverse pressure gradient • Process consists of series of diffusions in both rotor &

stator blade passages • Careful design of compressor blading necessary to prevent

wasteful losses and minimize stalling • Flow reversals may occur at mass flow conditions different

from blade design conditions FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Flow through stages in Axial Flow Compressor


Efficiency • Isentropic efficiency is ratio of ideal specific work

input, or total T rise, for given pressure ratio to actual • Definition of isentropic is adiabatic+reversible • Total T rise & power input to sustain given P ratio is

proportional to inlet total temperature • Polytropic efficiency is isentropic efficiency of an

infinitesimally small compression step, such that its magnitude is constant throughout • Isentropic efficiency falls as pressure ratio is increased

for same polytropic efficiency FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Efficiency Isentropic efficiency ηc

ηc

= (T03s – T01)/(T03 – T01)


Centrifugal Compressor Performance Curve

• Lets analyse what will occur when a valve placed in the

delivery line of a compressor running at constant speed is slowly opened • The variation in pressure ratio is shown above FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal Compressor Performance Curve • Point A occurs when the valve is shut & mass flow is

zero. It corresponds to centrifugal pressure head produced by action of impeller on the air trapped between the vanes. • At point B, efficiency and pressure ratio approach maximum value. Further increase in mass flow will result in fall of pressure ratio. • For mass flows greatly in excess of design mass flow, air angles will be widely different from vane angles leading to breakaway of air & fall in efficiency. • The pressure ratio drops to unity at 'C' , when the valve is fully open and all the power is absorbed in overcoming internal frictional resistances FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal Compressor Performance Curve - Surging • The operating point 'A' could be obtained but a part of the curve •

•

•

•

between 'A' and 'B' could not be obtained due to Surging. Surging is associated with sudden drop in delivery pressure & with violent aerodynamic pulsation which is transmitted throughout the machine For any operating point D on the part of characteristics curve having a positive slope, a decrease in mass flow will be accompanied by a fall in delivery pressure. If the pressure of the air downstream of the compressor does not fall quickly enough, the air will tend to reverse its direction and will flow back in the direction of the resulting pressure gradient. When this occurs, the pressure ratio drops rapidly causing a further drop in mass flow until the point 'A' is reached, where the mass flow is zero. FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal Compressor Performance Curve - Surging • Surging starts to occur in the diffuser passages where • •

• • •

flow is retarded by frictional forces near the vanes Tendency to surge increases with number of diffuser vanes Several diffuser channels to every impeller channel – tendency for air to flow up one channel & down another (conditions conducive to surging) Only in one pair of channels the delivery pressure will fall & increase likelihood of surging Thus number of diffuser vanes is less than no. of impeller vanes Surging is then not likely to occur FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal Compressor Performance Curve- Rotating Stall • It is another important cause of instability & poor

• •

• • •

performance which can exist in the nominally stable operating range. A,B & C are three consecutive flow channels When there is non‐uniformity in flow or geometry of channels between vanes or blades, breakdown can occur in one channel (say channel B) Air deflects in such a way that C receives fluid at reduced incidence & A at increased incidence Channel A stalls which reduces incidence in B enabling flow in that channel to recover Rotating stall may lead to aerodynamically induced vibrations leading to fatigue failures in other parts FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal Compressor Performance Curve • There is an additional limitation to the operating range,

between 'B' and 'C'. As the mass flow increases and the pressure decreases, the density is reduced and the radial component of velocity must increase. • At constant rotational speed this means an increase in resultant velocity and hence an angle of incidence at the diffuser vane leading edge. • At some point say 'E', the position is reached where no further increase in mass flow can be obtained no matter how wide open the control valve is ‐ CHOKING • This point represents the maximum delivery obtainable at the particular rotational speed for which the curve is drawn.


Centrifugal Compressor Analysis


Centrifugal Compressor Analysis • No work is assumed to be done in the diffuser • Energy absorbed is determined by inlet and outlet

conditions at the impeller • Air enters the impeller in axial direction, so initial angular momentum is zero. • Vanes have a curved axial portion for smooth entry of air. • Nomenclature: 

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α ‐ angle made by the leading edge of the vane with the tangential direction. Vr1‐ relative velocity of air at the inlet V2‐ absolute velocity of air at the impeller tip Vw2‐ tangential/whirl component of V2 U‐ Impeller speed at the tip


Centrifugal Compressor Analysis • Under ideal conditions whirl component of V2 is equal to • • • •

the impeller tip speed U Due to inertia, air trapped between the impeller vanes doesn’t move round with the impeller. This results in a higher static pressure at the leading face than the trailing face. Slip Factor, σ takes into account this effect; σ = Vw2/U A widely used expression for σ suggested by Stanitz which is the most suitable to radial vaned impellers σ = 1 – (0.63π/n) where n is number of vanes


Centrifugal Compressor Analysis • Theoretical work done: σU2 • Due to friction between casing and air carried round by

• • • •

the vanes and other losses like ‘windage’, actual work input is greater than theoretical Power input factor ψ takes this into account actual work done = ψσU2 Typical values for ψ lie between 1.035 – 1.04 Stagnation Temperature represents the total energy held by the fluid. No energy is added in the diffuser, so, stagnation temperature rise across the impeller is that equal to the whole compressor. FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal Compressor Analysis 

Adiabatic work done is given by

w = Cp(T02 – T01) 

If stagnation temperature at the outlet of the diffuser is T03 then T03 = T02

p03 / p01 = [1 + ηc(T03‐T01)/T01]Υ/Υ‐1


Axial Compressor Analysis – Velocity Triangles


Axial Compressor Analysis • Air approaches rotor with velocity V1 at angle α1 • • • •

in axial direction Combining V1 vectorially with blade speed U gives velocity relative to blade Vr1 at angle β1 Fluid leaves rotor with relative velocity Vr2 at angle β2 Air leaving rotor at angle α2 then passes to stator where it is diffused to velocity V3 at an angle α3 Typical design is such that V3 = V1 & α3=α1 FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Axial Compressor Analysis • Assuming Vf =Vf1=Vf2 the following equations emerge

U/Vf = tan α1 + tan β1 U/Vf = tan α2 + tan β2 • Power input is given by W = mcp(T02 ‐ T01) & W = mU(Vw2 – Vw1) • The expression can be put in terms of velocity & air angles to give W = mUVf (tan α2 ‐ tan α1) or W = mUVf (tan β1 ‐ tan β2) FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Axial Compressor Analysis 

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This input energy will be absorbed usefully in raising pressure of air & wastefully in overcoming various frictional losses Regardless of losses, the whole of input will reveal as rise in stagnation temp. of air

ΔT0S = T03‐T01 = (UVf /cp)(tan β2 ‐ tan β1) 

Pressure ratio is then given by

p03/p01 = [ 1 + ηs(T03‐T01)/T01]Υ/Υ‐1


Sizing Parameters - Centrifugal Mean Inlet Mach number

1. •

This is the Mach number at compressor face

•

While it is desirable to have high inlet mach no. to minimize frontal area, this leads to high relative velocities at first stage blade tip, & inefficiency.

•

Values between 0.4 – 0.6 are common

Tip relative Mach number

2. •

Conservative & ambitious design levels are 0.9 & 1.3

•

For a centrifugal rear stage of an axi‐centrifugal compressor even lower values might be inevitable


Sizing Parameters - Centrifugal Rotational Speed

3. •

Must be set to maximize efficiency by optimising specific speed, keeping other parameters within target levels

Pressure ratio & no. of stages

4. • •

Highest pressure ratio from a single stage is 9:1, and from two stages 15:1 Owing to ducting difficulties, unusual to use more than two centrifugal stages in series

Backsweep

5. • •

For max efficiency, backsweep angle of 40o is practical However this results in increased diameter for given mass flow & pressure ratio FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Sizing Parameters - Centrifugal Rim Speed

6. •

Exducer rim speed should not exceed around 500m/s for aluminium & 625m/s for titanium

Exducer Height

7. • •

Initially set to achieve target relative velocity ratio from inducer tip to exit of 0.5‐0.6 This should be ideally optimized by rig testing

Exit Mach number & Swirl Angle

8. • •

Where bend & axial straighteners are employed, exit mach no. & swirl angle must be less than 0.2 & 10o If bend & axial straighteners are not employed, swirl angle will be of order of 50o


Sizing Parameters - Axial Mean inlet Mach number

1. • •

Common values lie between 0.4 & 0.6 Highest level for aero‐engines in supersonic applications

Tip Relative Mach number

2. • • • •

The highest tip relative mach no. will occur on the first stage Inlet absolute gas velocity will usually be axial & may be considered constant across the annulus Conservative & ambitious design levels are 0.9 & 1.3 The latter requires high diffusion relative to blade to achieve subsonic conditions, which increases pressure losses

Stage Loading

3. • •

Measure of how much work is demanded of the compressor or stage It is the enthalpy increase per unit mass flow of air, divided by blade speed squared (Dimensionless) FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Sizing Parameters - Axial • Efficiency improves as loading is reduced, but more stages are

required for given pressure ratio • Loading along the pitch line should be 0.25 to 0.5 4.

Pressure ratio & number of stages • Achievable pressure ratio for given no. of stages governed

most importantly by good efficiency • Higher the overall pressure ratio in a given no. of stages, & hence loading, lower the efficiency 5.

Hade Angle • Angle of the inner or outer annulus line to the axial • A hade angle of upto 10o , but preferably less than 50 may be

used for outer annulus • Inner annulus line angle should be kept to less than 10o FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Sizing Parameters - Axial Axial Velocity & Axial Velocity Ratio

6. • • •

Axial velocity ratio is the axial velocity divided by blade speed on the pitch line Axial component of velocity is normally kept constant throughout the compressor Axial velocity ratio is normally btw 0.5 & 0.75

Aspect Ratio

7. • •

Defined as height divided by vane or blade chord Typical design levels are 1.5 – 3.5

Exit Mach number & Swirl Angle

8. • • •

Must be minimized to prevent downstream pressure loss Mach no. shouldn’t be higher than 0.35 (ideally 0.25) Exit swirl angle should be less than 10O (ideally 0)


Losses in Compressors 

Frictional Losses 

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Major portion of the losses is due to fluid friction in stationary and rotating blade passages Flow in impeller and diffuser is decelerating in nature Frictional losses are due to both skin friction and boundary layer separation Depend on the friction factor, length of the flow passage and square of the fluid velocity

Incidence Losses 

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During the off ‐design conditions, the direction of relative velocity of fluid at inlet does not match with the inlet blade angle Hence, fluid cannot enter the blade passage smoothly by gliding along the blade surface The loss in energy that takes place because of this is known as incidence loss


Losses in Compressors  

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This is sometimes referred to as shock losses. However, the word shock in this context should not be confused with the aerodynamic sense of shock

Clearance and leakage losses 

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Certain minimum clearances are necessary between the impeller shaft and the casing and between the outlet periphery of the impeller eye and the casing The leakage of gas through the shaft clearance is minimized by employing glands. The clearance losses depend upon the impeller diameter and the static pressure at the impeller tip. A larger diameter of impeller is necessary for a higher peripheral speed and it is very difficult in the situation to provide sealing between the casing and the impeller eye tip.


Losses in Compressors –Dependence of various losses with mass flow


Losses in Compressors 

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The leakage losses comprise a small fraction of the total loss. The incidence losses attain the minimum value at the designed mass flow rate. The shock losses are zero at the designed flow rate. However, Incidence losses comprise both shock losses and impeller entry loss due to a change in the direction of fluid flow from axial to radial direction in the vaneless space before entering the impeller blades. The impeller entry loss is very small compared to other losses. This is why the incidence losses show a non zero minimum value at the designed flow rate. FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal vs. Axial Flow Compressors Advantages of Axial • Frontal area is lower for given mass flow & pressure

• • • •

ratio. For ex. at pressure ratio of 5:1, axial compressor diameter would be half of centrifugal Weight is less because of lower engine diameter For mass flow rates > 5kg/s, axial flow compressor has greater isentropic efficiency Magnitude of above advantage increases with mass flow rate Owing to manufacturing difficulties there is practical upper limit of around 0.8m on diameter of centrifugal impeller, hence mass flow & pressure ratio capability FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal vs. Axial Flow Compressors Advantages of Centrifugal • Over 9:1 pressure ratio achievable in a single stage. For axial flow

compressor this may take between six to twelve stages • Centrifugal compressors are significantly lower in unit cost for same

mass flow rate & pressure ratio • At mass flow rates < 5kg/s isentropic efficiency is better, as in this

flow range axial flow compressor efficiency drops rapidly as size is reduced due to increasing levels of tip clearance, blade leading & trailing edge thicknesses • Centrifugal compressor is significantly shorter for given mass flow. This

advantage increases with pressure ratio • Exit mach no. will be lower in centrifugal compressor, hence reducing

pressure losses in the downstream duct • Centrifugal compressors are less prone to Foreign object damage FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Centrifugal vs. Axial Flow compressors 

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Axial flow compressors dominate where low frontal area, low weight & high efficiency are essential Axial flow compressors are the only choice at large sizes Centrifugal compressors dominate where unit cost is paramount, and at small size. The reason for high efficiency in axial compressors: The gas experiences less drastic changes of direction as it progresses through the stages of an axial machine. The general flow path in an axial compressor is in a predominantly axial direction ,with minor perturbations through each blade row. In the centrifugal compressor ,there are two 180 degrees turns in each stage, in addition to a spiral shaped path in the radial plane of each impeller. The shorter ,straighter flow path of the axial results in lower turbulence and turning losses FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

Summary 

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Compressors are machines which raise the pressure of a fluid using various energy transformations In Centrifugal Compressors pressurization is achieved by the action of a rotating impeller and subsequent conversion of kinetic energy in static pressure head in the diffuser. In Axial compressors, pressure ratio is achieved by passing the fluid through stages of rotors & stators Optimum values of sizing parameters for both centrifugal and axial flow compressors were discussed Frictional, Incidence and Clearance & Leakage Losses for compressors were discussed Both centrifugal & axial compressors have their own advantages & limitations when compared against each other FLOW THROUGH CENTRIFUGAL & AXIAL FLOW COMPRESSORS

References 

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Gas Turbine Theory by H.I.H. Saravanamuttoo, G.F.C. Rogers and H. Cohen Gas Turbine Performance by P.P. Walsh and P. Fletcher

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Introduction to the Gas Turbine by D.G. Shepherd

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NPTEL Online – IIT Kanpur

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Google Search Engine


Acknowledgements 

I would like to express my gratitude towards Prof. Subrata Sarkar from IIT‐ Kanpur, whose guidance & suggestions were invaluable in the preparation of this lecture


Compressors

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