Wall-pressure fluctuations in weakly compressible turbulent channel flow

Abstract

Wall-pressure fluctuations in turbulent wall-bounded flows are detrimental in many applications because they can cause structural vibrations and acoustic radiation. Their spectral behavior at subconvective wavenumbers are to date poorly understood and predicted, particularly in low-Mach-number flows. In this study, compressible direct numerical simulation is employed to elucidate the low-wavenumber behavior of wall-pressure fluctuations in turbulent channel flow and the effect of flow Mach number in the nearly incompressible regime. Simulations are conducted at bulk Mach numbers of 0.4, 0.2, and 0.1, and friction Reynolds number of 180. In addition to the convective ridge that is virtually Mach-number independent, acoustic ridges representing longitudinal and oblique waves are clearly identified in the two-dimensional wavenumber-frequency spectrum. The acoustic peaks are orders of magnitude weaker than the convective peak and decay with flow Mach number, but remain distinctly identifiable even at Mach 0.1. The acoustic energy in the supersonic wavenumber range is significantly enhanced by the onset of the first oblique mode but not much affected by the higher modes. The effect of a small, two-dimensional surface hump is also considered, which is shown to elevate the spectral level of the fluctuating wall pressure in the subconvective wavenumber range by several decades due to acoustic diffraction by the hump. [Work supported by the U.S. Office of Naval Research.]