IMPACT OF PRESSURE-GRADIENT CONDITIONS ON HIGH REYNOLDS NUMBER TURBULENT BOUNDARY LAYERS

Summary Mean velocity distributions in the overlap region, over the range of Reynolds numbers 10,000 < Reθ < 70,000, under five different pressure-gradient conditions are accurately described by a log law. The pressure-gradient conditions include adverse, zero, favorable and strongly favorable. The wall-shear stress was measured using oil-film interferometry, and hot-wire sensors were used to measure velocity profiles. Parameters of the logarithmic overlap region developed from these higher Reynolds number boundary layers continue to be consistent with our recent findings and to remain independent of Reynolds number. The best estimate of the log-law parameters from the zero-pressure gradient boundary layers is κ = 0.38, B = 4.1. However, the Karman "coefficient" (κ ) is found to vary considerably for the non-equilibrium boundary layers under the various pressure gradients. The results highlight the variation with pressure gradient not only in the outer region of the boundary layer but also within the inner region. INTRODUCTION & EXPERIMENTAL ARRANGEMENT Two independent experimental investigations of the behavior of turbulent boundary layers with increasing Reynolds number (Reθ) were recently completed (1). The experiments were performed in two facilities, the MTL wind tunnel at KTH and the NDF wind tunnel at IIT. While the KTH experiments were carried out on a flat plate, the model used in the NDF was a long cylinder with its axis aligned in the flow direction. Both experiments were conducted in a zero-pressure gradient, covered the range of Reynolds numbers based on the momentum thickness from 2,500 to 27,000, and utilized oil-film interferometry to obtain an independent measure of the wall-shear stress. Contrary to the conclusions of some earlier publications, careful analysis of the data revealed no significant Reynolds number dependence for the parameters describing the overlap region using the classical logarithmic relation. The parameters of the logarithmic overlap region were found to be constant and were estimated to be: κ = 0.38, B = 4.1. These two experiments have been recently extended to Reynolds numbers based on momentum thickness exceeding 70,000. The current experiments were also carried out in the National Diagnostic Facility (NDF) at IIT on a 10 m long and 1.5 m wide flat plate using free-stream velocities ranging from 30 to 85 m/s. Again, hot-wire anemometry and oil-film interferometry were used to measure the velocity profiles and the wall-shear stress, respectively. The design of the experiments, and in particular the location and spacing of the velocity profiles in the downstream direction and the hot-wire sensor in the wall-normal direction, developed to facilitate the evaluation of wall -normal and streamwise derivatives. The arrangement of the NDF was designed to allow the adjustment of the test-section ceiling to impart various pressure gradients. Several conditions were investigated so far, including: Adverse Pressure Gradient (APG), Zero Pressure Gradient (ZPG), Favorable Pressure Gradient (FPG), Strongly Favorable Pressure Gradient (SFPG), and Complex Pressure Gradient (CPG) as displayed in Figure 1.