Flow Noise from Small Gaps in Turbulent Boundary Layers

Abstract

The aeroacoustics of low-Mach-number boundary-layer flow over small gaps is studied using large-eddy simulation and Lighthill’s theory. Gap leading edge height (h1) is 13.3% of the thickness of unperturbed turbulent boundary layer at Re� = 4755. The effect of gap trailing edge height (h2) and width (W) on wall pressure fluctuations and radiated sound is investigated by considering different trailing edge heights (h2/h1 = 1/2, 1 and 2) and gap widths (W/h1 = 1, 2, 4 and 8). For the smallest gap width, the flow barely recognizes the existence of gap and, depending on the trailing edge height, is similar to that over a single backward, forward step or flat plate. As the gap width increases, the streamwise variation of root-mean-square pressure fluctuations exhibits characteristics of both backward and forward steps. The increase in trailing edge height results in larger pressure fluctuations, some of which are caused by the reattaching shear layer on top of the trailing edge. The peak pressure fluctuations occur near the trailing edge tip, or reattachment location if there is separation. The Green’s function valid for an acoustically compact gap configuration is computed numerically using Schwarz-Christoffel transformation and is used to evaluate the volume integral in the solution to Lighthill’s equation. The flow characteristics near the corner of gap leading edge and trailing edge, together with the Green’s function, determine the sound pressure spectrum. Gaps with larger width and/or larger trailing edge height generates sound spectrum similar to that of an equivalent single forward step. For gaps with the same leading and trailing edge heights, the sound spectrum displays a broad peak which becomes more pronounced as the width decreases. This is due to symmetric Green’s function which leads to acoustic cancellations at low frequencies.