Scaling of Sub-Convective Wall Pressure Fluctuations in a Turbulent Boundary Layer

Wall pressure fluctuations beneath turbulent boundary layers are of central importance in structural acoustics and flow-induced noise applications. Of particular interest are the sub-convective pressure fluctuations, which dominate low-wavenumber structural excitation but are notoriously difficult to measure because conventional arrays cannot spatially resolve the sub- convective region without contamination from the much more energetic convective ridge. The following work presents spatially resolved measurements of the wavenumber-frequency spectrum of wall pressure in a zero-pressure-gradient smooth-wall turbulent boundary layer over a wide range of Mach numbers (0.05 ≤ M∞ ≤ 0.190). An area-averaging sensor array was designed to suppress the high wavenumber energy for all nine flow conditions, and both convective and sub-convective scaling arguments are assessed qualitatively using the measurements. Scaling on the auto-spectrum produces collapse of the spectral shape in the convective region, while the sub-convective scaling goes as C_T*h^3*rho^2*u_tau^6*omega−3, augmented by an empirical correction factor, k_c*theta. The collapsed sub-convective data are consistent with Chase’s wavenumber white prediction of the sub-convective region. A superposition model combining an asymmetric convective ridge with the wavenumber white sub-convective floor is proposed, and fits all nine measurements with a single set of global parameters. The model is given as a step toward building an accurate predictive tool for the convective and sub-convective pressure fluctuations.