International Journal of Naval Architecture and Ocean Engineering

The Society of Naval Architects of Korea (대한조선학회)
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Modelling cavitating flow around underwater missiles

  • Published : 2011.12.31
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Abstract

The diffuse interface model of Saurel et al. (2008) is used for the computation of compressible cavitating flows around underwater missiles. Such systems use gas injection and natural cavitation to reduce drag effects. Consequently material interfaces appear separating liquid and gas. These interfaces may have a really complex dynamics such that only a few formulations are able to predict their evolution. Contrarily to front tracking or interface reconstruction method the interfaces are computed as diffused numerical zones, that are captured in a routinely manner, as is done usually with gas dynamics solvers for shocks and contact discontinuity. With the present approach, a single set of partial differential equations is solved everywhere, with a single numerical scheme. This leads to very efficient solvers. The algorithm derived in Saurel et al. (2009) is used to compute cavitation pockets around solid bodies. It is first validated against experiments done in cavitation tunnel at CNU. Then it is used to compute flows around high speed underwater systems (Shkval-like missile). Performance data are then computed showing method ability to predict forces acting on the system.

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References

  1. Davis, S.F., 1988. Simplified second order Godunov type methods. SIAM Journal on Scientific and Statistical Computing, 9, 445-473 https://doi.org/10.1137/0909030
  2. Favrie, N. Gavrilyuk, S. and Saurel, R., 2008. Solid-fluid diffuse interface model in cases of extreme deformations. Journal of Computational Physics, 228(16), pp. 6037-6077.
  3. Fedkiw, R. Aslam, T. Merriman, B. and Osher, S., 1999. A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method). Journal of Computational Physics, 152(2) , pp 457-492. https://doi.org/10.1006/jcph.1999.6236
  4. Glimm, J. Grove, J.W. Li, X.L. Shyue, K.M. Zhang, Q. and Zeng, Y., 1998. Three dimensional front tracking. SIAM Journal on Scientific and Statistical Computing, 19, pp. 703-727. https://doi.org/10.1137/S1064827595293600
  5. Hirt, C.W. and Nichols, B.D., 1981. Volume Of Fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39, pp. 201-255. https://doi.org/10.1016/0021-9991(81)90145-5
  6. Hou, T.Y. and Le Floch, P., 1994. Why non-conservative schemes converge to the wrong solution: error analysis, Mathematics of Computation, 62, pp. 497-530. https://doi.org/10.1090/S0025-5718-1994-1201068-0
  7. Kapila A.K. Menikoff R. Bdzil J.B. Son S.F. and Stewart D.S., 2001. Two-phase modeling of deflagration-todetonation transition in granular materials : Reduced equations. Physics of Fluids, 13 (10), pp. 3002-3024. https://doi.org/10.1063/1.1398042
  8. Le Metayer, O. Massoni, J. and Saurel, R., 2004. Elaboration des lois d'etat d'un liquide et de sa vapeur pour les modeles d'ecoulements diphasiques. Int. J. Thermal Sciences, 43 (3), pp. 265-276. https://doi.org/10.1016/j.ijthermalsci.2003.09.002
  9. Le Metayer, O. Massoni, J. and Saurel, R., 2005. Modeling evaporation fronts with reactive Riemann solvers. Journal of Computational Physics, 205, pp 567-610. https://doi.org/10.1016/j.jcp.2004.11.021
  10. Miller, G.H. and Puckett, E.G., 1996. A High-Order Godunov Method for Multiple Condensed Phases. Journal of Computational Physics, 128(1), pp 134-164 https://doi.org/10.1006/jcph.1996.0200
  11. Noh, W.F. and Woodward, P., 1976. Simple line interface calculation. Proceedings of the fifth international conference on numerical methods in fluid dynamics, Vol. 59, pp. 330-340.
  12. Perigaud, G. and Saurel, R., 2005. A compressible flow model with capillary effects. Journal of Computational Physics, Vol. 209, pp 139-178. https://doi.org/10.1016/j.jcp.2005.03.018
  13. Petitpas, F. Massoni, J. Saurel, R. Lapebie, E. and Munier, L., 2009a. Diffuse interface model for high speed cavitating underwater systems. International Journal of Multiphase Flow, 35(8), pp. 747-759. https://doi.org/10.1016/j.ijmultiphaseflow.2009.03.011
  14. Petitpas, F. Saurel, R. Franquet, E. and Chinnayya, A., 2009b. Modelling detonation waves in condensed materials: Multiphase CJ conditions and multidimensional computations. Shock Waves, 19(5), pp. 377-401. https://doi.org/10.1007/s00193-009-0217-7
  15. Saurel, R. Cocchi, J.P. and Butler, P.B., 1999. Numerical study of cavitation in the wake of a hypervelocity underwater projectile. Journal of Propulsion and Power, 15(4), pp. 513 - 522. https://doi.org/10.2514/2.5473
  16. Saurel, R. and Abgrall, R., 1999. A multiphase Godunov method for multifluid and multiphase flows. Journal of Computational Physics, 150, pp 425-467 https://doi.org/10.1006/jcph.1999.6187
  17. Saurel, R. and Le Metayer, O., 2001. A multiphase model for interfaces, shocks, detonation waves and cavitation. Journal of Fluid Mechanics, Vol. 431, pp 239-271 https://doi.org/10.1017/S0022112000003098
  18. Saurel, R. Le Metayer, O. Massoni, J. and Gavrilyuk, S., 2007. Shock jump relations for multiphase mixtures with stiff mechanical relaxation . Shock Waves, 16(3), pp 209-232 https://doi.org/10.1007/s00193-006-0065-7
  19. Saurel, R. Petitpas, F. and Abgrall, R., 2008. Modeling phase transition in metastable liquids. Application to cavitating and flashing flows. Journal of Fluid Mechanics, 607:313-350
  20. Saurel, R. Petitpas, F. and Berry, R.A., 2009. Simple and efficient relaxation for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures. Journal of Computational Physics, 228, pp 1678-1712 https://doi.org/10.1016/j.jcp.2008.11.002
  21. Saurel, R. Favrie, N. Petitpas, F. Lallemand, M.H. and Gavrilyuk, S., 2010. Modeling dynamic and irreversible powder compaction. Journal of Fluid Mechanics, Vol. 664, pp. 348-396. https://doi.org/10.1017/S0022112010003794
  22. Toro, E.F. Spruce, M. and Spears, W., 1994. Restoration of the contact surface in the HLL-Riemann solver. Shock Waves, Vol. 4, pp. 25-34 https://doi.org/10.1007/BF01414629
  23. Von Neuman, J. and Richtmyer, R., 1950. A method for the numerical calculation of hydrodynamic shocks. Journal of Appl. Phys., Vol. 21, pp. 232-237 https://doi.org/10.1063/1.1699639
  24. Wood, A.B. (1930) A textbook of sound. Bell and Sons Ltd, London

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