Direct numerical simulation of a supersonic turbulent boundary layer with hydrogen combustion

The complex behaviours of supersonic turbulent boundary-layer flows interacting with combustion is explored through the use of direct numerical simulations. The chosen flow model is a non-premixed hydrogen-air flame ignited within a three-dimensional supersonic turbulent flat-plate boundary layer operating at a Mach number of 2.33 and a friction Reynolds number of approximately 1000. The simulation involves a finite-rate model for the hydrogen-air reaction including 9 species and 19 steps with adiabatic non-catalytic wall conditions. The inlet flow consists of preheated air in the main stream and a hydrogen film injected in proximity to the cold wall, inducing mixing and ignition in the outer layer. The specific inlet configuration leads to two successive transition stages of distinct mechanisms, with the first stage related to the mixing-layer instability and the second one to the boundary-layer instability. The excess Reynolds stresses resulting from the transition exhibit a downstream decrease, with values being lower than canonical adiabatic profiles, particularly in the outer layer. This difference is attributed to the reduced local friction Reynolds numbers, associated with the non-classical wall-normal distributions of density and viscosity. The effect of combustion on the recovery process and skin friction is analysed in comparison with a supplemented chemistry-frozen setting. Velocity-temperature and velocity-species correlations are further examined. The wall-normal profiles of turbulent Prandtl number tend to classical non-reacting values and the turbulent Schmidt number is only slightly affected by the reaction. The strong Reynolds analogy linking velocity and temperature fluctuations is found to be invalid in the outer layer due to the presence of large-scale temperature fluctuations and the inhomogeneity of hydrogen gas distribution, as revealed by a spectrum analysis. A statistical analysis of elementary reactions at varying wall-normal distances is provided, highlighting the dominance of hydrogen atom depletion in the inner region and the prevalence of water vapour production in the outer region, together contributing to the chemical heat release across the boundary layer. Turbulence-chemistry interaction is assessed through a comparison of mean turbulent and laminar chemical heat release rates, showing significant differences of up to an order of magnitude. Using a simple diagnostic tool, the modelling of fluctuations associated with hydrogen gas and two intermediate products is found to be crucial for turbulent chemistry closure.