Lattice Boltzmann Method And Simulation Forsolid-Liquid Phase Change

In the solid-liquid phase change process,the specific volume changes slightly and the temperature is almost constant.Besides,a large amount of latent heat is absorbed or released.Owing to these characteristics,solid-liquid phase change has wide and important applications both in daily life and engineering technology.Study on phase change problem is always a challenging task,because of the dynamic evolution and nonlinear nature of the solid-liquid phase interface,as well as the complexity of the flow and heat transfer process.For the experiment study on a complex phase change problem,it may be difficult to reproduce the specific application and to reveal the detailed characteristics of the process.Thus,the numerical study is required.As compared with the conventional computational fluid dynamics method,the lattice Boltzmann method,which has mesoscopic background,has distinct advantages in grid generation and boundary treatment for complex geometry,consideration of many factors,massive parallel computing,etc.,so the lattice Boltzmann method is very suitable for the numerical study on a complex phase change problem.However,as a relatively new mesoscopic numerical technique,there are still many important issues that should be solved for the simulation of solid-liquid phase change by lattice Boltzmann method.Therefore,through theoretical analysis and numerical simulation,lattice Boltzmann method and accurate and efficient simulation for solid-liquid phase change is systematically studied in this thesis.The detailed research contents and main results are summarized as follows.1.The framework of the energy conservation equation for solid-liquid phase change is a convection-diffusion equation.Theoretical analysis on the lattice Boltzmann model for convection-diffusion equation is performed.It is found that the existing deviation term is induced by the influence of convection term,which is recovered at first-order,on diffusion term,which is recovered at second-order.By using the multiple-relaxation-time collision scheme and modifying the relaxation matrix,such influence is eliminated.Furthermore,by properly choosing the corresponding equilibrium moment function,a new multiplerelaxation-time lattice Boltzmann model for convection-diffusion equation is proposed.Through the Chapman-Enskog analysis,the present model can correctly recover the macroscopic convection-diffusion equation with no deviation term.2.A total enthalpy-based lattice Boltzmann method for solid-liquid phase change is developed.To precisely realize the nonslip velocity condition in solid phase,a volumetric lattice Boltzmann scheme is proposed,which can completely avoid the nonphysical flow.By combining the latent enthalpy with the sensible enthalpy and then adopting the total enthalpy distribution function,a total enthalpy-based lattice Boltzmann model is proposed.Both the enthalpy iteration procedure and linear equation system solving are avoided.By devising the equilibrium distribution function for total enthalpy,the thermal conductivity and specific heat in the model are decoupled,and thus the differences in thermophysical properties can be correctly handled.Moreover,the numerical diffusion across phase interface is revealed and found to be induced by the phase change process.By exploiting the multiple-relaxation-time collision scheme and setting the “magic” parameter one fourth,such numerical diffusion can be reduced dramatically.3.An immersed boundary-thermal lattice Boltzmann method for solid-liquid phase change is developed,in which the phase interface is represented as a sharp interface and the immersed boundary method is employed to treat the velocity and temperature interface conditions.Using this method,the motion of solid phase in phase change process can be directly simulated.From the viewpoint of physical reality,a local formula is proposed to compute the moving velocity of phase interface induced by phase change,which can avoid the computations of temperature gradients on both sides of the phase interface.As the phase interface evolves with time,the adaptive treatment of Lagrangian points and the identification of phase of Eulerian points are considered,which can guarantee the explicit tracking of phase interface.As an application,melting in a circular cylinder heated by the circular wall is directly simulated by the present method.It is found that the motion of solid phase can obviously accelerate the melting process.4.An adaptive mesh refinement approach for thermal lattice Boltzmann method is developed,which can be used to improve the accuracy and efficiency of the simulation of flow and heat transfer problem by lattice Boltzmann method.With the introduction of an indicator function,a grid generation strategy for adaptive multiblock grids is devised,which can guarantee the special interface structure between adjacent blocks and ensure that adjacent blocks only differ by one block level.From the viewpoint of the grid independence of the Chapman-Enskog expansion equation for multiple-relaxation-time lattice Boltzmann equation,the information exchange equations between coarse and fine blocks are directly deduced in the moment space.Based on this adaptive mesh refinement approach and the present total enthalpy-based lattice Boltzmann method for solid-liquid phase change,the melting processes in a square cavity with large Rayleigh numbers are successfully simulated with high accuracy and efficiency.5.By the lattice Boltzmann methods developed in the present thesis,two kinds of complex phase change problems are investigated.(1)On the basis of the Boussinesq approximation for natural convection,an approximation method is proposed to treat the difference in density between solid and liquid phases.Then a new dimensionless parameter,the Archimedes number,is introduced to characterize the difference in density.By using the present immersed boundary-thermal lattice Boltzmann method,the melting problem in a circular cylinder with the consideration of solid phase motion is directly simulated.It is found that the melting process can be accelerated either by increasing the Rayleigh number or the Archimedes number.However,the mechanisms of the acceleration are different and may coordinate or compete with each other.(2)The total enthalpy-based lattice Boltzmann method for solid-liquid phase change is extended to three-dimensional situation.Meanwhile,three-dimensional porous medium with foam structure is numerically constructed.And then,pore-scale numerical simulation of solid-liquid phase change problem in complex porous medium is carried out by using the present total enthalpy-based lattice Boltzmann method.The influences on the melting process of the thermal conductivity,porosity and pore density of the porous medium are investigated and revealed.