Finite volume method for radiative transport in multiphase flows with free surfaces

References

• F. H. Harlow and J. E. Welch, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface, Phys. Fluids, vol. 8, pp. 2182–2189, 1965.
   Web of Science ®Google Scholar
• W. F. Noh and P. Woodward, SLIC (Simple Line Interface Calculation) Lect. Notes Phys., vol. 59, pp. 330–340, 1976.
   Google Scholar
• C. W. Hirt and B. D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys., vol. 39, pp. 201–225, 1981.
   Web of Science ®Google Scholar
• O. Ubbink and R. I. Issa, A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes, J. Comp. Phys., vol. 153, pp. 26–50, 1999.
   Web of Science ®Google Scholar
• S. Muzaferija and M. Perić, Computation of Free Surface Flows Using Interface-Tracking and Interface-Capturing Methods, in O. Mahrenholtz and M. Markiewicz (eds.), Nonlinear Water Wave Interaction, Chapter 3, Computational Mechanics Publications, Southampton, pp. 59–96, 1998.
   Google Scholar
• S. Osher and J. A. Sethian, Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulation, J. Comp. Phys., vol. 79, pp. 12–49, 1988.
   Web of Science ®Google Scholar
• M. Sussman, P. Smereka, and S. Osher, A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, J. Comp. Phys., vol. 114, pp. 146–159, 1994.
   Web of Science ®Google Scholar
• A. Teskeredžić, I. Demirdžić, and S. Muzaferija, Numerical Method for Calculation of Complete Casting Process – Part I: Theory, Numer. Heat Trans. B, vol. 68, pp. 295–316, 2015.
   Web of Science ®Google Scholar
• L. A. Tarshis, S. O'Hara, and R. Viskanta, Heat Transfer by Simultaneous Conduction and Radiation for Two Absorbing Media in Intimate Contact, Int. J. Heat Mass Trans., vol. 12, pp. 333–347, 1969.
   Web of Science ®Google Scholar
• R. Siegel, Transient Thermal Analysis of Parallel Translucent Layers by Using Green's Functions, J. Thermophys. Heat Trans., vol. 13, pp. 10–17, 1999.
   Web of Science ®Google Scholar
• A. V. Gusarov, The Multiphase Radiation Transfer Model for Two-Phase Layered Systems, J. Quant. Spectro. Rad. Trans., vol. 116, pp. 156–168, 2013.
   Web of Science ®Google Scholar
• A. I. Shestakov, Multifrequency Radiation Diffusion Equations for Homogeneous, Refractive, Lossy Media and Their Interface Conditions, J. Comp. Phys., vol. 243, pp. 293–304, 2013.
   Web of Science ®Google Scholar
• H. Matshushima and R. Viskanta, Effects of Internal Radiative Transfer on Natural Convection and Heat Transfer in a Vertical Crystal Growth Configuration, Int. J. Heat Mass Trans., vol. 33, pp. 1957–1968, 1990.
   Web of Science ®Google Scholar
• E. W. Larsen, G. Thommes, A. Klar, M. Seaid, and T. Götz, Simplified PN Approximations to the Equations of Radiative Heat Transfer and Applications, J. Comp. Phys., vol. 183, pp. 652–675, 2002.
   Web of Science ®Google Scholar
• P. Łapka and P. Furmański, Fixed Cartesian Grid Based Numerical Model for Solidification Process of Semi-Transparent Materials I: Modelling and Verification, Int. J. Heat Mass Trans., vol. 55, pp. 4941–4952, 2012.
   Web of Science ®Google Scholar
• P. Łapka and P. Furmański, Fixed Cartesian Grid Based Numerical Model for Solidification Process of Semi-Transparent Materials II: Reflection and Refraction or Transmission of the Thermal Radiation at the Solid-Liquid Interface, Int. J. Heat Mass Trans., vol. 55, pp. 4953–4964, 2012.
   Web of Science ®Google Scholar
• S. H. Chan, D. H. Cho, and G. Kocamustafaogullari, Melting and Solidification with Internal Radiative Transfer – A Generalized Phase Change Model, Int. J. Heat Mass Trans., vol. 26, pp. 621–633, 1983.
   Web of Science ®Google Scholar
• S. Brandon and J. J. Derby, Heat Transfer in Vertical Bridgman Growth of Oxides: Effects of Conduction, Convection, and Internal Radiation, J. Cryst. Growth, vol. 121, pp. 473–494, 1992.
   Web of Science ®Google Scholar
• T. Tsukada, K. Kakinoki, M. Hozawa, and N. Imaishi, Effect of Internal Radiation Within Crystal and Melt of Czochralski Crystal Growth of Oxide, Int. J. Heat Mass Trans., vol. 38, pp. 2707–2714, 1995.
   Web of Science ®Google Scholar
• C. W. Lan, C. Y. Tu, and Y. F. Lee, Effects of Internal Radiation on Heat Flow and Facet Formation in Bridgman Growth of YAG Crystals, Int. J. Heat Mass Trans., vol. 46, pp. 1629–1640, 2003.
   Web of Science ®Google Scholar
• C. J. Jing, S. Ihara, K. I. Sugioka, T. Tsukada, M. Kobayashi, M. Mito, and C. Yokoyama, Global Analysis of Heat Transfer Considering Three-Dimensional Unsteady Melt Flow in CZ Crystal Growth of Oxide, J. Cryst. Growth, vol. 307, pp. 235–244, 2007.
   Web of Science ®Google Scholar
• C. J. Jing, S. Ihara, K. I. Sugioka, T. Tsukada, and M. Kobayashi, Global Analysis of Heat Transfer in CZ Crystal Growth of Oxide Taking into Account Three-Dimensional Unsteady Melt Convection: Effect of Meniscus Shape, J. Cryst. Growth, vol. 310, pp. 204–213, 2008.
   Web of Science ®Google Scholar
• C. Yao, B. T. F. Chung, and G. -X. Wang, Mushy Zone Equilibrium Solidification of a Semitransparent Layer Subject to Radiative and Convective Cooling, Int. J. Heat Mass Trans., vol. 45, pp. 2397–2405, 2002.
   Web of Science ®Google Scholar
• P. R. Parida, R. Raj, A. Prasad, and S. C. Mishra, Solidification of a Semitransparent Planar Layer Subjected to Radiative and Convective Cooling, J. Quant. Spectro. Radiat. Trans., vol. 107, pp. 226–235, 2007.
   Web of Science ®Google Scholar
• D. Makhanlall and L. H. Liu, Second Law Analysis of Coupled Conduction-Radiation Heat Transfer with Phase Change, Int. J. Therm. Sci., vol. 49, pp. 1829–1836, 2010.
   Web of Science ®Google Scholar
• S. C. Mishra, N. C. Behara, A. K. Garg, and A. Mishra, Solidification of a 2-D Semitransparent Medium Using the Lattice Boltzmann Method and the Finite Volume Method, Int. J. Heat Mass Trans., vol. 51, pp. 4447–4460, 2008.
   Web of Science ®Google Scholar
• B. Mondal and S. C. Mishra, Numerical Analysis of Solidification of a 3-D Semitransparent Medium in Presence of Volumetric Radiation, Int. J. Therm. Sci., vol. 48, pp. 1116–1128, 2009.
   Web of Science ®Google Scholar
• B. Yimer, Phase-Change Heat Transfer During the Cyclic Heating and Cooling with Internal Radiation and Temperature-Dependent Properties, Energy, vol. 23, pp. 929–935, 1998.
   Web of Science ®Google Scholar
• M. F. Modest, Radiative Heat Transfer, 3rd ed., Academic Press, New York, 2013.
   Google Scholar
• I. Demirdžić and M. Perić, Space Conservation Law in Finite Volume Calculations of Fluid Flow, Int. J. Numer. Meth. Fluids, vol. 8, pp. 1037–1050, 1988.
   Web of Science ®Google Scholar
• I. Demirdžić and S. Muzaferija, Numerical Method for Coupled Fluid Flow, Heat Transfer and Stress Analysis Using Unstructured Moving Meshes with Cells of Arbitrary Topology, Comput. Methods Appl. Mech. Eng., vol. 125, pp. 235–255, 1995.
   Web of Science ®Google Scholar
• C. D. Perez-Segarra, C. Farre, J. Cadafalch, and A. Oliva, Analysis of Different Numerical Schemes for the Resolution of Convection-Diffusion Equations Using Finite-Volume Methods on Three-Dimensional Unstructured Grids. Part I: Discretization Schemes, Numer. Heat Trans. B, vol. 49, pp. 333–350, 2006.
   Web of Science ®Google Scholar
• S. W. Chau, M. Perić, and S. Muzaferija, An Interface-Capturing Method for Prediction of Sloshing Problems, Proc. 22nd Natl. Conf. Theor. Appl. Mech., vol. 2, pp. 363–380, 1998.
   Google Scholar
• P. C. Sames, T. E. Schellin, S. Muzaferija, and M. Perić, Application of a Two-Fluid Finite Volume Method to Ship Slamming, J. Offshore Mech. Arctic Eng., vol. 121, pp. 47–52, 1999.
   Web of Science ®Google Scholar
• G. Pal and M. F. Modest, Advanced Differential Approximation Formulation of the P − N Method for Radiative Transfer, J. Heat Trans., vol. 137, pp. 233–240, 2015.
   Web of Science ®Google Scholar