Wall pressure fluctuations and flow-induced noise in a turbulent boundary layer over a bump

Abstract

Direct numerical simulations of a turbulent boundary layer over a bump were performed to examine the effects of surface longitudinal curvature on wall pressure fluctuations ($p_{w}$) and flow-induced noise. Turbulence statistics and frequency spectra were obtained to elucidate the response of wall pressure fluctuations to the longitudinal curvature and to the corresponding pressure gradient. Wall pressure fluctuations were significantly enhanced near the trailing edge of the bump, where the boundary layer was subjected to a strong adverse pressure gradient. Large-scale structures in the distribution of wall pressure fluctuations were observed to grow rapidly near the trailing edge of the bump and convect downstream. Acoustic sources of the Lighthill equations were investigated in detail at various longitudinal surface curvatures. The acoustic sources ($S$) were highest near the trailing edge of the bump, where the root mean square wall pressure fluctuations were greatest. The maximum correlation coefficient between $p_{w}$ and $S$ was located just above the location of maximum wall pressure fluctuations. Far-field acoustic density fluctuations were computed using the Lighthill acoustic analogy. We found that the surface dipole is dominant in the total acoustic field. The contribution of the volume quadrupoles to the total acoustic field gradually increases with increasing radius of the surface curvature ($\delta/\!R$).