Investigation of the Direct Measurement Algorithm to Experimentally Acquire the Wavenumber–Frequency Spectrum of the Turbulent Boundary Layer Wall Pressure Fluctuations Using a Linear Surface Array

Abstract The wavenumber–frequency spectrum (W–F spectrum) of turbulent boundary layer wall pressure fluctuations (TBL-WPFs) holds considerable significance in various engineering applications. Experimental assessments of the W–F spectrum are predominantly conducted using a surface array, with data processed through the direct measurement algorithm (DMA). In this study, a novel one-dimensional (1D) DMA, based on the cross spectrum matrix (CSM), was developed to obtain the W–F spectrum of TBL-WPFs using a linear surface array. This development was founded on the assumptions of temporal stationarity and spatial homogeneity; an averaging method is employed to reduce errors and enhance robustness. Additionally, the DMA is specifically designed for parallel computing, which significantly enhances efficiency. To validate the 1D DMA, an experiment was conducted in the wind tunnel, employing a 32-channel microelectromechanical systems (MEMS) linear surface array, alongside hot-wire tests to determine the boundary layer characteristics. The W–F spectral results were compared to the Chase I model. The study concluded that the DMA can effectively capture the acoustic region of the W–F spectrum and can provide accurate measurement results for the subconvective, convective, and viscous regions, thereby confirming the utility of the algorithm. Furthermore, the efficiency of parallel computing was analyzed, and the performance of the parallel computing capabilities of the DMA was evaluated. It is affirmed that parallel computing, when combined with the application of conjugacy, can decrease computational time to enhance efficiency, with its advantages becoming increasingly evident as the number of sensors in the surface array increases.