Automotive Engineering_Development of an Advanced Turbocharger Simulation Method for Cycle...
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Development of an advanced turbochargersimulation method for cycle simulation ofturbocharged internal combustion engines
W Zhuge1, Y Zhang1*, X Zheng1, M Yang1, and Y He2
1State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, Peoples Republic of China2R&D and Strategic Planning, General Motors Corporation, MI, USA
The manuscript was received on 24 July 2008 and was accepted after revision for publication on 4 February 2009.
DOI: 10.1243/09544070JAUTO975
Abstract: An advanced turbocharger simulation method for engine cycle simulation wasdeveloped on the basis of the compressor two-zone flow model and the turbine mean-line flowmodel. The method can be used for turbocharger and engine integrated design withoutturbocharger test maps. The sensitivities of the simulation model parameters on turbochargersimulation were analysed to determine the key modelling parameters. The simulation method
was validated against turbocharger test data. Results show that the methods can predict theturbocharger performance with a good accuracy, less than 5 per cent error in general for boththe compressor and the turbine. In comparison with the map-based extrapolation methodscommonly used in engine cycle simulation tools such as GT-POWERH, the turbochargersimulation method showed significant improvement in predictive accuracy to simulate theturbocharger performance, especially in low-flow and low-operating-speed conditions.
Keywords: turbocharger, internal combustion engine, cycle simulation
1 INTRODUCTION
Turbocharging is playing an increasingly important
role in developing internal combustion engines for
today and tomorrow. Turbocharger matching is the
key technique used to explore optimal solutions for
minimum fuel consumption and maximum transi-
ent response together with satisfying all given
constraints such as maximum turbine temperature,
turbocharger speed, compressor surge limit, max-
imum combustion pressure, and knock limit.Engine cycle simulation tools such as GT-POWERH
are commonly used for turbocharger matching (GT-
POWER is a registered trademark of Gamma Tech-
nologies). Compressors and turbines are defined as
maps within these simulation tools. These maps are
obtained from test data of available turbochargers.
Unfortunately, the test data of the turbocharger are
usually not sufficient for the turbocharger matching
simulation especially in low-flow and low-speed
regions. Furthermore, the testing maps of turbines
are often not available. In this case the turbocharger
matching has to resort to hands-on testing.
The map-based turbocharger matching method is
not efficient. There is a need to develop a model-
based method to perform turbocharger matching
without turbocharger testing maps. Compressors
and turbines are defined with simulation models
instead of maps within the method. The perfor-
mance of turbochargers could be changed easily by
adjusting the model parameters. An optimum match-
ing between the engine and the virtual turbochar-
ger could be achieved. The model-based method is
very useful for integrated engine and turbocharger
design.
Although the full three-dimensional (3D) compu-
tational fluid dynamics simulation is capable of
predicting the turbocharger performance, it is very
complicated and time consuming [1, 2]. It is not
suitable for engine cycle simulation because of itslarge computational footprint. Some researchers
*Corresponding author: Department of Automotive Engineering,
Tsinghua University, Tsinghua Park, Haidian District, Beijing,
100084, Peoples Republic of China.email: [email protected]
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have developed one-dimensional (1D) semiempirical
models for compressors and turbines performance
prediction [38]. These models are commonly used
for the preliminary design of compressors and turbines
and can predict the performance well in the design
conditions. In order to use these models for engine
cycle simulation, the performance prediction in off-
design conditions needs to be improved. Winkler
and Angstrom [9] used the semi-empirical turbine
model to generate the turbine map for diesel engine
simulation in transient operation. It was shown that
the model-generated turbine performance map data
agree well with the measured map data. However,
the compressor is still simulated using the test map.
The present paper develops a numerical method
to simulate automotive turbochargers in engine
cycle simulations. The simulation method is based
on the compressor two-zone flow model and the
turbine mean-line flow model. The performance
prediction in off-design conditions is improved. The
sensitivities of the model parameters on turbochar-
ger performance simulation were analysed to deter-
mine the key modelling parameters. The simulation
method was validated against turbocharger test data.
2 THE TURBOCHARGER SIMULATION METHOD
2.1 Compressor model
The compressor performance prediction is based on
the analysis of the internal gas flow of the impeller
using the COMPALH code of Concepts NREC Incor-
poration [3] (COMPAL is a registered trademark of
Concepts ETI, Inc.). The impeller flow is modelled
using the two-zone modelling equations established
by Japikse [3]. The basic idea of the two-zone model is
that the impeller exit flow can be conceptually
divided into a primary zone, which is an isentropic
core flow region with high velocities, and a secondary
zone, which is a low-momentum non-isentropic
region having all the losses occurring in the impeller.
The primary zone and secondary zone reach static
pressure balance at the impeller exit. A schematic
representation of the two-zone model is shown in
Fig. 1.
2.1.1 Primary zone equations
The equations for the primary zone are
W2p~W1t DR2 1
h2p~ h1zW21
2{
U212
{
W22p
2z
U222
2
P2p
Tk= k{1 2p
~P1
Tk= k{1 3
P2p
T2pr2p~
P1T1r1 4
b2p~b2bzd2p 5
Fig. 1 Schematic representation of the two-zone model
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where b2b is the exit blade angle, d2p is the exit flow
deviation angle, the subscript 1 denotes the impeller
inlet variable, and the subscript 1t denotes the inlet
tip component.
The diffusion ratio DR2
is calculated using the
correlation
DR2~ 1{gaCpai
1{gbCpbi
{1=26
where ga and Cpai are the diffusion efficiency and
ideal diffusion ratio respectively of the segment from
impeller inlet to throat, and gb and Cpbi are the
diffusion efficiency and ideal diffusion ratio respec-
tively of the segment from impeller throat to exit.
When the impeller flow stalls, DR2 will reach its
maximum value DRstall. Also
Cpai~1{1
AR2a~1{
cos b1cosb1b
27
Cpbi~1{1
AR2b~1{
AthA2 cosb2b
28
where b1b is the inlet blade angle, Ath is the impeller
throat area, and A2 is the exit area.
2.1.2 Secondary zone equations
The equations for the secondary zone are
W2s~x _mmtot
r2seA2 cosb2s9
h2s~ h1zW21
2{U21
{
W22s2z
U222
10
P2s~P2p 11
b2s~b2b 12
where mtot is the total mass flowrate.
2.1.3 Two-zone mixing equations
The equations for the two-zone mixing are
r2mCm2mA2~r2pCm2p 1{e A2zr2sCm2seA2 13
P2p{P2m
A2~r2mC2m2mA2{r2pC
2m2p 1{e A2
{r2sC22seA2 14
CpT02a~xCpT02sz 1{x CpT02p 15
h02m~CpT02azPrecirczPleakzPdf
_mmtot16
where T0 is the total temperature, h0 is the total
enthalpy, Precirc is the recirculation loss, Pleak is the
leakage loss, and Pdfis the disc friction loss. The Daily
Nece [10] correlation is used as the disc friction loss
model. Leakage loss is as modelled by Aungier [6].
2.1.4 Recirculation loss model
The recirculation loss is quite important for perfor-
mance prediction in off-design conditions. Japikse
[3] established a parabolic correlation between the
recirculation loss and operating mass flowrate accor-
ding to
Precirc~KrecircPEuler 17
Krecirc~a m{1 2zKrecirc-opt 18
a~a1, q1
a2, qw1
&19
m~_mm
_mmopt20
where PEuler is the Euler power, Krecirc is the
recirculation loss coefficient, a1 and a2 are correlation
coefficients, mopt is the optimum mass flowrate, andKrecirc-opt is the recirculation loss coefficient at the
best efficiency point, which is an empirical constant.
The Japikse model works well in the design rotating
speed conditions. In off-design rotating speed condi-
tions, the prediction error becomes larger since the
optimum recirculation loss coefficient Krecirc-opt is not
constant for different rotating speeds. The Japikse
model is modified for predicting compressor perfor-
mance better in off-design rotating speed conditions,
which is important for engine cycle simulations. The
modified model assumes a parabolic correlation bet-
ween Krecirc-opt and rotating speeds according to
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Krecirc-opt~an2zbnzc 21
n~
N
Ndesign 22
where a, b, and c are correlation coefficients and
Ndesign is the design rotating speed.
2.2 Turbine model
The turbine performance prediction is based on the
mean-line analysis of the internal gas flow of the turbine
using the RITALH code of Concepts NREC Incorpora-
tion [4] (RITAL is a registered trademark of Concepts
ETI, Inc.). The turbine flow is divided into seven control
sections. The computation stations are on the boundary
of these sections. Flow variables are solved at these
stations, from volute inlet (station 0) to exhaust diffuser
exit (station 7). The computation stations are shown in
Fig. 2. For the turbocharger without vaned nozzle and
diffuser, only the volute and rotor sections are solved.
The effects of a vaned nozzle as well as the inlet pulsat-
ing flow condition are not taken into account currently.
2.2.1 Volute section equations
The equations for the volute section are
Ch1~SR0C0
R123
Cm1~_mm
r1A1 1{B1 24
p01~p00{K p01{p1 25
where p0 is the total pressure, and the subscripts 0
and 1 denote the computation stations.
2.2.2 Rotor section equations
The equations for the rotor section are
r6W6A6 cosb6~r4W4A4 cosb4 26
Cp T04{T06 ~U4Ch4{U6Ch6 27
T6T06~1{W26
W26s1{T04
T06p6p04
k{1 =k" #28
W26s{W26~LizLpzLc 29
where W6s is the isentropic rotor exit relative vel-
ocity, Li is the incidence loss, Lp is the passage loss,
and Lc is the tip clearance loss.
The incidence and passage loss are modelled
using the NASA models [11, 12] according to
Li~12
W24 sin2i 30
where i5b4b4,opt is the angle between the incoming
flow and that at the best efficiency point (b4,opt is not
normally equal to the inlet blade angle, but is usually
negative)
Fig. 2 Turbine flow sections
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Lp~1
2Kp W
24 cos
2 izW26
31
where Kp is an empirical loss coefficient.
The tip clearance loss is modelled using theequation [4]
Lc~U34ZR
8pKxexCxzKrerCrzKxr
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexerCxCr
p 32
where Kx and Kr are discharge coefficients for the
axial and radial tip clearance respectively, Kxr is the
cross-coupling coefficient, and
Cx~1{R6t=R4
Cm4b4, Cr~
R6tR4
z{b4Cm6R6b6
33
2.3 Bearing loss model
The bearing loss is estimated according to the Petroff
equation [13]
LB~KBN
Ndesign
234
where KB is the coefficient determined by the
turbocharger bearing geometry and lubricant visc-osity.
The mechanical efficiency of the bearing can be
deduced from the bearing loss and the isentropic
efficiency of the turbine, which is obtained from the
turbine model.
gmech~1{LB
Wisgis35
where Wis is the isentropic turbine work and gis is the
isentropic turbine efficiency.
3 SENSITIVITY ANALYSIS OF MODELPARAMETERS
There are many parameters in the compressor and
turbine model equations. It will take great effort to
determine all these parameters accurately for every
turbocharger simulation. In order to reduce the
effort of parameter calibration, a sensitivity analysis
of the turbocharger model parameters on perfor-
mance prediction is conducted and the key para-
meters are determined. These key parameters are
determined by calibration against turbocharger
experimental test data. A key parameter databasecan be set up for different sizes of turbocharger. The
database can then be used for the simulation of
newly designed turbochargers.
3.1 Compressor key model parameters
The key parameters of the compressor model are the
impeller diffusion ratio and the recirculation loss
coefficient.
The impeller diffusion ratio DR2 is determined by
the diffusion efficiencies ga and gb, as well as by thestall diffusion ratio DRstall. The influence ofga on the
compressor performance prediction is shown in
Fig. 3. The parameter ga has a significant effect on
the performance prediction within the range of near-
design conditions. As ga increases from 0.4 to 0.7, the
predicted efficiency increases by 3.7 per cent and the
pressure ratio increases by 5.3 per cent.
Fig. 3 The influence ofga on the compressor efficiency and pressure ratio prediction
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The influence of gb on the compressor perfor-
mance prediction is shown in Fig. 4. The parameter
gb affects the performance prediction largely within
the range of high-flow conditions. As gb increases
from 20.3 to 0.3, the predicted efficiency increases
by 25.3 per cent and the pressure ratio increases by
22 per cent.
The influence of DRstall on the compressor
performance prediction is shown in Fig. 5. The
parameter DRstall affects the performance prediction
largely within the range of low-flow conditions. As
DRstall increases from 1.09 to 1.29, the predictedefficiency increases by 8.2 per cent and the pressure
ratio increases by 11 per cent.
The influence of the recirculation loss coefficient
Krecirc on the compressor performance prediction
is shown in Fig. 6. The coefficient has a signific-
ant effect on the efficiency prediction in off-design
conditions. The maximum difference between the
efficiency predictions using variable and fixed co-
efficients is 17 per cent.
3.2 Turbine key model parameters
The key parameters of the turbine model are the
volute swirl coefficient, the passage loss coefficient,
the clearance loss coefficients, and the rotor exit flow
deviation angle.
The influence of the volute swirl coefficient S on
the turbine performance prediction is shown in
Fig. 7. The coefficient has a significant effect on boththe turbine throughput and efficiency predictions.
As the coefficient increases from 0.75 to 0.90, the
predicted pressure ratio increases by 6 per cent and
the efficiency increases by 3.6 per cent.
The influence of the passage loss coefficient Kp on
the turbine performance prediction is shown in Fig. 8.
The coefficient affects largely the turbine efficiency
Fig. 4 The influence ofgb on the compressor efficiency and pressure ratio prediction
Fig. 5 The influence of DRstall on the compressor efficiency and pressure ratio prediction
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prediction. As the coefficient increases from 0.15 to
0.35, the predicted pressure ratio increases by 4.2 per
cent and the efficiency decreases by 8.4 per cent.
The influences of the clearance loss coefficients Kx
and Kr on the turbine performance prediction areshown in Fig. 9. The coefficients affect largely the
turbine efficiency prediction. As the coefficients
increase from 0.5 to 3, the predicted pressure ratio
increases by 3.3 per cent and the efficiency decreases
by 7.9 per cent.
The influence of the deviation angled
on the turbineperformance prediction is shown in Fig. 10. The
Fig. 6 The influence of Krecirc on the compressor efficiency and pressure ratio prediction
Fig. 7 The influence of S on the turbine throughput and efficiency prediction
Fig. 8 The influence of Kp on the turbine throughput and efficiency prediction
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predicted turbine throughput is largely affected by this
coefficient. As the deviation angle increases from 0u to
3u, the predicted pressure ratio decreases by 3.2 per
cent and the efficiency increases by 1.5 per cent.
4 VALIDATION OF THE SIMULATION METHOD
4.1 Turbocharger geometry measurement
The turbocharger simulation method is validated
against turbocharger test data. The geometry para-
meters of the turbocharger are obtained by scanning
the compressor and turbine impeller using optical
digitizing sensors and a three-coordinate measuring
machine. The created computer-aided design (CAD)
models of the compressor and turbine are shown in
Fig. 11.
4.2 Results of validation
The key parameters of turbocharger models are
calibrated using only some of the available turbo-
charger testing data. The calibrated models are val-idated against the additional experimental data. The
turbocharger test is conducted at General Motors.
The turbocharger is powered by compressed air hea-
ted to 600 uC on the test rig. The turbine power is
derived by the calculation of the compressor power.
4.2.1 Validation of the compressor simulationmethod
Three sets of compressor test data (140 000 r/min,
120 000 r/min, and 100 000 r/min) are used to cali-
brate the compressor model key parameters. Thevalues of the key modelling parameters are listed
Fig. 9 The influences of Kx and Kr on the turbine throughput and efficiency prediction
Fig. 10 The influence ofd on the turbine throughput and efficiency prediction
Fig. 11 Compressor and turbine CAD models
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in Table 1. The calibrated model is used for predict-
ing the turbocharger performance at 80 000 r/min.
Figure 12 shows the validation results. The solid
curves represent the prediction results and the
symbols represent the experimental data points.
Figure 12 shows that the predicted performance
curve agrees well with the experimental data points.
The maximum error of the pressure ratio prediction
error is 5.1 per cent. The maximum error of the
efficiency prediction is less than 5 per cent for most
points except for high-flow (near-choking) points.
Since the compressor is rarely operated in near-
choking conditions for a real engine, because of the
very low efficiency of the compressor operating in
these conditions, the prediction inaccuracy at near-
choking points is not very important. Therefore the
developed simulation method is accurate enough for
simulating compressor characteristics in engine
cycle simulations.
4.2.2 Validation of the turbine simulation method
Three sets of turbine test data (147750 r/min,
132970 r/min, and 118 220 r/min) are used to cali-
brate the turbine model key parameters. The values
of the key modelling parameters are listed in Table 2.
The calibrated model is used for predicting the
turbocharger performance at 103 420 r/min, 88 670 r/
min, and 73 860 r/min. Figure 13 shows the valida-
tion results. The solid curves represent the predic-
tion results and the symbols represent the experi-
mental data points.
Figure 13 shows that the predicted performance
curve agrees well with the experimental data points.
The maximum error of the pressure ratio prediction
error is 2.9 per cent. The maximum error of the
efficiency prediction is less than 5 per cent in most
points except for one point at the lowest operating
speed, the value for which is 6.2 per cent. The
developed simulation method is accurate enough for
simulating turbine characteristics in engine cycle
simulations.
4.3 Performance prediction with the GT-POWERextrapolation methods
The turbocharger test performance data for modelcalibration (three sets of test data) are input into GT-
POWER to generate the turbocharger performance
maps. The performance of the turbocharger in the
conditions of the model validation is predicted using
the GT-POWER map extrapolation method.
Figure 14 shows the validation results for the
compressor performance prediction by GT-POWER.
The solid curves represent the prediction results and
the symbols represent the experimental data points.
Table 1 Values of the key modellingparameters of the compressor
Parameter Value
ga 0.55gb 20.1
DRstall 1.19a1 0.75a2 0.125a 0.81b 21.54c 0.745
Fig. 12 Comparison of the predicted compressor pressure ratio and efficiency with validationdata
Table 2 Values of the key modellingparameters of the turbine
Parameter Value
S 0.82Kp 0.25
Kx 2Kr 2d 3uKB 1200
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In comparison with Fig. 12, the pressure ratio
prediction by GT-POWER is a little better than the
compressor simulation method but the efficiency
prediction is worse than the simulation method for
most points at 80 000 r/min. However, the efficiency
prediction in the near-choking condition by GT-
POWER is much better.
GT-POWER uses power curves to fit the input data
for the turbine. The equation used to calculate the
mass flow is
MR~Cmz 1{Cm BSRm 36
where MR is the mass flow ratio, which is the ratio of
the mass flow to the mass flow at the maximum
efficiency point, Cm is a coefficient, BSR is the
normalized blade speed ratio with respect to the
blade speed ratio at the maximum-efficiency point,
and m is the mass flow ratio exponent.
The equation for the efficiency curve at low BSR
(BSR,1) is
g~1{ 1{BSR b 37
where b is the efficiency curve shape factor at low
BSRs. The efficiency curve at high BSRs (BSR.1) is a
parabola drawn through the maximum-efficiency
point and the point at efficiency intercept at high
BSR (BSRi).
The values of the coefficients that determined the
shape of the fitting curves can be adjusted to fit the
data best. These coefficients are tuned using the test
data and are listed in Table 3.
Figure 15 shows the validation results for the
turbine performance prediction by GT-POWER.The solid curves represent the prediction results
and the symbols represent the experimental data
points. In comparison with Fig. 13, both the pressure
ratio prediction and the efficiency prediction by GT-
POWER are worse than the predictions by the
Fig. 13 Comparison of the predicted pressure turbine ratio and efficiency with validation data
Fig. 14 Comparison of the predicted compressor pressure ratio and efficiency by GT-POWER
with validation data
Table 3 Coefficients for the turbine data fitting
Coefficient Value
Cm 1.05m 2b 1.5
BSRi 2
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turbine simulation method. The maximum predic-
tion error of the efficiency prediction by GT-POWER
is 13 per cent.
5 CONCLUSIONS
A turbocharger simulation method for engine cycle
simulations was developed on the basis of the
compressor two-zone model and the turbine
mean-line flow model. The recirculation loss model
was improved for predicting the compressor perfor-
mance better in off-design conditions. The sensi-
tivities of the model parameters on turbocharger
simulation were analysed. The key modelling para-
meters were determined. For the compressor model,
the impeller diffusion ratio coefficients and the
recirculation loss coefficients are the key para-
meters. For the turbine model, the volute swirl
coefficient, the passage loss coefficient, the clear-
ance loss coefficients, and the rotor exit flow
deviation angle are the key parameters.
The models are calibrated using only a some of the
available turbocharger testing data, and the cali-
brated models were validated against the remaining
test data to evaluate the general predictive accuracy.
The results of the validation of the turbocharger
simulation methods against test data show that the
methods can predict the turbocharger performance
at a good accuracy, less than 5 per cent error in
general for both the compressor and the turbine. The
efficiency prediction in near-choking conditions of
the compressor needs to be improved.
In comparison with the conventional map-based
extrapolation approach commonly used in engine
cycle simulation tools such as GT-POWER, the tur-
bocharger simulation methods developed in this
study showed significant improvement in predictiveaccuracy to simulate the turbocharger performance,
especially in low-flow and low-operating-speed con-
ditions.
ACKNOWLEDGEMENTS
The authors would like to thank General Motors fortheir support. This work is also supported by theNational Natural Science Foundation of China (Project50706020) and the Open Research Fund Program ofthe National Key Laboratory of Diesel Engine Tur-bocharging Technology (Project 9140C3311010804).
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Fig. 15 Comparison of the predicted turbine pressure ratio and efficiency by GT-POWER withvalidation data
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APPENDIX
Notation
A area (m2)
AR area ratio
b blade heightB blocking coefficient
Cm absolute meridional velocity (m/s)
Cp specific heat (J/kg K)
Cpai, Cpbi ideal diffusion ratio
Ch absolute tangential velocity (m/s)
DRstall diffusion ratio when the compressor
impeller flow stalls
DR2 diffusion ratio of the compressor
rotor
h specific enthalpy
i incidence angle
K empirical loss coefficient
Krecirc recirculation loss coefficient
L energy lossm mass flowrate (kg/s)
N turbocharger operating speed
(r/min)
P pressure (Pa)
R radius
S swirl coefficient
T temperature (K)
U circumferential velocity (m/s)
W relative velocity (m/s)
z turbine rotor axial length
ZR blade number
b flow angle or blade setting angle
d deviation angle
e secondary zone area fraction
er radial tip clearance (m)
ex axial clearance (m)
g efficiency
ga, gb diffusion efficiencies
r density (kg/m3)
x secondary mass flow fraction
Subscripts
2s compressor exit secondary zone
variables
2p compressor exit primary zone
variables
2m compressor exit mixing flow
variables
s isentropic process
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