Comparison of sub-convective pressure fluctuations over a smooth and rough wall

Abstract

Sub-convective wall pressure fluctuations are compared for a smooth and rough surface with homogeneously distributed roughness elements. Limitations in measurement techniques make it challenging to measure the sub-convective pressure spectrum over smooth surfaces, and there are no general techniques for rough walls. The study presented here uses a recently developed approach to accurately measure the sub-convective pressure fluctuations, particularly at low-wavenumbers for a single flow condition for two surfaces. Correlations between different sensors suggest smaller scales in rough walls than in smooth walls. A significant expansion of the convective ridge is noticed. Normalizations of the wavenumber-frequency spectrum as ${\varphi }_{pp}(k_1{\delta }^{\ast },\omega {\delta }^{\ast }/U_c)U_c/{\tau }_w^2{\delta }^{{\ast }^2}$ shows a near-exact collapse at the convective peak. The normalized spectral levels show a difference of about 25 dB in the sub-convective domain due to rough wall convective ridge behavior. The absolute sub-convective pressure spectrum levels relative to 20 $\mu$Pa are about 30 dB below the convective pressure fluctuations for smooth walls. Rough wall measurements show absolute levels 15–20 dB higher than the smooth wall. A wavenumber-white behavior is observed at higher frequencies for smooth and rough walls. Both smooth and rough walls show a convection velocity dependent on frequency. The rough wall convective ridge width shows a frequency dependency, whereas the smooth wall convective ridge width collapses at all frequencies.