Measurements and model comparison of sub-convective pressure fluctuations in rough-wall turbulent boundary layers

The effect of roughness on the wall-pressure field generated by a turbulent boundary layer is a widely encountered but poorly understood phenomenon. Understanding and modelling these wall-pressure fields is important for the design and analysis of vehicles such as large-scale aircraft and marine vehicles. In particular, sub-convective wall-pressure fluctuations are a primary driver of structural vibration, which in turn leads to cabin noise and far-field sound radiation. This study uses a novel technique for the measurement of the continuous streamwise wavenumber–frequency spectrum of wall-pressure fluctuations beneath a turbulent boundary layer over a rough wall. Measurements were taken for long sampling durations, which are shown to be necessary for accurately capturing the statistical nature of the sub-convective wall-pressure fluctuations. Data have been compared across adverse, favourable and near-zero pressure gradient conditions, and three different Reynolds numbers. In all cases, the spectrum reveals an asymmetric convective ridge with a high dependency on frequency, a wavenumber-white behaviour at higher frequencies, and a difference between the convective ridge and the subconvective regime of 23–25 dB. Data are shown to collapse when normalising using a mixed scaling based on displacement thickness, convection velocity and wall shear stress. Measured data have been compared with the modified Corcos model and display poor agreement, particularly in the roll off from the convective ridge and in the behaviour at high frequency. Corrections to the modelled spectrum have been made through the estimation of the pressure spectrum due to scattering from roughness. Including the effects of scattering is insufficient in accounting for the differences between spectral models and measured data, indicating that it is likely the roughness sublayer that has a more significant effect on the wall-pressure spectrum than scattering alone.