Nonlinear enthalpy transformation for transient convective phase change in Smoothed Particle Hydrodynamics (SPH)

References

• A. Dalhuijsen and A. Segal, “Comparison of finite element techniques for solidification problems,” Int. J. Numer. Meth. Eng., vol. 23, no. 10, pp. 1807–1829, 1986. DOI: 10.1002/nme.1620231003.
   Web of Science ®Google Scholar
• P. L.-F. Liu, H. H.-J. Yeh, and C. Synolakis, Advanced Numerical Models for Simulating Tsunami Waves and Runup. Singapore: World Scientific, 2008. http://opac.inria.fr/record=b1120438.
   Google Scholar
• B. Cartwright, P. Groenenboom, and D. McGuckin, “Examples of ship motion and wash predictions by smoothed particle hydrodynamics (SPH),” in 9th Symposium on Practical Design of Ships and Other Floating Structures, Luebeck-Travemuende, Germany, 2004.
   Google Scholar
• A. Farrokhpanah and J. Mostaghimi, “Application of multiphase particle methods in atomization and breakup regimes of liquid jets,” in ASME 2014 4th Joint US–European Fluids Engineering Division Summer Meeting American Society of Mechanical Engineers, 2014.
   Google Scholar
• A. Farrokhpanah, B. Samareh, and J. Mostaghimi, “Droplet impact: a GPU based smoothed particle hydrodynamics (SPH) approach,” in ASME 2012 Fluids Engineering Division Summer Meeting American Society of Mechanical Engineers, 2012, pp. 615–623.
   Google Scholar
• X. Hu and N. Adams, “A multi-phase SPH method for macroscopic and mesoscopic flows,” J. Comput. Phys., vol. 213, no. 2, pp. 844–861, 2006. DOI: 10.1016/j.jcp.2005.09.001.
   Web of Science ®Google Scholar
• N. Grenier, D. Touze, M. Antuono, and A. Colagrossi, “An improved SPH method for multi-phase simulations,” in 8th International Conference on Hydrodynamics, ICHD, 2008.
   Google Scholar
• A. M. Tartakovsky, K. F. Ferris, and P. Meakin, “Lagrangian particle model for multiphase flows,” Comput. Phys. Commun., vol. 180, no. 10, pp. 1874–1881, 2009.
   Web of Science ®Google Scholar
• M. Passandideh-Fard and J. Mostaghimi, “Droplet impact and solidification in a thermal spray process: Droplet-substrate interactions,” in Proceedings of the 9th National Thermal Spray Conference, 1996.
   Google Scholar
• V. R. Voller and C. Prakash, “A fixed grid numerical modelling methodology for convection–diffusion mushy region phase change problems,” Int. J. Heat Mass Transfer, vol. 30, no. 8, pp. 1709–1719, 1987. DOI: 10.1016/0017-9310(87)90317-6.
   Web of Science ®Google Scholar
• B. Thomas, I. Samarasekera, and J. Brimacombe, “Comparison of numerical modeling techniques for complex, two-dimensional, transient heat-conduction problems,” MTB, vol. 15, no. 2, pp. 307–318, 1984. DOI: 10.1007/BF02667334.
   Google Scholar
• J. Hsiao and B. T. Chung, “An efficient algorithm for finite element solution to two-dimensional heat transfer with melting and freezing,” In: J. Heat Transfer, vol. 108, no. 2, pp. 462–464, 1986. DOI: 10.1115/1.3246948.
   Web of Science ®Google Scholar
• A. Farrokhpanah, M. Bussmann, and J. Mostaghimi, “New smoothed particle hydrodynamics (SPH) formulation for modeling heat conduction with solidification and melting,” Numer. Heat Transfer, Part B: Fund., vol. 71, no. 4, pp. 299–312, 2017. DOI: 10.1080/10407790.2017.1293972.
   Web of Science ®Google Scholar
• P. Cleary, J. Ha, J. Mooney, and V. Ahuja, “Effect of heat transfer and solidification on high pressure die casting,” in Proc. 13th Australasian Fluid Mechanics Conference, Melbourne, 1998, pp. 679–682.
   Google Scholar
• P. Cleary, J. Ha, M. Prakash, and T. Nguyen, “3D SPH flow predictions and validation for high pressure die casting of automotive components,” Appl. Math. Model., vol. 30, no. 11, pp. 1406–1427, 2006. DOI: 10.1016/j.apm.2006.03.012.
   Web of Science ®Google Scholar
• P. W. Cleary, “Extension of SPH to predict feeding, freezing and defect creation in low pressure die casting,” Appl. Math. Model., vol. 34, no. 11, pp. 3189–3201, 2010. DOI: 10.1016/j.apm.2010.02.012.
   Web of Science ®Google Scholar
• M. Zhang, H. Zhang, and L. Zheng, “Application of smoothed particle hydrodynamics method to free surface and solidification problems,” Numer. Heat Transfer, Part A: Appl., vol. 52, no. 4, pp. 299–314, 2007. DOI: 10.1080/00397910601150007.
   Web of Science ®Google Scholar
• M. Zhang, H. Zhang, and L. Zheng, “Simulation of droplet spreading, splashing and solidification using smoothed particle hydrodynamics method,” Int. J. Heat Mass Transfer, vol. 51, no. 13–14, pp. 3410–3419, 2008. DOI: 10.1016/j.ijheatmasstransfer.2007.11.009.
   Web of Science ®Google Scholar
• M. Zhang, H. Zhang, and L. Zheng, “Numerical investigation of substrate melting and deformation during thermal spray coating by SPH method,” Plasma Chem. Plasma Process, vol. 29, no. 1, pp. 55–68, 2009. DOI: 10.1007/s11090-008-9158-7.
   Web of Science ®Google Scholar
• J. J. Monaghan, H. E. Huppert, and M. G. Worster, “Solidification using smoothed particle hydrodynamics,” J. Comput. Phys., vol. 206, no. 2, pp. 684–705, 2005. DOI: 10.1016/j.jcp.2004.11.039.
   Web of Science ®Google Scholar
• Y. Cao, A. Faghri, and W. S. Chang, “A numerical analysis of Stefan problems for generalized multi-dimensional phase change structures using the enthalpy transforming model,” Int. J. Heat Mass Transfer, vol. 32, no. 7, pp. 1289–1298, 1989. DOI: 10.1016/0017-9310(89)90029-X.
   Web of Science ®Google Scholar
• J. J. Monaghan, “Smoothed particle hydrodynamics and its diverse applications,” Annu. Rev. Fluid Mech., vol. 44, no. 1, pp. 323–346, 2012. DOI: 10.1146/annurev-fluid-120710-101220.
   Web of Science ®Google Scholar
• A. M. Tartakovsky and P. Meakin, “A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and the two-dimensional Rayleigh–Taylor instability,” J. Comput. Phys., vol. 207, no. 2, pp. 610–624, 2005. DOI: 10.1016/j.jcp.2005.02.001.
   Web of Science ®Google Scholar
• D. W. Holmes, J. R. Williams, and P. Tilke, “Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media,” Int. J. Numer. Anal. Meth. Geomech., vol. 35, no. 4, pp. 419–437, 2011. DOI: 10.1002/nag.898.
   Web of Science ®Google Scholar
• J. J. Monaghan, “SPH without a tensile instability,” J. Comput. Phys., vol. 159, no. 2, pp. 290–311, 2000. DOI: 10.1006/jcph.2000.6439.
   Web of Science ®Google Scholar
• P. W. Cleary and J. J. Monaghan, “Conduction modelling using smoothed particle hydrodynamics,” J. Comput. Phys., vol. 148, no. 1, pp. 227–264, 1999. DOI: 10.1006/jcph.1998.6118.
   Web of Science ®Google Scholar
• S. Meng, R. Yang, J.-S. Wu, and H. Zhang, “Simulation of droplet spreading on porous substrates using smoothed particle hydrodynamics,” Int. J. Heat Mass Transfer, vol. 77, pp. 828–833, 2014. DOI: 10.1016/j.ijheatmasstransfer.2014.05.056.
   Web of Science ®Google Scholar
• V. Voller, A. Brent, and C. Prakash, “Modelling the mushy region in a binary alloy,” Appl. Math. Model., vol. 14, no. 6, pp. 320–326, 1990. DOI: 10.1016/0307-904X(90)90084-I.
   Web of Science ®Google Scholar
• S. Alavi, M. Passandideh-Fard, and J. Mostaghimi, “Simulation of semi-molten particle impacts including heat transfer and phase change,” J. Therm. Spray Tech., vol. 21, no. 6, pp. 1278–1293, 2012. DOI: 10.1007/s11666-012-9804-8.
   Web of Science ®Google Scholar
• H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. Oxford: Clarendon Press, 1959.
   Google Scholar
• A. Crowley, “Numerical solution of Stefan problems,” Int. J. Heat Mass Transfer, vol. 21, no. 2, pp. 215–219, 1978. DOI: 10.1016/0017-9310(78)90225-9.
   Web of Science ®Google Scholar
• C.-S. Keung, The Use of Sources and Sinks in Solving Two-Dimensional Heat Conduction Problems with Change of Phase in Arbitrary Domains, Columbia University, Diss., 1980.
   Google Scholar
• S. D. Aziz and S. Chandra, “Impact, recoil and splashing of molten metal droplets,” Int. J. Heat Mass Transfer, vol. 43, no. 16, pp. 2841–2857, 2000. DOI: 10.1016/S0017-9310(99)00350-6.
   Web of Science ®Google Scholar
• M. Pasandideh-Fard, S. Chandra, and J. Mostaghimi, “A three-dimensional model of droplet impact and solidification,” Int. J. Heat Mass Transfer, vol. 45, no. 11, pp. 2229–2242, 2002. DOI: 10.1016/S0017-9310(01)00336-2.
   Web of Science ®Google Scholar
• A. Farrokhpanah, T. W. Coyle, and J. Mostaghimi, “Numerical study of suspension plasma spraying,” J. Therm. Spray Tech., vol. 26, no. 1–2, pp. 12–36, 2017. DOI: 10.1007/s11666-016-0502-9.
   Web of Science ®Google Scholar
• M. Pasandideh‐Fard, Y. M. Qiao, S. Chandra, and J. Mostaghimi, “Capillary effects during droplet impact on a solid surface,” Phys. Fluids, vol. 8, no. 3, pp. 650–659, 1996. DOI: 10.1063/1.868850.
   Web of Science ®Google Scholar
• G. R. Johnson, R. A. Stryk, and S. R. Beissel, “SPH for high velocity impact computations,” Comput. Methods Appl. Mech. Eng., vol. 139, no. 1–4, pp. 347–373, 1996. DOI: 10.1016/S0045-7825(96)01089-4.
   Web of Science ®Google Scholar
• J. J. Monaghan and J. C. Lattanzio, “A refined particle method for astrophysical problems,” Astron. Astrophy., vol. 149, pp. 135–143, 1985.
   Web of Science ®Google Scholar
• G.-R. Liu and M. B. Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method. Singapore: World Scientific, 2003.
   Google Scholar