Hybrid LBM-FVM Methods And Simulations Of Natural Convection And Melting Process

Development of CFD involves very wide variation of scales ranging from,nano-/micro-,meso-and macroscales.Molecular dynamics can be applied to solve nano-and microscale problems while lattice Boltzmann method(LBM)and Monte Carlo method are typical mesoscopic scale methods.Finite volume method(FVM)and finite difference method,on the other hand,are suitable for solving the macroscale problems.Multiscale problems exsit in many industry fiels,especially in the high technology areas.Single scale numerical methods are not suitable for multiscale problem regarding applicability and calculation time.This thesis proposed several multiscale methods by combing several single scale methods.Combined LBM-FVM models are proposed for convection and melting problems.Firstly,several natural convection and low Prandtl convection problems are solved to discuss their heat transfer behaviors with the proposed numerical method.Then different types of melting processes are simulated with LBM,FVM and LBM-FVM,respectively.Non-dimensional parameters' effects to the melting problem are discussed based on these results.The following conclusions are reached:1.Combined LBM and FVM methods are proposed for pure fluid flow problem and fluid flow with heat transfer problem.Numerical results agree with reference results well.It indicates the proposed methods are reliable.2.A hybrid FVM and LBM approach is proposed for the fluid flow and heat transfer problem.LBM is applied to obtain the velocity fields and the temperature field is obtained by the FVM.The hybrid method,together with pure LBM and pure SIMPLE,are used to solve the natural convection in a squared cavity.The streamlines and temperature fields obtained by the three methods agree with each other very well for different Rayleigh numbers at 104,105 and 106.The hybrid method also has a good accuracy for the Nusselt number when comparing with the reference and the two pure methods results.Thus,the hybrid LBM-FVM is reliable for the natural convection simulation.This method is designed to take advantages of both LBM and FVM.It is well known that LBM has its advantage in solving complex geometry fluid flow while FVM has high efficiency for conservative laws.So this hybrid method can show its advantage in the case such as heat transfer in the complex geometry fluid flow problems.3.A pure incompressible fluid flow and a pure conduction problem are solved by LBM and MCM respectively.The results indicate LBM and MCM are valid for those problems.Then,a combined LBM-MCM approach is proposed for the fluid flow and heat transfer problem.The LBM is applied to solve the velocity field and the temperature field is obtained by the MCM.This combined method is employed to solve two cases natural convection in a cavity.The streamlines temperature field and Nusselt number obtained from the present LBM-MCM approach agree with that of the benchmark solutions well.Thus,the combined LBM-MCM is reliable for the natural convection simulation.4.Double MRT thermal LBM is applied to simulate the natural convection of fluid with low Prandtl number(310-–210-).The natural convection can reach to steady state or oscillate,which agree with the reference results well.Therefore,the double MRT thermal LBM is valid for simulation of natural convection of the fluid with low Prandtl numbers.With fixed Rayleigh number,lower Prandtl number leads to a weaker convection effect,longer oscillation period and higher oscillation amplitude for the cases reaching oscillatory solutions.At fixed Prandtl number,higher Rayleigh number leads to a more notable convection effect and longer oscillation period.5.LBM with interfacial tracking method is applied to simulate the melting problem.Both conduction and convection controlled melting problems are solved for validation.The numerical results agreed with the analytical results for conduction controlled melting.For convection controlled melting,the agreement between the results from the present method agreed with that in the reference very well.Therefore the proposed numerical method is valid for the melting problem simulation.6.Interfacial tracking method is applied to solve a melting problem in an enclosure with discrete heating at a constant rate.This method takes the advantages of fixed grid and deforming grid methods.The location of melting fronts,melt fraction and surface temperature at the surface of the heat blocks in the numerical results agreed with the experiment results well.So this interfacial method is suitable for this kind of melting problem.With increasing Stefan numbers,the natural convection affects the results more quickly and significantly.When applied to the cooling process,the cooling efficiency is best when the heaters combined together.Meanwhile,the temperatures of the heaters increase with the growing of the thermal resistance between the heaters and PCM.7.A hybrid lattice Boltzmann and finite volume method is developed for the melting problems.The interfacial tracking method is applied to obtain the location of the interface.Natural convection governed melting problems with different Stefan numbers are solved for validation.The numerical results agreed with the experimental results very well.Therefore the proposed numerical method is valid for the melting problem simulation.