Lesson 14Turbomachinery Design Considerations

8/10/2019 Lesson 14Turbomachinery Design Considerations

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Euler Pump Equation

titeiieec

c hhmvrvrg

mW

..

.


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Compressor

Axial Schematic


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Compressor

Centrifugal Schematic


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Compressor Typical Velocity Diagram


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Compressor Repeating Row Nomenclature


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Airfoil Pressure and Velocity


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Important Parameters

Compressor Efficiency, c

Stage Efficiency, s

Polytropic Efficiency, ec

Stage Pressure Ratio, s

Overall Pressure Ratio, c


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Degree of Reaction

Desirable value around 0.5

13

12

hh

hh

riseenthalpystaticstage

riseenthalpystaticrotor

Rco


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Diffusion Factor

Quantifies the correlation between total pressureloss and deceleration (diffusion) on the upper(suction) surface of blade (rotor and stator)

is the soliditythe ratio of airfoil chord tospacing

i

ei

i

e

avg

e

V

vv

V

VDasdefine

V

VVD

21m ax


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Diffusion Factor Data


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Hub, Mean, and Tip Velocity Diagrams


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Stall and Surge


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Parameters Affecting Turbine Blade

DesignVibration 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


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Turbine Prel im Design Focuses on Defining a

Flowpath that Meets Customer RequirementsCustomer Reqts/Desires

Performance Mission Cost & Risk

FN, SFC Reqts

Aero Technology

Life Reqts Mech. &

Cooling Technologies

PerformanceCycle Design Combustor

Design

MaterialSelections

Turbine

Aero Design

Manufacturing

Component

Temp to other

areas

Preliminary Design = Frozen Turbine Flowpath

Turbine

Mech DesignAN2

rh

a,bWcClearance

NoNo

Yes Meet Requirements


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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


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Turbine Nomenclature


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50% Reaction Turbine


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0% Reaction or Impulse Turbine


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Hub, Mean and Tip Velocity Diagrams


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Velocity Triangles

a1V1

rr

V2

V2R

u2

v2V2

b2

a2

1 2 3

a3

rV3R

V3

b3

V3R

u3

v3R= v3 + r

ABSOLUTE FLOW ANGLEStan

tan

a

a

22

2

33

3

v

u

v

u

RELATIVE BLADE ANGLES

tan

tan

b

b

22

2

2

2

33

3

3

3

v

u

v r

u

v

u

v r

u

R

R

Relating as and bs

v u r u

v u r u

2 2 2 2 2

3 3 3 3 3

tan tan

tan tan

a b

a b

tan tan tan tana a b b23

2

3 23

2

3 u

u

u

u


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TURBINE ANALYSIS

Velocity Triangles


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TURBINE ANALYSIS

Euler Turbine Equation:

Torque m

gr v r v

W mg

r v r v mc T T

ci i e e

tc

i i e e p ti te

v2V2

u2

inlet, i

v3u3

exit, e

V3convention:

v3= -vealso, ri= re= r

rg

v v c T Tc

p t t2 3 2 3


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TURBINE ANALYSIS

Turbine Efficiency:Adiabatic (Isentropic)

Polytropic

Stage Loading Coefficient, y:

Typical values: 1.3 - 2.2

t

s

s t t

1

1 1

s s

et t t 1

Stage work / mass

(Rotor Speed)2

g h

r

c t

2


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TURBINE ANALYSIS

axial velocity enter ing rotor

rotor speed

u

r2

Flow Coefficient, : Typical values 0.5 - 1.1

Degree of Reaction, R:

Rt= 0 Impulse turbine

Reaction turbine

R

h h

h h

T T

T Tt t t t t

enthalpy ri se in rotor

total enthalpy rise for stage

2 3

1 3

2 3

1 3

Rt0


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Turbine Mechanical Design

AN2

: Rotor Exit Annulus Area x [Max Physical Speed]2

Units: in2x RPM2x 1010, typical values: 0.5


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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 < 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 rh

2 Disk and Blade Attachment Stresses are a function of

rh2 and AN2


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Structures

- Rotational Stress (Centr i fugal 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


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Structures


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Structures


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Structures - Stress Calculations

- Rotational Stress (Centr i fugal 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 0 rH

T

T0

T+T

r

rH

Disk

r q

H

tr

r

rTE1

3

a

H

t

r

rTE21

3

a

q

radial stress

tangential stress


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Lesson 14Turbomachinery Design Considerations

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