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Numerical Simulation of Cavitating Flows with Different Cavitation and Turbulence Models

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Cavitation Instabilities and Rotordynamic Effects in Turbopumps and Hydroturbines

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 575))

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Abstract

The simulation of cavitating flows is a challenging problem both in terms of modelling the thermodynamic path during the phase transition and the complex interaction with the turbulence. Based on a one-fluid compressible Reynolds-Averaged Navier-Stokes (RANS) solver, a numerical study is proposed to investigate and to compare different turbulence and cavitation models (with and without thermal effects). Steady and unsteady numerical results are given for 1D rarefaction cases and 2D Venturi geometries for which experimental data are available.

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References

  • Aeschlimann, V., & Barre, S. (2009). PIV-LIF determination of mean velocity field and Reynolds stress tensor in a cavitatiting mixing layer. In 7th International Symposium on Cavitation CAV2009, Ann Arbor, USA.

    Google Scholar 

  • Aeschlimann, V., Barre, S., & Djeridi, H. (2011). Velocity field analysis in an experimental cavitating mixing layer. Physics of Fluids, 23, 055105.

    Article  Google Scholar 

  • Aeschlimann, V., Barre, S., & Djeridi, H. (2013). Unsteady cavitation analysis using phase averaging and conditional approaches in a 2D Venturi. Open Journal of Fluid Dynamics, 3, 171–183.

    Article  Google Scholar 

  • Ahn, S. J., & Kwon, O. J. (2013). Numerical investigation of cavitating flows for marine propulsors using an untructured mesh technique. International Journal of Heat and Fluid Flow, 43, 259–267.

    Article  Google Scholar 

  • Barre, S., Rolland, J., Boitel, G., Goncalves, E., & Patella, R. F. (2009). Experiments and modelling of cavitating flows in Venturi: Attached sheet cavitation. European Journal of Mechanics B/Fluids, 28, 444–464.

    Google Scholar 

  • Barret, M., Faucher, E., & Herard, J. M. (2002). Schemes to compute unsteady flashing flows. AIAA Journal, 40(5), 905–913.

    Google Scholar 

  • Besnard, D. C., & Harlow, F. H. (1988). Turbulence in multiphase flow. International Journal of Multiphase Flow, 14(6), 679–699.

    Article  MATH  Google Scholar 

  • Bilicki, Z., Kwidzinski, R., & Mohammadein, S. A. (1996). Evaluation of the relaxation time of heat and mass exchange in the liquid–vapour bubble flow. International Journal of Heat and Mass Transfer, 39(4), 753–759.

    Google Scholar 

  • Bois, G., Jamet, D., & Lebaigue, O. (2010). Towards large eddy simulation of two-phase flow with phase change: Direct numerical simulation of a pseudo-turbulent two-phase condensing flows. In 7th International Conference on Multiphase Flow, Tampa, USA.

    Google Scholar 

  • Charriere, B., Decaix, J., & Goncalves, E. (2015). A comparative study of cavitation models in a venturi flow. European Journal of Mechanics B/Fluids, 49, 287–297.

    Article  MathSciNet  Google Scholar 

  • Chen, Y., Lu, C. J., & Wu, L. (2006). Modelling and computation of unsteady turbulent cavitation flows. Journal of Hydrodynamics, 18(5), 559–566.

    Article  MATH  Google Scholar 

  • Choi, Y. H., & Merkle, C. L. (1993). The application of preconditioning to viscous flows. Journal of Computational Physics, 105(2), 207–223.

    Article  MathSciNet  MATH  Google Scholar 

  • Clerc, S. (2000). Numerical simulation of the homogeneous equilibrium model for two-phase flows. Journal of Computational Physics, 161(1), 354–375.

    Article  MathSciNet  MATH  Google Scholar 

  • Coutier-Delgosha, O., Fortes-Patella, R., & Reboud, J. L. (2002). Simulation of unsteady cavitation with a two-equation turbulence model including compressibility effects. Journal of Turbulence, 3(58).

    Google Scholar 

  • Davidson, L. (2006). Evaluation of the SST-SAS model: Channel flow, asymmetric diffuser and axi-symmetric hill. In Proceedings of ECCOMAS CFD 2006, Egmond aan Zee, The Netherlands.

    Google Scholar 

  • Decaix, J., & Goncalves, E. (2012). Time-dependent simulation of cavitating flow with \(k-\ell \) turbulence models. International Journal for Numerical Methods in Fluids, 68, 1053–1072.

    Google Scholar 

  • Decaix, J., & Goncalves, E. (2013a). Compressible effects modelling in turbulent cavitating flows. European Journal of Mechanics B/Fluids, 39, 11–31.

    Article  MathSciNet  MATH  Google Scholar 

  • Decaix, J., & Goncalves, E. (2013b). Investigation of three-dimensional effects on a cavitating venturi flow. International Journal of Heat and Fluid Flow, 44, 576–595.

    Article  Google Scholar 

  • Delannoy, Y., & Kueny, J. L. (1990). Two phase flow approach in unsteady cavitation modelling. Cavitation and Multiphase Flow Forum, ASME-FED, 98, 153–158.

    Google Scholar 

  • Downar-Zapolski, P., Bilicki, Z., Bolle, L., & Franco, J. (1996). The non-equilibrium relaxation model for one-dimensional flashing liquid flow. International Journal of Multiphase Flow, 22(3), 473–483.

    Article  MATH  Google Scholar 

  • Durbin, P. A. (2009). Limiters and wall treatments in applied turbulence modeling. Fluid Dynamics Research, 41(1), 012203.

    Article  MATH  Google Scholar 

  • Edwards, J. R., & Franklin, R. K. (2000). Low-diffusion flux splitting methods for real fluid flows with phase transition. AIAA Journal, 38(9), 1624–1633.

    Article  Google Scholar 

  • Elghobashi, S. E., & Abou-Arab, T. W. (1983). A two-equation turbulence model for two-phase flows. Physics of Fluids, 26(4), 931–938.

    Article  MATH  Google Scholar 

  • Fruman, D. H., Reboud, J. L., & Stutz, B. (1999). Estimation of thermal effects in cavitation of thermosensible liquids. International Journal of Heat and Mass Transfer, 42, 3195–3204.

    Article  MATH  Google Scholar 

  • Goncalves, E. (2011). Numerical study of unsteady turbulent cavitating flows. European Journal of Mechanics B/Fluids, 30(1), 26–40.

    Article  MathSciNet  MATH  Google Scholar 

  • Goncalves, E. (2013). Numerical study of expansion tube problems: Toward the simulation of cavitation. Computers & Fluids, 72, 1–19.

    Article  MathSciNet  Google Scholar 

  • Goncalves, E. (2014). Modeling for non isothermal cavitation using 4-equation model. International Journal of Heat and Mass Transfer, 76, 247–262.

    Article  Google Scholar 

  • Goncalves, E., & Charriere, B. (2014). Modelling for isothermal cavitation with a four-equation model. International Journal of Multiphase Flow, 59, 54–72.

    Article  Google Scholar 

  • Goncalves, E., & Decaix, J. (2012). Wall model and mesh influence study for partial cavities. European Journal of Mechanics B/Fluids, 31(1), 12–29.

    Article  MathSciNet  MATH  Google Scholar 

  • Goncalves, E., & Fortes, R. (2009). Patella. Numerical simulation of cavitating flows with homogeneous models. Computers & Fluids, 38(9), 1682–1696.

    Article  MATH  Google Scholar 

  • Goncalves, E., & Patella, R. F. (2010). Numerical study of cavitating flows with thermodynamic effect. Computers & Fluids, 39(1), 99–113.

    Article  MathSciNet  MATH  Google Scholar 

  • Goncalves, E., & Patella, R. F. (2011). Constraints on equation of state for cavitating flows with thermodynamic effects. Applied Mathematics and Computation, 217, 5095–5102.

    Google Scholar 

  • Goncalves, E., Champagnac, M., & Fortes, R. (2010a). Patella. Comparison of numerical solvers for cavitating flows. International Journal of Computational Fluid Dynamics, 24(6), 201–216.

    Article  MATH  Google Scholar 

  • Goncalves, E., & Fortes, R. (2010b). Patella, J. Rolland, B. Pouffary, and G. Challier. Thermodynamic effect on a cavitating inducer in liquid hydrogen. Journal of Fluids Engineering, 132, 111305.

    Article  Google Scholar 

  • Guillard, H., & Viozat, C. (1999). On the behaviour of upwind schemes in the low Mach number limit. Computers & Fluids, 28(1), 63–86.

    Article  MathSciNet  MATH  Google Scholar 

  • Hosangadi, A., & Ahuja, V. (2005). Numerical study of cavitation in cryogenic fluids. Journal of Fluids Engineering, 127(2), 267–281.

    Article  Google Scholar 

  • Hu, Z. M., Dou, H. S., & Khoo, B. C. (2011). On the modified dispersion-controlled dissipative (DCD) scheme for computation of flow supercavitation. Computers & Fluids, 40(1), 315–323.

    Article  MATH  Google Scholar 

  • Ihm, S. W., & Kim, C. (2008). Computations of homogeneous-equilibrium two-phase flows with accurate and efficient shock-stable schemes. AIAA Journal, 46(12), 3012–3037.

    Article  Google Scholar 

  • Ishii, C. M., & Hibiki, T. (2006). Thermo-fluid dynamics of two-phase flow. Springer.

    Google Scholar 

  • Jameson, A., Schmidt, W., & Turkel, E. (1981). Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes. In AIAA Paper, 81–1259.

    Google Scholar 

  • Ji, B., Luo, X., Wu, Y., Peng, X., & Duan, Y. (2013). Numerical analysis of unsteady cavitating turbulent flow and sheding horse-shoe vortex structure around a twisted hydrofoil. Interational Journal of Multiphase Flow, 51, 33–43.

    Article  Google Scholar 

  • Jones, W. P. (1979). Prediction methods for turbulent flows. In Von Karman Institute. Lecture Series 1979–2.

    Google Scholar 

  • Jones, W. P., & Launder, B. E. (1972). The prediction of laminarization with a two-equation model of turbulence. International Journal of Heat and Mass Transfer, 15, 301–314.

    Article  Google Scholar 

  • Kapila, A. K., Menikoff, R., Bdzil, J. B., Son, S. F., & Stewart, D. S. (2001). Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations. Physics of Fluids, 13(10), 3002–3024.

    Article  MATH  Google Scholar 

  • Kataoka, I., & Serizawa, A. (1989). Basic equations of turbulence in gas-liquid two-phase flow. International Journal of Multiphase Flow, 15(5), 843–855.

    Article  MATH  Google Scholar 

  • Kunz, R. F. Boger, D. A., Stinebring, D. R., Chyczewski, T. S., Lindau, J. W., Gibeling, H. J., Venkateswaran, S., & Govindan, T. R. (2000). A preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction. Computers & Fluids, 29(8), 849–875.

    Google Scholar 

  • Labourasse, E., Lacanette, D., Toutant, A., Vincent, S., Lubin, P., Lebaigue, O., Caltagirone, J.-P., & Sagaut, P. (2007). Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori test. The International Journal of Multiphase Flow, 33(1), 1–39.

    Google Scholar 

  • Lance, M., Marie, J. L., & Bataille, J. (1984). Construction of a model for liquid phase turbulence in bubble flow. La Houille Blanche, 3–4, 255–260.

    Article  Google Scholar 

  • Larocque, J., Vincent, S., Lacanette, D., Lubin, P., & Caltagirone, J.-P. (2010). Parametric study of LES subgrid terms in a turbulent phase separation. International Journal of Heat and Fluid Flow, 31, 536–544.

    Article  Google Scholar 

  • Liovic, P., & Lakehal, D. (2012). Subgrid-scale modelling of surface tension within interface tracking-based Large Eddy and Interface Simulation of 3D interfacial flows. Computers & Fluids, 63, 27–46.

    Article  MathSciNet  Google Scholar 

  • Liu, T. G., Khoo, B. C., & Xie, W. F. (2004). Isentropic one-fluid modelling of unsteady cavitating flow. Journal of Computational Physics, 201(1), 80–108.

    Google Scholar 

  • Menter, F. R. (2010a). The scale-adaptive simulation mathod for unsteady turbulent flow predictions. Part 1: Theory and model description. Flow, Turbulence and Combustion, 85(1), 113–138.

    Article  MATH  Google Scholar 

  • Menter, F. R. (2010b). The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 2: Application to complex flows. Flow, Turbulence and Combustion, 85(1), 139–165.

    Article  MATH  Google Scholar 

  • Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), 1598–1605.

    Article  Google Scholar 

  • Menter, F. R. (1997). Eddy viscosity transport equations and their relation to the \(k-\epsilon \) model. Journal of Fluids Engineering, 119, 876–884.

    Article  Google Scholar 

  • Menter, F. R., & Egorov, Y. (2004). Re-visiting the turbulent scale equation. In Proceeding IUTAM Symposium; One Hundred Years of Boundary Layer Research—Gottingen.

    Google Scholar 

  • Merci, B., Steelant, J., Vierendeels, J., Riemslagh, K., & Dick, E. (2000). Computational treatment of source terms in two-equation turbulence models. AIAA Journal, 38(11), 2085–2093.

    Article  Google Scholar 

  • Merkle, C. L., Feng, J., & Buelow, P. E. (1998). Computation modeling of the dynamics of sheet cavitation. In 3rd International Symposium on Cavitation CAV1998, Grenoble, France.

    Google Scholar 

  • Le Metayer, O., Massoni, J., & Saurel, R. (2004). Elaborating equations of state of a liquid and its vapor for two-phase flow models. International Journal of Thermal Sciences, 43, 265–276.

    Article  Google Scholar 

  • Petitpas, F., Massoni, J., Saurel, R., Lapedie, E., & Munier, L. (2009). Diffuse interface model for high speed cavitating underwater systems. International Journal of Multiphase Flow, 35, 747–759.

    Article  Google Scholar 

  • Petkovsek, M., & Dular, M. (2013). IR measurements of the thermodynamic effects in cavitating flow. International Journal of Heat and Fluid Flow, 44, 756–763.

    Article  Google Scholar 

  • Reboud, J.-L., Stutz, B., & Coutier, O. (1998). Two-phase flow structure of cavitation: Experiment and modelling of unsteady effects. In 3rd International Symposium on Cavitation CAV1998, Grenoble, France.

    Google Scholar 

  • Roe, P. L. (1981). Approximate Riemann solvers, parameters vectors, and difference schemes. Journal of Computational Physics, 43, 357–372.

    Article  MathSciNet  MATH  Google Scholar 

  • Sarkar, S. (1992). The pressure-dilatation correlation in compressible flows. Physics of Fluids, 4(12), 2674–2682.

    Article  Google Scholar 

  • Saurel, R., Cocchi, J. P., & Barry, P. (1999). Butler. Numerical study of cavitation in the wake of a hypervelocity underwater projectile. Journal of Propulsion and Power, 15(3), 513–522.

    Article  Google Scholar 

  • Saurel, R., Petitpas, F., & Abgrall, R. (2008). Modelling phase transition in metastable liquids: application to cavitating and flashing flows. Journal of Fluid Mechanics, 607, 313–350.

    Article  MathSciNet  MATH  Google Scholar 

  • Saurel, R., Petitpas, F., & Berry, A. (2009). Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures. Journal of Computational Physics, 228(5), 1678–1712.

    Article  MathSciNet  MATH  Google Scholar 

  • Schmidt, D., Rutland, C., & Corradini, M. L. (1999). A fully compressible, two-dimensional model of small, high-speed, cavitating nozzles. Atomization and Sprays, 9, 255–276.

    Article  Google Scholar 

  • Schmidt, S. J., Sezal, I. H., & Schnerr, G. H. (2006). Compressible simulation of high-speed hydrodynamics with phase change. In European Conference on Computational Fluid Dynamics ECCOMAS 2006, Delft, The Netherlands.

    Google Scholar 

  • Senocak, I., & Shyy, W. (2002). A pressure-based method for turbulent cavitating flow computations. Journal of Computational Physics, 176(2), 363–383.

    Article  MATH  Google Scholar 

  • Shin, B. R., Iwata, Y., & Ikohagi, T. (2003). Numerical simulation of unsteady cavitating flows using a homogeneous equilibrium model. Computational Mechanics, 30, 388–395.

    Article  MATH  Google Scholar 

  • Singhal, A. K., Athavale, M. M., Li, H., & Jiang, Y. (2002). Mathematical basis and validation of the full cavitation model. Journal of Fluids Engineering, 124(3), 617–624.

    Article  Google Scholar 

  • Sinibaldi, E., Beux, F., & Salvetti, M. V. (2006). A numerical method for 3D barotropic flows in turbomachinery. Flow Turbulence Combustion, 76, 371–381.

    Google Scholar 

  • Smith, B. R. (1994). A near wall model for the \(k-l\) two equation turbulence model. In AIAA 94–2386, 25th Fluid Dynamics Conference—Colorado Springs, Colorado.

    Google Scholar 

  • Spalart, P. R., & Allmaras, S. R. (1994). A one-equation turbulence model for aerodynamic flows. La Recherche Aérospatiale, 1, 5–21.

    Google Scholar 

  • Srinivasan, V., Salazar, A. J., & Saito, K. (2009). Numerical simulation of cavitation dynamics using a cavitation-induced-momentum-defect (CIMD) correction approach. Applied Mathematical Modelling, 33, 1529–1559.

    Article  MATH  Google Scholar 

  • Stutz, B. (1996). Analyse de la structure diphasique et instationnaire de poches de cavitation. Ph.D. thesis, Institut National Polytechnique de Grenoble.

    Google Scholar 

  • Toutant, A., Chandesris, M., Jamet, D., & Lebaigue, O. (2009). Jump conditions for filtered quantities at under-resolved discontinuous interface. Part 1: Theoretical development. International Journal of Multiphase Flow, 35, 1100–1118.

    Google Scholar 

  • Turkel, E. (1987). Preconditioned methods for solving the incompressible and low speed compressible equations. Journal of Computational Physics, 172(2), 277–298.

    Article  MathSciNet  MATH  Google Scholar 

  • Utturkar, Y., Wu, J., Wang, G., & Shyy, W. (2005). Recent progress in modelling of cryogenic cavitation for liquid rocket propulsion. Progress in Aerospace Sciences, 41, 558–608.

    Article  Google Scholar 

  • Venkateswaran, S., Lindau, J. W., Kunz, R. F., & Merkle, C. L. (2002). Computation of multiphase mixture flows with compressibility effects. Journal of Computational Physics, 180(1), 54–77.

    Google Scholar 

  • Ventikos, Y., & Tzabiras, G. (2000). A numerical method for the simulation of steady and unsteady cavitating flows. Computers & Fluids, 29(1), 63–88.

    Article  MATH  Google Scholar 

  • Viegas, J. R., & Rubesin, M. W. (1983). Wall–function boundary conditions in the solu tion of the Navier–Stokes equations for complex compressible flows. In AIAA 83–1694, 16th Fluid and Plasma Dynamics Conference, Danver, Massachussetts, 12–14 July 1983.

    Google Scholar 

  • Vincent, S., Larocque, J., Lacanette, D., Toutant, A., Lubin, P., & Sagaut, P. (2008). Computers & Fluids, 37, 898–906.

    Article  MathSciNet  Google Scholar 

  • Vortmann, C., Schnerr, G. H., & Seelecke, S. (2003). Thermodynamic modeling and simulation of cavitating nozzle flow. International Journal of Heat and Fluid Flow, 24, 774–783.

    Google Scholar 

  • De Vuyst, F., Ghidaglia, J. M., & Le Coq, G. (2005). On the numerical simulation of multiphase water flows with changes of phase and strong gradients using the Homogeneous Equilibrium Model. International Journal on Finite Volumes, 2(1), 1–36.

    Google Scholar 

  • Wallis, G. (1967). One-dimensional two-phase flow. New York: McGraw-Hill.

    Google Scholar 

  • Weller, H., Tabor, G., Jasak, H., & Fureby, C. (1998). A tensorial approach to computational continuum mechanics using objected-oriented techniques. Computers in Physics, 12, 620–631.

    Article  Google Scholar 

  • Wilcox, D. C. (1988). Reassement of the scale-determining equation for advanced turbulence models. AIAA Journal, 26(11), 1299–1310.

    Article  MathSciNet  MATH  Google Scholar 

  • Wilcox, D. C. (1998). Turbulence modeling for CFD. DCW Industries Inc.

    Google Scholar 

  • Wu, J., Wang, G., & Shyy, W. (2005). Time-dependent turbulent cavitating flow computations with interfacial transport and filter-based models. International Journal for Numerical Methods in Fluids, 49(7), 739–761.

    Google Scholar 

  • Zein, A., Hantke, M., & Warnecke, G. (2010). Modeling phase transition for compressible two-phase flows applied to metastable liquids. Journal of Computational Physics, 229(8), 2964–2998.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang, X. B., Qiu, L. M., Gao, Y., & Zhang, X. J. (2008). Computational fluid dynamic study on cavitation in liquid nitrogen. Cryogenics, 48, 432–438.

    Google Scholar 

  • Zhou, L., & Wang, Z. (2008). Numerical simulation of cavitation around a hydrofoil and evaluation of a RNG \(k-\varepsilon \) model. Journal of Fluid Engineering, 130(1), 011302.

    Article  Google Scholar 

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Acknowledgements

The author is grateful to Prof. Salvetti and Prof. d’Agostino for their invitation to the Udine summer school. The author expresses his gratitude to the French Space Agency CNES and to the SNECMA Space Engines Division to support these studies. The author thanks the IDRIS–CNRS supercomputing centre for providing us their computing resources.

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Authors and Affiliations

  1. LEGI Laboratory, University of Grenoble, Grenoble, France

    Eric Goncalves

  2. Institut Pprime, UPR 3346 CNRS, ENSMA, Futuroscope, Poitiers, France

    Eric Goncalves

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  1. Eric Goncalves
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Correspondence to Eric Goncalves .

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  1. Civil and Industrial Engineering De, Pisa University, Pisa, Italy

    Luca d'Agostino

  2. Civil and Industrial Engineering Dept., Pisa University, Pisa, Italy

    Maria Vittoria Salvetti

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Goncalves, E. (2017). Numerical Simulation of Cavitating Flows with Different Cavitation and Turbulence Models. In: d'Agostino, L., Salvetti, M. (eds) Cavitation Instabilities and Rotordynamic Effects in Turbopumps and Hydroturbines. CISM International Centre for Mechanical Sciences, vol 575. Springer, Cham. https://doi.org/10.1007/978-3-319-49719-8_8

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