Experimental study of the inner layer of an adverse-pressure-gradient turbulent boundary layer

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Abstract

We present an analysis of the inner layer of adverse-pressure-gradient turbulent boundary layers at Reynolds numbers up te Re-theta=57000. The major aim is to determine the resilience of the log-law, the possible change of the log-law slope and the appearance of a square-root law above the log-law at significant adverse pressure gradients. The second objective is to characterise the total shear stress. The third aim is to provide a well-defined test case for the validation and improvement of numerical flow simulation methods. We designed and performed a new wind-tunnel experiment, in which the turbulent boundary layer flow of interest develops on the side wall of the wind-tunnel and then follows an accelerating ramp and a long flat plate at almost zero pressure gradient. Then the flow enters into the adverse pressure gradient section, first along a curved surface and then on a flat plate. We use a large-scale overview particle imaging velocimetry method for characterising the streamwise evolution of the flow over a streamwise distance of 15 boundary layer thicknesses. In the focus region, we use microscopic and Lagrangian particle tracking velocimetry to measure the mean velocity and the Reynolds stresses down to the viscous sublayer. Oil-film interferometry is used for the complementary direct measurement of the wall shear stress. In the adverse pressure gradient region we observe a composite form of the mean velocity profile with a thin log law region and a square-root law above up to 12% boundary layer thickness. We find lower values for the log-law slope coefficient than for zero pressure gradient boundary layers, but the reduction is within the uncertainties in the measurement and possible history effects. The total shear stress and the turbulent viscosity in the inner layer can be described by an analytical model whose parameters are the pressure gradient parameter and the acceleration parameter based on the streamwise gradient of the wall shear stress. Then we use a data base of adverse pressure gradient turbulent boundary layer flows at large Reynolds numbers from the literature. We find that the mean velocity profiles for different flows almost collapse provided that both the pressure gradient parameter and the wall shear stress gradient parameter are close to each other. Finally we describe and discuss the effects of the convex curvature and the relaxation of upstream curvature effects on a flat plate. The streamwise eddy-turnover distance indicates that the flow relaxes fast in the inner layer, whereas the turnover length is strongly increasing in the outer part of the boundary layer.

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• Experimental study of the inner layer of an adverse-pressure-gradient turbulent boundary layer. (deposited 22 Nov 2019 16:44) [Currently Displayed]