外掠平板湍流边界层对流传热特性解析预测方法

An Analytical Method of Convective Heat Transfer Prediction in an Incompressible Turbulent Boundary Layer on a Flat Plate

摘要: 外掠平板湍流流动特性是研究湍流传热特性的基本问题之一，具有重要的理论意义和工程应用价值。将不可压缩湍流边界层划分为层流底层和湍流核心区，分别采用三次多项式和幂函数代表两个区域的速度场(温度场)分布，利用积分方法建立了动量方程和能量方程组并获得显式解析解，通过四阶龙格–库塔法得到速度和温度边界层厚度分布。与以往模型对比表明，选择1/5次幂函数在湍流核心区符合得较好。以此为基础同时获得了湍流边界层的对流热传递特性。获得的解析解与Blackwell、Moffat和Kays等人的试验结果，以及普朗特–泰勒二层模型和Schlichting经验公式对比表明具有较好的一致性，证明了理论模型的正确性。

Abstract: The study on the steady turbulent flows over a flat plate is one of the basic problems of convective heat transfer processes, which has the key theoretical significance and wide engineering applica-tions. The incompressible turbulent boundary layer is divided into the laminar sublayer and tur-bulent core zone, respectively, for steady turbulent flows over a flat plate, and both of the velocity and temperature profiles in respective zone are characterized by the cubic polynomial or power function. The momentum and energy equation groups are accordingly established by the integral method, and the analytical solutions of the integro-differential equation groups are obtained by carrying out the fourth-order Runge-Kutta method. It is shown that a 1/5 power function has the best agreement with the previous classical models in the turbulent core zone. The convective heat transfer characteristics and profiles on the wall are also obtained for steady turbulent flows. It is indicated that analytical solutions of the present model are in good agreement with the experi-mental measurements by Blackwell, Moffat & Kays, respectively, as well as Prandtl-Taylor’s tur-bulent two-layer theoretical model and Schlichting’s empirical formula, which validates the present theoretical solutions.