Improved Performance Model of Turbocharger Centrifugal Compressor

Improved Performance Model of Turbocharger Centrifugal Compressor

Mingyang Yang, Xinqian Zheng, Yangjun Zhang Zhigang Li Department of Automotive Engineering, Tsinghua

University, Beijing, 100084 Beijing Special Vehicle Institute,Beijing,100074

Proceedings of ASME Turbo Expo 2008: Power for Land, Sea and Air GT2008

June 9-13, 2008, Berlin, Germany

GT2008-50009

ABSTRACT This paper improves the conventional performance prediction

model by correlating recirculation loss at the outlet of compressor impeller with its rotational speeds. The validation is carried out on a gasoline engine turbocharger compressor. The result shows that accuracy of the new model is greatly improved over the whole operating speeds, which brings possibility to the high accurate performance prediction in off design condition and a powerful tool for the matching between turbocharger and engine.

1 INTRODUCTION A good matching between a turbocharger and an engine

should be firstly guarantied in order to get high performance for a turbocharged engine. The matching of compressor and engine is one of the most important procedures in the whole matching calculation. Usually this matching is performed on the base of maps of a compressor and an engine. The compressor map could be obtained by experimental measurement. However, besides its considerable expense of time and energy, experiments can not be carried out in the process of turbocharger preliminary design. On the other hand, only a limited rotational speeds and mass flowrate are covered for most of the maps. Although the mathematical interpolation could be used to estimate performance between measured points, it could not be reliably used to extrapolate performance since it has no physical basis [1]. Therefore, a reliable performance prediction over a wide operating range is quite necessary for the matching calculation between a turbocharger and an engine as well as a critical element in compressor design process. A reasonable 1-D model of compressor could have such a potential to provide a powerful tool for the matching calculation between turbocharger and engine as well as compressor preliminary design.

The recirculation loss, which is one of compositions of the parasitic loss in 1-D performance model of the centrifugal compressor, dominates the disc friction loss and the leakage loss under the off-design conditions, thus the predicted efficiency
curves are strongly influenced by the recirculation loss. This
loss results from the flow distortion at the impeller discharge section. When the flow is distorted severely enough, it is separated close to the shroud and locally the fluid moves inwards. Then the reversed flow is re-energized by the fluid in the impeller and recirculation loss is arisen from the process. Several empirical and semi-empirical correlations of the loss are available in the published literatures. Rodgers has suggested the following equation to estimate the value of recirculation loss [2]:

22r

1

0.032( )em

UIC

= （1）

No factor about the impeller outlet flow angle is involved in the correlation, which seems not consistent with the phenomenon. Like the blade loading loss in axial compressor, diffusion factor was introduced into the recirculation loss model by Dallenbach [3]: 2

r 0.02 taneI D 2α= （2）

Where is a diffusion factor defined as: D

2

1 11

2 2

0.751 2( (1 ) )s s

W hWD r rZWr rπ

Δ= − +

− +

2 （3）

In order to consider compressor stall, Aungier [4] introduced the blade stall limit of diffusion factor into the recirculation loss correlation at low flow rate region.

22

2

( 1) 2cot2

ure

m

WDI iC

β⎡ ⎤

2f D= − −⎢ ⎥⎣ ⎦

> （4）

H. W. Oh [5] used a hyperbolic function of impeller exit flow angle in the Dallenbach’s model to improve the accuracy of predicted performance according to experiment results.

However, it could be inferred that for the same inlet flow angle the recirculation loss is at the same level for different rotational speeds from above correlations. Thus the impact of
impeller rotational speed on recirculation loss is not fully
1 Copyright © 2008 by ASME

involved. Japikse’s model [6] is quite different from those loss models.

He suggested an empirical recirculation loss correlation curve (“bucket” model) as a function of no-dimensional mass flowrate based on lots of experimental data. Again the rotational speed is not involved in the model.

This paper is aimed at finding an improved recirculation loss model to consider the influence of rotational speed. Firstly, a new recirculation loss model is established on the base of Japikse’s model. Then the two-zone performance model system [6] including the new loss model is presented briefly. Performance prediction is performed on a gasoline turbocharger compressor. Results show that accuracy of prediction is improved apparently by the new model comparing to the original one.

NOMENCLATURE A Area

aAR Blade passage throat area and inlet area ratio

bAR Blade passage throat area and outlet area ratio

C Absolute velocity

pC Specific heat

paiC Ideal diffusion ratio of section ‘a’ in TEIS model

pbiC Ideal diffusion ratio of section ‘b’ in TEIS model

D Diffusion factor

DR Impeller diffusion ratio h enthalpy

I No dimensional loss

L Loss coefficient in volute

N Rotational speed

P Static pressure

Q Mass flow ratio

r Radii

T Temperature

U Impeller periphery velocity

W Relative velocity

eulerW Euler work

reW Recirculation loss

Z Blade number Greek Symbols α Meridional angle of absolute velocity β Meridional angle of relative velocity

bβ Blade angle

δ Deviation angle ε Area fraction of secondary flow

aη Effectiveness of section ‘a’ in TEIS model

bη Effectiveness of section ‘b’ in TEIS model

η Efficiency λ Volute inlet swirl parameter ρ Density χ Mass fraction of secondary flow

Subscripts

0 Stagnation condition 1 impeller inlet condition 2 impeller outlet condition 5 diffuser exit 6 volute throat m Meriditional direction θ tangential direction p primary zone s secondary zone re recirculation t impeller tip

2 TWO –ZONE MODEL SYSTEM

2.1 Assumptions and Model Establishment Because flow develops well in the impeller passage at design

point, the recirculation loss is usually considered to be negligible in the situation. However, in off-design conditions, the recirculation loss has a significant influence on the predicted performance [5, 6]. “Bucket” curve is a common approach which uses a piecewise parabola to fit recirculation loss value which is deduced from impeller tests. Therefore, this mode will be adapted to describe the relationship between recirculation loss and mass flow rate at the same rotational speed in this paper. On the other hand, the recirculation loss will vary with the rotational speeds. When the flow rate range of high efficiency is narrow on the compressor map, the highest efficiency for different rotational speeds is quite different from each other, as shown in upper part figure 2. The low part of the figure shows the recirculation loss distribution at different rotational speeds, which is deduced from the experimental test by the data reduction model in the code Compal of NREC-Concepts. It is apparent in this figure that the recirculation loss varies with the rotational speeds. This phenomenon is one of the mainly causes for variational best efficiency at different speeds. Figure 2 shows the performance map and recirculation loss for gasoline engine turbocharger compressor. In the upper of the figure, it can be seen that the high efficiency curve covers most of the rotational speeds. Different from the former impeller, the recirculation loss of this one is almost independent on rotational speeds, as shown in the low sub-figure. This phenomenon is reasonable. For most of gasoline engine turbocharger compressors, the sizes are always quite small. When the rotational speeds of those small compressors decrease, it is quite possible that Reynolds number of the impeller is below the critical value which is reported as around 105 level when characteristic length is defined as blade outlet wideness [7]. Once the low Reynolds number effect happens on the


development of blades boundary layer when the impeller works below the critical Reynolds number, the thickness of the boundary layer could increase evidently. The recirculation loss is influenced by the development of boundary layer development. Therefore, it is closed related with the impeller rotational speeds, especially for impellers which are operated around a critical Reynolds number.

The “bucket” model suggested by Japikse is presented as following:

21( 1re

design

QI cQ

= )− （5）

Where is an empirical coefficient. Because the model is consisted of two pieces of second order curves, the coefficient has two different values in different situations, as shown in following expression:

1c

1

1

2

, 1

, 1

design

design

QkQ

cQk

Q

⎧ <=⎪⎪= ⎨⎪ >⎪⎩

（6）

Where , are empirical coefficients. 1k 2kIt could be inferred from the above model that no factor of

rotational speeds is involved in it. This empirical recirculation loss works well for the single design rotational speed or the impeller of which the recirculation loss is almost independent on rotational speeds if the coefficient is chosen appropriately. However, it will be invalid in the off-design conditions for the impellers of which the recirculation loss is greatly influenced by rotational speeds.

In the loss models with diffusion factor and exit flow angle, the problem also exists. According to the expression (3), the diffusion factor is a depiction of relative velocity variation in the impeller and it is mainly influenced by the geometry of impeller. On the other hand, different kinds of deviation angle models or slip factor models were reported in literatures [7, 8, 9, 10], but still the geometry of impellers are almost the only factor involved. As a result, the recirculation loss models only with diffusion factor and exit flow angle are also needed to be improved by introducing the rotational speeds to consider rotational effect.

The recirculation loss model in this paper is based on the “bucket” model by using the code Compal of NREC-Concepts. A no-dimensional rotational speed is employed in the original model and a parabola is used to relate recirculation loss with rotational speeds.

0

0.1

0.2

0.3

0.4

0.2 0.4 0.6 0.8 1 1.2

mass flow rate（kg）/s

reci

rcul

atio

n lo

ss

45000

50000

55000

60000

Figure 1. Compressor map and reduced recirculation loss when mass flow rate range of high efficiency is wide


0

0.1

0.2

0.3

0.4

0 0.05 0.1 0.15 0.2mass flow rate (kg/s)

reci

rcul

atio

n lo

ss80000

100000

140000

180000

Figure 2. Compressor map and reduced recirculation loss when mass flow rate range of high efficiency is narrow

Before the new loss model is established, two assumptions are given as following:

1. The inlet flow angles of operated points with minimal recirculation loss are the same at different rotational speeds.

2. The “shapes” of the “bucket” curves at different rotational speeds are the same.

The no dimensional mass flow rate of minimal recirculation loss at each speed could be obtained from assumption 1, which is also used in the code Compal:

re opti design

design

Q QN N− = （7）

Where is the mass flow where the minimal recirculation loss is reached at a rotational speed.

re optiQ −

The second assumption is an approximation which assumes that the empirical coefficient in equation (5) is the same for all of the rotational speeds. There are errors between this assumption and theoretically correct situation, however, the model will be greatly simplified.

1c

The recirculation loss in following equations is no-dimensional and it is defined as:

rre

eeuler

WIW

= （8）

The model of minimal recirculation loss at each rotational speed is given as following:

2r 2 (e opti

design

NI cN− = 1)− （9）

Where is another empirical coefficient and it determines how much rotational speeds influence the recirculation loss. This coefficient should be related with the impeller geometry.

2c

According to the “bucket” model and the equation (9), the improved loss model is established:

2r 1 r( 1)e

re opti

QI c IQ −

−

= − + e opti （10）

The first item of the equation right part is “bucket” model. The mass flow rate is explained and determined in equation (7).

re optiQ −

2.2 Two-zone Model System The complete system of equations for the two-zone model

including vaneless diffuser and volute model is presented briefly as following. The flow is considered to be ideal gas. 2.2.1 Impeller equations

121 1(

1 1a pai b pbi

DR KC Cη η

=− −

)

R

(Diffusion ratio

from TEIS model) （11） Where the coefficient is a multiplier which is used to

correct the diffusion ratio at large mass flow rate. K

2 1p tW W D= (Diffusion ratio definition In TEIS

model) （12） 2 2 2

2 1 1 1 2( / 2 / 2) / 2p P p pC T C T W U W U= + − − + 22 (Ener

gy conservation) （13）

2 1

1 12 1

pk

k kp

P P

T Tk

− −

= (Gas dynamic) （14）

2 1

2 2 1 1

p

p p

P PT Tρ ρ

= (Gas state equation) （15）

2 2p b 2 pβ β δ= + (Deviation angle) （16）

Deviation angle 2 pδ is determined by the correlation between exit blade angle and exit flow angle. Velocity triangle and thermodynamic parameters of the primary flow are derived from iteration of above equations.

2 2 2 2

(1 )1cos( )p p p

mA W

χερ β

−= − (Wake fraction of

blade to blade space) （17）

22 2 2cos( )s

s s

mWAχ

ρ ε β= (Wake mass flow) （18）

2 2 2 22 1 1 1 2 2( / 2 / 2) / 2 / 2p s p sC T C T W U W U= + − − + (En

ergy conservation) （19）

2 pP P2s= (Unload tip condition) （20）

22

2 2 2 2

ps

s s p

PPT Tρ ρ

=p

(Gas state equation) （21）

The deviation angle of secondary flow is considered to be zero. Again, velocity triangle and thermodynamic parameters of


secondary flow are obtained by equations from (17) to (21).

2 2 2 2 2 2(1 )m m m ex p m p ex s m s exC A C A C Aρ ρ ε ρ= − + ε

2

(Mass conservation) （22）

2 2

2 22 2 2 2 2 2

( )

(1 )p m ex

m m m ex p m p ex s s ex

P P A

C A C A C Aρ ρ ε ρ

− =

− − − ε

(Momentum equation) （23）

02 02 02 r(1 ) ( ) /p m p s p p leak df eC T C T C T W W W mχ χ= + − + + + (Energy conservation) （24）

The state of mixture of the two zones near the exit of impeller is described by the equations of (22) ～(24).

In the equation (24), there are three kinds of parasitic loss which are leakage loss , disc friction loss and

recirculation loss respectively. The Daily and Nece [11] correlation is used as disc friction loss model. Leakage loss is modeled by Aungier [4]. The recirculation loss is determined by equation (10).

leakW dfW

reW

1.2.2 Vaneless diffuser equations Staniz equations [12] are adapted as vaneless diffuser model.

The skin friction coefficient in these equations is correlated to diffuser inlet Reynolds number. And then the velocity and thermodynamic parameters could be obtained from Staniz equations including momentum and energy conservation equations. 1.2.3 Volute equations

In order to simplify the model, a volute is modeled as two sections in series [6]. The first one is the section from the volute inlet to throat while the second one is the section from throat to outlet of the volute. Models are established separately for these two parts.

According to the conservation equations and gas state equations, the flow state at the volute exit could be determined.

With the equation system presented above, the flow parameters from impeller inlet to volute outlet are derived and then the 1-D performance prediction of the centrifugal compressor can be achieved.

3 VALIDATION OF THE IMPROVED MODEL In order to verify the recirculation loss correlation on the base

of two-zone model system presented in this paper, performance prediction is carried out on a gasoline engine turbocharger centrifugal compressor. The results including efficiency and pressure ratio are compared with that from original model and experiment test. Main specifications of the compressor are listed in Table 1 (angles are in meridional direction):

Table 1. main specifications of the Impeller Impeller

Inlet tip radii 19.7 Outlet blade angle -45° Inlet hub radii 6.6 Inlet hub angle -62° Outlet radii 26 Inlet tip angle -69° Blade outlet height 3.6 Blade thickness 1.36 Blade number 6

Vaneless Diffuser Outlet radii 93 Outlet height 3.3

Volute Throat radii 34 Outlet radii 43

The empirical coefficients in the model are presented in Table 2:

Table 2. main empirical coefficients of the model

2c K 1c

/ 1designQ Q <= / 1designQ Q >0.81 0.95

0.75 0.125

0

0.1

0.2

0.3

0.4

reci

rcul

atio

n lo

ss

deduced

140000120000

100000

80000

0

0.1

0.2

0.3

0.4

reci

rcul

atio

n lo

ss

80000100000

120000140000

new model

0

0.1

0.2

0.3

0.4

0 0.04 0.08 0.12 0.16mass flow rate（kg/s）

reci

rcul

atio

n lo

ss

140000

120000100000

80000 original model

Figure 3. Recirculation loss estimated by the new and original model as well as the reduced loss from experiment data


Figure 3 compares the recirculation loss estimated by the new and original “bucket” model as well as reduced recirculation loss from experimental measurement in the tested impeller at 4 rotational speeds. The upper sub-figure is the reduced loss from total pressure ratio and efficiency of the compressor via data reduction model in the code Compal. The middle one and the last one are the loss estimated by the new and original model separately. It is apparent that the minimal loss at different speeds is independent on rotational speeds for the original model, while it increases sharply as speeds reduce for the new one, which is the same variational manner as the experimental data reduced results.

Figure 4 and 5 compare the predicted performance by new and original models. The compressor performance including efficiency and pressure ratio are measured in the experiment and they are used to validate the predicted performance by the new model. In figure 4, it could be noticed that the predicted pressure ratio of the two models is almost the same at different speeds. This is reasonable because the parasitic loss which includes the recirculation loss doesn’t have impact on the exit total pressure. However, the predicted efficiency by two models at different speeds is quite different from each other, as shown in figure 5. As the speeds decrease from the design rotational speed, the difference between the results of original model and experiment test become prominent: the highest efficiency changes slightly with the rotational speeds for original “bucket” model, while it decreases obviously for the new one. It is can be seen that the result of new model can fit well with that of the experiment measurement. Apparently, the accuracy of results from the new model is greatly improved.

Figure 4. Comparison of predicted pressure ratio by original model and improved model as well as experimental measurement

Figure 5. Comparison of predicted efficiency by original model and improved model as well as experimental measurement

4 CONCLUSIONS AND DISSCUSION This paper presents an improved recirculation loss model

which correlates the loss with impeller rotational speeds directly. This new model is used in two-zone model system and then the performance prediction is carried out on a turbocharger centrifugal compressor. Two conclusions are drawn as following:

(1) The recirculation loss is correlated with impeller rotational speeds. This is evidently and important for the impeller of which the mass flow rate range of high efficiency curve is narrow.

(2) The accuracy of predicted efficiency is greatly improved by the new model over the whole rotational speed range.

Because gasoline turbochargers are usually in small size and the mass flow is quite small, the operated Reynolds number could be possible below the critical value (about 105) as rotational speed decreases and the performance degrades sharply due to blades boundary layer development. As a result, the original recirculation loss models without rotational speed factor will not work reliably. It seems that it is more reasonable to correlate the loss with the compressor Reynolds number. On the other hand, there are too many empirical coefficients in the “bucket” model and the predicted performance is strongly depended of the experience. Nevertheless, more experiment test should be carried out for further validation in future.


ACKNOWLEDGEMENT The author gratefully acknowledges GM cooperation for its support and experiment measurement. The author also would like to thanks senior engineers Weidong Xin, Junyue Zhang and Jizhong Zhang in National Key Lab. of Diesel Engine Turbocharger Tech. of China for their support.

REFERENCES [1] Shaaban, S., 2006, “Part-load Performance Prediction of

Turbocharged Engine,” 8th International Conference on Turbochargers and Turbocharging.

[2] Rodgers, C., 1961, “Influence of Impeller and Diffuser Characteristics and Matching on Radial Compressor Performance,” Centrifugal compressors, SAE.

[3] Dallenbach, F., “Study of Supersonic Radial Compressors for Refrigeration and Pressurization on Systems,” WADC TR 55-257, ASTIA Document NO. AD 110 467.

[4] Aungier R. H., 1995, “Mean Streamline Aerodynamic Performance Analysis of Centrifugal Compressors,” Trans. ASME, 117,360-366.

[5] Oh, H. W., and Yooh, E. S., 1997, “An Optimum Set of Loss Models for Performance Prediction of Centrifugal Compressors,” IMechE.

[6] Japikse. D., 1996, “Centrifugal Compressor Design and Performance,” Concepts ETI. Wilder.

[7] Wiesner, F. J., 1979, “A New Appraisal of Reynolds Number Effects on Centrifugal compressor performance,” Trans. ASME, Vol 101, 384-396.

[8] Wisner, F. J., 1967, “A Review of Slip Factor for Centrifugal Compressor,” ASME Journal of Engineer for Power, 89, PP. 558-572.

[9] Stodola, A., 1945, “Steam and Gas Turbine,” McGraw-Hill, New York.

[10] Paeng, K. S., and Chung, M. K., 2001, “A New slip factor for centrifugal impeller,” Proc. Inst. Mech. Eng., Vol 251 Part A, pp.645-649.

[11] Daily, J. W., and Nece, R. E., 1960, “Chamber Dimension Effects on Induced Flow and Frictional Resistance of Enclosed Rotating Disks.” Trans ASME Journ Basic Eng.

[12] Stanitz, J. D., 1952, “One-dimensional Compressible Flow in Vaneless Diffusers of Radial-and Mixed-flow Centrifugal Compressors, Including Effects of Friction, Heat Transfer and Area Change,” NACA TN 2610.


Improved Performance Model of Turbocharger Centrifugal Compressor

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