Journal of Thermal Science Vol.17, No.1

(2008) 21−27

DOI: 10.1007/s11630-008-0021-1

Article ID: 1003-2169(2008)01-0021-07

Use of partially shrouded impeller in a small centrifugal compressor Jin Tang

Teemu Turunen-Saaresti

Jaakko Larjola

Department of Energy and Environmental Technology, Lappeenranta University of Technology, Lappeenranta, Finland [email protected], [email protected], [email protected]

Numerical analysis is conducted for the 3-dimensional impeller and vaneless diffuser of a small centrifugal compressor. The influence of impeller tip clearance on the flow field of the impeller is investigated. Detailed investigation on the leaking flow across the tip clearance of the impeller shows that the leaking flow rate is higher near the exit of the impeller than that near the inlet of the impeller. Based on this phenomenon, a new partially shrouded impeller is designed. The impeller is shrouded near the exit of the impeller. Numerical results show that the secondary flow region becomes smaller at the exit of the impeller. Better performance is achieved than that with the unshrouded impeller.

Keywords: centrifugal compressor, tip clearance, partial shroud, CFD.

Introduction Centrifugal compressors are used quite widely in industrial refrigerators, turbochargers, small gas turbines and many other places. The pressure ratio of one centrifugal compressor stage is much higher than the pressure ratio of an axial compressor stage. The manufacturing costs of centrifugal compressors are also lower than multistage axial compressors. Centrifugal compressors are better options for simple and small systems which require smaller number of stages and lower costs. Due to manufacturing cost limit, most of the small centrifugal compressors are unshrouded. Thus the influence of the tip clearance is quite significant. The tip clearance effect has been known and investigated for quite a long time. Pampreen [1] has collected the data of six different centrifugal impellers and correlated the efficiency drop to the relative tip clearance at the impeller exit (shown in Fig. 1). The average line shows that there is 3% efficiency drop if the relative clearance increases by 10%. He has also concluded that

Fig. 1

Effect of tip clearance on the efficiency drop of centrifugal impellers[1]

the tip clearance has a pronounced influence on the performance of small centrifugal and axial compressors as compared to the Reynolds number effects. Ishida et al. [2] have measured velocity distribution at the exit of two

Received: November 2007 Jin Tang: Post Doctoral Researcher www.springerlink.com

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J. Therm. Sci., Vol.17, No.1, 2008

Nomenclature b d h m N p T t

height of blade, m diameter, m specific enthalpy, J/kg mass flow rate, kg/s rotating speed, rps pressure, Pa temperature, K tip clearance, m

different types of unshrouded centrifugal compressors under four different clearance conditions. When the tip clearance was increased, the input power and flow angle hardly changed in the radial impeller and were reduced in the backward-leaning impeller. Eum and Kang [3] have studied the effects of tip clearance on through flows and the performance of a centrifugal compressor impeller numerically with six different tip clearances. The results showed that the flow, pressure and entropy contours at the impeller exit were greatly influenced by the tip leakage flow. Meanwhile, predictions of the change in compressor characteristics due to the tip clearance have been carried out by many investigators. The efficiency drop can be correlated using the following equation: Δη 2ac (1) =− η b1 + b2 Eckert and Schnell [4] have used a = 0.9, while Pfleiderer [5] has chosen a = 1.5 to 3. Pampreen [1] has plotted the efficiency drop versus tip clearance for several centrifugal compressors (see Fig. 1). These data make some agreements with the correlation of Eckert and Schnell, with b1/b2 = 4 and η = 0.8. Japikse and Goebel [6] have made correlations of the size of tip clearance with the diffusion ratio and efficiency drop. Senoo and Ishida [7][8] have developed correlations to predict the drop of efficiency and pressure loss at design and off-design mass flows and speeds, which show good agreements with experimental data for high speed compressors[9]~[11]. Senoo [12] has further improved this theory and extended it to axial compressor rotors. Researchers have also tried to reduce the tip clearance effect in centrifugal compressors. Palmer and Waterman [13] have utilized splitter vanes in the impeller of the first and second stages of a two-stage centrifugal compressor, thereby reducing the vane loading. Partial shroud [14] has been found also effective to reduce the efficiency loss due to the tip clearance. Howard and Ashrafizaadeh [15] have numerically investigated the effects of lean angle modifications to a high performance centrifu-

Greek letters

η π

efficiency pressure ratio

Subscripts 1 2 d s t

impeller inlet impeller exit design isentropic total

gal compressor. They have found that an appropriate compound lean has beneficial effects, such as reducing leakage, reducing blade tip loading and increasing total pressure ratio, without sacrificing the efficiency. In the previous study [16], the influence of tip clearance to the compressor performance has been investigated numerically. In this paper, more information has been revealed. A new partially shrouded impeller has been developed to achieve higher efficiency of the compressor.

Numerical procedure Reynolds-averaged thin layer Navier-Stokes equations were solved by the Finite-Volume method. A quasi-steady approach was utilized with Roe’s flux-difference splitting. The effects of turbulence were evaluated with Chien’s κ−ε model. In most places y+ was less than 1 to get correct boundary layer information. The multi-grid method was used for the acceleration of convergence. The flow solver Finflo was used to solve the flow field. Finflo is a Navier-Stokes solver developed at Helsinki University of Technology [17]. The working fluid of the compressor is perfluoropentane, which is a heavy molecular weight gas. The ideal gas model is not suitable for the calculation. A practical real gas model using polynomial equations to calculate the gas properties has been applied for the study. In this real gas model, the temperature and pressure are independent variables. Density, internal energy, dynamic viscosity and thermal conductivity are functions of temperature and pressure. This real gas model is much faster than other real gas equations and easily generated from the property table. It has been proved to be suitable and efficient for modeling the superheated gas flow in the CFD process [16, 18, 19]. Figure 2 shows the density calculated by the real gas model and the ideal gas model. The dots represent the values from the property table. The dark mesh represents the values calculated by the real gas model, while the light mesh represents the values calculated by the ideal gas model.

Jin Tang et al.

Fig. 2

Use of partially shrouded impeller in a small centrifugal compressor

Density as a function of temperature and pressure, for the calculated case

The computational domain consists of one channel with an impeller and a vaneless diffuser. Table 1 shows the geometry parameters and operation conditions of the compressor. Figure 3(a) shows the surface grids of the computational domain. Clearance has also been modeled on the tip of the long blades and the splitter. Figure 3(b) shows the grids near the tip clearance at the impeller exit. To capture the flow across the tip clearance, 16 grid points between the blade tip and the shroud and also 16 grid points covering the blade thickness are applied. The number of grid points is about 110,000. The validation of the numerical procedure has been made previously [20]. Figure 4 shows the result of numerical calculations and measured values. Good agreement has been obtained and the numerical method has been proved adequate for the calculation.

Fig. 3

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(a) Surface grids of the computational domain (b) Grids near the tip clearance

Table 1

Geometry parameters and operation conditions of the compressor

d1t (m)

d1h (m)

d2 (m)

b2 (m)

Nd (rps)

0.0285

0.014

0.048

0.0018

800

md (kg/s)

p1t,d (Pa)

T1t,d (K)

πt-t,d

0.086

42000

291

2.87

Fig. 4

Total to total pressure ratio (a) and efficiency (b) of a water-treatment compressor [20].

Partially shrouded impeller and alternatives of clearance types As known [3,12], tip clearance leakage flow is the main reason of the drop of efficiency and pressure ratio. Detailed investigation of the leaking flow rate across the blade tip was made. Figure 5 shows the leaking flow rate at the tip of different positions along the impeller blade from the leading edge (0%) to the trailing edge (100%). It shows that the leaking flow rate is increased from the impeller leading edge and ends up of much higher leaking flow rate at the impeller trailing edge. There are three main reasons. First, the pressure and density are greater at the impeller exit. Second, the pressure gradient at the two sides of the impeller is greater at the impeller exit since the blade at the impeller exit is moving faster (linear velocity) than the inlet. Third, the relative size of the tip clearance is larger at the impeller exit. Based on the above information, a partially shrouded impeller was invented and calculated. Figure 6 shows the geometry of the partially shrouded impeller. The impeller is coated only at a small part near the impeller exit. Numerical calculations were made for two partially

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J. Therm. Sci., Vol.17, No.1, 2008

shrouded impellers: 36% of the blade length is coated, and 54% of the blade length (from leading edge of splitter blade) is coated. The clearance between the casing and the shroud at the shrouded part of the impeller which is needed in the real machine is not modeled. Geometry parameters of different partially shrouded cases are shown in table 2.

the channel height, which is called positive tip clearance. Figure 7 shows the two kinds of tip clearance configuration. Both clearances in the calculation are 0.3 mm for the positive clearance and the negative clearance. Geometry parameters of different unshrouded cases are shown in table 3.

Fig. 7 Fig. 5 Leaking flow rate across the tip clearance along the blade length Table 2

Geometry parameters of different partially shrouded impeller cases.

Positive clearance

0.048

0.0021

length of partial shroud 54 %

Negative clearance

0.048

0.0018

54 %

Negative clearance

0.048

0.0018

36 %

case

d2 (m)

Fig. 6

b2 (m)

Partially shrouded impeller

In the design procedure, the channel height at the impeller exit is usually well designed. For manufacturing, however, the blade height is of greater concern. For normal open wheeled compressors, this is not a big problem, but for small compressors, the difference of blade height and channel height would be great at the impeller exit. There are two alternatives of treating the difference. One is keeping the channel height as designed channel height, and decreasing the blade height, which is called negative tip clearance. The other is keeping the blade height as designed channel height, and increasing

Table 3

Tip clearance configuration

Geometry parameters of different unshrouded impeller cases. Case

d2 (m)

b2 (m)

Positive clearance No clearance (shrouded) Negative clearance

0.048 0.048 0.048

0.0018 0.0018 0.0015

channel height (m) 0.0021 0.0018 0.0018

Overall Performance of the Partially Shrouded Impeller The overall performance of the compressor with the partially shrouded impeller is shown in Fig. 8. The isentropic efficiency, total pressure rise and the total enthalpy rise of the compressor are increased as the shrouded part of the impeller grows. So basically the fully shrouded impeller gets the best performance and the fully unshrouded impeller gets the worst. Only the total enthalpy of the positive clearance and 54% partially shrouded impeller is higher than the total enthalpy of the fully shrouded impeller. This is because of the longer blade of the positive partial shroud in spanwise direction. The longer the blade, the more energy is transferred from the impeller blade to the fluid, and the greater the total enthalpy rise of the fluid. Figure 8 also shows that the increase of the isentropic enthalpy rise is not linear. The increase rate is higher when the shrouded part is smaller and lower when it is larger. Similar trends can also be found for the total pressure ratio and total enthalpy rise. So there is an optimization between the shrouded area and the isentropic efficiency of the compressor, that is, a compromise between cost and performance. Figure 8 also shows that the performance of the positive tip clearance is higher than the negative tip clear-

Jin Tang et al.

Use of partially shrouded impeller in a small centrifugal compressor

25

real compressor with partially shrouded impeller maybe 0.5-1 percentage lower than the calculated values. However, comparing the efficiency gained by the partially shrouded impeller, this efficiency drop is quite small.

Detailed Flow Field

(a) Isentropic efficiency

(b) Total pressure rise

(c) Total enthalpy rise Fig. 8

Influence of partial shroud to the performance of the compressor

ance, for both the fully unshrouded impeller and partially shrouded impeller. Due to the clearance and friction influence between the shroud and the casing of the compressor, in reality the performance of the shrouded impeller is lower than what is calculated here. From Harada [21], it is deduced that the performance of a shrouded impeller is about the same of an unshrouded impeller which has 3-4% relative clearance. According to Pampreen [1], the efficiency of a real shrouded impeller will be 1-1.5 percentage lower than what is calculated as a fully shrouded impeller here. Then the efficiency of the

The Mach number distributions of the different shroud configurations near the impeller shroud are shown in Fig. 9. It is seen that the area of the low speed flow region in sub-channel I is significantly reduced by the partially shroud, and the low speed flow region is closer to the suction side of the splitter. A similar reduction of the low speed flow can be seen in sub-channel II of the negative shrouded impeller. However, for the positive partially shrouded impeller, the low speed flow is greater than that of the unshrouded impeller and closer to the pressure side of the splitter. Figure 10 shows the relative Mach number distributions at the exit of the impeller. It is seen that the area of the low speed flow region is reduced most in the partially shrouded impeller than in the unshrouded impeller. The only different one is the positive clearance partially shrouded impeller. The low speed flow region in sub-channel I is larger than in the unshrouded impeller. However, the higher speed flow near the shroud of the unshrouded impeller is leaking flow. This means that the flow direction is more tangential. Careful observation at the flow near the pressure side of the impeller shows that the speed of the main flow is lower in the partially shrouded impeller. It means that the main flow is compressed less by the secondary flow of the partially shrouded impeller. The secondary effect is smaller in the positive clearance partially shrouded impeller. This is also proved by Fig. 11. From the distribution of the radial component of the flow momentum, it is seen that the region of the low radial speed region is smaller and closer to the suction side in the positive clearance partially shrouded impeller than in the unshrouded impeller. Figure 11 also shows that the speed of the main flow in the negative clearance unshrouded impeller is higher than that in the positive tip clearance unshrouded impeller. The smaller flow area at the impeller exit of the negative clearance unshrouded impeller is the main reason. The diffusion rate of the impeller is greater in the positive clearance unshrouded impeller than in the negative clearance unshrouded impeller, which is the same with the designed diffusion rate. Thus the speed of the flow at the impeller exit is of course smaller in the positive unshrouded impeller. In Fig. 11, the radial speed is also greater in the negative clearance unshrouded impeller than in the positive clearance unshrouded impeller. The larger diffusion rate in the positive partial shroud is also one reason for the large low speed flow in subchannel I of the positive clearance partially shrouded

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J. Therm. Sci., Vol.17, No.1, 2008

A B C D E F

Fig. 9

0.1 0.3 0.5 0.7 0.9 1.1

Distribution of the relative Mach number near the shroud of the impeller with different shroud configurations A B C D E F

Fig. 10

Distribution of the relative Mach number at the exit of the impeller with different shroud configurations A B C D E F

Fig. 11

0.2 0.3 0.4 0.6 0.7 0.8

0 100 200 300 400 500

Distribution of the radial component of the flow momentum at the exit of the impeller with different shroud configurations

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Use of partially shrouded impeller in a small centrifugal compressor

impeller. The diffusion rate is greater than the designed value, which may cause the separation. Due to the separation, the main flow is compressed. It is seen in Fig. 11 that the radial speed of the main flow in sub-channel I of the positive partially shrouded impeller is higher than that of the negative partially shrouded impeller. It also shows that the flow field uniformity of the negative clearance impeller is better than that of the positive clearance.

Conclusions A detailed study on the leaking flow rate across the tip clearance was made, and it was found that the leaking rate is much higher near the exit of the impeller than the inlet. A partial shroud near the exit of the impeller was carried out. The result shows that the flow field is greatly changed by the partially shrouded impeller. At the exit of the impeller, the big secondary flow region caused by the leaking flow becomes smaller and closer to the suction/shroud corner. The flow uniformity becomes better at the exit of the impeller. Better performance is achieved than with the unshrouded impeller. Meanwhile, the manufacturing cost of the impeller will be higher than the unshrouded impeller but a lot lower than the shrouded impeller if it is cut from one piece of metal.

Acknowledgements Financial support for this study provided by National Technology Agency of Finland (TEKES) is gratefully acknowledged. CSC–Scientific Computing Ltd. has provided the computational resources for the numerical work.

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[7] Senoo, Y. and Ishida, M.: Pressure loss due to the tip clearance of impeller blades in axial and centrifugal blowers. Journal of Engineering for Gas Turbines and Power. 108: 32−37. (1986). [8] Senoo, Y. and Ishida, M. (1987). Deterioration of compressor performance due to tip clearance of centrifugal impellers. Journal of Turbomachinery, 109: 55−61. [9] Klassen, H. A., Wood, J. R. and Schumann, L. F.: Experimental performance of a 13.65 centimetre tip diameter tandem-vaned swept back centrifugal compressor designed for a pressure ratio of 6, NASA TP 1091, (1977). [10] Klassen, H. A., Wood, J. R. and Schumann, L. F.: Experimental performance of a 16.10 centimetre tip diameter swept back centrifugal compressor designed for a pressure ratio of 6, NASA TM X-3552, (1977). [11] Beard, M. G., Pratt. C. M. and Timmis P. H.: Recent experience on centrifugal compressors for small gas turbines, ASME Paper No. 78-GT-193, (1978). [12] Senoo, Y.: Mechanics on the tip clearance loss of impeller vanes, Journal of Turbomachinery, 113: 680−685, (1991). [13] Palmer, D. L. and Waterman, W. F.: Design and development of an advanced two-stage centrifugal compressor, Journal of Turbomachinery, 117: 205−212, (1995). [14] Ishida, M., Ueki, H. and Senoo, Y.: Effect of vane tip configuration on tip clearance loss of a centrifugal impeller, Journal of Turbomachinery, 112:14−18, (1990). [15] Howard, J. H. G. and Ashrafizaadeh, M.: A numerical investigation of blade lean angle effects on flow in a centrifugal impeller, Journal of Engineering for Power. 97: 207−213, (1994). [16] Tang, J., Turunen-Saaresti, T., Reunanen, A., Honkatukia, J. and Larjola, J.: Numerical investigation of the effect of tip clearance to the performance of a small centrifugal compressor, Proceedings of the ASME Turbo Expo, 2006, pp. 411-418, May 6-11, Barcelona, Spain, (2006). [17] Siikonen, T., Rautaheimo, P. and Salminen, E.: Finflo user guide, version 7.2, Helsinki University of Technology, Laboratory of Applied Thermodynamics, (2004). [18] Turunen-Saaresti, T., Tang, J., van Buijtenen, J. and Larjola, J.: Experimental and numerical study of a real-gas flow in a supersonic ORC turbine nozzle, Proceedings of the ASME Turbo Expo 2006, pp.1527-1533, May 6-11, Barcelona, Spain, (2006). [19] Turunen-Saaresti, T., Tang, J. and Larjola, J.: A practical real-gas model in CFD, European conference on computational fluid dynamics 2006, Sep 5−-8, Egmond aan Zee, The Netherlands, (2006). [20] Pitkänen, H.: The CFD analysis of the impeller and vaneless diffuser of an industrial water-treatment compressor, Proceedings of the 1997 ASME International Mechanical Engineering Congress & Exposition, Nov 16−21 1997, Dallas, TX, USA, (1997). [21] Harada, H.: Performance characteristics of shrouded and unshrouded impellers of a centrifugal compressor, Journal of Engineering for Gas Turbines and Power, Transactions of the ASME, Vol. 107, No. 3, pp. 528−533, (1985).