The momentum integral-based method developed by Mehdi and White (Exp Fluids 50(1):43–51. https://doi.org/10.1007/s00348-010-0893-1 , 2011) for determining wall skin friction in turbulent wall-bounded flow is evaluated in separated flows in which independent estimates of wall skin friction are known. Owing to flow complexities, a direct measurement of the wall skin friction in separated flow is experimentally challenging. In this pursuit, the momentum integral-based method is particularly attractive as the method is mathematically exact and determination of the wall skin friction only requires measurement of the wall-normal profile of mean velocity and Reynolds shear stress. The present analysis uses existing experimental particle image velocimetry and direct numerical simulation data of flow over a backward-facing step as well as DNS over a smooth hump to demonstrate that the method is viable. The method is also shown to be viable in estimating the wall skin friction in flows over non-flat geometries.

中文翻译：

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评估分离流动中壁面摩擦的动量积分法

Mehdi 和 White 开发的基于动量积分的方法（Exp Fluids 50(1):43–51. https://doi.org/10.1007/s00348-010-0893-1, 2011）用于确定湍流中的壁面摩擦壁面流动在分离的流动中进行评估，其中壁面摩擦的独立估计是已知的。由于流动的复杂性，直接测量分离流动中的壁面摩擦在实验上具有挑战性。在这种追求中，基于动量积分的方法特别有吸引力，因为该方法在数学上是精确的，壁面摩擦的确定只需要测量平均速度和雷诺剪切应力的壁面法向剖面。本分析使用现有的实验粒子图像测速法和后向台阶上的流动直接数值模拟数据以及平滑驼峰上的 DNS 来证明该方法是可行的。该方法还被证明在估计非平坦几何体上流动的壁面摩擦方面是可行的。