基于格子Boltzmann方法的粘弹性流体圆柱绕流分析

Analysis of viscoelastic fluid flow around a cylinder based on lattice Boltzmann method

将光滑界面法引入到格子Boltzmann方法中分析粘弹性流体绕流问题,分别采用单松弛模型和对流扩散模型求解运动方程和Oldroyd-B本构方程,针对圆形和椭圆内部边界条件,给出连续界面插值函数,在此基础上,运用光滑界面法将内部边界转换为作用力项施加到演化方程中。首先分析圆柱绕流问题,给出不同材料参数情况下的流场分布和阻力系数计算结果,比较发现与宏观数值模拟结果相吻合。将模型拓展到绕椭圆流动中,分析椭圆形状和材料参数对粘弹性流体绕柱流的影响,发现随着椭圆长轴与短轴比值的增加和维森伯格数的增加,阻力系数逐渐下降,并且长短轴比对迭代收敛有较大影响。

The smooth profile method is introduced into the lattice Boltzmann method to analyze the flow of a viscoelastic fluid around a circular cylinder and an elliptical cylinder.The single relaxation model and advection-diffusion model are used to solve the equation of motion and Oldroyd-B constitutive equation respectively.For circular and elliptical internal boundary conditions,the continuous interface interpolation function is given.On this basis,the internal boundary is transformed into a force term and applied to the evolution equation by using the smooth profile method.Firstly,the flow around the cylinder is analyzed,and the calculation results of the flow field and drag coefficient under different material parameters are given,which are found to be consistent with the macro numerical simulation results,through comparison.The model is extended to the flow around an elliptical cylinder,and the effects of the ellipse shape and viscoelastic material parameters on the flow are analyzed.It is found that the drag coefficient decreases with the increase of the ratio of the major axis to the minor axis of the cylinder and Weissenberg number,and the ratio of the major axis to the minor axis has a great influence on the convergence of iterations.