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Turbomachinery -15

Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion

Turbomachinery

Compressors

Turbomachinery -16


Compressor Analysis

• From Euler turbomachinery (conservation) equations need to understand change in tangential velocity to relate to forces on blades and power

• Analyze cascade flow to find c

12 rcrcm

12 12 cucumW

Mechanics and Thermodynamics of

Propulsion, Hill and Peterson

2

Turbomachinery -17


Cascade Analysis

• You have previously analyzed flow

over a “blade” (airfoil!!)

– but in blade’s reference frame

• But here there are moving

(e.g. rotor) and stationary

(stator) blades

– e.g., for compressor

12 rotor

23 stator

• Use velocity triangles to switch

between frames Mechanics and Thermodynamics of


z

Turbomachinery -18


Velocity Triangles

• Two reference frames to use for fluid velocity

– engine’s

– blade’s

• Difference due to blade motion

• For cascade flow

– u is in direction

– define angles (,) for each ref. frame

c

w

uwc

c

u

w

z

c u

w

u

3

Turbomachinery -19


Rotor Velocity Triangles

• Blade moves in direction, and in

cascade flow, fixed r, so let ui=U

• Also have general relations

– e.g.,

• Therefore

uwc

z

1ii zz cw c

U

w

2Ucwii

izii iiccc tansin

2tan

2,1

22

22

zcUc

wUc

1tan11

zcc



Turbomachinery -20


Single-Stage Characteristics

(Axial Compressor)

• Goal - determine how compressor performance, e.g., Prc, affected by changes in operating conditions

• Start by analyzing single-stage (of) compressor

• Rotor (12)

– Euler

– at fixed radial location

• Stator (23)

• So for stage

1212 12 ooR hhmcucumW

1212 ooR hhmccUmW

2,12,1 ohcU

230 ooS hhW

2,12,13,1 cUhh oo

while no work, there is still

torque on stator blades

4

Turbomachinery -21


Stage Loading Coefficient

• So

• Interpretation

• Typical design values

(axial comp.)

U

c

U

ho 2,13,1

2

cityrotor velo

increase tan vel~

rotorKE

Work/mass

1.033.0~

stage

loading

coeff

2,13,1 cUho

Turbomachinery -22


Stage Pressure Ratio

• Recall press. ratio for adiabatic compressor with thermally and calorically perfect gas

1

1

3

01

3 11

o

ost

o

T

T

p

p1

1

131

o

oost

T

TT

1

1

3,11

op

o

stTc

h

1

2

1

23,11

1

U

h

RT

U o

o

st

1

Rcp

1

1

2

1

3 2,111

U

c

RT

U

p

p

o

st

o

o

U

c

U

ho 2,13,1

2

5

Turbomachinery -23


Compressor Pressure Ratio

• Stage compression ratio depends on

1. stage loading coefficient,

• c and U

2. blade Mach number,

• rotor blade speed (U = r)

• stage inlet stagnation temperature, To1

3. stage efficiency, st

1

1

2

1

3 2,111

U

c

RT

U

p

p

o

st

o

o

1oRTU

Turbomachinery -24


Blade Loading and Flow Coefficient

• What effects c

• From velocity triangle expressions, we had

• Assume axial vel. ~constant through stage

1tan11

zcc 2tan

22 zcUc

12 tantan12,1

zz ccUUU

c

zzz ccc

21

12 tantan12,1

U

c

U

cz

U

czFlow

Coefficient Typical values (axial comp.)

0.50.1 Mechanics and Thermodynamics of Propulsion, Hill and Peterson

6

Turbomachinery -25


Blade Design Influence

• What controls stage loading?

1. =cz/U • relative flowrate through stage,

proportional to mass flow rate

2. 1

• inlet flow angle - from previous stage or inlet guide vanes

3. 2

• flow angle leaving rotor blade in rotor reference frame blade design angle (flow follows airfoil?)

– best performance: rotor leading edge match to 1; similarly for stator leading edge (2)

12 tantan12,1

U

c

U

cz



Turbomachinery -26


Compressor Example • Axial air compressor stage with design point created for:

1. 8,000. rpm rotor with 0.30 m mean design radius

2. 100. m/s axial velocity (constant through stage), 36.4 m/s inlet tangential velocity

3. 50. rotor blade trailing edge angle (wrt to axis and opposite to rotation), and 20. stator blade’s trailing edge angle

4. 95% estimated adiabatic stage efficiency @ design point

5. 298 K inlet temperature

• Determine at design point:

1. rotor speed (m/s)

2. stage flow coefficient

3. required power per unit mass flowrate (kJ/kg)

4. stagnation pressure ratio across stage

• Assume - calorically/thermally perfect gas, zero radial velocity

7

Turbomachinery -27


Compressor Example

• Rotor speed

• Flow coefficient

• Specific power

smmrev

radrev

rrev

radrpmNrU

2513.0.

2sec60

000,8

.

2)(

398.0251

.100

sm

sm

U

cz

213 UhhmW ooa

21 tantan1

2=50

3=20 1

U

cz1=100m/s

c1=36.4m/s

20100

4.36tan 11

381.050tan364.0398.01

kg

kJ

kg

kg

s

m

s

m

m

W

a

1.24065,24381.02512

22

Turbomachinery -28


Compressor Example

• Pressure Ratio

1

1

22,111

U

c

RT

UPr

o

stst

5.32

381.02982884.1

25114.195.01

KkgKJ

sm

Blade M = 0.73

3.1stPr

8

Turbomachinery -29


Single Stage Compressor: Off-Design

• Near design point, flow follows blade

U

cC

U

c

U

cz

az

1tantan1 12

2,1

12

1

3 11

U

cCUC

p

p zabst

o

o

U

c2,1

U

cz

Design

Point rP

U

cz

Design

Point

1. As flowrate changes (e.g.,

fixed U), work doesn’t

– e.g. for higher mass flowrate

less work done per unit

mass

2. Near design point, flow

follows blade

– farther away, flow separates

AND efficiency drops

Actual Actual

Turbomachinery -30


Single-Stage (Axial) Compressor Map

Mechanics and Thermodynamics of Propulsion, Hill and Peterson

corro TT 1 corro pp 1

11 oRPMo TNRTU

1ochokedz Tpmc

Why?

1

1

22,111

U

c

RT

UPr

o

stst

Throttled

• Measured single- stage performance

– cz replaced by corrected mass flow rate

– U replaced by corrected RPM

• blade Mach #

• Drop in efficiency off design point

9

Turbomachinery -31


Efficiency Losses

• Profile/Blade Losses

– flow not following blade/airfoil

– boundary layer separation, po loss

– but not explain all the losses

• Tip Losses

– flow around blade tip (clearance between blade and casing or hub); like wing tip vortices

• Secondary Flow

– 3-d flow associated with boundary layers – especially at casing and hub, also induced by tip flow

st

1

0.6

st

1

0.6

cascade data

actual

tip 2nd

profile

Hydrodynamics of Pumps, Christopher

Brennen 1994

Turbomachinery -32


Centrifugal (Single-Stage) Compressor Map

• Characteristics similar to axial compressors

– much higher stage pressure ratio

– lower peak efficiencies

– flatter map at max pressure ratio


also less susceptible to FOD

10

Turbomachinery -33


Multistage Compressors • What can happen in a multistage

(axial) compressor

– exit of one stage influences

following stage

• Consider: 1st stage with

at design RPM

– so 2nd stage sees lower

and even lower cz (), pushes

cz even lower for 3rd stage…

– gets worse with each successive

stage until positive incidence stall


designstst PrPr

m

designmm

Turbomachinery -34


Multistage Compressors

• If for first stage, later stages will eventually have negative incidence stall

• Similar behavior if sudden change in RPM for fixed

• If cz/U increases too much, final stages throttled and can give pressure drop (negative pressure rise)

• So multistage compressors susceptible to off-design performance problems

designmm

m


11

Turbomachinery -35


Multistage Comp.: Off-Design Operation

Gas Turbine Theory, Cohen, Rogers and Saravanamuttoo

Turbomachinery -36


Starting Issues

• What happens in multistage compressor at start up (low RPM)

• Initially p and ~constant but area increasing down-stream, so low cz in first stages, but high in last stages

– both ends can be stalled


12

Turbomachinery -37


Solutions for Multistage Compressors

• Problems

– off-design for

given RPM

– incidence angle

does not match

blade angle

– wrong RPM for

given

m

• Solutions

– bleed valves to

remove mass

between stages

– variable stator and

inlet guide vane

angles

– LP and HP

sections with

different RPM

m

Turbomachinery -38


Compressor Stability (Surge)

• Dynamic instability problem

– leads to periodic mass flow rate (and pressure) fluctuations


13

Turbomachinery -39


Surge Margin

margin


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