Sound generation by turbulent boundary-layer flow over small steps

Abstract

The aeroacoustics of low-Mach-number boundary-layer flow over backward and forward facing steps is studied using large-eddy simulation and Lighthill's theory. The Reynolds number based on the step height and free-stream velocity ranges from 21000 to 328 as the step height is varied from 53% to 0.83% of the unperturbed boundary layer thickness at the step. For the largest step size, statistics of wall pressure fluctuations such as the root mean square values and frequency spectral density yield favourable comparisons with available experimental measurements. A low-frequency Green's function for the step geometry, valid for an acoustically compact step height, is employed to evaluate the volume integral in the solution to Lighthill's equation. Consistent with the result of previous theoretical studies, the steps act primarily as a dipole source aligned in the streamwise direction. The sound from the forward step is shown to be significantly louder than that from the backward step and the underlying reason is analysed in terms of source strength and distribution relative to the Green's function. The forward step generates stronger sources in regions closer to the step corner, which is heavily weighted by the Green's function. A detailed analysis of flow field and Green's function weighted sources reveals that the backward step generates sound mainly through a diffraction mechanism, while the forward step generates sound through a combination of diffraction and turbulence modification by the step. As the step height decreases, the difference in noise level between forward and backward steps is much reduced as turbulence modification becomes less significant.