明渠柱体上游马蹄涡的运动学特征研究

马蹄涡是水下柱体结构周围床面冲刷的主要动力。为掌握马蹄涡的运动学特征,引入了基于旋转强度的马蹄涡识别方法,提出了基于椭圆涡拟合的马蹄涡特征提取方法,其中,椭圆涡由Oseen涡和倾斜单向剪切流叠加而成。基于上述方法,通过开展明渠圆柱绕流PIV实验,对柱体上游对称面时均流场中马蹄涡的运动学特征进行了研究。结果表明,在柱体雷诺数大于104的紊流柱体绕流中,马蹄涡上游的流动分离点随柱体雷诺数的增大而缓慢向下游移动,但马蹄涡的位置保持不变,涡中心距柱体中轴约0.67D(D为柱体直径或宽度),距床面约0.06D;随着柱体雷诺数的增大,马蹄涡的半径不变而强度增加,使得马蹄涡作用于床面的剪切应力增大。研究结果建立了客观提取马蹄涡运动学特征的数学方法,得到了流动分离点、马蹄涡位置等运动学特征随水流条件的变化规律,揭示了明渠柱体绕流与其它流动中柱体绕流的差异,初步构建了马蹄涡的动力作用概念模型。

Kinematic characteristics of horseshoe vortex upstream of circular cylinders in open channel flow

To investigate the kinematic characteristics of horseshoe vortex upstream of cylinders, the swirling strength method is introduced to identify horseshoe vortices, and a method of fitting the local velocity field with an elliptic vortex are proposed to characterize these vortices. The elliptic vortex is constructed by overlapping the Oseen vortex with an inclined unidirectional shear flow. The proposed methods were used to investigate the time-averaged horseshoe vortex upstream of a circular cylinder in open channel flow. The time averaged horseshoe vortex is captured by averaging instantaneous velocity fields measured with PIV. The results show that, in flows with cylinder Reynolds number larger than 10⁴, the position of horseshoe vortex is unchanged while the upstream separation point moves downstream slowly. The distances from the vortex center to the cylinder axis and the bed are 0.67D and 0.06D, respectively, with D being the cylinder diameter. Comparing with those in open channel flows,the horseshoe vortex and separation point in turbulent boundary layers are further upstream. With the increasing of cylinder Reynolds number, the horseshoe vortex strengthens itself but keeps the size unchanged, results in increasing shear stress on the bed. The dependence of vortex-induced shear stress with the flow strength indicates that it is physically reasonable to formulate equations for local scour based on the kinematic characteristics of horseshoe vortex.