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Modeling of turbulent, isothermal and cryogenic cavitation under attached conditions

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Abstract

Cavitation is often triggered when the fluid pressure is lower than the vapor pressure at a local thermodynamic state. The present article reviews recent progress made toward developing modeling and computational strategies for cavitation predictions under both isothermal and cryogenic conditions, with an emphasis on the attached cavity. The review considers alternative cavitation models along Reynolds-averaged Navier–Stokes and very lager eddy simulation turbulence approaches to ensure that the computational tools can handle flows of engineering interests. Observing the substantial uncertainties associated with both modeling and experimental information, surrogate modeling strategies are reviewed to assess the implications and relative importance of the various modeling and materials parameters. The exchange between static and dynamic pressures under the influence of the viscous effects can have a noticeable impact on the effective shape of a solid object, which can impact the cavitation structure. The thermal effect with respect to evaporation and condensation dynamics is examined to shed light on the fluid physics associated with cryogenic cavitation. The surrogate modeling techniques are highlighted in the context of modeling sensitivity assessment.

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Abbreviations

σ ∞ :

Free stream cavitation number; cavitation number based on the free stream temperature

σ :

Local cavitation number; cavitation number based on the local temperature

B :

B-factor

Cε1, Cε2, σ ε , σ k :

Coefficients of k–ε turbulence model

C :

Heat capacity

C p :

Pressure coefficient

D :

Characteristic length scale

f :

Filter function

f v :

Vapor mass fraction

h :

Enthalpy

I :

Turbulence intensity

K :

Turbulent kinetic energy

L :

Latent heat

m+, m−:

Source and sink terms in the cavitation model

Pr :

Prandtl number

P t :

Production term of turbulent kinetic energy

P v :

Saturation vapor pressure

P diff :

L2 norm between experiment and predicted pressure

Re :

Reynolds number

S :

Sensitivity indices

T :

Temperature

T diff :

L2 norm between experiment and predicted temperature

t ∞ :

Reference time scale (t ∞ = L/U ∞)

U ∞ :

Reference velocity

u :

Velocity

U v,n :

Normal component of the vapor velocity moving away from the interface

U I,n :

Normal interfacial velocity

V :

Total variance

Δν :

Difference of specific volume during phase change in Clapeyron equation

ΔT*:

Reference temperature drop

x :

Space variable

α l :

Liquid volume fraction

ρ :

Density

μ :

Dynamic viscosity

μ T /μ L |inlet:

Eddy-to-laminar viscosity ratio at the inlet

\({\phi_m}\) :

Mixture property

ε :

Turbulent dissipation rate

Δ:

Filter size in filter-based model

δ * :

Displacement thickness

j :

Component

l :

Liquid

L :

Laminar

m :

Mixture property

T :

Turbulent

v :

Vapor

ω :

Free stream quantities

References

  1. Utturkar Y., Wu J., Wang G., Shyy W.: Recent progress in modeling of cryogenic cavitation for liquid rocket propulsion. Prog. Aerosp. Sci. 41(7), 558–608 (2005)

    Article  Google Scholar 

  2. Knapp R.T., Daily J.W., Hammitt F.G.: Cavitation. McGraw-Hill, New York (1970)

    Google Scholar 

  3. Brennen C.E.: Cavitation and Bubble Dynamics, Oxford Engineering & Sciences Series 44. Oxford University Press, Oxford (1995)

    Google Scholar 

  4. Joseph D.D.: Cavitation in a flowing liquid. Phys. Rev. E. 51(3), 1649–1650 (1995)

    Article  Google Scholar 

  5. Joseph D.D.: Cavitation and the state of stress in a flowing liquid. J. Fluid Mech. 366, 367–378 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Lemmon, E.W., McLinden, M.O., Huber, M.L.: REFPROP: Reference Fluid Thermodynamic and Transport Properties. NIST Standard Database 23, version 7.0 (2002)

  7. Sonntag R.E., Borgnakke C., Wylen G.J.: Fundamentals of T thermodynamics. Wiley, New York (2004)

    Google Scholar 

  8. Ruggeri, R.S., Moore, R.D.: Method for Prediction of Pump Cavitation Performance for Various Liquids, Liquid Temperatures and Rotative Speeds. NASA TN D-5292 (1969)

  9. Goel T., Zhao J., Thakur S., Haftka R.T., Shyy W., Zhao J.: Surrogate model-based strategy for cryogenic cavitation model validation and sensitivity evaluation. Int. J. Numer. Meth. Fluids. 58, 969–1007 (2008)

    Article  MATH  Google Scholar 

  10. Wang G., Senocak I., Shyy W., Ikohagi T., Cao S.: Daynamics of attached turbulent cavitating flows. Prog. Aerosp. Sci. 37, 551–581 (2001)

    Article  Google Scholar 

  11. Kubota A., Kato H., Yamaguchi H., Maeda M.: Unsteady structure measurement of cloud cavitation on a foil section using conditional sampling technique. J. Fluid Eng-T. ASME 111, 204–210 (1989)

    Article  Google Scholar 

  12. Leroux J.B., Astolfi J.A., Billare J.Y.: An experimental study of unsteady partial cavitation. ASME 26, 94–101 (2004)

    Google Scholar 

  13. Kawanami Y., Kato H., Tanimura M., Tagaya Y.: Mechanism and control of cloud cavitation. J. Fluid Eng-T. ASME. 119, 788–794 (1997)

    Article  Google Scholar 

  14. Laberteaux K.R., Ceccio S.L.: Partial cavity flows. Part 1. Cavities forming on models without spanwise variation. J. Fluid Mech. 431, 1–41 (2002)

    Article  Google Scholar 

  15. Callenaere M., Franc J.P., Michel J.M., Riondet M.: The cavitation instability induced by the development of a re-entrant jet. J. Fluid Mech. 444, 223–256 (2001)

    Article  MATH  Google Scholar 

  16. Gopalan S., Katz J.: Flow structure and modeling issues in the closure region of attached cavitation. Phys. Fluids 12(4), 895–911 (2000)

    Article  MATH  Google Scholar 

  17. 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)

    Article  Google Scholar 

  18. Laberteaux K.R., Ceccio S.L.: Partial cavity flows. Part 2. Cavities forming on test objects with spanwise variation. J. Fluid Mech. 431, 43–63 (2002)

    Article  Google Scholar 

  19. Sarosdy, L.R., Acosta, A.J.: Note on Observations of Cavitation in Different Fluids. Paper 60-WA-83, ASME Winter Annual Meeting, New York (1961)

  20. Hord, J.: Cavitation in Liquid Cryogens II-Hydrofoil. NASA CR-2156 (1973)

  21. Kazuki, N., Satoshi, H., Shinichi, T., Yoshiki, Y., Tsutomu, T., Mamoru, O.: Thermodynamic effects on cryogenic cavitation flow in orifice. In: Proceedings of the 7th International Symposium on Cavitation, August 17–22, 2009, Ann Arbor, MI, USA. CAV2009, Paper No. 36

  22. Huang D.G., Zhuang Y.Q.: Temperature and cavitation. IMechE 222, 207–211 (2008)

    Article  Google Scholar 

  23. Cervone A., Bramanti C., Rapposelli E., Agostino L.: Thermal cavitation experiments on a NACA 0015 hydrofoil. ASME 128, 326–331 (2006)

    Article  Google Scholar 

  24. Yuka, I., Naoya, O., Yoshiki, Y., Toshiaki, I.: Numerical invetigation of thermodynamic effect on unsteady cavitation in cascade. In: Proceedings of the 7th International Symposium on Cavitation, August 17–22, 2009, Ann Arbor, MI, USA. CAV2009, Paper No. 78

  25. Gustavsson J.P.R., Denning K.C., Segal C.: Incipient cavitation studied under strong thermodynamic effect. AIAA J. 47(3), 710–716 (2009)

    Article  Google Scholar 

  26. Chen Y., Hesiter S.D.: A numerical treatment for attached cavitaition. J. Fluids Eng. 116, 613–618 (1994)

    Article  Google Scholar 

  27. Deshpande M., Feng J., Merkle C.L.: Numerical modeling of the thermodynamic effects of cavitation. J. Fluids Eng. 119, 420–427 (1997)

    Article  Google Scholar 

  28. Shyy, W., Udaykumar, H.S., Rao, M.M., Smith, R.W.: Computational Fluid Dynamics with Moving Boundaries. Taylor & Francis, Washington, DC (1996, revised printing 1997, 1998, 2001)

  29. Ye T., Mittal R., Udaykumar H.S., Shyy W.: An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Computat. Phys. 156, 209–240 (1999)

    Article  MATH  Google Scholar 

  30. Ye T., Shyy W., Chung J.C.: A fixed-grid, sharp-interface method for bubble dynamics and phase change. J. Computat. Phys. 174, 781–815 (2001)

    Article  MATH  Google Scholar 

  31. Chen S., Doolen D.: Lattice Boltzmann method for fluid flows. Ann. Rev. Fluid Mech. 30, 329–364 (1998)

    Article  MathSciNet  Google Scholar 

  32. Huang D., Zhuang Y., Cai R.: A computational method for cavitational flows based on energy conservation. IMechE 207, 1333–1338 (2007)

    Google Scholar 

  33. Edward J.R., Franklin R.K., Liou M.S.: Low-diffusion flux-splitting methods for real fluid flows with phase transition. AIAA J. 38(9), 1624–1633 (2000)

    Article  Google Scholar 

  34. Wang G., Ostoja-Starzewski M.: Large eddy simulation of a sheet/cloud cavitation on a NACA0015 hydrofoil. Math. Model. 31, 417–447 (2006)

    Google Scholar 

  35. 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 

  36. Wu J.Y., Wang G.Y., Shyy W.: Time-dependent turbulent cavutating flow computations with interfacial transport and filter-based models. Int. J. Numer. Methods Fluids 49(7), 739–761 (2005)

    Article  MATH  Google Scholar 

  37. Merkle, C.L., Feng, J., Buelow, P.E.O.: Computational modeling of sheet cavitation. In: Proceedings of the 3rd International Symposium on Cavitation, Grenoble, France (1998)

  38. Kunz R.F., Boger D.A., Stinebring D.R., Chyczewski T.S., Lindau J.W., Gibeling H.J., Venkateswaran S., Govindan T.R.: A preconditioned Navier–Stokes method for two phase flows with application to cavitation prediction. Comput. Fluids 29, 849–875 (2000)

    Article  MATH  Google Scholar 

  39. Hosangadi A., Ahuja V.: A numerical study of cavitation in cryogenic fluids. J. Fluids Eng. 127, 267–281 (2005)

    Article  Google Scholar 

  40. 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)

    Article  MATH  Google Scholar 

  41. 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)

    Article  MATH  Google Scholar 

  42. Ha, C.T., Park, W.G., Merkle, C.L.: Multiphase flow aanlysis of cylinder using a new cavitation model. In: Proceedings of the 7th International Symposium on Cavitation, August 17–22, 2009, Ann Arbor, MI, USA. CAV2009, Paper No. 99

  43. Li X., Wang G., Yu Z., Shyy W.: Multiphase fluid dynamics and transport processes of low capillary number cavitating flows. Acta Mech. Sin. 25, 161–172 (2008)

    Article  Google Scholar 

  44. Singhal A.K., Li H., Athavale M.M., Jiang Y.: Mathematical basis and validation of the full cavitation model. J. Fluids Eng. 124(3), 617–625 (2002)

    Article  Google Scholar 

  45. Hosangadi, A., Ahuja, V.A.: Numerical of cavitation in cryogenic fluids. Part II: new unsteady model for dense cloud. cavitation. In: Proceedings of 6th International Symposium on Cavitation, September 2006. Wageningen, Netherlands

  46. 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; pp. 1–16 (2007)

  47. Giorgi, M.G.D., Ficarella, A., Chiara, F., Laforgia, D.: Experimental and numerical investigations of cavitating flows. In: Proceedings of 35th AIAA Fluids Dynamics Conference and Exhibit, June. Toronto, Ontario, Canada (2005)

  48. Aliabadi, S., Tu, S.Z., Watts, M.D.: Simulation of hydrodynamic cavitating flows using stabilized finite element method. In: Proceedings of 43th AIAA Aerospace Science Meeting and Exhibit, January. Reno, Nevada (2005)

  49. Tani, N., Nagashima, T.: Numerical analysis of cryogenic cavitating flow on hydrofoil-comparison between water and cryogenic fluids. In: Proceedings of 4th International Conference on Launcher Technology, Liege, Belgium, December 3–6 (2002)

  50. Yao W., Morel C.: Volumetric interfacial area prediction in upward bubbly two-phase flow. Int. J. Heat Mass Transf. 47, 307–328 (2004)

    Article  MATH  Google Scholar 

  51. Mimouni S., Boucker M., Lavieville J., Guelfi A., Bestion D.: Modeling and computation of cavitation and boiling bubbly flows with the NEPTUNE_CFD Code. Nucl. Eng. Des. 238, 680–692 (2008)

    Article  Google Scholar 

  52. Kubota A., Kato H., Yamaguchi H.: A new modeling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section. J. Fluids Mech. 240, 59–96 (1992)

    Article  Google Scholar 

  53. Xing T., Frankel S.H.: Effect of cavitation on vortex dynamics in a submerged laminar jet. AIAA J. 40, 2266–2276 (2002)

    Article  Google Scholar 

  54. Shyy W., Thakur S.S., Ouyang H., Liu J., Blosch E.: Computational Techniques for Complex Transport Phenomenon. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  55. Dahm, W.J.A.: Introduction to Turbulent Flows, Physical Concept, Statistical Theory, and Engineering Modeling. University of Michigan (2007)

  56. Launder B.E., Spalding D.B.: The numerical computation of turbulent flow. Comp. Meth. Appl. Mech. Eng. 3, 269–289 (1974)

    Article  MATH  Google Scholar 

  57. Ruprecht, A., Helmrich, T., Buntic, I.: Very large eddy simulation for the prediction of unsteady vortex motion. In: Conference on Modeling Fluid Flow (CMFF’05), The 12th International Conference on Fluid Flow Technologies, September 3–6. Budapest, Hungary (2005)

  58. Germano M., Piomelli U., Moin P., Cabot W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3(7), 1760–1765 (1991)

    Article  MATH  Google Scholar 

  59. Smagorinsky J.: General circulation experiments with the primitive equations 1. The basic experiment. Mon. Weather Rev. 91(3), 99–164 (1963)

    Article  Google Scholar 

  60. Fasel H.F., Seidel J., Wernz S.: A methodology for simulations of complex turbulent flows. J. Fluids Eng. 124, 933–942 (2002)

    Article  Google Scholar 

  61. Johansen S.T., Wu J.Y., Shyy W.: Filter based unsteady RANS computational. Int. J. Heat Fluid Flow 25, 10–21 (2005)

    Article  Google Scholar 

  62. Shur M.L., Spalart P.R., Strelets M.H., Travin A.K.: A hybrid RANS-LES approach with delayed-DES and wall-modeled LES capability. Int. J. Heat Fluid Flow 29, 1638–1649 (2008)

    Article  Google Scholar 

  63. Chauvet N., Deck S., Jacquin L.: Zonal detached eddy simulation of a controlled propulsive jet. AIAA J. 45(10), 2458–2473 (2007)

    Article  Google Scholar 

  64. Strelets, M.: Detached eddy simulation of massively separated flows. AIAA 2001-0879 (2001)

  65. Home D., Lightstone M.F., Hamed M.S.: Validation of DES-SST based turbulence model for a fully developed turbulent channel flow problem. Numer. Heat Transf. Part A 55, 337–361 (2009)

    Article  Google Scholar 

  66. Menter, F.R.: Zonal two equation k−ω turbulence models for aerodynamic flows. AIAA Paper 93-2906 (1993)

  67. Tseng C., Shyy W.: Modeling for isothermal and cryogenic cavitation. Int. J. Heat Mass Transf. 53, 513–525 (2010)

    Article  MATH  Google Scholar 

  68. Yu D., Mei R., Luo L., Shyy W.: Viscous flow computations with the method of lattice Boltzmann equation. Prog. Aerosp. Sci. 39, 329–367 (2003)

    Article  Google Scholar 

  69. Mei R., Yu D., Shyy W., Luo L.S.: Force evaluation in the lattice Boltzmann method involving curved geometry. Phys. Rev. E 65, 1–14 (2002)

    Article  Google Scholar 

  70. Lee T., Lin C.: A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio. J. Computat. Phys. 206, 16–47 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  71. Shan X., Chen H.: Lattice Boltzmann model of simulating flows with multiple phases and components. Phys. Rev. E 47, 1815–1819 (1993)

    Article  Google Scholar 

  72. Shan X., Chen H.: Simulation of non-ideal gases and liquid–gas phase transitions by the lattice Boltzmann equation. Phys. Rev. E 49, 2941–2948 (1994)

    Article  Google Scholar 

  73. Swift M., Osborn W., Yeomans J.: Lattice Boltzmann simulation of nonideal fluids. Phys. Rev. Lett. 75, 830–833 (1995)

    Article  Google Scholar 

  74. He X., Shan X., Doolen G.D.: A discrete Boltzmann equation model for non ideal gases. Phys. Rev. E 57, R13–R16 (1998)

    Article  Google Scholar 

  75. He X., Chen S., Zhang R.: A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability. J. Computat. Phys. 152, 642–663 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  76. Sankaranarayanan K., Shan X., Kevrekidis I.G., Sundaresan S.: Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method. J. Fluid Mech. 452, 61–96 (2002)

    Article  MATH  Google Scholar 

  77. Holdych D.J., Georgiadis J.G., Buckius R.O.: Migration of a van der Waals bubble: lattice Boltzmann formulation. Phys. Fluids. 13, 817–825 (2001)

    Article  Google Scholar 

  78. Nourgaliev R., Dinh T., Theofanous T., Joseph D.: The lattice Boltzmann method: theoretical interpretation, numerics and implications. Int. J. Multiph. Flow. 29, 117–169 (2003)

    Article  MATH  Google Scholar 

  79. Chang Q., Iwan J., Alexander D.: Application of the lattice Boltzmann method to two-phase Rayleigh–Benard convection with a deformable interface. J. Computat. Phys. 212, 473–486 (2006)

    Article  MATH  Google Scholar 

  80. Inamuro T., Ogata T., Tajima S., Konishi N.: A lattice Boltzmann method for incompressible two-phase flows with large density difference. J. Computat. Phys. 198, 628–644 (1998)

    Article  Google Scholar 

  81. Zheng H.W., Shu C., Chew Y.T.: A lattice Boltzmann model for multiphase flows with large density ratio. J. Computat. Phys. 218, 353–371 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  82. Li, D.Q.I., Naoya, O., Lindell, P., Toshiaki, I.: A modified SST K-turbulence model to predict the steady and unsteady sheet cavitation on 2D and 3D hydrofoils. In: Proceedings of the 7th International Symposium on Cavitation, August 17–22, 2009, Ann Arbor, MI, USA. CAV2009, Paper No. 107

  83. Kim, S.E.: A numerical study of unsteady cavitation on a hydrofoil. In: Proceedings of the 7th International Symposium on Cavitation, August 17–22, 2009, Ann Arbor, MI, USA. CAV2009, Paper No. 56

  84. Rouse, H., McNown, J.S.: Cavitation and pressure distribution, head forms at zero angle of yaws flow phenomenon. Studies in Engineering, Bulletins 32, State University of Iowa (1948)

  85. Shen, Y., Dimotakis, P.: The influence of surface cavitation on hydrodynamic forces. In: Proceedings of the 22nd. ATTC, St. Johns, 44–53 (1989)

  86. Tseng, C., Shyy, W.: Surrogate-based modeling of cryogenic turbulent cavitating flows. In: Proceedings of the 7th International Symposium on Cavitation, August 17–22, 2009, Ann Arbor, MI, USA. CAV2009, Paper No. 77

  87. Sobol I.M.: Sensitivity analysis for nonlinear mathematical models. Math. Model. Computat. Exp. 1(4), 407–414 (1993)

    MATH  MathSciNet  Google Scholar 

  88. Queipo N.V., Haftka R.T., Shyy W., Goel T., Vaidyanathan R., Tucker P.K.: Surrogate based analysis and optimization. Prog. Aerosp. Sci. 41, 1–28 (2005)

    Article  Google Scholar 

  89. Goel T., Haftka R.T., Shyy W., Queipo N.V.: Ensemble of multiple surrogates. Struct. Multidisciplin. Optim. 33(3), 199–216 (2007)

    Article  Google Scholar 

  90. Myers R.H., Montgomery D.C.: Response Surface Methodology. Wiley, New York (1995)

    MATH  Google Scholar 

  91. Matheron G.: Principles of geostatistics. Econ. Geol. 58, 1246–1266 (1963)

    Article  Google Scholar 

  92. Orr, M.J.L.: Introduction to Radial Basis Function Networks, Center for Cognitive Science, Edinburg University, EH 9LW, Scotland, UK (1996). http://www.anc.ed.ac.uk/~mjo/rbf.html

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Michigan, 2350 Hayward, Ann Arbor, MI, 48109, USA

    Chien-Chou Tseng

  2. School of Astronautics, Harbin Institute of Technology, 92 West Da-Zhi Street, Harbin, 150001, China

    Yingjie Wei

  3. School of Vehicle and Transportation Engineering, Beijing Institute of Technology, 5 South Zhongguancun Street, Beijing, 100081, China

    Guoyu Wang

  4. Department of Aerospace Engineering, University of Michigan, 1320 Beal, Ann Arbor, MI, 48109, USA

    Wei Shyy

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  1. Chien-Chou Tseng
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Tseng, CC., Wei, Y., Wang, G. et al. Modeling of turbulent, isothermal and cryogenic cavitation under attached conditions. Acta Mech Sin 26, 325–353 (2010). https://doi.org/10.1007/s10409-010-0342-7

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