1-D Model of Radial Turbocharger Turbine Calibrated by Experiments
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Transcript of 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
Company Logo
ContentsIntroductionDemands on a turbochargerTypes of turbine characteristics1-D model of a radial turbineModel calibration procedureResults of calibrationExamples of predictionsConclusions
2002-01-0377
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
2002-01-0377
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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ContentsIntroductionDemands on a turbochargerTypes of turbine characteristics1-D model of a radial turbineModel calibrationResults of calibrationExamples of resultsConclusions
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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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Types of turbine characteristics
02P-447
Standard form
of turbine
characteristic.
Strong
dependence
on pressure
ratio.
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Range of turbine operation
Types of turbine characteristics
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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Types of turbine characteristics
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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Types of turbine characteristics
maximumefficiency
nominalvelocity ratio
nominal dischargecoefficient
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Both pressureand velocityratioinfluencesmust beconsidered:nominalvalues
Types of turbine characteristics
efficiency
dischargecoefficient
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Both pressureand velocityratioinfluencesmust beconsidered:relative(normalized)valuescompared tonominalones
ContentsIntroductionDemands on a turbochargerTypes of turbine characteristics1-D model of a radial turbineModel calibrationResults of calibrationExamples of resultsConclusions
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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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ContentsIntroductionDemands on a turbochargerTypes of turbine characteristics1-D model of a radial turbineModel calibrationResults of calibrationExamples of resultsConclusions
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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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ContentsIntroductionDemands on a turbochargerTypes of turbine characteristics1-D model of a radial turbineModel calibrationResults of calibrationExamples of resultsConclusions
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Results of calibration
Exit flow angles
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Results of calibration
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Eficiencies of both nozzle ring and impeller
Results of calibration
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Results of calibration
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Results of calibration
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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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Examples of resultsMeasurement and simulation with constantand variable tuning parameters at differentpressure ratios πT
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πT=1.6
Examples of resultsMeasurement and simulation with constantand variable tuning parameters at differentpressure ratios πT
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πT=2.0
Examples of resultsMeasurement and simulation with constantand variable tuning parameters at differentpressure ratios πT
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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
ContentsIntroductionDemands on a turbochargerTypes of turbine characteristics1-D model of a radial turbineModel calibrationResults of calibrationExamples of resultsConclusions
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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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