A vibration-based method to estimate the low-wavenumber wall pressure field in a turbulent boundary layer

When an elastic structure is excited by a low-speed turbulent flow, it generates flow-induced vibration which is primarily due to the low-wavenumber components of the wall pressure field (WPF) beneath the turbulent boundary layer (TBL). Therefore, to accurately predict the vibration response of the structure, an accurate estimation of the low-wavenumber WPF is needed. While existing TBL models for WPF well predict the convective region, they exhibit significant discrepancies in predicting the low-wavenumber levels. This numerical study aims to explore the feasibility of estimation of the low-wavenumber WPF by analysing vibration data obtained from a structure excited by a TBL. An inverse method is proposed based on the relationship between the TBL forcing function and structural vibrations in the wavenumber domain. The random TBL force is simulated with deterministic loading using the uncorrelated wall plane wave technique. A model of a simply supported plate under a TBL excitation is developed to demonstrate the proposed method. The plate's acceleration data is then used to estimate the WPF in the low-wavenumber range. It is shown how using multiple discrete frequencies in the analysis can reduce the required snapshots for accurate estimation of the WPF.