Automotive Engineering_Development of an Advanced Turbocharger Simulation Method for Cycle Simulation of Turbocharged Internal Combustion Engines

7/28/2019 Automotive Engineering_Development of an Advanced Turbocharger Simulation Method for Cycle Simulation of Tu

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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]

661


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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

662 W Zhuge, Y Zhang, X Zheng, M Yang, and Y He


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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

An advanced turbocharger simulation method 663


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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).

REFERENCES

1 Dawes, W. N. Development of a 3D NavierStokessolver for application to all types of turbomachin-ery. ASME paper 88-GT-70, 1988.

2 Dawes, W. N. The extension of a solution adaptivethree-dimensional NavierStokes solver towardgeometries of arbitrary complexity. J. Turbomach-inery, 1993, 115, 283295.

3 Japikse, D. Centrifugal compressor design andperformance, 1996 (Concepts ETI, Wilder, Ver-mont).

4 Monstapha, H., Zelestus, M. F., Baines, N. C., and

Japikse, D. Axial and radial turbines, 2003 (Con-cepts ETI, Wilder, Vermont).

5 Rodgers, C. Meanline performance prediction ofradial inflow turbines, VKI Lecture Series, 1987(von Kaman Institute, Rhode-St, Genoese).

6 Aungier, R. H. Mean streamline aerodynamicperformance analysis of centrifugal compressors.J. Turbomachinery, 1995, 117, 360366.

7 Oh, H. W., Yoon, E. S., and Chung, M. K. Sys-tematic two-zone modelling for performance pre-diction of centrifugal compressors. Proc. IMechE,Part A: J. Power and Energy, 2002, 216, 7587. DOI:10.1243/095765002760024854.

8 Swain, E. Improving a one-dimensional centrifugalcompressor performance prediction method. Proc.

Fig. 15 Comparison of the predicted turbine pressure ratio and efficiency by GT-POWER withvalidation data



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IMechE, Part A: J. Power and Energy, 2005, 219,653659. DOI: 10.1243/095765005X31351.

9 Winkler, N. and Angstrom, H. E. Study of meas-ured and model based generated turbine perfor-mance maps within a 1D model of a heavy-duty

diesel engine operated during transient conditions.SAE paper 2007-01-0491, 2007.10 Daily, J. W. and Nece, R. E. Chamber dimension

effects on induced flow and frictional resistanceof enclosed rotating disks. Trans. ASME J. BasicEngng, 1960, 82, 217232.

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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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Automotive Engineering_Development of an Advanced Turbocharger Simulation Method for Cycle Simulation of Turbocharged Internal Combustion Engines

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