有吹吸速度的外掠多孔平板湍流边界层的积分方法

The integral method for turbulent momentum boundary layers on a porous plate with uniform blowing and suction

摘要:

具有吹吸速度的外掠多孔平板湍流流动特性是研究发散冷却和气膜冷却的基础，具有重要的理论研究意义. 将湍流速度边界层划分为层流底层和湍流核心区，采用三次多项式和1/5次幂函数分别代表流体沿两个区域厚度方向的速度分布，通过积分方法建立了动量方程，利用四阶龙格-库塔法求解得到可渗透壁面湍流边界层速度场的理论解析解，同时获得了壁面摩擦系数. 对比表明，解析解与Whitten、Blackwell试验结果以及Kays的经验公式符合得较为满意，证明了所提出的湍流理论模型的正确性.

Abstract:

The turbulent boundary layer with injection and suction is of fundamental interest for the analytical research in the field of transpiration or film cooling, which has an important theoretical significance. The momentum boundary layer is divided into the viscous sublayer and turbulent core zone for steady turbulent flows on a porous flat plate, and the velocity distributions in the two zones are approximated by the cubic polynomial and 1/5 power functions, respectively. An integral method is used to recast the momentum equations into the integro-differential equation groups, and the analytical solutions of velocity boundary layers through the permeable surfaces are obtained by employing the fourth-order Runge-Kutta method. Following the foregoing analytical results, the profile of skin friction factor on the wall is also obtained. It is showed that the proposed analytical solutions have a satisfactory agreement with the existing experimental measurements carried out respectively by Whitten and Blackwell, and also with the empirical formula of Kays.