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

DOI：

 作者 单位 邮编 李勇 华东理工大学机械与动力工程学院 200237 李汉清 华东理工大学机械与动力工程学院 何录武 华东理工大学机械与动力工程学院

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,通过比较发现,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 viscoelastic fluid around a cylinder and an elliptical cylinder. The single relaxation model and advection–diffusion model are used to solve the motion equation 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 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 flow field distribution and drag coefficient under different material parameters are given. Through comparison, it is found that it is consistent with the macro numerical simulation results. The model is extended to the flow around an ellipse, and the effects of 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 major axis to minor axis and Weissenberg number, and the ratio of major axis to minor axis has a great influence on the convergence of iteration.
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