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

通过数值求解摄动方程，研究了平均速度为Blasius型的层流边界层在流线曲率离心力和系统旋转引起的科里奥利力作用下的稳定性，得到了以下理论结果：(1)当科里奥利力作用于凹面时，边界层更不稳定，在较低的壁曲率处产生涡旋。当科里奥利力较大时，即使在凸面上也会出现Goetler涡。(2)在压力梯度相反的拉米亚尔边界层中，科里奥利力对壁面的作用促进了Goertler涡的产生。为了验证计算结果，制作了一条通道截面曲率半径和长宽比分别为1000 mm和8的弯曲通道，并安装在直径为3000 mm的转台上。空气通过一个二维喷嘴被引入，并沿轴向无氮排放。在雷诺数Re分别为40,000和80,000的定常流道中，用热线探头测量了凹凸表面上边界层的性质。结果表明，离心力对边界层的发展有较大影响，加速了凹面边界层向浑浊状态的转变，但对凸面边界层的湍流运动有抑制作用，阻碍了边界层向湍流状态的转变。

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.