纵掠平板速度和温度边界层湍流转捩区的积分方法

An integral method of the laminar-turbulent transition zone for momentum and thermal boundary layer flows on a flat plate

摘要:

转捩边界层内壁面摩擦和传热特性急剧变化，转捩区的速度和温度分布特性研究具有重要理论意义. 以外掠平板空气为研究对象，将自然转捩边界层沿厚度方向划分为层流底层和准湍流层两部分，采用三次多项式代表层流底层、1/7.5和1/7幂指数函数代表准湍流层速度和温度分布，利用积分方法建立了动量和能量积分方程组，获得了转捩区速度场和温度场的显式表达式，同时确定了壁面摩擦系数和努塞尔数大小，通过四阶龙格-库塔算法获得了动量和热边界层厚度大小，同数值解、Dhawan & Narasimha解(D-N解)和Coupland基准实验结果对比表明，给定条件下理论解精度达到4.8%，证明了理论模型的正确性，对提出的转捩边界层特征参数进行了参数研究，并给出间歇因子对层流底层的影响规律.

Abstract:

It is of very important theoretical significance to study the velocity and temperature distributions for transitional boundary layers with abrupt changes of wall friction and heat transfer. The momentum and thermal boundary layers are divided into the laminar sublayer and quasi-turbulent layer for natural transition flows on a flat plate, and the velocity (or temperature) profiles in the two zones are represented by the cubic polynomial and 1/7.5 (or 1/7) power functions, respectively. An integral method is used to recast the momentum and energy equations into the integro-differential equation groups, and the closed-form analytical solutions of velocity and temperature for transition boundary-layers are obtained by employing the fourth-order Runge-Kutta method. Following the foregoing analytical results, the characteristics of local skin friction factor as well as Nusselt number is also obtained. It is showed that the present analytical solutions can be validated by comparing with the Dhawan and Narasimha’s solution (D-N solution), Coupland’s T3A benchmark experimental and proposed numerical results, respectively, and the accuracy of analytical solution can reach 4.8% for the specified conditions in this paper. The two key parameters affecting the profiles of velocity and temperature of the transition boundary layer are also proposed and analyzed, and it is found that an intermittency factor has a crucial effect on the distributions of velocity and temperature across the laminar sublayer of transition regions.