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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 78, 2020 - Issue 7
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Original Articles

A novel fixed-grid interface-tracking algorithm for rapid solidification of supercooled liquid metal

ORCID Icon, ORCID Icon, , & ORCID Icon
Pages 306-320 | Received 02 May 2020, Accepted 30 Jun 2020, Published online: 20 Jul 2020

References

  • R. Scardovelli and S. Zaleski, “Direct numerical simulation of free-surface and interfacial flow,” Annu. Rev. Fluid Mech., vol. 31, no. 1, pp. 567–603, 1999. DOI: 10.1146/annurev.fluid.31.1.567.
  • D. Juric and G. Tryggvason, “A front-tracking method for dendritic solidification,” J. Comput. Phys., vol. 123, no. 1, pp. 127–148, 1996. DOI: 10.1006/jcph.1996.0011.
  • H. S. Udaykumar, R. Mittal, and W. Shyy, “Computation of solid–liquid phase fronts in the sharp interface limit on fixed grids,” J. Comput. Phys., vol. 153, no. 2, pp. 535–574, 1999. DOI: 10.1006/jcph.1999.6294.
  • P. Zhao and J. C. Heinrich, “Front-tracking finite element method for dendritic solidification,” J. Comput. Phys., vol. 173, no. 2, pp. 765–796, 2001. DOI: 10.1006/jcph.2001.6911.
  • P. Zhao and J. C. Heinrich, “Numerical approximation of a thermally driven interface using finite elements,” Int. J. Numer. Meth. Eng., vol. 56, no. 11, pp. 1533–1547, 2003. DOI: 10.1002/nme.621.
  • A. Yadav, A. Kumar, P. Gupta, and D. K. Sinha, “Numerical study of temperature distributions and solidification pattern in the weld pool of arc welded plate,” Defect Diffus. Forum, vol. 392, pp. 218–227, 2019. DOI: 10.4028/www.scientific.net/DDF.392.218.
  • N. Al-Rawahi and G. Tryggvason, “Numerical simulation of dendritic solidification with convection: Three-dimensional flow,” J. Comput. Phys., vol. 194, no. 2, pp. 677–696, 2004. DOI: 10.1016/j.jcp.2003.09.020.
  • A. Karma and W. J. Rappel, “Quantitative phase-field modelling of dendritic growth in two and three dimensions,” Phys. Rev. E, vol. 57, no. 4, pp. 4323–4349, 1998. DOI: 10.1103/PhysRevE.57.4323.
  • A. Yadav, A. Ghosh, and A. Kumar, “Thermal transport phenomena in multi-layer deposition using arc welding process,” in 3D Printing and Additive Manufacturing Technologies, L. J. Kumar, P. M. Pandey, D. I. Wimpenny, Eds. Singapore: Springer, 2019, pp. 15–27.
  • C. Beckermann, H. J. Diepers, I. Steinbach, A. Karma, and X. Tong, “Modeling melt convection in phase-field simulations of solidification,” J. Comput. Phys., vol. 154, no. 2, pp. 468–496, 1999. DOI: 10.1006/jcph.1999.6323.
  • W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, “Phase-field simulation of solidification,” Annu. Rev. Mater. Res., vol. 32, no. 1, pp. 163–194, 2002. DOI: 10.1146/annurev.matsci.32.101901.155803.
  • A. Yadav, A. Ghosh, and A. Kumar, “Experimental and numerical study of thermal field and weld bead characteristics in submerged arc welded plate,” J. Mater. Process. Technol., vol. 248, pp. 262–274, 2017. DOI: 10.1016/j.jmatprotec.2017.05.021.
  • I. Harary, V. Dubovsky, E. Assis, G. Ziskind, and R. Letan, “Solidification of subcooled gallium poured into a vertical cylindrical mold,” Int. J. Thermodyn., vol. 19, no. 1, pp. 36–41, 2016. DOI: 10.5541/ijot.5000155486.
  • E. Günther, H. Mehling, and S. Hiebler, “Modeling of subcooling and solidification of phase change materials,” Model. Simul. Mater. Sci. Eng., vol. 15, no. 8, pp. 879–892, 2007. DOI: 10.1088/0965-0393/15/8/005.
  • A. Y. Uzan, Y. Kozak, Y. Korin, I. Harary, H. Mehling, and G. Ziskind, “A novel multidimensional model for solidification process with supercooling,” Int. J. Heat Mass Transf., vol. 106, pp. 91–102, 2017. DOI: 10.1016/j.ijheatmasstransfer.2016.10.046.
  • A. D. Brent, V. R. Voller, and K. J. Reid, “Enthalpy-porosity technique for modeling convection-diffusion phase change: Application to the melting of a pure metal,” Numer. Heat Transf., vol. 13, no. 3, pp. 297–318, 1988. DOI: 10.1080/10407788808913615.
  • S. Mishra, S. Chakraborty, and T. DebRoy, “Probing liquation cracking and solidification through modeling of momentum, heat, and solute transport during welding of aluminum alloys,” J. Appl. Phys., vol. 97, no. 9, pp. 094912, 2005. DOI: 10.1063/1.1886272.
  • R. K. Shukla, V. Patel, and A. Kumar, “Modeling of rapid solidification with undercooling effect during droplet flattening on a substrate in coating formation,” J. Therm. Spray Technol., vol. 27, no. 3, pp. 269–287, 2018. DOI: 10.1007/s11666-017-0666-y.
  • K. Yokoi, “Efficient implementation of THINC scheme: a simple and practical smoothed VOF algorithm,” J. Comput. Phys., vol. 226, no. 2, pp. 1985–2002, 2007. DOI: 10.1016/j.jcp.2007.06.020.
  • W. D. Bennon and F. P. Incropera, “A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems - II. Application to solidification in a rectangular cavity,” Int. J. Heat Mass Transf., vol. 30, no. 10, pp. 2171–2187, 1987. DOI: 10.1016/0017-9310(87)90095-0.
  • C. G. Levi and R. Mehrabian, “Heat flow during rapid solidification of undercooled metal droplets,” Metall. Trans. A, vol. 13, no. 2, pp. 221–234, 1982. DOI: 10.1007/BF02643312.
  • T. W. Clyne, “Numerical treatment of rapid solidification,” Metall. Trans. B, vol. 15, no. 2, pp. 369–381, 1984. DOI: 10.1007/BF02667341.
  • G. X. Wang and E. F. Matthys, “Numerical modelling of phase change and heat transfer during rapid solidification processes: Use of control volume integrals with element subdivision,” Int. J. Heat Mass Transf., vol. 35, no. 1, pp. 141–153, 1992. DOI: 10.1016/0017-9310(92)90015-K.
  • M. F. Ashby and D. R. Jones, Engineering Materials, vol. 2, 3rd ed. Butterworth: Heinemann, 2006.
  • H. Liu, M. Bussmann, and J. Mostaghimi, “A comparison of hyperbolic and parabolic models of phase change of a pure metal,” Int. J. Heat Mass Transf., vol. 52, no. 5–6, pp. 1177–1184, 2009. DOI: 10.1016/j.ijheatmasstransfer.2008.08.030.
  • G. L. Buchbinder and V. A. Volkov, “Heat transfer in rapidly solidifying supercooled pure melt during final transient,” Phys. A, vol. 391, no. 23, pp. 5935–5947, 2012. DOI: 10.1016/j.physa.2012.07.028.
  • P. Reddy, V. Patel, A. Yadav, S. Patel, and A. Kumar, “Modelling and simulation of equilibrium and non-equilibrium solidification in laser spot welding,” IOP Conf. Ser. Mater. Sci. Eng., vol. 310, pp. 012092, 2018. DOI: 10.1088/1757-899X/310/1/012092.
  • S. D. Peteves and R. Abbaschian, “Growth kinetics of solid-liquid Ga interfaces: Part II Theoretical,” Metall. Trans. A, vol. 22, no. 6, pp. 1271–1286, 1991. DOI: 10.1007/BF02660659.
  • H. Zhang, X. Y. Wang, L. L. Zheng, and S. Sampath, “Numerical simulation of nucleation, solidification, and microstructure formation in thermal spraying,” Int. J. Heat Mass Transf., vol. 47, no. 10–11, pp. 2191–2203, 2004. DOI: 10.1016/j.ijheatmasstransfer.2003.11.030.
  • S. B. Al-Omari and E. Elanajjar, “Experimental study on the enhancement of heat transfer between water integrated with higher thermal conductivity liquid,” Int. Commun. Heat Mass Transf., vol. 45, pp. 95–99, 2013.
  • C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” J. Comput. Phys., vol. 39, no. 1, pp. 201–225, 1981. DOI: 10.1016/0021-9991(81)90145-5.
  • S. V. Patankar, “Numerical heat transfer and fluid flow,” in Series in Computational Methods in Mechanics and Thermal Sciences, W. J. Minkowycz and E. M. Sparrow, Eds. New York: McGraw-Hill Book Company, 1980.
  • D. L. Turcotte and G. Schubert, Geodynamics. Cambridge: Cambridge University Press, 2002.
  • W. H. Reed and T. R. Hill, Triangular Mesh Methods for the Neutron Transport Equation. Proceedings of the American Nuclear Society, USA. Los Alamos Scientific Laboratory, 1973.

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