On the challenges of estimating the low-wavenumber wall pressure field beneath a turbulent boundary layer using a microphone array

The low-wavenumber components of the turbulent boundary layer (TBL) wall pressure field (WPF) are known to be the primary cause of structural vibration in low-Mach number flows, despite the maximal energy of the TBL being at the convective wavenumber. Existing semi -empirical TBL models show good agreement in predicting the WPF levels in convective region but differ significantly in the low-wavenumber domain. This study aims to highlight the challenges of estimating the low-wavenumber WPF in a TBL using a microphone array. A regularized Fourier-based approach is proposed to numerically study the estimation of the low-wavenumber WPF. Performance of the proposed method is initially evaluated by comparing the estimated WPF against a closed-form input TBL model. Effects of sensor spacing, co-array factor, and sensor distribution on the estimation of the low-wavenumber WPF levels are then investigated. To mimic experimental measurements a virtual acoustic experiment is proposed, involving the synthesis of snapshots of TBL-induced WPF. It is demonstrated that although with relatively small number of snapshots the convective region can be identified, a significant number of snapshots is required to well estimate the TBL low-wavenumber region.