Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation · 2009. 4....

1Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation

A. Alexiou & K. Mathioudakis

Laboratory of Thermal TurbomachinesNational Technical University of Athens

Direct-Transfer Pre-Swirl System:Performance Modelling, Validation and Optimisation




Paper Objectives

Ø Construct a model of a gas turbine direct-transfer pre-swirl air system using models of its individual components

Ø Validate the modelling against experimental results from 3 different publicly available test cases

Ø Optimise the design of such a system on its own and as part of a complete engine performance model



qMODELLING PHILOSOPHY

qMODEL VALIDATION

o Test Case 1

o Test Case 2

o Test Case 3

q DESIGN OPTIMISATION

o System Level

o Engine Level

q CONCLUSION

Contents



Direct Transfer Pre-Swirl Air System

Pre-swirlNozzle

ReceiverHole

InnerLabyrinth

Seal

OuterLabyrinth

Seal

Cover-plate

Pre-swirlChamber

To BladeCooling Passage

Pre-swirlNozzle

ReceiverHole

InnerLabyrinth

Seal

OuterLabyrinth

Seal

Cover-plate

Pre-swirlChamber

To BladeCooling Passage

Important ParametersRelative Total Temperature

Tt,rel,RH

Discharge Coefficient

CD,RH

Swirl Ratio

β = Vφ / Ω rΩ

(RH)

(PN)



Modelling Philosophy

1 2 3 4

5

8

6

7Pre-swirlNozzle

ReceiverHole

Pre-swirlChamber

InnerLabyrinth

Seal

OuterLabyrinth

Seal

12

3

4

5

8

6

7

Connected components communicate through their external interfaces by exchanging a pre-defined set of variables. For describing flow conditions, these variables are mass flow, total temperature, total pressure and swirl angle. The exit flow conditions of a component are linked to the corresponding inlet ones through the conservation equations for mass, energy, axial and angular momentum, the component characteristics and appropriate empirical correlations.



Cavity Component Model

Ø Arbitrary geometry (discs, cones, cylinders)Ø J Input flows and N output flowsØ Fully mixed flowØWork and heat transfer from surrounding K surfacesØMixing pressure losses

Ω

rK, AKrm

r

zin outrN, AN

rJ, AJ

mixSTATOR

ROTOR

Q



Orifice Component Model

α

Ω

L

rf

U

V

Vrel

φ

z1

2

d

Vφ

ir

α

Ω

L

rf

U

V

Vrel

φ

z1

2

d

Vφ

ir

Ø Axial & radial holesØ Rotating & stationary

Discharge Coefficient CD corrected through correlations for:ü Hole Reynolds numberü Inlet corner radiusü Hole lengthü Pressure ratioü Incidence angle

( ) i:DRe:D3'dL,2dr,21D CC1ffff1C f ∆+−⋅⋅⋅⋅−=

α−

α⋅

−= φ−

cosVVU

taniis

1,1

Incidence Angle Definition



Labyrinth Seal Component Model

Ω

1 2

cp

STATOR

ROTOR

FIN

Ω

1 2

cp

STATOR

ROTOR

FIN

)PR1ln(nPR1

TR

PCAm

t

2t

1,t

1,tD +

−⋅

⋅⋅Γ⋅⋅=&

02.0pcpc

n1n1

1

+⋅

−−

=Γ

For flow through straight, staggered and stepped labyrinth seals

CD = 0.71 for 1.3 < c/t < 2.3




qMODEL VALIDATION

o Test Case 1

o Test Case 2

o Test Case 3


o System Level

o Engine Level

q CONCLUSIONS

Contents



Validation Test Case 1: Geis et al. (2004)

0.98

0.99

1

1.01

1.02

1.03

0 0.5 1 1.5 2 2.5 3 3.5βmix

T t,r

el,R

H /

T t,P

N

-0.2

-0.1

0

0.1

0.2

0.3

MR [N

m]

Geis et al. (2004) Measured Temparatures

Present Work Predicted Temparatures

Present Work Predicted Moments

Tt,rel,RH

Tt,PN



Validation Test Case 2: Lewis et al. (2006) - I

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0.0 0.5 1.0 1.5 2.0 2.5 3.0

βin

Θ

Present WorkTheoreticalComputed

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamberPre-swirl

Nozzles

ReceiverHoles

Pre-swirlChamber

( )2RH

2RH,rel,tPN,tP

rTTC2

⋅Ω

−⋅⋅=Θ

2RH

S

2

RH

PNin rm

M21rr2

⋅Ω⋅⋅

−−

⋅β⋅=Θ

&

Theoretical Value of Θ



Validation Test Case 2: Lewis et al. (2006) - II

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8βmix

CD

Present WorkCFDMeasured

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamberPre-swirl

Nozzles

ReceiverHoles

Pre-swirlChamber



Validation Test Case 2: Lewis et al. (2006) - III

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0.0 0.5 1.0 1.5 2.0

βmix

Θ

( )

⋅⋅Ω−=Θ

P

2RH

2

RH,rel,tPN,t C2rTT

1P

2RH

2

P

2RH

2

mixC2

rC2

r=β

⋅⋅Ω

⋅⋅Ω⋅Θ=Θ′



Validation Test Case 3: Chew et al. (2003)

-0.5

0

0.5

1

1.5

0 0.5 1 1.5

βmix

Θ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Present WorkMeasured

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

Inner Labyrinth

Seal

Outer Labyrinth

Seal

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

Inner Labyrinth

Seal

Outer Labyrinth

Seal

CD

Θ'

CD




qMODEL VALIDATION

o Test Case 1

o Test Case 2

o Test Case 3


o System Level

o Engine Level

q CONCLUSIONS

Contents



Optimisation: System Level

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5 3 3.5 4βin,RH

Θ

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CD,RH

CD Θ



Optimisation: Engine Level - I

H.P. CompressorBurner

H.P.Turbine

Pre-SwirlSystem

H.P.Compressor

Pre-SwirlSystem

H.P.Turbine

Burner



Optimisation: Engine Level - II

0.9

0.95

1

1.05

-5 0 5 10Change in Pre-swirl Nozzle Angle (deg)

β mix

-2

-1

0

1

2

3

4

Inci

denc

e A

ngle

i (d

eg)



Optimisation: Engine Level - III

0.87

0.92

0.97

1.02

Fuel Flow

Θ

βmix=1 at design

βmix=1.01 at design




qMODEL VALIDATION

o Test Case 1

o Test Case 2

o Test Case 3


o System Level

o Engine Level

q CONCLUSIONS

Contents



Conclusions

Ø A generic approach for modelling direct-transfer pre-swirl air systems using object-oriented simulation principles is presented. Ø Three components (orifice, cavity and labyrinth seal) are combined together to simulate different experimental pre-swirl systems found in the open literature. The predicted results are consistent with the experimental data and computational results reported in the relevant references. Ø The ease with which the proposed approach allows different pre-swirl system configurations to be constructed and evaluated, both on their own and as part of a complete engine performance model is demonstrated. Ø Since the approach presented allows components to be represented in varied levels of detail, it is possible to create more realistic models early in the engine design process.



Cavity Component Equations (I)

( )∑ ∑= =

φφ =⋅⋅−⋅⋅J

1j

K

1kkj,in,j,inj,inmix,mmix MVrmVrm &&

( )mix,kmix,kmixkkk,mk VrVrArC5.0M φφ −⋅Ω⋅−⋅Ω⋅ρ⋅⋅⋅⋅=

( )∑ ∑= =

⋅Ω+=⋅⋅−⋅⋅J

1j

K

1kkj,in,tj,pj,inmix,tmix,pmix MQTCmTCm &&

Angular Momentum Conservation Equation → Vφ,mix

Energy Conservation Equation → Tt,mix

Moment exerted by fluid on each surrounding surface, Mk (from drag force equation):



Friction Coefficients

( ) 2.05

o

i8.0m Rer

r1sin07288.0C −ϕ− ⋅

−⋅θ⋅=

fm CrL2C ⋅⋅π⋅=

( )[ ] 2f10f 6.0CRelog07.4C −ϕ −⋅⋅=

For free disks or cones with non-zero inner radius and half angle θ:

For a smooth cylinder of length L:

where



Cavity Component Equations (II)

Mixing total pressure, Pt,mix

( )refSSav TTAhQ −⋅⋅=

Axial momentum equation → Ps,mix:

Convective heat transfer, Q:

( ) ( )( )

ζ+

⋅−⋅ζ−⋅=

−γγ

1

mix,s

Pmixmix,tmix,smix,t T

CmQT1PP

&

( )( )mix,tis,mix,t

mix

mix,zmix

J

1jj,inj,in,sj,in,zj,in

mix,s PPA

VmAPVmP −−

⋅−⋅+⋅=

∑=

&&



Orifice Component Equations

( )

21

22,1,12,2

1

1,t

2,s

1,t

1,t1

1,t

2,s1,this

VVrVr2

PP

1P

12

PP

Am

−⋅−⋅⋅Ω⋅+

−⋅

ρ⋅

−γ

γ⋅⋅

⋅ρ⋅=

φφφ

γ−γ

γ

&

1-D, isentropic, compressible expansion of a perfect gas from the upstream total pressure to the downstream static pressure and considering the work transfer to the fluid:

Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation · 2009. 4....

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Transcript of Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation · 2009. 4....