基于SPH方法的幂律流体突缩型管路流动过程仿真

摘要

The flowing characteristics of the power-law fluid in the sharply contractive pipe were simulated with the smoothed particle hydrodynamics （SPH） method. The control equations of SPH fluid dynamics were deduced, which imposed boundary conditions by penalty function, avoided so-called stretching instability by artificial stress and regulated the particle distribution with XSPH method. The SPH solving formula of power-law model is proposed and the algorithms of shear rate and viscosity term are presented. The formula was verified by a calculation example of Poiseuille flow. The flowing characteristics of both power-law fluid and Newtonian fluid in sharply contractive pipe were obtained. The flowing characteristics of the power-law fluid are analyzed and discussed.%应用光滑粒子流体动力学（SPH）方法进行了幂律型流体的突缩型管路流动过程仿真。推导了SPH形式的流体动力学控制方程，应用罚方法施加边界条件，应用人工应力消除拉伸不稳定现象，应用XSPH方法规范粒子秩序。提出了幂律型本构关系的SPH求解方法，推导了剪切速率及粘性项的计算公式。应用Poiseuille流算例对本文的幂律型本构求解方法进行了验证，获取了幂律型流体在突缩管中的流动特性，并与水的流动特性进行了对比分析。讨论了流动特性的成因。