Experimental analysis of the log law at adverse pressure gradient

Abstract

The experimental data for the mean velocity are analysed in the inner layer for a turbulent boundary layer at significant adverse pressure gradient and Reynolds numbers up to. The aim is to determine the resilience of the log law for the mean velocity, the possible change of the von Kármán constant and the appearance of a square-root law above the log law at significant adverse pressure gradients. In the wind-tunnel experiment, the adverse pressure gradient is imposed by an -shaped deflection of the contour model which is mounted on a wind-tunnel sidewall. A large-scale particle imaging velocimetry method is applied to measure the streamwise evolution of the flow over a streamwise distance of 15 boundary layer thicknesses. In the adverse pressure gradient region, microscopic and three-dimensional Lagrangian particle tracking velocimetry are used to measure the mean velocity and the Reynolds stresses down to the viscous sublayer. Oil-film interferometry is used to determine the wall shear stress. The log law in the mean-velocity profile is found to be a robust feature at adverse pressure gradient, but its region is thinner than its zero pressure gradient counterpart, and its slope is altered. A square-root law emerges above the log law, extending to the wall distance the log law typically occupies at zero pressure gradient. Lower values for are found than for zero pressure gradient turbulent boundary layers, but the reduction is within the uncertainty of the measurement.