矩形腔内Stokes流动混合过程追踪模拟

TRACE SIMULATION OF STOKES FLOW IN RECTANGULAR CAVITIES

基于涡量-速度方法建立了矩形腔上盖拖动的数学模型,采用交错网格,对腔内Stokes流动进行了有限体积数值模拟研究,得到了不同长高比的矩形腔内速度场及流函数分布.发现随着长高比的增大,中垂线的水平速度分布逐渐向无限大长高比得到解析解抛物线分布靠近.采用4阶Runge-Kutta方法对示踪剂混合过程进行前锋追踪模拟,得到了不同时刻示踪剂的混合图像.结果表明,示踪剂界面随时间呈线性增长,而且长高比越大,示踪剂界面的增长越快.

Based on the vortex-velocity method, the mathematical model of the upper lid-driven rectangular cavities is estabilished. A staggered grid arrangement is used in which the dependent variables are located at different mesh points in the computational domain. The finite volume method is adopted to simulate the Stokes flow in such cavities. The distributions of the velocities and streamlines are obtained for different aspect ratios. It is found that the velocity distribution along the vertical centerline is increasingly approaching the parabolic shape with the increase of the aspect ratio, which is that of the analytical solution drived from the hypothsis of infinite aspect ratio.Adopting fourth order Runge-Kutta scheme, the front trace simulation is carried out during the course of mixing and the mixing patterns of tracers for different time are captured with result that the growth of interface increases linearly with time. In addtioton, The larger the aspect ratio is, the faster the growth of interface is.