基于积分方法的外掠平板湍流温度场的解析解

The analytical solutions of temperature field based on an integral method for turbulent thermal boundary layer flows over 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. 本文将外掠平板湍流温度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1/5次幂函数描述温度场的分布规律，用积分方法建立能量方程，利用四阶龙格-库塔算法得到湍流温度场理论解，以此为基础获得了壁面处的对流换热特性，与Blackwell、Moffat和Kays等人的试验结果对比表明本文解析解的正确性，获得的理论解与经典普朗特-泰勒二层理论模型也具有较好的一致性.

Abstract:

A steady turbulent flow over a flat plate is one of the basic problems of convective heat transfer processes, with the key theoretical significance and wide engineering applications. In this paper, the thermal boundary layer for steady turbulent flows over a flat plate is divided into the laminar sublayer and turbulent core zone. The temperature profile in respective zone is described by the cubic polynomial and 1/5 power function, respectively. Accordingly, the energy equations are established for the thermal boundary layer based on the integral method, and the analytical solutions of the integro-differential equation groups are obtained by employing the fourth-order Runge-Kutta method. Compared with the experimental results measured by Blackwell, Moffat and Kays, respectively, it is indicated that the analytical solutions in this paper are correct, and these theoretical solutions also agree well with those obtained from the classical Prandtl-Taylor’s turbulent two-layer theoretical model.