基于积分法的粗糙壁面湍流边界层发展预测

壁面粗糙度对湍流的影响研究是流体动力学的热点问题。利用边界层积分法对零压力梯度下棱锥形粗糙壁面湍流边界层的发展进行预测分析。首先，以2个几何统计参数对棱锥形的粗糙形态进行描述，通过对试验数据的拟合分析，确定粗糙度函数的具体形式；然后，利用动量积分方程和壁面律求解出粗糙壁面湍流边界层厚度和局部摩擦系数沿流向的变化情况。计算结果与试验数据吻合较好，表明采用积分法预测粗糙壁面湍流边界层的发展精度较高，适于工程应用。

Prediction of the Development of Turbulent Boundary Layers on Rough Walls Based on the Integration Method

The effect of wall roughness on the turbulent flow has long been an important research topic inthe field of fluid dynamics. The development of turbulent boundary layers on rough walls with pyramidroughness elements in zero pressure gradient is conducted in this paper, using the integration method ofboundary layers. Firstly, the pyramid roughness texture is characterized with two geometric statistical pa-rameters, and the specific form of the roughness function is next determined by fitting the experimental da-ta. Then, the streamwise development of the boundary layer thickness and local friction factor are solvedbased on the momentum integral equation and the wall law. The calculation is observed to be in reasonableagreement with the experimental data, which validates the accuracy and simplicity of the integration meth-od in predicting the development of turbulent boundary layers on rough walls.