Numerical Methods Of Flow And Heat Transfer In Complex Geometries And Porous Media Based On Lattice Boltzmann Method

The flow and heat transfer in complex geometries and porous media can be encountered in nature and industrial applications and its related studies play important role in mechanical engineering,energy engineering and chemical engineering,etc.Due to the complicated interactions between heat,fluid phase and solid phase,the theoretical and experimental methods are difficult to obtain the flow and heat transfer characteristics.However,as an alternative method,the numerical simulation method gradually becomes a widely accepted approach by its particular advantage.In recent years,lattice Boltzmann method(LBM)gets the favor of the CFD community,and is very suitable for studying the flow and heat transfer in complex geometries and porous media.Althouth some results of research on these flow and heat transfer using LBM have been achieved,there are still many problems needed to be solved.The main contents of this thesis are as follows:One is LB models for flow and heat transfer in complex geometries:Firstly,we propose a modified momentum exchange method based on volumetric lattice Boltzmann model.The idea of the improvement is to remove the restriction that the boundary points must be set as the midpoints of the grid lines or the intersection of the grid lines with the solid boundaries.In computational procedure,the geometric conservation law is satisfied.As a result,the nonphysical oscillatory of the force acts on the solid particle is avoided.Moreover,a generalized explicit time marching scheme is introduced to resolve the motion of particle in the problems with the ratio of particle density/fluid density is close to or less than 1.Secondly,we propose an iterative immersed boundary-lattice Boltzmann mothod for flow and heat transfer problems with complex boundaries.Through selecting the appropriate relaxation parameter and number of iterations,the present method can accurately satisfy the Dirichlet velocity and temperature boundary conditions.Thirdly,based on the interfacial jump conditions and interpolation formulas in the non-smooth domain,we propose a novel immersed boundary-lattice Boltzmann mothod to treat the Neumann temperature boundary condition.We also simulate the natural convection in a concentric horizontal annulus with a constant heat flux wall using this method,and find a new steady solution.Fourthly,a unified governing equation for temperature in both fluid and solid regions is derived.Through introducing a source term,we prove the conjugate interface conditions can be satisfied automatically.Based on the unified governing equation,we propose a full Eulerian model for conjugate heat transfer.The other is LB models for flow and heat transfer in porous media at the representative-elementary volume scale:Firstly,a multiple-relaxation-time lattice Boltzmann model for the flow and heat transfer in a hydrodynamically and thermally anisotropic porous medium is proposed.By selecting the appropriate equilibrium distributions,relaxation matrix and discrete force/heat source terms,the present lattice Boltzmann model can recover the correct Darcy-Brinkman-Forchheimer and energy equations with anisotropic permeability and thermal conductivity through the Chapman-Enskog procedure.Especially,natural convection in a cavity with two anisotropic porous layers is investigated.The numerical results indicates that,the use of anisotropic porous layer with some optimal parameters can produce higher rate of heat transfer compared with the isotropic porous layer.Secondely,based on the Darcy-Brinkman-Forchheimer equation,a finite volume method with lattice Boltzmann flux scheme is proposed for incompressible porous media flow.The fluxes across the cell interface are calculated by reconstructing the local solutions of the generalized lattice Boltzmann method for porous media flow.The time-scaled midpoint integration rule is adopted to discrete the governing equation,which relaxes the stability limit on the time step.