Two-Relaxation-Time Lattice Boltzmann Simulations For Simulating Flow And Heat Transfer In Porous Media

The phenomenon of heat transfer in geotechnical media is widely used in mining engineering,and the geotechnical media is a typical porous medium.its internal structure is extremely complex,and it is far difficult to study the internal flow and heat transfer process than a single medium.The flow and heat transfer problems in geotechnical porous media are multi-scale and nonlinear.Numerical simulation is one of the crucial means to study the flow and heat transfer of geotechnical porous media.Lattice Boltzmann method(LBM)exhibits several distinctive advantages over the continuum-based numerical methods,such as local nature of operations,easy implementation of complex boundary conditions with elementary mechanical rules,inherently parallel nature,and avoiding solving the Poisson equation for pressure field of incompressible flows.Owing to its distinctive advantages,the LB method can provide an efficient and reliable method to study the flow and heat transfer phenomenon in geotechnical porous media.Currently,the theoretical system for the REV-scale lattice Boltzmann method for single-phase flow of geotechnical media is still incomplete,and the study of thermal convection at the REV scale is still in the exploration stage.The REV scale lattice Boltzmann model of thermal flow in porous media are mostly based on the BGK model or the MRT model,which have poor numerical stability,few adjustable parameters or complex operation.It is very necessary to develop the REV scale lattice Boltzmann model with good stability and high calculation accuracy.The two-relaxation-time(TRT)lattice Boltzmann model has well numerical stability and is simpler than the multiple-relaxation-time(MRT)lattice Boltzmann model.Therefore,in order to enrich the theoretical system of single-phase heat transfer at the REV scale and develop the lattice Boltzmann model for large-scale porous medium heat flow in engineering calculation,the REV-scale two-relaxation-time(TRT)lattice Boltzmann model of convection and heat transfer of geotechnical porous medium is deeply studied in this paper.The main work of this article as follows:(1)The second chapter introduces the basic theoretical knowledge and fundamental models of the lattice Boltzmann method.This paper summarizes the basic ideas,history of lattice Boltzmann method and the boundary processing format used in numerical simulation,focusing on the specific form of frequently-used discrete velocity model,incompressible lattice Boltzmann model and incompressible thermal lattice Boltzmann model.(2)The third chapter develops the TRT-LB model of incompressible flow and heat transfer phenomenon,which divides the external force terms into symmetric and asymmetric parts according to the idea of the double relaxation ideas.The characteristics of the flow heat transfer are studied by model experiment,and the influence law of the flow heat transfer is calculated and analyzed by the numerical simulation method.Through the comparisons of the temperature contour diagram and its streamline plot,focusing on the analysis of the quantitative data,the numerical simulation results prove that the model has a high ability to deal with the flow heat transfer problem.(3)In the framework of the dual distribution function,based on the core of the TRT model.And considering the heat flow case with an internal heat source based on the chapter three.Consequently the fourth chapter constructs a thermal two-relaxation-time lattice Boltzmann model of the REV scale.The temperature and velocity field evolution equations in the model are restored to the macroscopic flow equation using the Chapman-Enskog analysis.Through three numerical examples of mixed convection of parallel plate channel,natural convection in the cavity and porous cavity thermal convection with heat source,the results prove that the present model is stable and efficient.And comparing the results with the relevant analytical or numerical solutions obtained in previous studies,the numerical results of the TRT-LB model agree well with the analytical solution,as well as the convergence speed of the model has the second order accuracy.In addition,the accuracy of the simulation results can be found from the flow lines and isotherms as well as the velocity and temperature distribution maps of the horizontal surface.Through quantitative analysis,the average Nusselt number of the thermal wall surface and the maximum dimensionless temperature under different conditions can further verify the reliability of the model.