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A GT-POWER Based PredictiveA GT-POWER Based Predictive Radial Turbine Model

(P t)(Progress report)

Jan Macek Oldřich Vítek Ján BuričJan Macek, Oldřich Vítek, Ján BuričCzech Technical University in Prague,

Josef Božek Research CenterJosef Božek Research Center

Overview of Presentation1. Introduction 2. Tools for 1-D Simulation of a Radial Turbine3 Application of 1 D Modules to In Turbine Flow3. Application of 1-D Modules to In-Turbine Flow

Simulation 4. Calibration of a 1-D Turbine Model5 Examples of Results5. Examples of Results6. Conclusion and Prospects

Goals: To simulate interaction between exhaust pressure waves and a turbinepressure waves and a turbine.To extrapolate a turbine map keeping physical meaning of it.

2

1. Introduction: State-of-the-Art Att t t d ib t t bi• Attempts to describe pressure waves at a turbine(or compressor) since 1960’s to present: simple, schematic models using “1D” central streamline w/o g /realistic geometry.

• “1D” central streamline steady model developed and successfully calibrated (SAE 2002 SAE 2008)and successfully calibrated (SAE 2002, SAE 2008)

• Measurements at model turbine pulsator testbeds or directly at an engine- use of results with use of results with

/ l ti ?/ l ti ?mass/energy accumulation?mass/energy accumulation?• Tools for 3-D CFD simulations – time and computer time and computer

capacitycapacity requirementrequirementss.capacity capacity requirementrequirementss.• Tools for 1-D simulations (nearly) ready for

application (SAE 2008).

3

1. Introduction: MotivationhNeed for more accurate turbine model based

IntroductionIntroductionTools for 1-D Simulation of a Radial TurbineApplication of 1-D hNeed for more accurate turbine model based

on experiments suitable for engine/TC simulation and matching and natural

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelR lt

TURBINE PARAMETERS = f(deg CA)

1 1

1.2

;

3gextrapolation of a turbine map (based on physics) to high pressure ratios (supercritical) and wide range of blade speed ratio (low

ResultsConclusion and Prospects

mm 1206

gine

BoreNumber of cylinders

0 8

0.9

1

1.1ic

ienc

y et

aT;

effic

ient

muT

;tio

x=u

/c s

]

1 5

2

2.5

tio p

i T [

1]

and wide range of blade speed ratio (low number of cylinders per a manifold branch).Diabatic turbine modelling.

r.p.m. 2000Turbocharger speed r.p.m. 90 000

deg CA 10.2Turbine stator deg CA 8.2T bi t d CA 2 1

Manifold

elay

of

pres

s.

wav

e as

sage

Eng

Engine speed

0.6

0.7

0.8

sent

ropi

c Ef

fiis

char

ge C

oeVe

loci

ty R

at [ 1

0 5

1

1.5

Pres

sure

Rat

eta T u/c shTime scales of turbine unsteadiness: large

(transient response), medium (exhaust pressure waves) small (impeller channel

Turbine rotor deg CA 2.1deg CA 33.7

Turbine revolution deg CA 8.0Turbine stator deg CA 27.1Turbine rotor deg CA 6 8

Manifold

De p w

pa

Del

ay o

f flo

w s

ingl

e pa

ssag

e0.4

0.5

90 180 270 360Crank Angle [deg from CTDC]

Is Di

0

0.5 Peta T u/c s

mu T pi T

pressure waves), small (impeller channel passage).hMedium scales should be addressed.

Turbine rotor deg CA 6.8f

Heisler Engine Technology SAE 1998

Crank Angle [deg from CTDC]

4

Medium scales should be addressed. Heisler, Engine Technology. SAE 1998

1. Introduction: MotivationhNeed for more accurate turbine model based

IntroductionIntroductionTools for 1-D Simulation of a Radial TurbineApplication of 1-D N li d V l it M f R di l T bihNeed for more accurate turbine model based

on experiments suitable for engine/TC simulation and matching and natural

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelR lt

Normalized Velocity Maps of Radial Turbine

1.0 1.1

Radial Turbine at High Pressure RatioOptimum Velocity Ratio

0.90 1.20

simulation and matching and natural extrapolation of a turbine map (based on physics) to high pressure ratios (supercritical)


0.8

0.9

Effi

cien

cy

1]

1.0

1.1

effi

cien

t [1

]

0 80

0.85

nd

0 80

1.00

Exit

Mac

h

p y ) g p ( p )and wide range of blade speed ratio (low number of cylinders per a manifold branch).0.6

0.7

Isen

trop

ic E

eta

nom

[

0.9

1.0

sch

arge

Coe

mu

T n

om [

0.75

0.80

ic E

ffici

ency

an

city

Rat

io [1

]

0.60

0.80

icie

nt ;

Noz

zle

umbe

r [1

]

0.4

0.5

orm

aliz

ed I

eta

T/

0.8

0.9

Rel

ativ

e D

ism

u T

/m

0.70

Isen

trop

iVe

loc

0.40

scha

rge

Coe

ffi Nu

u/cs opt

eta T max

0.2

0.3

0 600 0 800 1 000 1 200 1 400 1 600 1 800

No

0.7

0.8

R

0.60

0.65

1 5 2 0 2 5 3 0 3 5 4 00.00

0.20 Dis

mu T nom

Nozzle Mach #

5

0.600 0.800 1.000 1.200 1.400 1.600 1.800

Normalized Blade Speed Ratio x/x nom [1]

1.5 2.0 2.5 3.0 3.5 4.0

Pressure Ratio pi T [1]

1. Introduction: Motivation

hM fl ibl t bi d l f

IntroductionIntroductionTools for 1-D Simulation of a Radial TurbineApplication of 1-DhMore flexible turbine model for

different layouts with integrated boost t l EGR it bl t di

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelR lt control or EGR suitable at medium

time-scale accuracy.ResultsConclusion and Prospects

hTwin-scroll with pressure wave shift and assymetry due to scroll design, WG inlet,

hIntegrated WG chamber or outlet diffuser.

etc.

6

1. Introduction: Motivation

hM fl ibl t bi d l f

IntroductionIntroductionTools for 1-D Simulation of a Radial TurbineApplication of 1-DhMore flexible turbine model for

different layouts with integrated boost t l EGR it bl t di

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelR lt control or EGR suitable at medium

time-scale accuracy.ResultsConclusion and Prospects

hDifferent variable geometries.hOutlet diffuser with unsteady flow.

7

Introduction Tools for 1Tools for 1--D D Simulation of a Simulation of a Radial TurbineRadial TurbineApplication of 1-D M d l t I

2. Tools for 1-D Simulation of a Radial TurbineModules to In-

Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults

a Radial TurbineModules and solvers for 1-D “Pipe” with variable cross/section area, source terms for enthalpy andResults

Conclusion and Prospects

cross/section area, source terms for enthalpy and momentum, external acceleration (rotating pipe) and curvature.Modules for flow momentum mixing/ splitting (“Flow splits”).Modules for orifices with variable discharge coefficient/area and sensor/signal processor/actuator h ichains.

1-D central streamline, steady flow turbine model. Definition of loss and flow separation coefficients

8Definition of loss and flow separation coefficients.

2. Tools for 1-D Simulation of a Radial Turbine


Modules with external

a Radial TurbineModules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults Modules with external

acceleratin: splitting an impeller into parts with


impeller into parts with different orientation to axis of rotation

r x, w

axis of rotationrεr εa

wu

aεt

9t

2. Tools for 1-D Simulation of a Radial T bine


Transformation modules must be

a Radial TurbineModules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults Transformation modules – must be

“programmed” separately to change total enthalpy by a source term (“heat transfer”)


u2

enthalpy by a source term ( heat transfer ) and velocity (pipe cross-section) maintaining all static state parameters and g pmass flow rate

I

IleakNI

m

mmm −=•

•••Δ

cu3

uNIrefI

NrN

IIrIref

wwA

mcw

222

2222

αβ

ρtantan −

=

== c3

w3

10( ) ( )IN

rIrelI

IrI

wmcwhhmH

w

22

22

222

22

000

22

22βα tantan −−=

−=−=

••Δ



Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults

Modules and solvers for 1-D “Pipe” with variable cross/section area, source terms for enthalpy and( ) ( )wACwAm sgeomD ηρρ ==•

2222ResultsConclusion and Prospects

cross/section area, source terms for enthalpy and momentum, external acceleration (rotating pipe) and curvature.

( ) ( )whhΔhhhhhw

lostss

sgeomD

ηη

ηρρ

=−

=+−=−=2

2201201201

22

2222

22Modules for flow momentum mixing/ splitting (“Flow splits”).

Cp Pκκ

ηη

⎥⎤

⎢⎡

⎟⎞

⎜⎛

−

2

1

02

22

Modules for orifices with variable discharge coefficient/area and sensor/signal processor/actuator h i

w2

CppT= cΔh P

plost =⎥⎥⎥

⎦⎢⎢⎢

⎣⎟⎟⎠

⎞⎜⎜⎝

⎛− 2

201

0201 1

chains.1-D central streamline, steady flow turbine model. Definition of loss and flow separation coefficients

C ;C+1

1 = DP

ηη =

⎦⎣

11Definition of loss and flow separation coefficients.

C + 1 P



Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults

Modules and solvers for 1-D “Pipe” with variable / ti t f th l d


cross/section area, source terms for enthalpy and momentum, external acceleration (rotating pipe) and curvature – transformation of absolute to relative;;

π II nD

wmw ==

•

2curvature – transformation of absolute to relative coordinates and back.Modules for orifices with variable discharge

;; Tu

ref

ref nw

rTpA

w == 2

2

2 60

Modules for orifices with variable discharge coefficient/area and sensor/signal processor/actuator chains.

tantan γδref

urefw

ww ±=

22 ( )tantan δγ

f

ref

w

wwcKhhq −=−

=−= 22222

22

0201 2m

12n)dissipatiokin.en.oft (assessmen

cosδref

transfww =

3. Application of 1-D Modules to In-Turbine Flow Simulationheat sink h0-h0rel

heat sink h0rel-h0CP for Borda-Carnot compensationA3 =var for outlet kinetic energy

Introduction Tools for 1-D Simulation of a Radial TurbineApplication ofApplication of

Stator –Impeller

TurbineImpeller RP 4A A / β

FlowConnection

C =K

Impeller –

StatorUnsteady Flow Pipe P1Flow

Connection

Turbine Nozzle P2Aout=Aref/cosα2

l C

FlowConnection

C 1

CP for Borda-Carnot compensationCP and A2 for incidence loss

FlowConnection

C 1

Application of Application of 11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulation

pP3 Aout=Aref/cosβ3

press. loss C PI

CI,=Ksep StatorP4

ImpellerLeakages

half scroll length

y pCD =1 press. loss C PN CD=1 CD=1

Existing 1-D turbine model for steady flow: Turbine

speedTurbine

transformation into unsteady 1-D scheme

speedtorque

( )δγ 22222

22

0201 2tantan −=

−±=−= refwwchhq m

13 2008-01-0295

3. Application of 1-D Modules to In-Turbine Flow Simulation

Introduction Tools for 1-D Simulation of a Radial TurbineApplication ofApplication of

Unsteady Flow Pipe P1Flow

ConnectionTurbine

Nozzle P2Flow

ConnectionTurbine

Impeller RP 4Flow

Connection

Impeller –

Stator

In Turbine Flow SimulationApplication of Application of 11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulation

Stator –Impeller

FlowConnection

half scroll length

y pμ=1

Connection Impeller RP 4 StatorP4

pP3

Connection

ImpellerLeakages

Turbine speedTurbine

1-D turbine model for unsteady model: transformation 1-D solvers using

speedtorque

gsensor/signal processor/actuator chains and interpolation of turbine features

14

p


Introduction Tools for 1-D Simulation of a Radial TurbineApplication of Application of 11 D M d l tD M d l t11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulationCalibration of a 1-D Turbine

Amended modules

ModelResultsConclusion and Prospects

Sources and sinks of total enthalpy (heating, cooling) in energy conservation b d t t l d t ti t t

;;π

TI

uI

ref nD

wmw ==

•

22 60based on total and static states

measured upstream a transformation module tan

;;

γf

Tu

ref

ref

wwrTpA

±

2

2

2 60

module.Input of flow cross-section according to empirically corrected exit angles at of( )

tantan γδref

uref

wcKhh

www

−

±=

22222

22empirically corrected exit angles at of

nozzle and impeller.( )

n)dissipatiokin.en.oft(assessmen

tantan δγ

reftransf

ref

ww

wwcKhhq

=

−==−= 222220201 2

m

15

n)dissipatiokin.en.oft (assessmen cosδtransfw


Introduction Tools for 1-D Simulation of a Radial TurbineApplication ofApplication of Turbine Flow SimulationApplication of Application of 11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulationCalibration of a 1-D Turbine

Borda Carnot pressure recovery has to becompensated at transformation pipe1-D Turbine


compensated at transformation pipeconnections (in a different way for subsonic and sonic regions)Carnot/Borda Pressure "Loss"g )Amendment of rothalpy and centrifugal acceleration terms into energy and

Carnot/Borda Pressure Loss

00 1 2 3 4 5 6

Pipe Flow Area/Nozzle Flow Area

0

momentum conservation equations.-10

-5

nt

Rel

ated

to

rgy

of w

2

-0.2

-0.1

nt

Rel

ated

to

rgy

of w

3

dze D ideal diffuser (w_3)

dze B related to w_3

25

-20

-15

oss

Coe

ffic

ien

Kin

etic

En

e

0 5

-0.4

-0.3

oss

Coe

ffic

ien

Kin

etic

En

edze B related to w_2

16-30

-25Lo

-0.6

-0.5 Lo



Turbine torque has to be calculated from the change of angular momentum1-D Turbine


the change of angular momentum.Turbine power from the torque and speed; coupling to a compressor∫∫∫∫∫ ⎞⎛∂ →→→→→→→

input - outputaccumulationangular accelerationspeed; coupling to a compressor.Instantaneous turbine efficiency is influenced by accumulation( )

∫∫∫∫∫

⎪⎫

⎪⎧ +⎥

⎤⎢⎡ ++

=⎟⎠⎞

⎜⎝⎛ ×−×

∂∂

−=Δ

•

∂

→→→→→→

→

→

VV

bladesgasT

wrmr

dAnccrdVcrt

M

εω

ρρ

cos

.,

flow accelerationinfluenced by accumulation.( )

( )⎪⎪⎪⎪⎪

⎪⎪⎪⎪⎪

+⎥⎦⎤

⎢⎣⎡ +−

+⎥⎦⎢⎣++

⎤⎡ ⎞⎛⎤⎡ ⎞⎛∂

•

→→•→→•→→ n i

iint

wrmr

wrmr

εω

εω

cos

cosflow acceleration

( )∑

⎪⎪⎪

⎪⎬

⎪⎪⎪

⎪⎨

+⎟⎠⎞

⎜⎝⎛ −+−

⎦⎣≈⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ ×+⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ ×−Δ×

∂∂

−=••i

ioutiint

iout

inout mmwrr

crmcrmVcrt

εω

ρ

cos

17 ⎪⎪⎪

⎭⎪⎪⎪

⎩−− j

tjjjjj dtdw

rmdtdrm εω cos2



Leakage flows.1-D Turbine ModelResultsConclusion and Prospects

Windage losses and mechanical efficiency prediction.Input of additional pressure losses (incidence angle, ...) as the sink term

f t d fl tiof momentum and flow separation losses.Backflo s th o gh impelle channelsBackflows through impeller channels.Twin scroll flow mixing.V l l d t diff

18Vaneless nozzle or downstream diffuser.

4. Calibration of 1-D Turbine Model

To build GT Power model:

Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D To build GT Power model:

Experiments at a turbine (reduced mass flow-rate & turbine efficiency at different PR and

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a Calibration of a 11--D Turbine D Turbine ModelModel rate & turbine efficiency at different PR and

BSR u/cs)Geometrical data for 1-D model

ModelModelResultsConclusion and Prospects

G t i l t f GT P d lGeometrical data for 1-D modelCalibration of steady 1-D model using optimizer for the best fit of results for sets of

Geometrical parameters for GT Power modelCalibration of GT Power model at steady flow using optimizeroptimizer for the best fit of results for sets of experiment results at similar PR and BSR ranges

flow using optimizerUse of GT Power model for unsteady simulationsgTransfer of parameters into GT Power model and unsteady simulations

simulations.

19


The first calibration procedure using “the

Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D

Calibration errors may be reduced: TheThe first calibration procedure using “the best fit model parameters” using non-linear regression published in SAE 2002-01-0337

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a Calibration of a 11--D Turbine D Turbine ModelModel

ΔμT [1] 5%

Calibration errors may be reduced: The experimental data subdivided into smaller groups in dependence on turbine speedregression published in SAE 2002 01 0337 More flexible approach based on general optimization methods (e.g., genetic


groups in dependence on turbine speed.

optimization methods (e.g., genetic algorithms) finding generally valid fixed parameters.

Pareto frontierΔηT [1]

5%

20


The first calibration procedure using “the

Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D The first calibration procedure using the

best fit model parameters” using non-linear regression was published in SAE 2002-01-0337 It fi d i bl lib ti

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a Calibration of a 11--D Turbine D Turbine ModelModel 0337. It finds variable ccalibartion

parameters. More suitable approach is based on general


More suitable approach is based on general optimization methods (e.g., genetic algorithms) finding generally valid fixedparametersparameters.

Calibration errors due to the variability of parameters may be reduced: Theparameters may be reduced: The experimental data can be subdivided into smaller groups in dependence on turbine

21

s a g oups d p d o u bspeed and/or pressure ratio.

5. Examples of ResultsIntroduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D

f fTurbine map represented by calibration parameters: examples of

l d d h ff

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l f

Examples of prediction of a turbine discharge coefficient and efficiency -

d flexit angles and discharge coefficients. (“efficiencies”)

Examples of Examples of ResultsResultsConclusion and Prospects

48.0

49.0

50.0

deg.

]

Pressure Ratio 1.664.0

65.0

[deg

.]

0.9

1.0

[1]

steady flow.The unsteady 1-D model has used

41 0

42.0

43.0

44.0

45.0

46.0

47.0

Impe

ller E

xit A

ngle

[d

Pressure Ratio 1.6Pressure Ratio 2.0Pressure Ratio 2.4

61.0

62.0

63.0

Noz

zle

Rin

g E

xit A

ngle

Pressure Ratio 1.6Pressure Ratio 2.0Pressure Ratio 2.4

0.7

0.8

Isen

trop

ic E

ffici

ency

Nozzle Efficiency at Pressure Ratio 1.6Nozzle Efficiency at Pressure Ratio 2.0Nozzle Efficiency at Pressure Ratio 2.4Impeller Efficiency at Pressure Ratio 1.6Impeller Efficiency at Pressure Ratio 2.0

only simplified losses yet, i.e., no look-up tables and no correction of

40.0

41.0

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

BSR [1]

60.00.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

BSR [1]

0.60.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

BSR [1]

Impeller Efficiency at Pressure Ratio 2.4

incidence angle loss.

22BSR [1] BSR [1]


5. Examples of ResultsT f f 1 D t d d l i t GT

Velocity Map of a Radial Turbine

0.9Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l f

Transfer of 1-D steady model into GT Power:

y Turbine map calculated from steady and 1-D0.7

0.8

0.9

y et

a T

Examples of Examples of ResultsResultsConclusion and Prospects

y Turbine map calculated from steady and 1 D unsteady models for the set of presure and blade speed ratios.

y Turbocharger test rig model used for steady0.5

0.6

0.7c

Effi

cien

cy[1

]

Isentropic Efficiency at Pressure Ratio=1 50.8

0.9

1 data based on MS ExcelEfficiencydata based on 1-D GT-PowerEfficiency

y Turbocharger test-rig model used for steady flow tests.

y Turbine used at 4 cylinder engine.0.3

0.4

Isen

trop

ic Isentropic Efficiency at Pressure Ratio=1.5Isentropic Efficiency at Pressure Ratio=2.0Isentropic Efficiency at Pressure Ratio=2.5Isentropic Efficiency at Pressure Ratio=3.0Isentropic Efficiency at Pressure Ratio=3.5Di h C ffi i t t P R ti 1 5

1

0 4

0.5

0.6

0.7

eff_

T

y Tested cases: 8Turbine map predicted by 0-D MS Excel model

interpolated by the standard GT-Power procedure

0.20.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0

Bl d S d R ti [1]

Discharge Coefficient at Pressure Ratio=1.5Discharge Coefficient at Pressure Ratio=2.0Discharge Coefficient at Pressure Ratio=2.5Discharge Coefficient at Pressure Ratio=3.0Discharge Coefficient at Pressure Ratio=3.50.6

0.7

0.8

0.9

T

0.1

0.2

0.3

0.4

80-D MS Excel model interpolated in a look-up table

81-D unsteady model

Blade Speed Ratio [1]

0 2

0.3

0.4

0.5

mi_

T

data based on MS ExcelDischarge Coefficient

00 0.2 0.4 0.6 0.8 1 1.2 1.4

x

238Turbine map predicted by 1-D unsteady model

interpolated by the standard GT-Power procedure0

0.1

0.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

x

data based on 1-D GT-PowerDischarge Coefficient


Test at simulated turbocharger test-rig (turbine loaded by a compressor). Turbine operation close to optimum efficiency before

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l f operation close to optimum efficiency before

sonic limit is reached.Examples of Examples of ResultsResultsConclusion and Prospects

24


fApplication of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l f

Comparison of 0-D and 1-D turbine models at a 4 cylinder, single exhaust

f ldExamples of Examples of ResultsResultsConclusion and Prospects

manifold at 1200 rpm

25

5. Examples of Resultsf


Comparison of engine parameters using both models

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l fExamples of Examples of ResultsResultsConclusion and Prospects

26

6. Conclusion and Prospectsh St d d l h b lid t d d d f

Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D h Steady model has been validated and prepared for

expected application. h The work on fully unsteady model in progress,

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l f application of detailed loss model will be done

soon. h Models under development:

Examples of ResultsConclusion and Conclusion and ProspectsProspects

Models under development:hTwin scroll model (momentum exchange,

backflow to the other manifold branch, assymetry of flows)assymetry of flows)hImpeller channel unsteadiness due to rotation

along scroll. Use of unsteady channel-switching model f om PWS (COMPREX®) SAE 2004 01model from PWS (COMPREX®) SAE 2004-01-1000

27

6. Conclusion and ProspectsU f i i i


h Use of experiments at an engine in operation with a help of “TPA” from GT Power

Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l f PowerExamples of ResultsConclusion and Conclusion and ProspectsProspects

1

0.6

0.8

0

0.2

0.4

etaT

s,m

-0.4

-0.2

0

28

-180 0 180 360 540 720

Crank Angle [deg]

etaTs,m etatsmap U/Cs

6. Conclusion and ProspectsIntroduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D

f

Scroll Flow Split FS1

Turbine Nozzle N1

Turbine

Impeller Leakage 1

Turbine Nozzle N2


Impeller Leakage 2


Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l f

Future comprehensive model of a turbine: scroll/blades/impeller

Stator – Impeller

P1

speed

Stator – Impeller

P2

Turbine Impeller RP 1

Turbine Impeller RP 2

Impeller – Stator P1

Impeller – Stator P2 Scroll Flow Split FS1 Scroll Flow Split FS2

Examples of ResultsConclusion and Conclusion and ProspectsProspects

interactionTurbine

Nozzle N1 ImpellerLeakage 1

TurbineNozzle N2

ImpellerLeakage 2


Turbine speed

g

Stator – Impeller

P1

Stator –Impeller

P2 Turbine

Impeller RP 2 Impeller – Stator P2

TurbineImpeller RP 1

Impeller –Stator P1

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A GT-POWER Based Predictive Radial Turbine Model

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Turbine Model

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Q ?Questions?

30

Transformation StatorImpellerInputs (1...upstream, 2...downstream, 0 .. total)

)actuatedbladesofangle(

,...,,,,,,,,, = 11010101111

Ap

Acc

cTphTpv

pp κρ

)actuated ,2

wh of efficiency isentropic(

)actuatedblades,ofangle(,,2

→−= 11

22

ηC

Ap

p

ref

Δ

γ

actuated)

,Connection Flow in ncontractio flow oft coefficien(2

= KCη

sepD

statorimp ... impstator ...

actuated)

→+→−

=11

K

31

Transformation StatorImpellerVelocity and total state transformation

•

;;π

TI

u

ref

Iref n

Dw

rTpA

mw == 22

2 60

tantan γδf

urefw

KwwrT

+=

2

( )tantan δγref

ref

cwKTT

w

−+= 222

0102 2

( )tantan δγref

p

wKwhh

c

−+= 2220102

2

32 n)dissipatio kin.en. oft (assessmen cosδ

reftransf

ww =

Transformation StatorImpellerOutputs

,,,ρ 2022 whm•

)flow of angle(,,, δ02Tww transfref

33

agta gt-power based predictivepower based ... gt-power based predictivepower based predictive radial...

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