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Analysis of Two-Phase Cavitating Flow with Two-Fluid Model Using Integrated Boltzmann Equations

Published online by Cambridge University Press:  03 June 2015

Shuhong Liu ,
Yulin Wu ,
Yu Xu  and
Hua-Shu Dou
Shuhong Liu
Affiliation:
State Key Laboratory of Hydro Science and Hydraulic Engineering, Tsinghua University, Beijing 100084, China
Yulin Wu*
Affiliation:
State Key Laboratory of Hydro Science and Hydraulic Engineering, Tsinghua University, Beijing 100084, China
Yu Xu
Affiliation:
Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100080, China
Hua-Shu Dou*
Affiliation:
Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, Zhejiang, China
*
Email: wyl-dhh@tsinghua.edu.cn
Corresponding author. Email: huashudou@yahoo.com
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Abstract

In the present work, both computational and experimental methods are employed to study the two-phase flow occurring in a model pump sump. The two-fluid model of the two-phase flow has been applied to the simulation of the three-dimensional cavitating flow. The governing equations of the two-phase cavitating flow are derived from the kinetic theory based on the Boltzmann equation. The isotropic RNG k — ε — kca turbulence model of two-phase flows in the form of cavity number instead of the form of cavity phase volume fraction is developed. The RNG k—ε—kca turbulence model, that is the RNG k — e turbulence model for the liquid phase combined with the kca model for the cavity phase, is employed to close the governing turbulent equations of the two-phase flow. The computation of the cavitating flow through a model pump sump has been carried out with this model in three-dimensional spaces. The calculated results have been compared with the data of the PIV experiment. Good qualitative agreement has been achieved which exhibits the reliability of the numerical simulation model.

Keywords

76T1076M12Cavitating flowtwo-fluid modelRNG k–ε–kca turbulence modelBoltzmann equationskinetic theory
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 5 , October 2013 , pp. 607 - 638
Copyright
Copyright © Global-Science Press 2013

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References

[1]Yamaguchi, H. and Kato, H., On application of nonlinear cavity flow theory to thick foil sections, Proc. Conf. Cavitation, Inst. Mech. Eng., Edinburgh, Scotland, 1983.Google Scholar
[2]Brewer, W. H. and Kinnas, S. A., Experimental and computational investigation of sheet cavitation on a hydrofoil, in FED Cavitation and Multiphase Flow, ASME FED 210, Matsumoto, Y. and Katz, J., eds., American Soc. of Mechanical Engineers, New York, USA, 1995, pp. 1–15.Google Scholar
[3]Pellone, C. and Peallat, J. M., Non-linear analysis of three-dimensional partially cavitating hydrofoil, in Proc. of the International Symposium on Cavitation, Des Carenes, B. D., Ed., Deauville, France, May 2-5, 1995, EPFL, Lausanne, Switzerland (1995), pp. 63–67.Google Scholar
[4]Lange, D.F.De and Bruin, G.J. De, Sheet cavitation and cloud cavitation re-entrant jet and three-dimensionality, Appl. Scic Res., 58 (1998), pp. 91–114.CrossRefGoogle Scholar
[5]Kubota, A., Kato, H. and Yamaguch, H., A new modeling of cavitating flows, a numerical study of unsteady cavitation on a hydrofoil section, J. Fluid Mech., 240 (1992), pp. 59–96.Google Scholar
[6]Song, C. C. S., He, J., Zhou, F. and Wang, G., Numerical Simulation of Cavitating and Non-cavitating Flows over a Hydrofoil, SAFL project report No. 402, St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, USA, 1997.Google Scholar
[7]Arndt, R. E. A., Kjeldsen, M., Song, C. C. S. and Keller, A., Analysis of cavitation wake flows, in Proc. of the 21st IAHR Symposium on Hydraulic Machinery and Systems, Avellan, F., Ciocan, G. and Kvicinsky, S., Eds., Lausanne, Switzerland, September 9-12, Inter. Assoc. on Hydraulic Research, Section on Hydraulic Machinery and System, Lausanne, Switzerland (2002), Paper No. A91-XOBKLURZ.Google Scholar
[8]Qin, Q., Song, C. S. S. and Arndt, R. E., Numerical study of unsteady turbulent wake behind a cavitating hydrofoil, in Proc. of 5th International Symposium on Cavitation, CAV2003, Matsumoto, Y. and Tsujimoto, Y. Eds. Osaka, Japan, November 1-4, 2003, Osaka University, Osaka, Japan, Paper No. EM.003 (2003).Google Scholar
[9]Chen, Y., Y. and Heister, D., A numerical treatment for attached cavitation, J. Fluids Eng., 116 (1994), pp. 613–618.Google Scholar
[10]Deshpande, M., Feng, J. and Merkle, C. L., Numerical modeling of the thermodynamic effects of cavitation, J. Fluids Eng., 119 (1997), pp. 420–426.Google Scholar
[11]Ventikos, Y. and Tzabiras, G., A numerical method for the simulation of steady and unsteady cavitating flows, Computer Fluids, 29 (2000), pp. 63–88.Google Scholar
[12]Singhal, A. K., Vaidya, N. and Leonard, A. D., Multi-dimensional simulation of cavitating flows using a PDF model for phase change, In: Proceeding of ASME Fluids Engineering Division Summer Meeting, Vancouver, 4 (1997), pp. 1–8.Google Scholar
[13]Merkle, C. L., Feng, J. Z. and Buelow, P. E., Computational modeling of the dynamics of sheet cavitation, in Proc. Third Int. Symposium on Cavitation, Michel, J.-M. and Kato, H. Eds., April 7-10, 1998, Grenoble, France, EPFL, Lausanne, Switzerland (1998), pp. 307–311.Google Scholar
[14]Kunza, R. F., Bogera, D. A., Stinebringa, D. R., Chyczewskia, T. S., Lindaua, J. W., Gibelinga, H. J., Venkateswaranb, S. and Govindanc, T. R., A preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction, Comput Fluids, 29 (2000), pp. 849–875.Google Scholar
[15]Senocak, I. and Shyy, W., A pressure-based method for turbulent cavitating flow computation, J. Comput. Phys., 176 (2002), pp. 363–383.Google Scholar
[16]Rieger, R., Mehrdimensionale Berechnung zweiphasiger Stroemungen, PhD-Thesis, Technical University Graz, Graz, Austria, 1992.Google Scholar
[17]Grogger, H. A. and Alajbegovic, A., Calculation of the cavitation flow in venturi geometries using two fluid model, in Proc. of ASME Fluids Eng. Division Summer Meeting, Freitas, C.J. Ed., Washington D. C., USA, June 22-25, 1998, American Soc. of Mechanical Engineers, New York, USA (1998), Paper No. FEDSM98-5295.Google Scholar
[18]Tang, X. L. and Wu, J., An improved les on dense particle-liquid turbulent flows using integrated Boltzmann equations, Can. J. Chem. Eng., 85 (2007), pp. 137–150.CrossRefGoogle Scholar
[19]Chen, X., Dynamic Theory and Its Application in Thermophysics and Fluid Flow, Tsinghua University Press, Beijing, China, 1996, pp. 58–66, 67–74 (in Chinese).Google Scholar
[20]Brennen, C. E., Cavitation and Bubble Dynamics, Oxford University Press, New York, USA, 1995, Chapter 2, pp. 1–10.Google Scholar
[21]Ishii, M., Thermo-Fluid Dynamic Theory of Two-Phase Flow, 1975, Eyrolles, Paris.Google Scholar
[22]Zhou, L. X., Theory of Gas-Particle Two-Phase Flow and Combustion and Its Numerical Simulation, Publisher of Sciences in China, 1994.Google Scholar
[23]Wu, Y. L., Numerical Simulation of Liquid-Particle Two-Phase Flows Through Hydraulic Machinery by Two-Fluid Model (Chapter 3), Abrasive Erosion and Corrosion of Hydraulic Machinery, Editors: Duan, C.G. and Karelin, V.Y., Imperiral College Press, London, 2002.Google Scholar
[24]Singhal, A. K., Li, H. Y., Athavale, M. M. and Jiang, Y., Mathematical basis and validation of the full cavitation model, in Proc. of ASME FEDSM’01, 2001 ASME Fluids Eng. Division Summer Meeting, Katz, J., Ed., New Orleans, Louisiana, May 29-June 1, 2001, American Soc. of Mechanical Engineers, New York, USA, 1997, Paper No. FEDSM2001-18015.Google Scholar
[25]Ji, B., Luo, X. W., Wu, Y. L., Peng, X. X. and Duan, Y. L., Numerical analysis of unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoil, Submitted to International Journal of Multiphase Flow, 2012, (accepted).Google Scholar