浸没边界-简化热格子Boltzmann方法研究及其应用

针对流固耦合传热问题,本文提出了一种基于浸没边界-简化热格子玻尔兹曼方法(immersed boundary method-simplified thermal lattice Boltzmann method,IB-STLBM)的耦合模型.不同于传统的格子玻尔兹曼方法使用分布函数演化流场和温度场,简化热格子玻尔兹曼方法(simplified thermal lattice Boltzmann method,STLBM)的演化过程不需要依赖分布函数,只涉及平衡态分布函数和非平衡态分布函数,能够直接演化宏观量,极大减小了计算过程中所占用的虚拟内存,简化了边界条件的实现方式,同时具有较高的稳定性.传统的浸没边界法对流场的计算采用欧拉网格,对固体边界采用拉格朗日网格,认为固体边界是对流场产生某种体积力.在应用浸没边界法时,汲取介观的思想,把固体的介入看作是对流场的干扰,打破了固体附近流体介观微团颗粒原始的平衡状态,这种干扰可以看作是在耦合边界上产生的一个非平衡项,可用非平衡态分布函数来表示.基于此,在模型中浸没边界法与简化热格子玻尔兹曼方法更紧密联系在一起,更大程度发挥二者的优点,整个计算过程更加简单直观,符合物理特性.通过对热圆柱绕流和内含热颗粒的封闭方腔自然对流问题的模拟以及对其结果的分析,验证了该算法在求解流固耦合传热问题的有效性和可行性. 

IMMERSED BOUNDARY-SIMPLIFIED THERMAL LATTICE BOLTZMANN METHOD FOR FLUID-STRUCTURE INTERACTION PROBLEM WITH HEAT TRANSFER AND ITS APPLICATION

An Immersed boundary-simplified thermal lattice Boltzmann method(IB-STLBM) for fluid-structure interaction problem with heat transfer is developed in this work. In the IB-STLBM, an effective simplified thermal lattice Boltzmann method without the evolution of distribution is used for the intermediate flow field. Different from the stander thermal lattice Boltzmann method, STLBM directly updates the macroscopic variables instead of the distribution functions, which offers several distinct benefits：lower cost in virtual memories, simpler implementation of physical boundary condition and higher numerical stability. In addition, from the mesoscopic view, the existence of solid boundary in the field is considered as an interference of system, which breaks the original equilibrium state of fluid particle, and a non-equilibrium state occurs on the fluid-structure interaction physics boundary. On this basis, in the present IB-STLBM, fluid-structural interaction duo to Immersed boundary appearance in the fluid can be expressed by the non-equilibrium distribution function, which is calculated by the popular non-equilibrium bounce-back boundary condition of the LBM. Hence, the solution procedure of present IB-STLBM can satisfy the non-slip boundary by a simpler way. Numerical experiments for the forced convection over a stationary heated circular cylinder and natural convection in a square cavity with a circle particle are presented to verify the stability, the capability and the flexibility of IB-STLBM for fluid-structure interaction problem with heat transfer. In the case of a stationary heated circular cylinder, quantitative and qualitative comparisons are carried out with previous study. The results of the drag coefficient and the avenge Nusselt numbers on the cylinder are in accordance with the results of previous study. From the case of natural convection in a square cavity with a circle particle, some interesting phenomena can be found. First, the temperature field is clearly stirred by the suspended particle. Second, the temporal trajectories of the particle exhibited regular changes. Third, the particle enhances heat transfer and the average Nusselt numbers periodically oscillate with time.