High Reynolds Number Turbulent Boundary Layers Subjected to Various Pressure-Gradient Conditions

摘要

Mean velocity distributions in the overlap region, over the range of Reynolds numbers 10,000 < Re_(theta) < 70,000, under five different pressure-gradient conditions are accurately described by a log law. The pressure-gradient conditions include adverse, zero, favorable, strongly favorable, and a complex gradient. 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 k = 0.384, B = 4.127. However, the Karman "coefficient" (k) 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. A slightly modified version of the almost century old Prandtl-Karman skin friction relation provides an exceptional agreement with all three sets of data (Hites, Osterlund, and Christophorou) for zero pressure gradient conditions.