5b - Axial Compressors Common

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AER510: AEROSPACE PROPULSION 5. Axial Compressors A. M. Steinberg c2012

5. Axial Compressors

Coverage of this section:

Characteristic Performance Surge

Rotating Stall

Boundary Layer Limitations

Cascade Aerodynamics Cascade performance Compressor efficiency

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5b.1 Characteristic performance of axial compressors

We will now consider the characteristic behavior of a single- ormulti-stage axial compressor operating between stations 2 and 3

using dimensional analysis. Two performance characteristics areimportant, the stagnation pressure ratio p03/p02 and the efficiencyr. A complete set of independent variables describing the

performance of the compressor is given by:

p03, r = f( m, p02, T02, , , R, , design, D)

where is the rotational speed of the shaft, is the kinematicviscosity, and D is a characteristic dimension of the compressor.

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Dimensional analysis

Using dimensional analysis, we can reduce the nine independentvariables in four dimensions to five non-dimensional groups:

p03

p02, r = f

m

RT02p02D2

,D

RT02,

D2

, , design

The second and third terms on the right can be recognized at ablade Mach number and Reynolds number.

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For a fixed design of an engine operating with air (we will leave inD for now), the relationship reduces to

p03

p02, r = f

m

T02

p02D2,

DT02

,D2

In our discussion of turbulence, we saw that at very high Reynolds

numbers, the details of the solution become independent of theReynolds number; all changing Re does is set the smallest scales atwhich the energy is dissipated. That is not to say that the highReynolds number is not important, only that the solution becomesinsensitive to Reynolds number. Assuming a sufficiently high bladeReynolds number,

p03

p02

, r = fm

T02

p02

,

T024
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No difference in the functional relationship is made if the variables

on the right are multiplied by a constant. Introducing a standardtemperature of 288.15 K and standard pressure of 101.325 kPa,the temperature and pressure at the compressor inlet can benormalized as:

=T02

T0,std

=p02

p0,std

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Replacing the shaft angular velocity with the shaft RPM, N, thefunctional relationship can be expressed as

p03

p02 , r = f

m ,

N

This relationship allows test data at particular flight conditions tobe related to other conditions.

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Axial Compressor Performance

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Axial Compressor Performance

Below some critical mass flow rate, the compressor does notoperate. This is referred to as the surge line.

As the mass flow rates increase, the slopes of the performancecurves approach . This is associated with negative flowseparation as the back stages acting a throttle for the forwardstages.

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5b.2 Surge

As the name implies, the phenomenon of surge refers to a locus ofunstable compressor operating conditions that are characterized byperiodic surging flow through. This instability can easily lead topressure oscillations that are violent enough to destroy thecompressor blades. Avoiding or minimizing surge therefore is ofcritical importance in compressor design.

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5b.2 Surge

Concept for surge analysis

To understand surge, we will consider a compressor stage that isexhausting into a plenum in which the flow is controlled by athrottle. A throttle is simply a device that has a relationshipbetween the flow rate and stagnation pressure change over thethrottle (i.e. a valve). Hence, the throttle mimics the behavior ofdownstream stages.

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5b.2 Surge

Description of Surge

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5b.2 Surge

In this model, an operating point is identified as theintersection of the throttle characteristics with the compressorstage performance.

Whether or not surge occurs depends on the slopes of thestage and throttle characteristics at the intersections.

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5b.2 Surge

If the slope of the throttle characteristic is greater than thatof the compressor characteristic, the operating point is stable(points A, B, C, and D).

A momentary increase of mass flow will be met by a throttledemand for a pressure rise greater than that caused by the

compressor. The throttle will therefore push back against theincreased flow rate, returning it to normal

The same is true for a decrease in flow rate.

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5b.2 Surge

If the slope of the throttle characteristic is less than that ofthe compressor characteristic, the operating point is stable(points A, B, C, and D).

A momentary increase of mass flow will be met by a throttledemand for a lower rise greater than that caused by thecompressor. The throttle will therefore pull in more flow,further increasing the flow rate.

The point of neutral stability is point E.

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5b.3 Stall

The surge phenomenon can be seen as a coupling between

compressor stall and the combustion chamber characteristics. Wepreviously gave a quick overview of stall, as explained by changesin angle of attack on the compressor blades during deviations fromdesign flow conditions. In practice, not all compressor blades stallsimultaneously. That is, a stalled blade acts as a blocker for theflow. This results in a change in the inflow for the surroundingblades, causing increased or decreased angles of attack at adjacentblades. The result is referred to as rotating stall.

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5b.3 Stall

Rotating Stall

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5b.4 Simplified analysis of stall and surge

A simple yet useful analysis of of stall and surge wasperformed by Greitzer (1976).

The analysis states that the onset of surge in a compressorcoupled to a combustion chamber is dictated by the ratio oftwo characteristic timescales.

Compressor flow-through time r Vr/ma Plenum charge time

pprRT2

Vpma

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5b.4 Simplified analysis of stall and surge

The compressor pressure rise scales with the rotational speed

pr (r)2

and the compressor temperature scales as a speed of sound squared

T2 a22

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Greizter has shown that whether a disturbance results in stall orsurge is described by a parameter

B r2a2

Vp

Vr

pr

For low B (around 0.6-0.7) systems settle into rotating stall. As Bincreases to around 1.5, the stall instability causes surge.

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5b.5 Boundary Layer Limitations

In compressors, there are two types of boundary layers that mayseparate:

End wall boundary layers At outer housing or along shaft

Blade boundary layers

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5b.5.1 End wall separation

End wall separation occurs on the walls of the outer compressorhousing or drive shaft between the blades.

The 2D turbulent boundary layer will separate for

Cp =p

12

u2> C

p

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We will assume that each row of blades in the compressor acts as a2D diffuser with a small pressure rise.

Rotor: Cp,r =p2 p1

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1w21Stator: Cp,s =

p3 p212

2c22

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In between each set of blades, we can apply Bernoullis equation. Ifwe assume a small pressure rise over each set of blades and amoderate Mach number, the density can be considered constant.

For a rotor stage:

p1 +1

21w

21 = p2 +

1

22w

22 p2 p1 =

1

21w

21

1

w2

w1

2

Cp,r = 1

w2

w1

2Cp,s = 1

c3

c2

2

A limitation on Cp implies a limit on the change in azimuthalvelocity over each set of blades.

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If the axial velocity is approximately constant through the stage

w1 cos 1 = cz = w2 cos 2 c2 cos 2 = cz = c3 cos 3

which gives

Cp,r = 1cos2 1cos2 2

Cp,s = 1cos2 1cos2 2

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Allowable angle combinations for different pressure coefficients

Cp,r = 1 cos2 1cos2 2

Cp,s = 1 cos2 1cos2 2

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5b.6 Cascade Aerodynamics

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In order to consider the separation of flow over the blade surface,we first need to introduce the concept of cascade aerodynamics. Acascade is a linear array of stationary blades that is constructed formeasuring the performance of blading schemes similar to real

compressors. A cascade does of end walls, but they are generallyporus and boundary layer suction is applied so that the flowbetween blades is as 2D as possible.

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The objective of cascade studies is to relate the the fluid turningangles to the blade geometry and to measure losses in stagnationpressure due to friction. The effects of separation are observedwhen the fluid exit angle deviates markedly from the blade exitangle and the stagnation pressure losses rise rapidly.

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Cascade Wind Tunnel

A typical cascade wind tunnel has well conditioned inflow and a rowof blades for which the angle relative to the flow can be adjusted.

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Note that, while cascades are used to study compressorcomponents, no work is being done to the flow. While there will bea static pressure rise due to the torque on the flow, there will be nowork done on the flow. Hence, for an adiabatic system, the

stagnation temperature does not change and the stagnationpressure decreases due to friction. However, the stagnationpressure loss over a cascade row is closely related to the efficiencyof a working compressor.

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5b.6.1 Dimensional analysis for cascades

We are interested in the flow exit angle and stagnation pressure lossover the cascade. A complete set of independent parameters is:

ii, p0 = f(wi, i, s, C,,, T1, p1, , R, blade shape)

where s, C, and are the spacing, chord, and stagger.

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We can take this set of 11 independent variables and write 7non-dimensional groups as:

ii,p0

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1w21= f

i,

wiC

, ,

wiRT1

,C

s, , , blade shape

This set of seven groups is too many to consider simultaneously, so

we will assume for now that the Reynolds number and Machnumber do not have a major influence (we will look at this in moredetail later). For a fixed blade shape with a constant and R gas,the relationship reduces to

ii,p0

12

1w21= f

i,

C

s,

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Cascade Test Data

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5b.6.2 Compressor Efficiency

Cascade tests are a primary means of determining the efficiency ofdifferent blading schemes. This is done by determining thestagnation pressure rise, or alternatively the increase in entropy tothe blading parameters.

In the design of a compressor, we are concerned with three types of

efficiency Overall Efficiency, r: the adiabatic efficiency of the entire

compressor, which we have previously defined and used.

Stage Efficiency, sr: the adiabatic efficiency of a single stage.

Polytropic Efficiency, pr: the efficiency for an infinitesimalcompression.

For small amounts of compression over single stages, pr sr.What is the relationship between r and pr

sr?

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Consider an incremental pressure rise from p0 p0 + dp0. Notethat we are considering a general definition of the efficiency that

involves doing work on the fluid, NOT the processes occurring in acascade.

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5b - Axial Compressors Common

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