Application of the diagnostic plot in estimation of the skin friction in turbulent boundary layer under an adverse pressure gradient

The paper concerns the problem of determining friction velocity in wallbounded flows affected by an adverse pressure gradient (APG). In the work of Niegodajew et al. [22] the corrected Clauser chart method (CCCM) for such flow conditions was proposed. This approach utilises the mean velocity profiles and turbulence intensity profiles to accurately estimate the friction velocity. In another work, Drozdz et al. [27] presented a modified version of the diagnostic-plot scaling (DPS) which allows for direct reconstruction of turbulence intensity profiles based on the local mean velocity profile, even when the flow is affected by a strong pressure gradient. This paper is aimed at verifying whether, when combining both of these methods (i.e. DPS and CCCM), the friction velocity can be accurately determined for APG flow conditions and one can possibly take advantage from both methods. The analysis revealed that the new approach is able to predict the friction velocity with uncertainty less than 5% for all the considered cases for the Clauser–Rotta parameter β < 17. Lastly, DPS-CCCM was also confronted with two empirical approaches (from available literature) allowing for estimation of the friction velocity under APG conditions. The performance of DPS-CCCM was found to be better than the ones of two other empirical approaches.