Turbomachinery Design
Considerations
EGR 4347 Analysis and Design of
Propulsion Systems
Euler Pump Equation
.
.
m
reve  ri vi   m hte  hti 
Wc 
gc
.
Compressor
Axial Schematic
Compressor
Centrifugal Schematic
Compressor Typical Velocity Diagram
Compressor Repeating Row Nomenclature
Airfoil Pressure and Velocity
Important Parameters
•
•
•
•
•
Compressor Efficiency, c
Stage Efficiency, s
Polytropic Efficiency, ec
Stage Pressure Ratio, s
Overall Pressure Ratio, c
Degree of Reaction
o
rotor static enthalpyrise
Rc 
stage static enthalpyrise
h2  h1

h3  h1
• Desirable value around 0.5
Diffusion Factor
• Quantifies the correlation between total pressure
loss and deceleration (diffusion) on the upper
(suction) surface of blade (rotor and stator)
Vmax  Ve
D
Vavg
define as
Ve vi  ve
D  1 
Vi
2Vi
•  is the solidity – the ratio of airfoil chord to
spacing
Diffusion Factor Data
Hub, Mean, and Tip Velocity Diagrams
Stall and Surge
Parameters Affecting Turbine Blade
Design
Vibration Environment
Tip Shroud
Number of Blades
Airfoil Shape
Inlet Temperature
Blade Cooling
Material
Trailing-Edge Thickness
Allowable Stress Levels (AN2)
(N = Speed, RPM)
Service Life Requirements
Turbine Prelim Design Focuses on Defining a
‘Flowpath’ that Meets Customer Requirements
Customer Req’ts/Desires
Performance
Mission
FN, SFC Req’ts
Aero Technology
Cost & Risk
Life Req’ts Mech. &
Cooling Technologies
Performance
Cycle Design
Turbine
Aero Design
Combustor
Design
AN2
rh
a,b
Wc
Clearance
Material
Selections
Turbine
Mech Design
Manufacturing
No
No
Meet Requirements
Yes
Preliminary Design = “Frozen” Turbine Flowpath
Component
Temp to other
areas
Turbine Mechanical Detailed Design
• Detailed Design Accomplishes Two Functions:
– Verify Assumptions/Choices Made in Preliminary Design
– Provide Detailed Geometry Required to Achieve Preliminary Design
Goals
• Detail Mechanical Design Disciplines:
–
–
–
–
–
–
Materials Selection - satisfy life/performance goals
Secondary Flow Analysis - define/control nonflowpath air (e.g. cooling)
Heat Transfer - component temperature definition
Stress Analysis - component stresses
Vibration Analysis - design to avoid natural frequencies
Life Analysis - define component life for all failure modes
Turbine Nomenclature
50% Reaction Turbine
0% Reaction or Impulse Turbine
Hub, Mean and Tip Velocity Diagrams
Velocity Triangles
1
2
3
“ABSOLUTE” FLOW ANGLES
V 3R
V1
V3
a1
V 3R
b2
V 2R
V2
r
r
u2
a2
V2
v2
b3
u3
v
tan a 2  2
u2
r
a3
v
tan a 3  3
u3
v3R = v 3 +  r
“RELATIVE” BLADE ANGLES
v
v  r
tan b 2  2 R  2
u2
u2
v 3 R v 3  r
tan b3 

u3
u3
Relating a’s and b’s
v 2  u 2 tan a 2  r  u 2 tan b 2
v3  u 3 tan a 3  r  u 3 tan b3
u3
u3
tan a 2 
tan a 3  tan b2 
tan b3
u2
u2
TURBINE ANALYSIS –
Velocity Triangles
TURBINE ANALYSIS
• Euler Turbine Equation:
m

Torque     ri v i  re v e 
gc
m


Wt   
 p  Tti  Tte 
 ri vi  re ve   mc
gc
u2
V2
v2
inlet, i
V3
u3
exit, e
r
 v2  v3   c p Tt 2  Tt 3 
gc
v3
convention:
v3 = -ve
also, ri = re= r
TURBINE ANALYSIS
• Turbine Efficiency:
– Adiabatic (Isentropic)
– Polytropic
t 
1  s
1  s
 t 1  t
  1 e
s  s t  t  t
• Stage Loading Coefficient, y:
Stage work / mass gc h t


2
r 2
(Rotor Speed)
– Typical values: 1.3 - 2.2
TURBINE ANALYSIS
• Flow Coefficient, : Typical values 0.5 - 1.1

axial velocity entering rotor u 2

rotor speed
r
• Degree of Reaction, °R:

h2  h3
T2  T3
enthalpy rise in rotor
Rt 


total enthalpy rise for stage h t1  h t 3 Tt1  Tt 3
– °Rt = 0 Impulse turbine

– R t  0 Reaction turbine
TURBINE ANALYSIS
Pti  Pte
ft 
• Pressure Loss Coefficient, ft:
Pte  Pe
Tip Leakage
Cooling Loss
Profile Loss
Endwall Loss
• Velocity Ratio, VR: Typical values: 0.5 - 0.6
rotor speed
VR 
vel equivalent of the change in total enthalpy
r
1
VR 

2g c h t
2
Turbine Mechanical Design
• AN2: Rotor Exit Annulus Area x [Max Physical Speed]2
– Units: in2 x RPM2 x 1010, typical values: 0.5<AN2<10 x1010
– Typical Limits:
• Cooled Blade < 5 x 1010
• Advanced Technology < 6.5 x 1010
• Uncooled Solid Blade < 10 x 1010
• LPT < 7 x 1010
– Use max physical speed; not design point or TO speed
– Blade Airfoil Stress is Primarily Driven by AN2
– Blade Pull Load Driven by AN2
Turbine Mechanical Design –
Hub and Tip Speed Limits
• rh2: Hub radius x 2/60 x Max Physical RPM
– Units: ft/s
– Typical Values:
• HPT - 1000 ft/s < rh2 < 1500 ft/s
• LPT - 500 ft/s < rh2 < 1000 ft/s
– Use max physical RPM; not design point or TO speed
– Disk Stress is Driven Primarily by rh2
– Disk and Blade Attachment Stresses are a function of
rh2 and AN2
Structures
- Rotational Stress (Centrifugal Stress)
- Bending Stress due to the lift of “airfoils”
- Buffet/Vibrational Stress
- Flutter due to resonant response
- Torsion from shaft torque
- Thermal Stress due to temperature gradients
- FOD
- Erosion, Corrosion, and Creep
Structures
Structures
Structures - Stress Calculations
- Rotational Stress (Centrifugal Stress)
-- Same as for compressor, c, blade
- Disk Thermal Stress, t
-- assume T = T(r) = T0 + T(r/rH)
-- a - coef of linear thermal expansion
-- E - Modulus of Elasticity
r
q r
H
radial stress
tangential stress
Disk
T+T
T
T0
0
 tr 
rH
r
aET 
3
r
1 
 rH



aET 
r 
1  2 
 tq 
3 
rH 