1-D Model of Radial Turbocharger Turbine Calibrated by Experiments

1-D Model of Radial TurbochargerTurbine Calibrated by

Experiments

Jan Macek, Jiří Vávra, Oldřich VítekCzech Technical University in Prague,

Josef Božek Research Center

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ContentsIntroductionDemands on a turbochargerTypes of turbine characteristics1-D model of a radial turbineModel calibration procedureResults of calibrationExamples of predictionsConclusions

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Introduction

Motivation - recent demands on aturbocharging

downsizing of engines - efficiency,emissions - requires high boostpressureoptimum turbine efficiency!simulation is an unavoidable toolcorrect turbine characteristics needed!

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Introduction

Turbine characteristics predictionresults of experiments carried out in areasonable range (velocity ratio, pressureratio,…) should be extrapolated;appropriate form for extrapolation needed;extrapolation to high pressure ratio using1-D model is cheap and flexible only if themodel is calibrated!

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ContentsIntroductionDemands on a turbochargerTypes of turbine characteristics1-D model of a radial turbineModel calibrationResults of calibrationExamples of resultsConclusions

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Demands on turbocharger

Boost pressure ratio higher than ~ 2 requires

high efficiency of a turbocharger

Compressor/turbine interaction

compressor input keeps turbocharger speed near

to optimum turbine efficiency if properly tuned

pulse exhaust manifolds require compromise

turbine setting concerning its averaged efficiency

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Demands on turbochargerPulse exhaust manifolds require compromiseturbine setting concerning averagedefficiency

TURBINE PARAMETERS = f(deg CA)

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

100 150 200 250 300 350 400

Crank Angle [deg from CTDC]

Ise

ntr

op

ic E

ffic

ien

cy

eta

T;

Dis

ch

arg

e C

oe

ffic

ien

t m

uT

Ve

loc

ity

Ra

tio

x=

u/c

s

[ 1

]

0

0.5

1

1.5

2

2.5

3

Pre

ss

ure

Ra

tio

p

i T

[1

e ta T u/c s

mu T pi T

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Types of turbine characteristics

Operation parameters

pressures p0T1, pT2 and pressure ratio

gas temperatures T0T1 , T0T2

turbine speed nT and reduced speed

Performance parameters - standard characteristics

reduced flow rate

isentropic efficiency

2

10

T

TT p

p=π

10T

TTred T

nn =

10

10

T

TTTred p

Tmm

&& =

( )

−−=

−κκ

πη1

102010 1 TTpTTpTs TcTTc

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02P-447

Standard form

of turbine

characteristic.

Strong

dependence

on pressure

ratio.

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Range of turbine operation


Standard form

of turbine

characteristic.

Big efficiency

changes, strong

pressure/speed

dependence.

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Range of turbine operation

Types of turbine characteristicsTurbine flow rate depends on its speed, noton pressures only

Standard form of turbine characteristics isnot suitable for extrapolation.

Derived (“dimensionless”) form ofcharacteristics should eliminate mainpressure dependencies.

Mutual substitution of both types is provided.

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Types of turbine characteristicsDerived operation parameters eliminating mainpressure dependence

pressure ratio

turbine velocity ratio

Mach number calculated from impeller circumferrence

velocity

2

10

T

TT p

p=π

1010

max,

T

TM

T

DTu T

nKa

uM ==

−==

−κκ

π1

10max, 12; TTps

s

DT Tccc

ux

nTred

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Types of turbine characteristicsPerformance parameters eliminating main pressuredependence

discharge coefficient

isentropic efficiency( )

2

22010

s

TTpTs c

TTc −=η

( )TT

TT

TrefT p

TmA πψ

µ11

10

10&=

−=

−κκ

π1

10 12 TTps Tcc( )

111

12

12

12

2

−∗−+

∗−−

+=>

+

=

≤

−

⟨κκ

κκ

κππ

κκ

π

ππππ

at

ψ

at rc.

TT

T

TTκκ+

TκTp

mTred

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Turbine Characteris tics at Engine with Puls e Manifold

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

Ve loc ity Ratio [1]

Isen

trop

ic E

ffic

ienc

y;

Dis

char

ge C

oeff

icie

nt

[1]

0

0.5

1

1.5

2

2.5

3

Pre

ssur

e ra

tio

[1]

Discharge Coefficient

Isentropic Efficiency

Pressure Ratio

Both

pressure

and velocity

ratio

influences

must be

considered

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maximumefficiency

nominalvelocity ratio

nominal dischargecoefficient

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Both pressureand velocityratioinfluencesmust beconsidered:nominalvalues


efficiency

dischargecoefficient

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Both pressureand velocityratioinfluencesmust beconsidered:relative(normalized)valuescompared tonominalones


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1-D modelof a radialturbine

Inlet scroll

Nozzlering

Impeller

OutletOutletdiffuserdiffuser

Impeller incidenceImpeller incidenceloss and relativeloss and relative

motionmotion

LLeeaakkaaggee

ImpellerImpellerwindagewindage

Flowseparation

• flow rateinfluenced bylosses and flowseparation

• efficiencylosses due tofriction andflow separation(wakes)

• windage

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1-D model of a radial turbine

c2w3

u2 u3

c3w2Iw2N

t +

r or a +

angle +α2

β2N

β3

α3

Velocity transformation

Impeller incidenceImpeller incidenceloss and relativeloss and relativemotionmotion

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1-D model of a radial turbine

s

∆hN

01 02 I

s3s3 N

3s3 I

∆hI

∆hIi loss

h02 N

1

2 N 2 I

0 rel2 N 0 rel2 I

c12/2

03

0 rel3

c22/2

PT/mT w2N2/2 w2I

2/2

-u2I2/2-u3I

2/2

w32/2s2

c32/2

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1-D model of a radial turbineSummary of model features

Flow through a nozzle channel withdissipation in turbulent boundary layersInfluence of centrifugal and Coriolisacelerations (rotating channel)Incidence angle loss at impellerLeakages at impeller shroud and hub(different impact of centrifugal force fields)Flow separation at shroud surfaceIterations based on the case ofincompressible liquid

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Model calibrationCalibration according to performancevariables - both flow rate (dischargecoefficient) and turbine efficiency determinedby experimentsExperiments at different operationparameters

turbine speedpressure ratioupstream turbine temperaturevelocity ratio, pressure ratio and Mach numbercalculations

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Model calibrationTuning parameters

exit angles at a nozzle ring and impeller - 2isentropic efficencies - 2incidence loss coefficient - 1leakage discharge coefficients at impeller shroudand hub - 2flow contraction coefficient due to flowseparation at impeller shroud - 1windage loss coefficient of an impeller - 1TOTAL 9

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Model calibrationCalibration procedure - step 1 -representation of experiments - turbinedriven by compressed air and loaded bydynamometer or a special compressor

regression representation of results ofexperiments (enables later interpolation ofperformance parameters)sets of performance and operation parameteroccurrences - using interpolation of measuredparameters in reasonable neighborhoods ofmeasured points

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Model calibrationCalibration procedure - step 2 - features of amodel:

sensitivity analysis of performance parameters atdifferent operation ones to changes of tuningparametersregression substitution of results at two levels -dependencies on operation and tuningparameterscreation of a non-linear set of equations withunknown tuning parameters if both if both performanceperformanceand and operationoperation parameters assumed to be defined parameters assumed to be defined

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Model calibrationCalibration procedure - step 3 -

interpolation of the results of experimentsusing their regression representation in areasonable neighborhood of a measured points -providing 9 equations9 equations for 9 unknownssolving the nonlinear set of equations from thestep 1repeating for different operation points untildependence of tuning parameters on operationparameters is provided.

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Results of calibration

Exit flow angles

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Eficiencies of both nozzle ring and impeller


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Examples of resultsMeasurement and simulation with constantand variable tuning parameters at differentpressure ratios πT

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πT=1.6


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πT=2.0


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πT=2.4

Examples of resultsDifferences of performance parameters independence on either optimum or constantvelocity ratio are significant at high pressureratios.A compressor keeps an uncontrolled turbineroughly at constant velocity ratio!

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Examples of results

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Total turbine

characteristics

for different

pressure

ratios in

dependence

on a velocity

ratio

Examples of resultsPositive influence of an outlet diffuser

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w/ diffuser of bigDout/Din

originalturbine

w/ diffuser of smallDout/Din


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Conclusions1-D model of a radial turbine has beenvalidated by experiments.

Calibrating procedures were developed.

Direct links of results to 1-D codes of cyclesimulation are provided at different levels

ya standard turbine characteristics, employed bymost of ICE simulation codes;

ythe modules in the form of special pipe elementsfor advanced engine codes.

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ConclusionsThe model provides moreover simulationtools foryvaneless components upstream a turbine

impeller,

ya vaneless axial-radial diffuser downstream aturbine impeller,

yinvestigation of the limit of sonic critical stateand its impact on a flow rate and isentropicefficiency,

ya mixing in a shear layer downstream a twin-entry scroll with different inlet pressures.

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Acknowledgements

This research has been supported by theproject „Research Centers“ of the Ministry ofEducation , Czech Republic, #LN00B073.This help is gratefully appreciated..

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The End

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1-D Model of Radial Turbocharger Turbine Calibrated by Experiments

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