Study on Goertler and T-S Type Instability of Boundary Layr Flow on Rotating Curved Wall

通过数值求解平均速度为Blasius型的层流边界层在流线曲率离心力和系统旋转科里奥利力作用下的扰动方程，研究了层流边界层在流线曲率离心力和系统旋转科里奥利力作用下的稳定性，得到了以下理论结果。(1)当科氏力作用于凹面时，边界层更不稳定，在壁面曲率较低时产生涡。当科氏力较大时，哥特勒涡即使在凸面上也会出现。(2)在具有逆压梯度的层流边界层中，作用于壁面的科里奥利力促进了戈特勒涡的发生。为了验证计算结果，制作了曲率半径为1000mm、通道截面长径比为8的弯曲通道，安装在直径为3000mm的转台上。空气通过一个二维喷嘴引入，并沿轴方向排出。利用热丝探针在沿通道中心线插入的薄弯曲板上测量了凹凸表面的边界层性质。实验是在雷诺数Re = 40000和80000的通道稳态下进行的。得到了以下结果：离心力对边界层的发展有较大的影响，加速了凹侧边界层向湍流状态的过渡，而对凸侧边界层的湍流运动有抑制作用，延缓了向湍流状态的过渡。

Stability of laminar boundary layer having a mean velocity of Blasius type was studied by solving numerically the perturbation equations when the boundary layer is subject to the centrifugal force due to the streamline curvature and the Coriolis force due to the system rotation and the following results have obtained theoretically.(1) When the Coriolis force acts toward the concave surface, the boundary layer is more unstable and vortices are generated at a lower value of wall curvature. With larger Coriolis force, Goetler vortices would appear even on a convex surface.(2) In a lamianr boundary layer with an adverse pressure gradient occurrence of the Goertler vortices are promoted by the Coriolis force acting toward the wall surface.In order to verify the calculation results, a curved channel whose radius of curvature and aspect ratio of the channel section are equal to 1000mm and 8, respectively, was made and mounted on a rotating table of 3000mm diameter. Air was introduced through an two-dimensional nozzle and exhaused azially theou the axis. The natue of the boundary layer on a convex and concave surfaces were ezmained on a thin durved plate inserted along the centerline of the channel using a hot wire probe.Experiments were carried out in a stationary state of the channel at the Reynolds numbers of Re = 40,000 and 80,000. The following results were obtained.The centrifugal force causes a large effect on the development of the boundary layer and accelerate the transition to the turbuent state in the concave side but the force suppresses the turbulent motion in the boundary layer on the convex side and deleys the transition to the turbulent state.