| Convective heat transfer is a common problem in nature and engineering practice.The study of its mechanism plays an important role in guiding life practice and indus-trial production.The driving force of the flow comes from the buoyancy caused by the density difference.The density difference can be caused by the temperature difference,the solute composition difference,the chemical reaction and so on.In order to study the buoyancy-driven flow,the lattice Boltzmann method is used to study the thermal con-vection.Compared with traditional methods,this method has the advantages of clear physical background,simple boundary processing and good parallelism.The main con-tents and achievements of present work are as follows:1.In this thesis,the accuracy of the coupled lattice BGK model is analyzed and discussed,and the proper equilibrium distribution function with good accuracy is point-ed out.Based on the analysis of the force model,we also give the heat source model which satisfies the conservation of mass,momentum and energy.In addition,a simpler calculation method of viscous dissipative power in lattice Boltzmann method is given.Because it only involves the computation of local data,the equation has good parallelism.Compared with the exact solution,experimental data and other numerical simulations,the accuracy of the proposed model is further verified.2.For the treatment of thermal boundary,we have pointed out the heuristic bound-ary treatment for the dual distribution model.Although there are some errors in treating curved boundary,the heuristic boundary scheme has many advantages,such as high ac-curacy,good stability,and conservative quantity,which make it occupy an important position in boundary treatment.Especially when treating straight boundary,it is the best choice of boundary treatment.In addition,with the popularization of massively parallel computing,heuristic boundary conditions are widely used because they do not destroy the parallelism of lattice Boltzmann methods.Therefore,the heuristic boundary fitted to the coupled lattice BGK model is very necessary in thermal lattice Boltzmann method.In addition,we also discuss the immersed boundary method which can deal with the large deformation and movable boundary very well,and propose a simple form of the thermal immersed boundary-lattice Boltzmann method for the coupled lattice BGK model.3.In the simulation of Rayleigh-Benard convection,we discussed two dimension-al and three dimensional flows respectively.In two-dimensional flow,we focus on the stability of convection and the efficiency of convective heat transfer,and analyze the ef-fect of the width-height ratio of convective units.At the same time,the mixed boundary conditions are introduced.On one hand,the influence of the mixed boundary conditions on the convective heat transfer efficiency of the steady heat convection is discussed.In general,mixed boundary conditions can reduce the convective heat transfer efficiency,except when they can produce "resonance" conditions with convective.On the other hand,we analyze the effect of the mixed boundary on the structure of the solution when thermal convection entering the oscillatory state.The mixed boundary condition makes the thermal convection oscillate earlier and destroy the periodicity of the oscillatory so-lution,so that it turns out to be chaotic.4.In the simulation of three-dimensional Rayleigh-Benard convection,we ana-lyzed and discussed the basic solutions of several kinds of flows,and the stability of the basic solutions.After introducing the viscous dissipative power and the influence of rotating coordinate system,we analyzed the important role of viscous dissipative power in the stability of flow and discussed its influence on the solution structure.In the dis-cussion of the rotating coordinate system,we find that the dimensionless wave number which actually controls the flow stability and convective heat transfer efficiency should be corrected and measured by the equivalent dimensionless wave number proposed in this thesis. |
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