Effect of a downstream ventilated gas cavity on turbulent boundary layer wall pressure fluctuation spectra

Abstract

An analytical and experimental investigation is made of the effect of a 2-D ventilated gas cavity on the spectrum of turbulent boundary layer wall pressure fluctuations upstream of a gas cavity on a plane rigid surface. The analytical model predicts the ratio of the wall pressure spectrum in the presence of the cavity to the blocked wall pressure spectrum that would exist if the cavity were absent. The ratio is found to oscillate in amplitude with upstream distance (−x) from the edge of the cavity. It approaches unity as −ωx∕Uc→∞, where ω is the radian frequency and Uc is the upstream turbulence convection velocity. To validate these predictions an experiment was performed in a water tunnel over a range of mean flow velocities. Dynamic wall pressure sensors were flush mounted to a flat plate at various distances upstream from a backward facing step. The cavity was formed downstream of the step by injecting carbon dioxide gas. The water tunnel measurements confirm the predicted oscillatory behavior of the spectral ratio, as well as its relaxation to unity as −ωx∕Uc→∞. For −ωx∕Uc>7 the cavity has a negligible influence on the upstream wall pressure fluctuations.