Direct Computation of Wall-Pressure Fluctuations in Weakly Compressible Turbulent Wall-Bounded Flows

Knowledge of wall-pressure fluctuations in turbulent wall-bounded flows is important for predictions of structural vibration and noise. In this study, compressible direct numerical simulations with a sixth-order, non-dissipative finite difference scheme are employed to accurately capture the spatiotemporal characteristics of wall-pressure fluctuations in low-Mach-number turbulent wall-bounded flows. Turbulent channel flow simulations are conducted at bulk Mach numbers 0.4, 0.2 and 0.1, and friction Reynolds number 180. In addition to the convective ridge that is virtually Mach number independent, acoustic ridges, whose magnitudes are orders of magnitude lower, are identified in the two-dimensional wavenumber-frequency spectrum. At lower frequencies, the acoustic ridges represent propagating longitudinal and oblique waves that match the theoretical predictions of two-dimensional duct modes with a uniform mean flow. They decay with decreasing Mach numbers but remain distinctly identifiable even at Mach 0.1. At high frequencies, in contrast, no propagating waves are found, and the spectral level in the supersonic wavenumber range is broadly elevated and increases with decreasing Mach number. At Mach 0.4, two additional simulations are carried out, one in a plane channel at friction Reynolds number 500 to explore the Reynolds number effect, and the other in a channel with a surface hump at friction Reynolds number 180 to examine the impact of surface inhomogeneity. A strong Reynolds number dependence is observed in the subconvective wavenumber region, where the spectral level shows a significant elevation with increasing Reynolds number, especially at higher frequencies. The presence of the small two-dimensional hump along the spanwise direction is shown to vastly increase the acoustic energy for both longitudinal and oblique modes as well as the broadband subconvective spectral level as a result of diffraction and turbulence generation induced by the hump. Moreover, the fluctuating wall pressure beneath a flat-plate turbulent boundary layer is investigated at freestream Mach number 0.4 and momentum-thickness Reynolds numbers up to 1918. The results reveal the presence of acoustic ridges associated with longitudinally propagating waves in the two-dimensional wavenumber-frequency spectra. These acoustic ridges are less prominent compared with their counterparts in the plane channel. With proper frequency scaling, the convective ridges in TBL and plane-channel flows are found to be nearly identical. A small two-dimensional surface hump is found to substantially increase the acoustic energy for the downstream propagating waves downstream of the hump, but has less impact on the upstream region.