幂律流体圆柱绕流的格子波尔兹曼模拟

基于插值补充格子波尔兹曼方法和幂律流体的本构方程，建立了贴体坐标系下适用于幂律流体的格子波尔兹曼模型，模拟了幂律流体的圆柱绕流问题，采用非平衡外推格式处理圆柱表面的速度无滑移边界，利用应力积分法确定曳力系数和升力系数，并与基于标准的格子波尔兹曼方法和有限容积法获得的数值数据进行对比，吻合良好. 进行了网格无关性验证之后，分析了稳态流动时，不同雷诺数下幂律指数对于尾迹长度、分离角、圆柱表面黏度分布、表面压力系数及曳力系数的影响，以及非定常流动中，幂律指数对于流场、曳力系数、升力系数和斯特劳哈尔数的影响. 获得的变化规律与基于其他数值模拟方法得到的结果相一致，充分验证了模型的有效性和正确性. 结果表明:插值补充格子波尔兹曼方法可以用来模拟幂律流体在具有复杂边界流场内的流动问题，通过引入不同的非牛顿流体本构方程，该方法还可以进一步应用于其他类型的非牛顿流体研究中. 

LATTICE BOLTZMANN SIMULATION OF A POWER-LAW FLUID PAST A CIRCULAR CYLINDER

Based on the interpolation-supplemented lattice Boltzmann method and constitutive equation for power-law fluid, a lattice Boltzmann model for power-law fluid in body-fitted coordinates is proposed and applied to simulate steady and unsteady flows of a power-law fluid past a circular cylinder, respectively. The non-equilibrium extrapolation boundary scheme is adopted for the non-slip velocity at the circular cylinder surface. The drag coefficient and lift coefficient are calculated by integrating the total stresses on the boundary of the circular cylinder, respectively, and the results are in good agreement with those obtained by using the conventional lattice Boltzmann method and finite volume method. After performing the grid sensitivity tests, in terms of steady flow, the effects of power-law index on the wake length, separation angle, viscosity distribution over cylinder surface, pressure coefficient and drag coefficient are further analyzed. Moreover, as for unsteady flow, the influences of power-law index on the flow field, drag coefficient, lift coefficient and Strouhal number are investigated. The validation and capability of the model are demonstrated by the good agreement between the simulation results and the ones obtained by other numerical simulation methods. The simulations show that the interpolation-supplemented lattice Boltzmann method can be used to study power-law fluid flow in flow field with complex boundaries, and it can be further applied to study other types of non-Newtonian fluid flow problems by using different constitutive equations.