AN INTEGRAL METHOD FOR ESTIMATING WALL FRICTION VELOCITY IN TURBULENT BOUNDARY LAYERS

Turbulent boundary layer (TBL) flows widely exist in nature, as well as in aerospace and environmental engineering applications. Wall friction velocity serves as an important parameter for both theoretical analysis and practical applications in TBL, and its accurate prediction holds significant value from scientific and engineering perspectives. Based on an integral analysis of the Reynolds-averaged momentum equation, an integral method is proposed to determine the wall friction velocity in TBL using the wall-normal profiles of the mean velocity and Reynolds shear stress. The method only requires the mean profiles in the outer layer of the TBL at a single streamwise location, which significantly reduces the dependence on the near-wall data. A number of direct numerical simulation and experimental data available in the literature are used to evaluate the performance of the proposed method. The wall friction velocities obtained using the present method agree with those published values, typically within \pm 3\text% . In addition, it is found that the lower and upper integration limits, as well as the boundary layer thickness have insignificant effects on the accuracy of the method. We also compared the present approach with other integral methods in the literature, demonstrating that the predictive accuracy of wall friction velocity in TBL is highly dependent on the total shear stress model used. In summary, the proposed method shows high accuracy and good robustness in both the incompressible smooth- and rough-wall TBL under zero pressure gradient. The present study provides theoretical guidance for the accurate prediction and control of turbulent wall friction drag in the major engineering applications, such as aerospace, and energy and power systems.