Effect of film Mach number on supersonic film cooling using direct numerical simulation

Supersonic film cooling serves as an effective thermal protection method for hypersonic vehicles. This study performs direct numerical simulations of supersonic film injection into a hypersonic turbulent boundary layer (Mach 6), investigating the influence of film Mach number Mac on cooling performance and flow characteristics. Mean flow field data reveal that increasing Mac extends absolute effective cooling length, but is less cost-effective in terms of effective cooling length per unit film mass flow rate. Further analysis reveals that the diminished cost-effectiveness results from earlier boundary layer transition relative to the effective cooling length, which enhances turbulent mixing in the effective cooling region. Turbulent kinetic energy (TKE) evolution demonstrates that in the wall-jet region, the turbulent intensity at the lowest Mac (Mac=2) displays a one-peak pattern that differs significantly from the two-peak distributions under higher Mac conditions, which stems from the lowest film mass flow rate that causes rapid complete mixing. Bypass transition occurs in the boundary layer beneath the film. Although the absolute location of the transition onset is insensitive to Mac, the downstream turbulence development shows altered characteristics with increasing Mac, as evidenced by the peak TKE levels and spanwise length scales of turbulent structures. Interestingly, greater scale disparity between the turbulent structures near the wall and in the mixing layer is observed as Mac increases, which is attributed to the reduced spanwise scales of near-wall streaks. The increase in Mac results in decelerated turbulence development, extending the absolute streamwise distance required for the film to be completely dissipated.