Effects of Mach number on space-time characteristics of wall pressure fluctuations beneath turbulent boundary layers

Wall pressure fluctuations beneath turbulent boundary layers are a fundamental source of aerodynamic noise by exciting the wall structure, with their space-time characteristics serving as the basic ingredient for predicting the wall structural response. To this end, direct numerical simulations of fully developed compressible turbulent boundary layers at Mach numbers of 0.5, 1.2, and 2.0 are conducted to investigate wall pressure fluctuations comprehensively. The effects of Mach number on the single-point statistics of wall pressure fluctuations are assessed to be very weak. Regarding the space-time characteristics, the convection velocity U_c determined by the space-time correlation of wall pressure fluctuations increases slightly with the Mach number, which only reflects the convective behavior of turbulent vortices. On the wavenumber–frequency spectrum, characteristic peaks of both the acoustic wave and convective vortices are identified. Due to the aerodynamic heating at supersonic conditions, the thermal effect on acoustic speed should be taken into account in determining the acoustic wavenumber. By introducing a convective Prandtl–Glauert parameter, a refined relation is proposed to provide a more accurate depiction of the acoustic domain in the wavenumber–frequency spectrum.