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Turbomachinery -15
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
Turbomachinery
Compressors
Turbomachinery -16
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
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Turbomachinery -17
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Propulsion, Hill and Peterson
z
Turbomachinery -18
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Mechanics and Thermodynamics of
Propulsion, Hill and Peterson
Turbomachinery -20
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
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Turbomachinery -21
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Mechanics and Thermodynamics of
Propulsion, Hill and Peterson
Turbomachinery -26
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
Centrifugal (Single-Stage) Compressor Map
• Characteristics similar to axial compressors
– much higher stage pressure ratio
– lower peak efficiencies
– flatter map at max pressure ratio
Mechanics and Thermodynamics of Propulsion, Hill and Peterson
also less susceptible to FOD
10
Turbomachinery -33
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Mechanics and Thermodynamics of Propulsion, Hill and Peterson
designstst PrPr
m
designmm
Turbomachinery -34
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Mechanics and Thermodynamics of Propulsion, Hill and Peterson
11
Turbomachinery -35
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
Multistage Comp.: Off-Design Operation
Gas Turbine Theory, Cohen, Rogers and Saravanamuttoo
Turbomachinery -36
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Mechanics and Thermodynamics of Propulsion, Hill and Peterson
12
Turbomachinery -37
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
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
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
Compressor Stability (Surge)
• Dynamic instability problem
– leads to periodic mass flow rate (and pressure) fluctuations
Mechanics and Thermodynamics of Propulsion, Hill and Peterson
13
Turbomachinery -39
Copyright © 2014,2015 by Jerry M. Seitzman. All rights reserved. AE4451 Propulsion
Surge Margin
margin
Mechanics and Thermodynamics of Propulsion, Hill and Peterson