A new lattice Boltzmann model for solid–liquid phase change

Abstract The solid–liquid phase change problems were solved by the lattice Boltzmann method in this paper. By modifying the equilibrium distribution function for the temperature, a new approach was developed to treat the latent-heat source term. As compared with the previous work, the approach developed in this paper could avoid iteration steps or solving a group of linear equations, which guaranteed this approach’s high efficiency. The phase interface was traced by updating the total enthalpy, and the moving interface was treated by the immersed moving boundary scheme proposed by Noble and Torczynski for simulation of particulate suspensions. The approach was firstly validated by the problem of conduction-induced melting in a semi-infinite space, and good agreement with the analytical result was obtained. Then it was used to simulate melting problems coupled with natural convection, which demonstrated that the approach could produce consistent results as compared with other numerical method.

[1]  B. Cook,et al.  Three‐dimensional immersed boundary conditions for moving solids in the lattice‐Boltzmann method , 2007 .

[2]  J. R. Torczynski,et al.  A Lattice-Boltzmann Method for Partially Saturated Computational Cells , 1998 .

[3]  Suman Chakraborty,et al.  An enthalpy-based lattice Boltzmann model for diffusion dominated solid–liquid phase transformation , 2005 .

[4]  D. Chatterjee.  Lattice Boltzmann Simulation of Incompressible Transport Phenomena in Macroscopic Solidification Processes , 2010 .

[5]  W. Miller,et al.  Growth kinetics and melt convection , 2004 .

[6]  Bastien Chopard,et al.  Lattice Boltzmann model for melting with natural convection , 2008 .

[7]  S. Succi,et al.  Phase-field lattice kinetic scheme for the numerical simulation of dendritic growth. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Raymond Viskanta,et al.  Transient natural convection of low‐Prandtl‐number fluids in a differentially heated cavity , 1991 .

[9]  Wei Ge,et al.  Direct numerical simulation of particle-fluid systems by combining time-driven hard-sphere model and lattice Boltzmann method , 2010 .

[10]  Alan Solomon,et al.  Some remarks on the Stefan problem , 1966 .

[11]  Suman Chakraborty,et al.  A hybrid lattice Boltzmann model for solid–liquid phase transition in presence of fluid flow , 2006 .

[12]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases : an account of the kinetic theory of viscosity, thermal conduction, and diffusion in gases , 1954 .

[13]  Dipankar Chatterjee.  An enthalpy-based thermal lattice Boltzmann model for non-isothermal systems , 2009 .

[14]  John R. Williams,et al.  A direct simulation method for particle‐fluid systems , 2003 .

[15]  M. Salcudean,et al.  On numerical methods used in mathematical modeling of phase change in liquid metals , 1988 .

[16]  Jeng-Rong Ho,et al.  LATTICE BOLTZMANN METHOD FOR THE HEAT CONDUCTION PROBLEM WITH PHASE CHANGE , 2001 .

[17]  Marcel Lacroix,et al.  Melting driven by natural convection A comparison exercise: first results , 1999 .

[18]  S. Succi,et al.  A Lattice Boltzmann Model for Anisotropic Crystal Growth from Melt , 2002 .

[19]  S. Chakraborty,et al.  An enthalpy-based hybrid lattice-Boltzmann method for modelling solid–liquid phase transition in the presence of convective transport , 2007, Journal of Fluid Mechanics.

[20]  Fulvio Stella, Marilena Giangi.  MELTING OF A PURE METAL ON A VERTICAL WALL: NUMERICAL SIMULATION , 2000 .

[21]  S. Succi,et al.  Lattice Boltzmann phase-field modelling of binary-alloy solidification , 2006 .

[22]  Xiaowen Shan,et al.  SIMULATION OF RAYLEIGH-BENARD CONVECTION USING A LATTICE BOLTZMANN METHOD , 1997 .

[23]  Dmitry Medvedev,et al.  Lattice Boltzmann scheme for crystal growth in external flows. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Mohsen Eshraghi,et al.  An implicit lattice Boltzmann model for heat conduction with phase change , 2012 .

[25]  S. Chakraborty,et al.  An enthalpy-source based lattice Boltzmann model for conduction dominated phase change of pure substances , 2008 .

[26]  Dieter Wolf-Gladrow,et al.  A lattice Boltzmann equation for diffusion , 1995 .

[27]  W. Miller.  The lattice Boltzmann method: a new tool for numerical simulation of the interaction of growth kinetics and melt flow , 2001 .

[28]  S. Argyropoulos,et al.  Mathematical modelling of solidification and melting: a review , 1996 .

[29]  S. Succi,et al.  Mesoscopic Models of Liquid/Solid Phase Transitions , 1998 .

[30]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[31]  Jure Mencinger,et al.  Numerical simulation of melting in two-dimensional cavity using adaptive grid , 2004 .

[32]  B. Shi,et al.  Discrete lattice effects on the forcing term in the lattice Boltzmann method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.