DOI QR코드

DOI QR Code

Simulation of free falling rigid body into water by a stabilized incompressible SPH method

  • Aly, Abdelraheem M. (Civil Engineering Department, Faculty of Engineering, Kyushu University) ;
  • Asai, Mitsuteru (Civil Engineering Department, Faculty of Engineering, Kyushu University) ;
  • Sonoda, Yoshimi (Civil Engineering Department, Faculty of Engineering, Kyushu University)
  • Received : 2011.05.12
  • Accepted : 2011.07.28
  • Published : 2011.09.25

Abstract

A stabilized incompressible smoothed particles hydrodynamics (ISPH) method is utilized to simulate free falling rigid body into water domain. Both of rigid body and fluid domain are modeled by SPH formulation. The proposed source term in the pressure Poisson equation contains two terms; divergence of velocity and density invariance. The density invariance term is multiplied by a relaxed parameter for stabilization. In addition, large eddy simulation with Smagorinsky model has been introduced to include the eddy viscosity effect. The improved method is applied to simulate both of free falling vessels with different materials and water entry-exit of horizontal circular cylinder. The applicability and efficiency of improved method is tested by the comparisons with reference experimental results.

Keywords

References

  1. Ellero M., Serrano, M. and Espanol, P. (2007), "Incompressible smoothed particle hydrodynamics", J. Comput. Phys., 226(2), 1731-1752. https://doi.org/10.1016/j.jcp.2007.06.019
  2. Gingold, R.A. and Monaghan, J.J. (1977), "Smoothed particle hydrodynamics: theory and application to nonspherical stars", Mon. Not. R. Astron. Soc., 181, 375-89. https://doi.org/10.1093/mnras/181.3.375
  3. Gotoh, H., Sakai, T. (2006), "Key issues in the particle method for computation of wave breaking", Coast. Eng., 53(2-3), 171-179. https://doi.org/10.1016/j.coastaleng.2005.10.007
  4. Greenhow, M. and Lin W. (1983), "Non-linear free surface effects: experiments and theory", Report Number 83-19, Department of Ocean Engineering, Massachusetts Institute of Technology.
  5. Greenhow, M. and Moyo, S. (1997), "Water entry and exit of horizontal circular cylinders", Philos. T. R. Soc. A., 355(1724), 551-563. https://doi.org/10.1098/rsta.1997.0024
  6. Hirt, C.W. and Nichols, B.D. (1981), "Volume of fluid (VOF) method for dynamics of free boundaries", J. Comput. Phys., 39(1), 201-225. https://doi.org/10.1016/0021-9991(81)90145-5
  7. Hui, Sun and Odd, M. Faltinsen (2006), "Water impact of horizontal circular cylinders and cylindrical shells", Appl. Ocean Res., 28 (5), 299-311. https://doi.org/10.1016/j.apor.2007.02.002
  8. Khayyer, A., Gotoh, H. and Shao, S. (2008), "Corrected incompressible SPH method for accurate water-surface tracking in breaking waves", Coast. Eng., 55(3), 236-250. https://doi.org/10.1016/j.coastaleng.2007.10.001
  9. Khayyer, A., Gotoh, H. and Shao, S. (2009), "Enhanced predictions of wave impact pressure by improved incompressible SPH methods", Appl. Ocean Res., 31(2), 111-131. https://doi.org/10.1016/j.apor.2009.06.003
  10. Kleefsman, K.M.T., Fekken, G., Veldman, A.E.P., Iwanowski, B. and Buchner, B. (2005), "A volume-of-fluid based simulation method for wave impact problems", J. Comput. Phys., 206(1), 363-393. https://doi.org/10.1016/j.jcp.2004.12.007
  11. Koshizuka, S,, Nobe, A. and Oka, Y. (1998), "Numerical analysis of breaking waves using the moving particle semiimplicit method", Int. J. Numer. Meth. Fl., 26, 751-769. https://doi.org/10.1002/(SICI)1097-0363(19980415)26:7<751::AID-FLD671>3.0.CO;2-C
  12. Koshizuka, S. and Oka, Y. (1996), "Moving-particle semi-implicit method for fragmentation of incompressible fluid", Nucl. Sci. Eng., 123(3), 421-434. https://doi.org/10.13182/NSE96-A24205
  13. Lee, E.S., Laurence, D., Stansby, P.K., Violeau, D. and Moulinec C. (2006), "2D flow past a square cylinder in a closed channel", SPHERIC Newsletter, No. 3.
  14. Lee, E.S., Moulinec, C., Xu, R., Violeau, D., Laurence, D. and Stansby P. (2008), "Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method", J. Comput. Phys., 227 (18), 8417-8436. https://doi.org/10.1016/j.jcp.2008.06.005
  15. Lee, B.H., Park, J.C., Kim, M.H., Jung, S.J., Ryu, M.C. and Kim, Y.S. (2010), "Numerical simulation of impact loads using a particle method", Ocean Eng., 37(2-3), 164-173. https://doi.org/10.1016/j.oceaneng.2009.12.003
  16. Lin, P.Z. (2007), "A fixed-grid model for simulation of a moving body in free surface flows", Comput. Fluids, 36(3), 549-561. https://doi.org/10.1016/j.compfluid.2006.03.004
  17. Liu, H., Gong, K. and Wang, B.L. (2009), "Modelling water entry of a wedge by multiphase SPH method", SPHERIC Newsletter, No. 9.
  18. Lucy, L.B. (1977), "A numerical approach to the testing of the fusion process", Astron J., 88, 1013-24.
  19. Miyata, H. and Park, J.C. (1995), Chap.5, "Wave breaking simulation", In: (Ed. Rahman, M.), Potential Flow of Fluids, Computational Mechanics Publications, UK, 149-176.
  20. Morris, J.P., Fox, P.J. and Zhu, Y. (1997), "Modeling Low Reynolds Number Incompressible Flows Using SPH", J. Comput. Phys., 136(1), 214-226. https://doi.org/10.1006/jcph.1997.5776
  21. Oger, G., Doring, M., Alessandrini, B. and Ferrant, P. (2006), "Two-dimensional SPH simulations of wedge water entries", J. Comput. Phys., 213(2), 803-822. https://doi.org/10.1016/j.jcp.2005.09.004
  22. Panahi, R., Jahanbakhsh, E. and Seif, M.S. (2006), "Development of a VoF-fractional step solver for floating body motion simulation", Appl. Ocean Res., 28(3), 171-181. https://doi.org/10.1016/j.apor.2006.08.004
  23. Shao, S.D. and Lo, E.Y.M. (2003), "Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface", Adv. Water Resour., 26(7), 787-800. https://doi.org/10.1016/S0309-1708(03)00030-7
  24. Shao, S. (2009), "Incompressible SPH simulation of water entry of a free-falling object", Int. J. Numer. Meth. Fl., 59(1), 91-115. https://doi.org/10.1002/fld.1813
  25. Sussman, M., Smereka, P. and Osher, S. (1994), "A level set approach for computing solutions to incompressible two-phase flow", J. Comput. Phys., 114, 146-159. https://doi.org/10.1006/jcph.1994.1155
  26. Tanaka, M. and Masunaga, T. (2010), "Stabilization and smoothing of pressure in MPS method by Quasi-Compressibility", J. Comput. Phys., 229(11), 4279-4290. https://doi.org/10.1016/j.jcp.2010.02.011
  27. Tyvand, P. and Miloh, T. (1995), "Free-surface flow due to impulsive motion of a submerged circular cylinder", J. Fluid Mech., 286, 67-101. https://doi.org/10.1017/S0022112095000656
  28. Violeau, D. and Issa, R. (2007), "Numerical modelling of complex turbulent free-surface flows with the SPH method: an overview", Int. J. Numer. Meth. Fl., 53(2), 277-304. https://doi.org/10.1002/fld.1292
  29. Zhao, R., Faltinsen, O. and Aarsnes, J. (1997), "Water entry of arbitrary two-dimensional sections with and without flowA@separation", Twenty-first Symposium on Naval Hydrodynamics, Trondheim, Norway, 408-423.

Cited by

  1. TSUNAMI RUN-UP SIMULATION BY ISPH METHOD WITH HIGH RESOLUTION GEOMETRICAL MODELING vol.69, pp.4, 2013, https://doi.org/10.2208/jscejseee.69.I_622
  2. A FLUID-RIGID BODY SIMULATION BY USING THE SPH METHOD AND ITS APPLICATION TO BRIGDE RUNOFF SIMULATION vol.70, pp.2, 2014, https://doi.org/10.2208/jscejam.70.I_329
  3. Numerical simulations of impact flows with incompressible smoothed particle hydrodynamics vol.28, pp.6, 2014, https://doi.org/10.1007/s12206-014-0120-8
  4. Analysis of unsteady mixed convection in lid-driven cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics method vol.25, pp.8, 2015, https://doi.org/10.1108/HFF-10-2014-0305
  5. Review of ship slamming loads and responses vol.16, pp.4, 2017, https://doi.org/10.1007/s11804-017-1437-3
  6. Double-diffusive natural convection in an enclosure filled with nanofluid using ISPH method vol.55, pp.4, 2016, https://doi.org/10.1016/j.aej.2016.06.036
  7. A numerical study on unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies using the ISPH method 2018, https://doi.org/10.1108/HFF-02-2017-0058
  8. An incompressible smoothed particle hydrodynamics method for natural/mixed convection in a non-Darcy anisotropic porous medium vol.77, 2014, https://doi.org/10.1016/j.ijheatmasstransfer.2014.06.044
  9. Double-diffusive natural convection in an enclosure including/excluding sloshing rod using a stabilized ISPH method vol.73, 2016, https://doi.org/10.1016/j.icheatmasstransfer.2016.01.008
  10. Modelling of Non-Darcy Flows through Porous Media Using Extended Incompressible Smoothed Particle Hydrodynamics vol.67, pp.3, 2015, https://doi.org/10.1080/10407790.2014.955772
  11. Modeling of multi-phase flows and natural convection in a square cavity using an incompressible smoothed particle hydrodynamics vol.25, pp.3, 2015, https://doi.org/10.1108/HFF-05-2014-0161
  12. ISPH method for double-diffusive natural convection under cross-diffusion effects in an anisotropic porous cavity/annulus vol.26, pp.1, 2016, https://doi.org/10.1108/HFF-03-2015-0085
  13. Three-Dimensional Incompressible Smoothed Particle Hydrodynamics for Simulating Fluid Flows Through Porous Structures vol.110, pp.3, 2015, https://doi.org/10.1007/s11242-015-0568-8
  14. Numerical Analysis of Liquid Sloshing Using the Incompressible Smoothed Particle Hydrodynamics Method vol.7, pp.2, 2015, https://doi.org/10.1155/2014/765741
  15. Development of Empirical Formulation for Bow Flare Slamming and Deck Wetness for Displacement Vessels pp.1993-5048, 2018, https://doi.org/10.1007/s11804-018-0045-1
  16. Towards development of a reliable fully-Lagrangian MPS-based FSI solver for simulation of 2D hydroelastic slamming vol.7, pp.3, 2011, https://doi.org/10.12989/ose.2017.7.3.299
  17. Water entry of decelerating spheres simulations using improved ISPH method vol.30, pp.6, 2011, https://doi.org/10.1007/s42241-018-0133-3
  18. Fluid Structure Interaction of Buoyant Bodies with Free Surface Flows: Computational Modelling and Experimental Validation vol.11, pp.5, 2011, https://doi.org/10.3390/w11051048
  19. Mixed Convection in an Inclined Nanofluid Filled-Cavity Saturated With a Partially Layered Porous Medium vol.11, pp.4, 2011, https://doi.org/10.1115/1.4042352
  20. Natural convection in a nanofluid-filled cavity with solid particles in an inner cross shape using ISPH method vol.141, pp.None, 2011, https://doi.org/10.1016/j.ijheatmasstransfer.2019.06.090
  21. Natural Convection from Heated Shape in Nanofluid-Filled Cavity Using Incompressible Smoothed Particle Hydrodynamics vol.33, pp.4, 2011, https://doi.org/10.2514/1.t5665
  22. Natural convection from cross blade inside a nanofluid-filled cavity using ISPH method vol.30, pp.10, 2011, https://doi.org/10.1108/hff-12-2019-0863
  23. Motion of circular cylinders during natural convection flow in X-shaped cavity filled with a nanofluid using ISPH method vol.31, pp.5, 2021, https://doi.org/10.1108/hff-04-2020-0231
  24. ISPH simulations of natural convection from rotating circular cylinders inside a horizontal wavy cavity filled with a nanofluid and saturated by a heterogeneous porous medium vol.230, pp.5, 2021, https://doi.org/10.1140/epjs/s11734-021-00050-y