Multivariate Statistics Analysis of the Pressure Field Induced by High-Speed Turbulent Boundary Layers

摘要

A DNS database of turbulent boundary layers with the freestream Mach number spanning from M_∞ = 2.5 to M_∞ = 14 is utilized to study multivariate statistics of pressure fluctuations induced by high-speed turbulent boundary layers. The multivariate pressure statistics include pressure correlations and coherence at multiple wall-normal locations, including those within the boundary layer and in the free stream. Within the boundary layer, the extent of pressure-correlation contours increases in both streamwise and spanwise directions as the wall-normal height increases, and variations in the freestream Mach number and the wall temperature do not seem to cause substantial differences in the size of large-scale pressure structures. In the free stream, however, the acoustic pressure structures exhibit a significant reduction in spatial length scales and structure angles as compared with those in the outer region of the boundary layer, and pressure wave fronts are found to be significantly shallower as Mach number increases. For all wall-normal locations, the coherence of pressure fluctuations attains much higher values at low frequencies and decays at high frequencies, with the spanwise coherence decaying substantially faster than the streamwise coherence. The coherence length increases with wall-normal coordinate within the boundary layer in both streamwise and spanwise directions. In the free stream, the streamwise coherence length and the Lagrangian correlation length are similar to those close to the wall, and such an apparent match indicates that the acoustic sources are located near the wall and is consistent with the 'Mach wave radiation' concept.