Numerical Study of Pressure Fluctuations due to a Mach 6 Turbulent Boundary Layer

Abstract

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a Mach 6 turbulent boundary layer with nominal freestream Mach number of 6 and Reynolds number of Reτ ≈ 464. The emphasis is on comparing the primarily vortical pressure signal at the wall with the acoustic freestream signal under higher Mach number conditions. Moreover, the Mach-number dependence of pressure signals is demonstrated by comparing the current results with those of a supersonic boundary layer at Mach 2.5 and Reτ ≈ 510. It is found that the freestream pressure intensity exhibits a strong Mach number dependence, irrespective of whether it is normalized by the mean wall shear stress or by the mean pressure, with the normalized fluctuation amplitude being significantly larger for the Mach 6 case. Spectral analysis shows that both the wall and freestream pressure fluctuations of the Mach 6 boundary layer have enhanced energy content at high frequencies, with the peak of the premultiplied frequency spectrum of freestream pressure fluctuations being at a frequency of ωδ/U∞ ≈ 3.1, which is more than twice the corresponding frequency in the Mach 2.5 case. The space-time correlations indicate that the pressure-carrying eddies for the higher Mach number case are of smaller size, less elongated in the spanwise direction, and convect with higher convection speeds relative to the Mach 2.5 case. The demonstrated Mach-number dependence of the pressure field, including radiation intensity, directionality, and convection speed, is consistent with the trend exhibited in experimental data and can be qualitatively explained by the notion of 'eddy Mach wave' radiation. NomenclatureC p heat capacity at constant pressure, J/(K·kg) C pp Space-time correlation coefficient of the pressure field, dimensionless C v heat capacity at constant volume, J/(K·kg)

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