改进近场动力学方法在圆柱绕流问题中的应用

Application of an Improved Bond-based Peridynamic Method to Analysis of Flow around a Cylinder

在传统近场动力学键理论方法的基础上,考虑粒子邻域范围内粒子间的法向键力作用,并引入了切向键力作用,提出一种改进的近场动力学键理论方法。该方法假设速度场在粒子邻域范围内线性变化,根据均质不可压缩牛顿流体的运动特性,推导出基于拉格朗日描述的近场动力学形式的流体运动控制方程,分别考虑法向键力与压力、切向键力与黏性力的关系,克服了传统近场动力学键理论方法难以描述流体黏性力的局限性。采用Fortran语言编程,利用改进的近场动力学键理论方法模拟计算了低雷诺数时无限域圆柱绕流问题算例,并与有限体积法的模拟结果进行对比,分析了在x、y方向速度场的分布、速度最大值的误差。结果表明:本文提出的改进近场动力学键理论方法与有限体积法的模拟结果在x、y方向速度场的分布、变化趋势基本一致,且终止时刻速度最大值误差分别为6.4%、22.6%,从而验证了该方法的可行性和有效性,可为近场动力学方法在流体问题领域中的应用提供参考。

Based on the traditional peridynamics bond based theory,this paper proposes an improved bond based peridynamic method which considers the normal bonding force and the tangential bonding force between each pair of particles in the neighbor horizon of the basic particle. The improved bond based peridy namic method derives the equation of motion method described by Lagrange for homogeneous incompressible Newtonian fluid by assuming that the velocity field changes linearly in the neighbor horizon. The derivation process of this method considers the relation between the normal bonding force and pressure and the relation between the tangential bonding force and viscous force in peridynamics respectively. Therefore this method is able to overcome the limitation of fluid viscous force described by the traditional peridynamic bond based theory. The numerical example uses Fortran to program, and realizes numerical simulation of fluid flowing around a cylinder in infinite field at a low Reynolds number,and compares with the results of the finite volume method. The results show that the fluid velocity results of the improved bond-based peridynamic method are basically consistent with those of Fluent and the errors of the maximum velocity are 6.40% and 22.6% respectively, which indicates that the improved bond based peridynamic method pro posed in the paper is feasible and effective to handle the problem for corresponding fluid problems and the research provides reference for the application of peridynamic method in the field of fluid problems.