Turbomachinery Design Considerations
EGR 4347 Analysis and Design of Propulsion Systems
Euler Pump Equation
titeiieec
c hhmvrvrg
mW
..
.
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
• Desirable value around 0.513
12
hh
hh
riseenthalpystaticstage
riseenthalpystaticrotorRco
Diffusion Factor
• Quantifies the correlation between total pressure loss and deceleration (diffusion) on the upper (suction) surface of blade (rotor and stator)
is the solidity – the ratio of airfoil chord to spacing
i
ei
i
e
avg
e
V
vv
V
VDasdefine
V
VVD
21max
Diffusion Factor Data
Hub, Mean, and Tip Velocity Diagrams
Stall and Surge
Parameters Affecting Turbine Blade Design
Vibration Environment
Tip Shroud
Inlet Temperature
Blade Cooling
Material
Number of Blades
Airfoil Shape
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 Cost & Risk
FN, SFC Req’tsAero Technology
Life Req’ts Mech. &Cooling Technologies
PerformanceCycle Design Combustor
Design
MaterialSelections
TurbineAero Design
Manufacturing
ComponentTemp to other
areas
Preliminary Design = “Frozen” Turbine Flowpath
TurbineMech Design
AN2
rh
Wc
Clearance
NoNo
Yes Meet Requirements
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
V 1
rr
V 2
V 2 R
u 2
v 2V 2
2
2
1 2 3
3
rV 3 R
V 3
3
V 3 R
u 3
v3 R = v 3 + r
“ABSOLUTE” FLOW ANGLES
tan
tan
22
2
33
3
v
u
v
u
“RELATIVE” BLADE ANGLES
tan
tan
22
2
2
2
33
3
3
3
v
u
v r
u
v
u
v r
u
R
R
Relating ’s and ’s
v u r u
v u r u2 2 2 2 2
3 3 3 3 3
tan tan
tan tan
tan tan tan tan 2
3
23 2
3
23
u
u
u
u
TURBINE ANALYSIS – Velocity Triangles
TURBINE ANALYSIS
• Euler Turbine Equation:
Torquemg
r v r v
Wm
gr v r v mc T T
ci i e e
tc
i i e e p ti te
v2V2
u2
inlet, i
v3 u3
exit, e
V3convention:
v3 = -ve
also, ri = re= r
rg
v v c T Tc
p t t2 3 2 3
TURBINE ANALYSIS• Turbine Efficiency:
– Adiabatic (Isentropic)
– Polytropic
• Stage Loading Coefficient, :
– Typical values: 1.3 - 2.2
ts
st t
1
1 1
s s
et t t 1
Stage work / mass
(Rotor Speed)2g h
rc t
2
TURBINE ANALYSIS
axial velocity entering rotor
rotor speedu
r2
• Flow Coefficient, : Typical values 0.5 - 1.1
• Degree of Reaction, °R:
– °Rt = 0 Impulse turbine
– Reaction turbine
Rh hh h
T TT Tt
t t t t
enthalpy rise in rotortotal enthalpy rise for stage
2 3
1 3
2 3
1 3
Rt 0
• Pressure Loss Coefficient, t:
• Velocity Ratio, VR: Typical values: 0.5 - 0.6
tti te
te e
P P
P P
VR
VRr
g hc t
rotor speedvel equivalent of the change in total enthalpy
2
12
TURBINE ANALYSIS
Tip Leakage
Profile Loss
Endwall Loss
Cooling Loss
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
• rh2: Hub radius x 2/60 x Max Physical RPM– Units: ft/s
– Typical Values:
• HPT - 1000 ft/s < rh2 < 1500 ft/s
• LPT - 500 ft/s < rh2 < 1000 ft/s
– Use max physical RPM; not design point or TO speed
– Disk Stress is Driven Primarily by rh2
– Disk and Blade Attachment Stresses are a function of rh2 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)-- - coef of linear thermal expansion-- E - Modulus of Elasticity 0 rH
T
T0
T+T
r
rH
Disk
r
Htr r
rTE1
3
Ht r
rTE21
3
radial stress
tangential stress