三个物体水动力相互作用的研究

Research on hydrodynamic interactions among three bodies

该文对二维不可压缩无黏流场中三个圆形物体之间的水动力相互作用问题进行了理论上的探讨。根据无耗散系统中的Lagrange方程,导出了这三个物体在水动力相互作用下的动力学方程组。采用Ronge-Kutta数值方法对此六个一阶方程组数值求解,能够计算出这三个物体在水动力相互作用下的运动速度和轨迹。数值结果预测了几种不同排列、速度分布和物体尺寸下的三个圆形物体在流场中运动的轨迹以及它们的实时速度、空间位置关系。发现了一些有兴趣的现象。

Hydrodynamic interactions between three circular cylinders immersed in a two dimensional unbounded and incompressible inviscid liquid are theoretically investigated in this paper. Based on the Lagrange equations in a Hamiltonian system, the dynamical equations of motion of these three bodies in consideration of hydrodynamic interactions are derived, and then the six ordinary differential equations can be numerically integrated using the Runge-Kutta numerical approach to predict the velocities and relative positions of the three bodies. Numerical results present trajectories and instantaneous velocities of these bodies in cases of different initial configurations, initial velocities and size ratios, and some interesting and important phenomena subsequently are identified.