双板驱动矩形空腔STOKES流动的数值模拟

用边界元方法对A =1.5 ,s为任意值时的双板驱动矩形空腔Stokes流动进行数值模拟 .研究了矩形空腔内涡旋生成和发展的规律 .数值计算结果表明 :在s的绝对值不太大的范围内 ,伴随s的增加 ,矩形空腔内涡旋的生成、发展过程可由s的 5个临界点分成 6个阶段 .第一个临界点 ,s =- 8.5 5 ,1个涡旋变成 2个涡旋 .第二个临界点 ,s =- 0 .118,2个涡旋变成 1个涡旋 .第三个临界点 ,s =- 0 .0 0 0 1,1个涡旋变成 3个涡旋 .第四个临界点 ,s =0 .0 5 ,3个涡旋变成 2个涡旋 .第五个临界点 ,s=15 5 ,2个涡旋变成 3个涡旋 .s =- 1时的数值计算结果与理论分析结果以及实验结果比较完全一致 ,令人非常满意 .特别是 ,本文方法适用于不同高宽比和任意速率比的矩形空腔驱动流动问题 ,因此不但具有方法上的理论意义 ,而且数值计算结果还具有工程应用上的实际意义 .

Numerical Simulation of Stokes Flow in a Double-Lid-Driven Cavity

Stokes flow is simulated numerically within a rectangular double-lid-driven cavity by using boundary element method when the cavity aspect ratio A=1.5 and the speed ratio s is a parameter. To obtain the flow regular as s increases, the velocity fields of numerical simulation are used to reveal changes in flow structures as s is varied. The numerical investigations show that the process of vortex arising or merging is divided into 6 phases at 5 critical points as s increases in the scope of |s| moderate. The first critical point is when s=-8.55, and one vortex becomes two. The second critical point is when s=-0.118, and two vortexes became into one. The third critical point is when s=-0.0001, and one vortex becomes three. The fourth critical point is when s=0.05 and three vortexes become two. The fifth critical point is when s=155 and two vortexes become three. When s=-1, the numerical results are in good agreement with previous experimental and analytical ones, showing that the method is very effective and reliable in researching and solving Stokes flows within double-lid-driven as A is varied. The method is of great significance in that it not only suits the arbitrary speed ratio but also fits the cavity aspect ratio as well.