Large-eddy simulations of conical hypersonic turbulent boundary layers over cooled walls via volumetric rescaling method

Abstract

Large-eddy simulations (LES) of a hypersonic boundary layer on a 7 deg-half angle cone are performed to investigate the effects of highly-cooled walls (wall-to-recovery temperature ratio of T_w / T_r = 0.1) on fully developed turbulence and to validate a newly developed rescaling method based on volumetric flow extraction. Two Reynolds numbers are considered, Re_m = 4.1e6 1/m and 6.4e6 1/m, at freestream Mach numbers of M = 7.4. A comparison with a reference laminar-to-turbulent simulation, capturing the full history of the transitional flow dynamics, reveals that the volumetric rescaling method can generate a synthetic turbulent inflow that preserves the structure of the fluctuations. Equilibrium conditions are recovered after approximately 40 inlet boundary layer thicknesses. Numerical trials show that a longer streamwise extent of the rescaling box increases numerical stability. Analyses of turbulent statistics and flow visualizations reveal strong pressure oscillations, up to 50% of local mean pressure near the wall, and two-dimensional longitudinal wave structures resembling second-mode waves, with wavelengths up to 50% of the boundary layer thickness, and convective Mach numbers of M_c = 4.5. It is shown that their quasi-periodic recurrence in the flow is not an artifact of the rescaling method. Strong and localized temperature fluctuations and spikes in the wall-heat flux are associated with such waves. Very high values of temperature variance near the wall result in oscillations of the wall-heat flux exceeding its average. Instances of near-wall temperature falling below the imposed wall temperature of T_w = 300 K result in pockets of instantaneous heat flux oriented against the statistical mean direction.