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

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Large-eddy simulations (LES) of a hypersonic boundary layer on a 7^∘ -half-angle cone are performed to investigate the effects of highly cooled walls (wall-to-recovery temperature ratio of Tw / Tᵣ ~ 0.1 ) on fully developed turbulence and to validate a newly developed rescaling method based on volumetric flow extraction. Two Reynolds numbers are considered, Reₘ = 4.1 × 10⁶\ m⁻¹ and 6.4 × 10⁶\ m⁻¹ , at free-stream 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 Mc 4.5 . It is shown that their quasi-periodic recurrence in the flow is not an artefact 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 Tw=300 K result in pockets of instantaneous heat flux oriented against the statistical mean direction.