Secondary Air System Component Modelling For Engine Performance Simulations · 2008. 6. 20. · ¾Describe an object-oriented approach for modelling Secondary Air Systems ¾Present

1Secondary Air System Component Modelling For Engine Performance SimulationsA. Alexiou & K. Mathioudakis

Laboratory of Thermal TurbomachinesNational Technical University of Athens

Secondary Air System Component Modelling For Engine Performance Simulations

A. Alexiou &

K. Mathioudakis


Paper Objectives

Describe an object-oriented approach for modelling Secondary Air Systems

Present the detailed modelling of some typical Secondary Air System components

Validate the modelling against publicly available experimental and/or computational results

Demonstrate the integration of such components in a whole engine performance model


SECONDARY AIR SYSTEM MODELLINGCOMPONENT MODELS

o Generic Componento Orifice Componento Labyrinth Seal Component

IMPLEMENTATION & VALIDATIONo Simulation Environment Overviewo Test Cases

Pre-Swirl ChamberRotating CavitiesRotating HolesPre-swirl System with Labyrinth Seals

o Whole Engine ModelSUMMARY & CONCLUSIONS

Contents


Secondary Air System Schematic

ORIFICESROTATING

DISC CAVITIESLABYRINTH

SEALS

PRE-SWIRL SYSTEM

DRIVE CONE CAVITY

RIM SEAL

ORIFICESROTATING

DISC CAVITIESLABYRINTH

SEALS

PRE-SWIRL SYSTEM

DRIVE CONE CAVITY

RIM SEAL


Secondary Air System Modelling: Current Approach

Dedicated Air System Model

Engine Performance Model

Values

for Bleeds & Returns for particular engine running conditions

DisadvantagesThe Secondary Air System is a “black box” for the

performance engineer.The Air System designer cannot assess autonomously the

system performance as part of the whole engine model.Increased scope for error during data exchange.


Secondary Air System Modelling: Proposed Approach

AdvantagesIndividual components or entire air systems can be integrated

transparently in whole engine performance models.Different air system design configurations can be constructed and

compared in a generic, flexible and intuitive manner.Component changes visible during model exchanging.

Secondary Air System (SAS) components directly integrated in

engine model. Boundary conditions (IN/OUT m, Pt, Tt, Vφ) communicated

through appropriate Ports.SAS component

(pre-swirl system)SAS Port







Contents


Component Models

Using the advantages of object-oriented modelling (such as encapsulation, inheritance, abstraction aggregation and polymorphism), it is possible to create secondary air system models for a variety of engine configurations using three main components: generic, orifice

and labyrinth seal.

For a specified component geometry, the inlet flow conditions (m, Pt, Tt, Vφ) are linked to the outflow ones through the conservation equations for mass flow, energy, axial and angular momentum.

The component’s performance can be calculated for any valid combination of input/output variables and component characteristics.


Generic Component Model

Ω

rK

, AKrm

r

zin out

rN

, AN

rJ

, AJ

mix

STATOR

ROTOR

Q

Arbitrary geometry (discs, cones, cylinders)J Input flows and N output flowsFully mixed flowWork and heat transfer from surrounding K surfacesSAS examples: pre-swirl system chamber, compressor inter-disc cavities,

drive-cone cavity


Generic 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):


Generic 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 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

Axial & radial holesRotating & stationary

is

hD m

mC =

Discharge Coefficient CD

corrected through correlations for:

Hole Reynolds numberInlet corner radiusHole lengthPressure ratioIncidence angle

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


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⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−γγ⋅

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅ρ⋅=

φφφ

γ−γ

γ

α−⎟⎟⎠

⎞⎜⎜⎝

⎛α⋅

−= φ−

cosVVU

taniis

1,1 α−⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

α⋅

+−= φ−

cosVV)VU(

taniis

21,z

21,1

Incidence Angle DefinitionAxial Holes Radial Holes

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:


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







Contents


Simulation Environment Overview

libraries

palette

Output Window

Engine Diagram(schematic view)

Experiment EL file(Simulation View)

Experiment Results(Simulation View)

Component EL file(Code View)


Test Cases: Pre-Swirl Chamber

( )2RH

2RH,rel,tPN,tP

rTTC2

⋅Ω

−⋅⋅=Θ

Adiabatic Effectiveness

PN

in,in r

V⋅Ω

=β φ

Inlet Swirl ratio

2RH

S

2

RH

PNin rm

M21rr2

⋅Ω⋅⋅

−−⎟⎟⎠

⎞⎜⎜⎝

⎛⋅β⋅=Θ

Theoretical value of Θ

( )P

RH,mix,RH2

RHmix,tRH,rel,t C2

Vr2rTT

⋅

⋅⋅Ω⋅−⋅Ω+= φ

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

Relative Total Temperature



-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-swirlChamber

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

Lewis et al, ASME GT-2006-90132



0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0βin

β mix

Present WorkComputed

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber




Geis

et al, J. Eng. Gas Turbine and Power, 126 (4), pp. 809-815

0.97

0.98

0.99

1

1.01

1.02

1.03

0 0.5 1 1.5 21/βmix

T t,re

l,RH /

T t,P

N

Measured (PR=1.10) Present Work (PR=1.10)Measured (PR=1.35) Present Work (PR=1.35)

Tt,rel,RHTt,PN



Geis


-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.5 1 1.5 21/βmix

MR [N

m]

Measured (PR=1.10) Present Work (PR=1.10)Measured (PR=1.35) Present Work (PR=1.35)

ROTOR



Geis


50

100

150

200

250

0 50 100 150 200Ωrm [m/s]

V φ,m

ix [

m/s

]

Present WorkMeasuredIsentropic


Test Cases: Rotating Cavities

Alexiou et al, Int. J. Experimental Heat Transfer, 13, pp. 299-328

0

0.01

0.02

0.03

0.04

0.05

0 2 4 6 8 10 12 14Bo

ΔT/

T

Present WorkMeasured

SHAFT

DISCSSHROUD

CA

VITY

SHAFT

DISCSSHROUD

CA

VITY


Test Cases: Rotating Holes –

Axial

Dittmann

et al, J. Eng. Gas Turbine and Power, 127, pp. 383-388

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45Incidence Angle, i (deg)

CD

Present WorkMeasured

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

L/d=5.66r/d=0.2α=0°NRH

=24



Axial

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-swirlChamber

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber


L/d=1.25r/d=0α=0°NRH

=60


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6βmix

CD

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber


Axial

Chew et al, ASME GT-2003-38084

L/d=0.86r/d=0α=0°NRH

=72


0.0

0.1

0.2

0.3

0.4

0.5

0.6

20 25 30 35 40 45Incidence Angle, i (deg)

CD

Measured: ΔΩ=0Present Work ΔΩ=0Measured: ΔΩ>0Present Work ΔΩ>0

ROTOR

SHAFT

ROTOR

SHAFT


Radial

Alexiou et al, Int. J. Heat and Fluid Flow, 21, pp. 701-709

L/d=0.45r/d=0.067α=0°NRH

=12


Test Cases: Pre-swirl System with Labyrinth Seals

-0.5

0

0.5

1

1.5

0 0.5 1 1.5

βmix

ΘPresent WorkMeasured

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

Inner Labyrinth

Seal

Outer Labyrinth

Seal

Pre-swirlNozzles

ReceiverHoles

Pre-swirlChamber

Inner Labyrinth

Seal

Outer Labyrinth

Seal

Chew et al, ASME GT-2003-38084


Whole Engine Model (I)

Pre-Swirl System

H.P.C. Air System


Whole Engine Model (II)

0.964

0.968

0.972

0.976

0.98

0.984

0.988

0.8 0.85 0.9 0.95 1 1.05 1.1βmix

T t,re

l,RH/T

t,PN

0.6

0.62

0.64

0.66

0.68

0.7

CD







Contents


Summary & Conclusions

An approach for modelling secondary air systems within an object-oriented environment for gas turbine engine performance simulations was presented.

The modelling of selected components was presented in detail. The components were used to simulate various air system configurations and the predicted results are consistent with available experimental data and computational results.

An example of adding parts of an air system to a whole engine performance model was given to demonstrate the benefits of this approach.

The flexibility of the simulation environment and the generality of the component modelling approach allow easily different air system configurations to be constructed and evaluated, both on their own and as part of a complete engine performance model.

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.


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


Heat transfer Coefficient Correlations

Natural Convection from a Vertical Plate:

Natural Convection from Upper Surface of heated Plate:

Forced Convection from a Flat Plate:

Lk

Pr492.01

Ra67.068.0h 94

169

25.0

av ⋅

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+

⋅+=

LkRa1.0h 31av ⋅⋅=

for Ra < 109 for Gr > 109

LkRa54.0h 25.0av ⋅⋅= L

kRa15.0h 31av ⋅⋅=

for 104

≤

Ra < 107 107

≤

Ra < 1011

LkRePr036.0h 8.0z

31av ⋅⋅⋅=

LkRePr662.0h 5.0z

31av ⋅⋅⋅=

for Rez

< 5×105 for Rez

≥

5×105

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Secondary Air System Component Modelling For Engine Performance Simulations · 2008. 6. 20. · ¾Describe an object-oriented approach for modelling Secondary Air Systems ¾Present