DOI QR코드

DOI QR Code

Incompressible smoothed particle hydrodynamics modeling of thermal convection

  • Moballa, Burniadi (Department of Mechanical Engineering, National Taiwan University of Science and technology) ;
  • Chern, Ming-Jyh (Department of Mechanical Engineering, National Taiwan University of Science and technology) ;
  • Odhiambo, Ernest (Department of Mechanical Engineering, National Taiwan University of Science and technology)
  • 투고 : 2013.03.12
  • 심사 : 2013.05.07
  • 발행 : 2013.09.01

초록

An incompressible smoothed particle hydrodynamics (ISPH) method based on the incremental pressure projection method is developed in this study. The Rayleigh-B$\acute{e}$nard convection in a square enclosure is used as a validation case and the results obtained by the proposed ISPH model are compared to the benchmark solutions. The comparison shows that the established ISPH method has a good performance in terms of accuracy. Subsequently, the proposed ISPH method is employed to simulate natural convection from a heated cylinder in a square enclosure. It shows that the predictions obtained by the ISPH method are in good agreements with the results obtained by previous studies using alternative numerical methods. A rotating and heated cylinder is also considered to study the effect of the rotation on the heat transfer process in the enclosure space. The numerical results show that for a square enclosure at, the addition of kinetic energy in the form of rotation does not enhance the heat transfer process. The method is also applied to simulate forced convection from a circular cylinder in an unbounded uniform flow. In terms of results, it turns out that the proposed ISPH model is capable to simulate heat transfer problems with the complex and moving boundaries.

키워드

참고문헌

  1. Angeli, D., Levoni, P. and Barozzi, G.S. (2008), "Numerical predictions for stable buoyant regimes within a square cavity containing a heated horizontal cylinder", Int. J. Heat Mass Transfer, 51 (3-4), 553-565. https://doi.org/10.1016/j.ijheatmasstransfer.2007.05.007
  2. Bonet, J. and Lok, T.S. (1999), "Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations", Comput. Meth. Appl. Mech. Eng., 180(1-2), 97-115. https://doi.org/10.1016/S0045-7825(99)00051-1
  3. Brookshaw, L. (1985), "A method of calculating radiative heat diffusion in particle simulations", Proceedings of the Astronomical Society of Australia, 6(2), 207-210. https://doi.org/10.1017/S1323358000018117
  4. Chandrasekhar, S. (1961), Hydrodynamic and Hydromagnetic Stability, Clarendon Press , Oxford, UK.
  5. Chern, M., Borthwick, A. and Taylor, R.E. (2006), "Pseudospectral element model for free surface viscous flows", Int. J. Numer. Meth. Heat Fluid Flow, 15(6), 517-554.
  6. Chorin, A.J. (1968), "Numerical solution of the Navier-Stokes equations", Math. Comput., 22(104), 745-762. https://doi.org/10.1090/S0025-5718-1968-0242392-2
  7. Cleary, P.W. (1998), "Modeling confined multi-material heat and mass flows using SPH", Appl. Math. Model., 22(12), 981-993. https://doi.org/10.1016/S0307-904X(98)10031-8
  8. Cleary, P.W. and Monaghan, J.J. (1999), "Conduction modelling using smoothed particle hydrodynamics", J. Comput. Phys., 148(1), 227-264. https://doi.org/10.1006/jcph.1998.6118
  9. Coutanceau, M. and Bouard, R. (1977), "Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow", J. Fluid Mech., 79(2), 231-256. https://doi.org/10.1017/S0022112077000135
  10. Cummins, S.J. and Rudman, M. (1999), "An SPH projection method", J. Comput. Phys., 152(2), 584-607. https://doi.org/10.1006/jcph.1999.6246
  11. Ghaddar, N.K. and Thiele, F. (1994), "Natural convection over a rotating cylindrical heat source in a rectangular enclosure", Numer. Heat Tr. A-Appl., 26(6), 701-717. https://doi.org/10.1080/10407789408956018
  12. Gingold, R.A. and Monaghan, J.J. (1977), "Smoothed particle hydrodynamics-theory and application to non-spherical stars", Mon. Not. R. Astron. Soc., 181, 375-389. https://doi.org/10.1093/mnras/181.3.375
  13. Goda, K. (1979), "A multistep technique with implicit difference schemes for calculating two-or threedimensional cavity flows", J. Comput. Phys., 30(1), 76-95. https://doi.org/10.1016/0021-9991(79)90088-3
  14. Gray, D.D. and Giorgini, A. (1976), "The validity of the Boussinesq approximation for liquids and gases", Int. J. Heat Mass Transfer, 19(5), 545-551. https://doi.org/10.1016/0017-9310(76)90168-X
  15. Hu, X.Y. and Adams, N.A. (2007), "An incompressible multi-phase SPH method", J. Comput. Phys., 227(1), 264-278. https://doi.org/10.1016/j.jcp.2007.07.013
  16. Kim, J. and Choi, H. (2004), "An immersed-boundary finite-volume method for simulation of heat transfer in complex geometries", J. Mech. Sci. Tech., 18(6), 1026-1035.
  17. Kum, O., Hoover, W.G. and Posch, H.A. (1995), "Viscous conducting flows with smooth-particle applied mechanics", Phys. Review E, 52(5), 4899-4908. https://doi.org/10.1103/PhysRevE.52.4899
  18. Lastiwka, M., Quinlan, N.J. and Basa, M. (2009), "Permeable and non-reflecting boundary conditions in SPH", Int. J. Numer. Meth. Fluid., 61(7), 709-724. https://doi.org/10.1002/fld.1971
  19. Lee, E.S., Moulinec, C., Xu, R. and Violeau, D. (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
  20. Liu, G.R. and Liu, M.B. (2003), Smoothed Particle Hydrodynamics a Meshfree Particle Method, World Scientific, Singapore.
  21. Liu, M.B. and Liu, G.R. (2010), "Smoothed particle hydrodynamics (SPH): an overview and recent developments", Arch. Comput. Meth. Eng., 17(1), 25-76. https://doi.org/10.1007/s11831-010-9040-7
  22. Lucy, L.B. (1977), "A numerical approach to the testing of the fission hypothesis", Astronom. J., 82(12), 1013-1024. https://doi.org/10.1086/112164
  23. Monaghan, J.J. (1992), "Smoothed particle hydrodynamics", Ann. Review Astronom. Astrophys., 30, 543-574. https://doi.org/10.1146/annurev.aa.30.090192.002551
  24. Monaghan, J.J. (2012), "Smoothed particle hydrodynamics and its diverse applications", Ann. Review Fluid Mech., 44, 323-346. https://doi.org/10.1146/annurev-fluid-120710-101220
  25. Monaghan, J.J. (1989), "On the problem of penetration in particle methods", J. Comput. Phys., 82(1), 1-15. https://doi.org/10.1016/0021-9991(89)90032-6
  26. Morris, J.P., Fox, P.J. and Zhu, Y. (1997), "Modeling low Reynolds number incompressible flowsusing SPH", J. Comput. Phys., 136(1), 214-226. https://doi.org/10.1006/jcph.1997.5776
  27. Moukalled, F. and Acharya, S. (1996), "Natural convection in the annulus between concentric horizontalcircular and square cylinders", J. Thermophys. Heat Transfer, 10(3), 524-531. https://doi.org/10.2514/3.820
  28. Noor, D.Z., Chern, M.J. and Horng, T.L. (2009), "An immersed boundary method to solve fluid-solidinteraction problems", Comput. Mech., 44(4), 447-453. https://doi.org/10.1007/s00466-009-0384-5
  29. Oger, G. et al. (2007), "An improved SPH method: Towards higher order convergence", J. Comput. Phys., 225(2), 1472-1492. https://doi.org/10.1016/j.jcp.2007.01.039
  30. Ouertatani, N., Ben Cheikh, N., Ben Beya, B. and Lili, T. (2008), "Numerical simulation of two-dimensional Rayleigh-Benard convection in an enclosure", Comptes Rendus Mecanique, 336(5), 464-470. https://doi.org/10.1016/j.crme.2008.02.004
  31. Pacheco-Vega, A., Pacheco, J.R. and Rodic, T. (2007), "A general scheme for the boundary conditionsin convective and diffusive heat transfer with immersed boundary methods", J. Heat Transfer, 129(11), 1506-1516. https://doi.org/10.1115/1.2764083
  32. Pan, D. (2006), "An immersed boundary method on unstructured cartesian meshes for incompressible flows with heat transfer", Numer. Heat Transfer, 49(3), 277-297. https://doi.org/10.1080/10407790500290709
  33. Peng, Y., Chew, Y.T. and Shu, C. (2003), "Numerical simulation of natural convection in a concentricannulus between a square outer cylinder and a circular inner cylinder using the Taylor-series-expansion and least-squares-based lattice Boltzmann method", Phys. Review E, 67(2), 026701. https://doi.org/10.1103/PhysRevE.67.026701
  34. Rosenfeld, M., Kwak, D. and Vinokur, M. (1991), "A fractional step solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems", J. Comput. Phys., 94(1), 102-137. https://doi.org/10.1016/0021-9991(91)90139-C
  35. Shao, S. and Lo, E.Y. (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
  36. Shu, C. and Zhu, Y. (2002), "Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder", Int. J. Numer. Meth. Fluids, 38(5), 429-445. https://doi.org/10.1002/fld.226
  37. Sigalotti, L., Klapp, J., Sira, E., Meleán, Y. and Hasmy, A. (2003), "SPH simulations of time-dependent Poiseuille flow at low Reynolds numbers", J. Comput. Phys., 191(2), 622-638. https://doi.org/10.1016/S0021-9991(03)00343-7
  38. Szewc, K., Pozorski, J. and Tanière, A. (2011), "Modeling of natural convection with smoothedparticle hydrodynamics: Non-Boussinesq formulation", Int. J. Heat Mass Transfer, 54(23-24), 4807-4816. https://doi.org/10.1016/j.ijheatmasstransfer.2011.06.034
  39. Temam, R. (1968), "Une methode d'approximation de la solution des 'equations de Navier-Stokes", Bull. Soc. Math. Fr., 96, 115-152.
  40. Xu, R., Stansby, P. and Laurence, D. (2009), "Accuracy and stability in incompressible SPH (ISPH)based on the projection method and a new approach", J. Comput. Phys., 228(18), 6703-6725. https://doi.org/10.1016/j.jcp.2009.05.032

피인용 문헌

  1. Smoothed Particle Hydrodynamics Modeling of Natural Convection Around a Heated Horizontal Cylinder: A Comparison With Experiments vol.143, pp.4, 2013, https://doi.org/10.1115/1.4049495