用格子Boltzmann模型模拟垂直平板间的热对流

Simulation of thermal convection in a vertical slot using the lattice Boltzmann model

引入一个新的能量分布函数 ,利用该能量分布函数与粒子速度分布函数耦合来求解一个热流场 .因而 ,这一能量分布函数与粒子速度分布函数和Boltzmann方程构成了一个新的格子Boltzmann模型 .这一模型满足质量、动量和能量守恒的准则 .用该模型对垂直平板间的狭缝热对流进行了数值模拟 ,数值结果表明 ,在Prandtl数为 1,Grashof数在 1 3× 10 2 — 1× 10 6 之间时 ,流场将出现多个旋涡结构的流型 .

A new distribution function of energy is introduced and coupled with a velocity distribution function of particle and applied to study a hot fluid field. Thus, a new lattice Boltzmann model is constructed by both energy and velocity distribution functions and Boltzmann equation in the BGK form, which satisfies the conservation criteria of mass, momentum and energy. Thermal convection in a vertical slot is calculated by using the present lattice Boltzmann model. The numerical results have shown that multi-vortexes in the flow field will take place for Prandtl number Pr=1 and Grashof number 1.3×10 2<Gr<1×10 6. The numerical results are in good agreement with Lee's studies.