The randomness and determinacy of wall pressure fluctuations in incompressible flow

Wall pressure fluctuations caused by turbulent boundary layers have a significant impact on aircraft structural vibration and cabin noise. This study aims to investigate the mechanism of turbulence-induced pressure fluctuations by focusing on the randomness of wall pressure fluctuations, analyzed in both the time-frequency and spatial-wavenumber domains using measured data obtained from a phase array in a wind tunnel. Three roughness elements were designed and installed upstream of the plate to manipulate the turbulent boundary layer at a specific Mach number. The results of the investigation demonstrate that the disturbance strength induced by the roughness element influences the randomness of wall pressure fluctuations, in addition to the parameters utilized for data analysis. Generally, stronger turbulence fluctuations tend to decrease the randomness of pressure fluctuations. Moreover, wall pressure fluctuations also exhibit certain statistical principles that cannot be precisely calculated using mathematical expressions, highlighting their inherent randomness. Further investigation into randomness in the spatial-wavenumber domain revealed the hydrodynamic modes of turbulence fluctuations with varying convection velocity analyzed through wavenumber maps computed using the beamforming algorithm. These modes with variable convective speed significantly contribute to the generation of randomness in wall pressure fluctuations. Both the time-frequency domain and the spatial-wavenumber domain affect the randomness characteristics of wall pressure fluctuations. However, such effects are not easily discernible through a rudimentary analysis of the space-time correlation of turbulence fluctuations.