基于涡量-流函数法的二维顶板驱动方腔内涡旋分析

Generation and Development of Vortex in Two-dimensional Lid-driven Square Cavity

本文采用MATLAB编程,利用涡量-流函数法求解二维顶板驱动方腔内流动,对比分析了不同雷诺数时,二维顶板驱动方腔内涡旋的变化情况.采用有限差分法对二维顶板驱动方腔内不可压黏性流动的连续性方程和动量方程进行离散求解计算,得到了方腔内的流函数和涡量分布,以此分析方腔内涡旋随雷诺数的变化.结果表明:雷诺数对二维顶板驱动方腔内流函数分布影响较大.随着雷诺数的增大,方腔内流动的复杂度增加,表现为次级涡旋数量增加,且各个次级涡旋的涡心位置和涡面面积也呈现各异的规律变化.主涡涡面变化较小,但涡心随着雷诺数的增大而向方腔中心移动;由于二维方腔流动为带奇性流动,主涡涡心最终均未位于方腔中心.

Based on vortex stream function method,this article compares and analyzes the generation and development of vortex in two-dimensional lid-driven square cavity with different reynolds numbers. The continuity equation and momentum equation of incompressible viscous flow in a two-dimensional lid-driven square cavity are discretized by the finite difference method,and the flow function and vorticity distribution in the two-dimensional lid-driven square cavity are obtained. Results show that the reynolds number has a great influence on the flow function distribution in a two-dimensional lid-driven square cavity. Along with the increase of reynolds number,the complexity of the square cavity flow increases,the number of the secondary vortex increase,and the position of the secondary vortex core and the vortex surface area leads to the different regular changes. The main vortex change is small,but the vortex core along with the increase of reynolds number move to the cavity center. But the main vortex centers are not located in the center of the square cavity because the flow in the square cavity is singular.