Turbomachinery
Design and Analysis
AE4803
Turbomachinery -1
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
Turbomachinery Design
• So let’s say you completed a simple, single-point
design of a turbofan engine for an aircraft flying at
M=0.85 at 30 kft with the outcome
Cycle Design
– Prc = 54
– T4 = 1420 K
Black Box
– wt = 632 kJ/kg
Analysis
(no help)
• How do you design the turbomachinery:
compressor(s), turbine(s) that can achieve this
performance?
– begin with review of what turbomachinery looks like
Turbomachinery -2
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
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Axial (Flow) Compressors and Turbines
• Turbomachinery made up of many parts
– compressor Stator/Stator Vanes
Inlet Guide Vanes
Shaft
Casing
Rotor/Rotor blades
– turbine
Stage=Rotor/Stator Pair
Rotor
Nozzle
Elements of Gas Turbine Propulsion, Mattingly
AE4803
Turbomachinery -3
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
Axial Compressors and Turbines
• Turbomachinery made up of many parts
Disk (blades attached to it)
• Blisk if blades integrated into disk
(Turbine)
Rotor
Blade
Spool - compressor and turbine
rotors on common shaft
braytonenergy.net
Elements of Gas Turbine Propulsion, Mattingly
Turbomachinery -4
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
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Axial Compressors and Turbines
• Turbomachinery made up of many parts
Spool
• compressor and turbine rotors on common shaft
GE F404 LP spool
turbine
1 rotor (1 stage)
compressor
3 rotors (3 stages)
Mechanics and Thermodynamics of Propulsion, Hill and Peterson
AE4803
Turbomachinery -5
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
Axial Compressors and Turbines
• Turbomachinery made up of many parts
– most engines have
at least two spools
– e.g., concentric
shafts
3 stage LP
compressor
7 stage HP
compressor
Elements of Gas Turbine Propulsion, Mattingly
GE F404
Prc~26
Prstage~1.4
Mechanics and Thermodynamics of Propulsion, Hill and Peterson
Turbomachinery -6
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
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Turbomachinery
Aerothermodynamics
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Turbomachinery -7
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
Turbomachinery Conservation Equations
• How to analyze the performance of
turbomachinery to enable design?
• Start by
developing Shaft
conservation
equations
Turbomachinery -8
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
Tip
Hub or Root
Rotor
Blades
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Coordinate System
• First need to define appropriate control volume
and coordinate
system for rotating
machinery
– axisymmetric

r
z
Casing
Mechanics and Thermodynamics of Propulsion, Hill and Peterson
Turbomachinery -9
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
AE4803
Fixed vs. Rotating Frames of Reference
• Since some blades are rotating (rotors) and
some are stationary (stators), we will find it
helpful to use 2
Radial
c
reference frames
Velocity r
for defining
cz
Axial
velocity
c
Velocity
Azimuthal
1. fixed (“lab”
Velocity
or engine)

ref. frame  c
2. rotating

ref. frame  w
Turbomachinery -10
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
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Fixed vs. Rotating Frames of Reference
• How to we convert velocities from one ref.
frame to another?
– Galilean transform




v new  v old  v rel
vrel is relative velocity of new
reference frame with
respect to old

u
• What is the relative velocity
between our 2 ref. frames?
– the (local) blade velocity!
u r   r
  
w  c u
Turbomachinery -11
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
AE4803
Euler Turbomachinery Equations
• Mass
CV for one
blade row

d
0   dV    c  nˆ dA
CS
dt CV
steady
0  0  m 2  m 1
m 2  m 1  m
• Angular Momentum(engine
frame)
torque
– CM law   d mrc 
dt

d
   rc dV   rc c  nˆ dA
CV
CS
dt
0 for steady…if we time avg. over high freq.
fluctuations that result from blades going by

   rc c  nˆ dA  m rc 2  rc 1 
CS
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blade
disk
rh rm rt
for prelim. design, typically use the
“mean” radius location (between
tip and hub)  pitchline (or meanline)
(rc) represents a spatially
reasonable starting point if rm>>rt-rh
averaged (integrated) property
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
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Euler Turbomachinery Equations
• So   m rc 2  rc 1 
– what about power?
• Power/Energy
– from mechanics
 rc 2  rc 1 
W    m
W m  rc 1, 2 r = blade speed  u W m  uc 1, 2
– from thermodynamics
W m  h?o 2  ho1  h0 1, 2  uc 1, 2
steady, adiabatic,
uniform
for equations as written
, W  0 for compressor
 rev  min  2 
  N



 min  60sec  rev 
 N rpm  30
, W  0 for turbine
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Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
Euler Turbomachinery Equations
• So having used both
mechanics (mass &
momentum) and
thermodynamics
(energy) across our
control volume
W m  uc   ho
we can relate the TD property changes
across turbomachinery blade rows to the
induced azimuthal velocity changes
• Using a constant pitchline approach (r1  r2)
uc  ho
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Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
for axial machines
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Other Important Definitions
• Reaction (Degree of Reaction)
R
hrotor energy change across rotor
hstage  energy change across stage
~
protor
pstage
– balance torque, p gradient between rotor/stator
• Flowfields (axial machines)
– while real machines have 3-d flows, easier to
consider 2-d flows (different “planes”)
• Throughflow Field (r-z plane)
r
– not including  variations
z
– disk replaces blades
(actuator disk theory)
AE4803
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Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
Other Important Definitions
• Cascade Field (-z plane)
– not including r variations
– like unwrapping blade to look
at array of airfoil sections
– will focus on this for 2-d design
• Secondary Field (r- plane)
– not including z variations
– low velocity in boundary layers
blade
along blades/walls
– pressure gradients produce
secondary (rotational) flows
– leads to reduced performance
(efficiency loss)
Turbomachinery -16
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
blade

z
r

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Turbomachinery
Cascade Analysis
Turbomachinery -17
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
AE4803
Cascade Analysis
• Historically, much of turbomachinery
blade design was based on

measurements of cascade data
in wind tunnels
• Extrapolating this to real
turbomachinery assumes
quasi-steady, 2-d flow
– not really true, but cascade results still relevant
and characteristics derived from cascade analysis
often satisfactory for preliminary design
• Modern design based on CFD analysis combined with
experimental testing
Turbomachinery -18
Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
z
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2
Cascade Geometry
• Typical airfoil properties
– camber line shape and angle, 
– chord, b
– thickness (t) profile and tmax/b
– leading and trailing edge radii

• Cascade properties
1
– pitch, s ( 2r / # blades)
– solidity,   b / s
– stagger angle, 
(between chord and axial*)
s
– blade inlet angle,* 1
– blade exit angle,* 2

camber
b line
chord
line
suction
surface
pressure
surface

z
  1  2
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Copyright © 2014,2015, 2018, 2019 by Jerry M. Seitzman. All rights reserved.
*some engine companies use
normal ( direction) as reference
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