A robust post-processing method to determine skin friction in turbulent boundary layers from the velocity profile

Abstract

The present paper describes a method to extrapolate the mean wall shear stress, $$\tau _{wall}$$ , and the accurate relative position of a velocity probe with respect to the wall, $$\Delta y$$ , from an experimentally measured mean velocity profile in a turbulent boundary layer. Validation is made between experimental and direct numerical simulation data of turbulent boundary layer flows with independent measurement of the shear stress. The set of parameters which minimize the residual error with respect to the canonical description of the boundary layer profile is taken as the solution. Several methods are compared, testing different descriptions of the canonical mean velocity profile (with and without overshoot over the logarithmic law) and different definitions of the residual function of the optimization. The von Karman constant is used as a parameter of the fitting process in order to avoid any hypothesis regarding its value that may be affected by different initial or boundary conditions of the flow. Results show that the best method provides an accuracy of $$\Delta u_\tau \le 0.6\,\%$$ for the estimation of the friction velocity and $$\Delta y^+\le 0.3$$ for the position of the wall. The robustness of the method is tested including unconverged near-wall measurements, pressure gradient, and reduced number of points; the importance of the location of the first point is also tested, and it is shown that the method presents a high robustness even in highly distorted flows, keeping the aforementioned accuracies if one acquires at least one data point in $$y^+<10$$ . The wake component and the thickness of the boundary layer are also simultaneously extrapolated from the mean velocity profile. This results in the first study, to the knowledge of the authors, where a five-parameter fitting is carried out without any assumption on the von Karman constant and the limits of the logarithmic layer further from its existence.