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Acta Mechanica Sinica

, 27:473 | Cite as

Turbulence and cavitation models for time-dependent turbulent cavitating flows

  • Ying-Jie WeiEmail author
  • Chien-Chou Tseng
  • Guo-Yu Wang
Research Paper

Abstract

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure at a local thermodynamic state, and the flow is frequently unsteady and turbulent. To assess the state-of-the-art of computational capabilities for unsteady cavitating flows, different cavitation and turbulence model combinations are conducted. The selected cavitation models include several widely-used models including one based on phenomenological argument and the other utilizing interface dynamics. The k-ɛ turbulence model with additional implementation of the filter function and density correction function are considered to reduce the eddy viscosity according to the computed turbulence length scale and local fluid density respectively. We have also blended these alternative cavitation and turbulence treatments, to illustrate that the eddy viscosity near the closure region can significantly influence the capture of detached cavity. From the experimental validations regarding the force analysis, frequency, and the cavity visualization, no single model combination performs best in all aspects. Furthermore, the implications of parameters contained in different cavitation models are investigated. The phase change process is more pronounced around the detached cavity, which is better illus-trated by the interfacial dynamics model. Our study provides insight to aid further modeling development.

Keywords

Cavitation Turbulence model Cavitation model Hybrid model 

Nomenclature

σ

Local cavitation number; cavitation number based on the local temperature

Cɛ1,Cɛ2, σɛ, σk

Coefficients of k-ɛ turbulence model

C

Chord length of hydrofoil

L

Characteristic length scale

I

Turbulence intensity

k

Turbulent kinetic energy

.m+, .m

Source and sink terms in the cavitation model

p

Pressure

pv

Saturation vapor pressure

Re

Reynolds number

t

Reference time scale, t = L/U

U

Reference velocity scale

u

Velocity

Uv,n

Normal component of the vapor velocity moving away from the interface

UI,n

Normal interfacial velocity

x

Space variable

αl

Liquid volume fraction

ρ

Density

µ

Dynamic viscosity

µTL|inlet

Eddy-to-laminar viscosity ratio at the inlet

ϕm

Mixture property

ɛ

Turbulent dissipation rate

Δ

Filter size in filter-based model

References

  1. 1.
    Utturkar, Y., Wu, J., Wang, G., et al.: Recent progress in modeling of cryogenic cavitation for liquid rocket propulsion. Progress in Aerospace Sciences 41(7), 558–608 (2005)CrossRefGoogle Scholar
  2. 2.
    Knapp, R.T., Daily, J.W., Hammitt, F.G.: Cavitation. McGraw-Hill. New York (1970)Google Scholar
  3. 3.
    Brennen, C.E.: Cavitation and Bubble Dynamics. Oxford Engineering & Sciences Series 44, Oxford University Press (1995)Google Scholar
  4. 4.
    Joseph, D.D.: Cavitation in a flowing liquid. Phys. Review E 51(3), 1649–1650 (1995)CrossRefGoogle Scholar
  5. 5.
    Joseph, D.D.: Cavitation and the state of stress in a flowing liquid. Journal of Fluid Mechanics 366, 367–378 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Kubota, A., Kato, H., Yamaguchi, H., et al.: Unsteady structure measurement of cloud cavitation on a foil section using conditional sampling technique. J. Fluid Eng-T. ASME 111, 204–210 (1989)CrossRefGoogle Scholar
  7. 7.
    Leroux, J.B., Astolfi, J.A., Billare, J.Y.: An experimental study of unsteady partial cavitation. ASME 26, 94–101 (2004)Google Scholar
  8. 8.
    Kawanami, Y., Kato, H., Tanimura, M., et al.: Mechanism and control of cloud cavitation. J. Fluid Eng-T. ASME 119, 788–794 (1997)CrossRefGoogle Scholar
  9. 9.
    LaCallenaere, M., Franc, J.P., Michel, J.M., et al.: The cavitation instability induced by the development of a re-entrant jet. J. Fluid Mech. 444, 223–256 (2001)Google Scholar
  10. 10.
    Gopalan, S., Katz, J.: Flow structure and modeling issues in the closure region of attached cavitation. Phys. Fluids 12(4), 895–911 (2000)zbMATHCrossRefGoogle Scholar
  11. 11.
    Li, C.Y., Ceccio, S.L: Interaction of single travelling bubbles with the boundary layer and attached cavitation. J. Fluid Mech. 322, 329–353 (1996)CrossRefGoogle Scholar
  12. 12.
    Chen, Y., Hesiter, S. D.: A numerical treatment for attached cavitaition. J. Fluids Eng. 116, 613–618 (1994)CrossRefGoogle Scholar
  13. 13.
    Deshpande, M., Feng, J., Merkle, C.L.: Numerical modeling of the thermodynamic effects of cavitation. J. Fluids Eng. 119, 420–427 (1997)CrossRefGoogle Scholar
  14. 14.
    Huang, D., Zhuang, Y., Cai, R.: A computational method for cavitational flows based on energy conservation. IMechE 207, 1333–1338 (2007)Google Scholar
  15. 15.
    Edward, J.R., Franklin, R.K., Liou, M.S.: Low-diffusion flux-splitting methods for real fluid flows with phase transition. AIAA Journal 38(9), 1624–1633 (2000)CrossRefGoogle Scholar
  16. 16.
    Delannoy, Y., Kueny, J.L.: Cavity flow prediction based on the Euler equations. ASM Cavitation and Multiphase Flow Forum. ASME-FED 98, 153–158 (1990)Google Scholar
  17. 17.
    Wu, J.Y., Wang, G.Y., Shyy, W.: Time-dependent turbulent cavutating flow computations with interfacial transport and filter-based models. International Journal for Numerical Methods in Fluids 49(7), 739–761 (2005)zbMATHCrossRefGoogle Scholar
  18. 18.
    Merkle, C.L., Feng, J., Buelow, P.E.O.: Computational modeling of sheet cavitation. Proc. 3rd International Symposium on Cavitation, Grenoble, France 1998Google Scholar
  19. 19.
    Kunz, R.F., Boger, D.A., Stinebring, D.R., et al.: A preconditioned Navier-Stokes method for two phase flows with application to cavitation prediction. Comput. Fluids 29, 849–875 (2000)zbMATHCrossRefGoogle Scholar
  20. 20.
    Hosangadi, A., Ahuja, V.: A numerical study of cavitation in cryogenic fluids. Journal of Fluids Engineering 127, 267–281 (2005)CrossRefGoogle Scholar
  21. 21.
    Senocak, I., Shyy, W.: Interfacial dynamics-based modeling of turbulent cavitating flows. Part 1: model development and steady-state computations. Int. J. Numer. Meth. Fluids 44, 975–995 (2004)zbMATHCrossRefGoogle Scholar
  22. 22.
    Senocak, I., Shyy, W.: Interfacial dynamics-based modeling of turbulent cavitating flows. Part 2: time-dependent computations. Int. J. Numer. Meth. Fluids 44, 997–1016 (2004)zbMATHCrossRefGoogle Scholar
  23. 23.
    Utturkar, Y., Wu, J., Wang, G., et al.: Recent progress in modeling of cryogenic cavitation for liquid rocket propulsion. Progress in Aerospace Sciences 41(7), 558–608 (2005)CrossRefGoogle Scholar
  24. 24.
    Tseng, C., Shyy, W.: Modeling for isothermal and cryogenic cavitation. Int. J. Heat Mass Transfer 53, 513–525 (2010)zbMATHCrossRefGoogle Scholar
  25. 25.
    Tseng, C., Shyy, W.: Surrogate-based modeling of cryogenic turbulent cavitating flows. CAV2009, Paper No. 77. Proceedings of the 7th International Symposium on Cavitation, August 17–22, 2009, Ann Arbor, Michigan, USAGoogle Scholar
  26. 26.
    Li, X., Wang, G., Yu, Z., et al.: Multiphase fluid dynamics and transport processes of low capillary number cavitating flows. Acta Mechanica Sinica 25, 161–172 (2008)CrossRefGoogle Scholar
  27. 27.
    Singhal, A.k., Li, H., Athavale, M.M., et al.: Mathematical basis and validation of the full cavitation model. J. Fluids Eng. 124(3), 617–625 (2002)CrossRefGoogle Scholar
  28. 28.
    Hosangadi, A., Ahuja, V.A.: Numerical of cavitation in cryogenic fluids. Part 2 — new unsteady model for dense cloud. cavitation. 6th International Symposium on Cavitation, Wageningen, Netherlands. Sep. 2006Google Scholar
  29. 29.
    Hosangadi, A., Ahuja, V., Ungewitter, R.J.: Simulations of rotational cavitation instabilities in the SSME LPFP inducer. In: 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit; 1–16. 2007Google Scholar
  30. 30.
    Coutier-Delgosha, R., Fortes-Patella, O., Reboud, J.L.: Evaluation of the turbulence model influence on the numerical simulations of unsteady cavitation. Journal of Fluids Engineering 125, 38–45 (2003)CrossRefGoogle Scholar
  31. 31.
    Ahuja, V., Hosangadi, A., Arunajatesan, S.: Simulations of cavitating flows using hybrid unstructured meshes. Journal of Fluids Engineering 123, 123–331 (2001)CrossRefGoogle Scholar
  32. 32.
    Shyy, W., Thakur, S.S., Ouyang, H., et al.: Computational Techniques for Complex Transport Phenomenon. Cambridge University Press (2007)Google Scholar
  33. 33.
    Launder, B.E., Spalding, D.B.: The numerical computation of turbulent flow. Comp. Meth. Appl. Mech. Eng. 3, 269–289 (1974)zbMATHCrossRefGoogle Scholar
  34. 34.
    Johansen, S.T., Wu, J.Y., Shyy, W.: Filter based unsteady RANS computational. International Journal of Heat and Fluid Flow 25, 10–21 (2005)CrossRefGoogle Scholar
  35. 35.
    Shyy, W., Udaykumar, H.S., Rao, M.M., et al.: Computational Fluid Dynamics with Moving Boundaries, Taylor & Francis, Washington, DC (1996); Dover, New York (2007)Google Scholar
  36. 36.
    Francois, M., Shyy, W.: Computations of drop dynamics with the immersed boundary method; Part 1-numerical algorithm and buoyancy induced effect. Numerical Heat Transfer, Part B 44, 101–118 (2003)CrossRefGoogle Scholar
  37. 37.
    Francois, M., Shyy, W.: Computations of drop dynamics with the immersed boundary method; Part 2-drop impact and heat transfer. Numerical Heat Transfer, Part B 44, 119–143 (2003)CrossRefGoogle Scholar
  38. 38.
    Ye, T., Shyy, W., Chung, J.C.: A fixed-grid, sharp-interface method for bubble dynamics and phase change. Journal of Computational Physics 174, 781–815 (2001)zbMATHCrossRefGoogle Scholar
  39. 39.
    Wang, G., Zhang, B., Huang, B., et al.: Unsteady dynamics of cloudy cavitating flows around a hydrofoil. CAV2009, Paper No. 9. In: Proceedings of the 7th International Symposium on Cavitation, August 17–22, 2009, Ann Arbor, Michigan, USAGoogle Scholar
  40. 40.
    Wang, G., Senocak, I., Shyy, W., et al.: Dynamics of attached turbulent cavitating flows. Progress in Aerospace Sciences 37, 551–581 (2001)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Mechanical EngineeringUniversity of MichiganAnn ArborUSA
  3. 3.School of Vehicle and Transportation EngineeringBeijing Institute of TechnologyBeijingChina

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