Direct numerical simulations (DNS) of high–temperature supersonic turbulent channel flow of equilibrium air are conducted at constant dimensional wall temperature 1733.2 K. The Mach number based on the bulk velocity and the speed of sound at the isothermal wall is 3.0, and the Reynolds number based on the bulk density, bulk velocity, channel half–width, and viscosity at the isothermal wall is 4880. Bidirectional coupling (BC) and unidirectional influence (UI) conditions are investigated, conditions which take account, respectively, of the influence of turbulence on chemistry and the influence of chemistry on turbulence, and just the influence of turbulence on chemistry. The reliability of the DNS data for the UI condition is verified by comparison with the results of Coleman et al. [J. Fluid Mech. 305, 159–183 (1995)]. The results of present research show that the many turbulent statistics and instantaneous structures which hold for calorically perfect gas also hold for equilibrium air, even for the BC condition. The coupling condition has no significant influence on the van Driest transformed mean velocity and turbulent kinetic energy budget. The magnitudes of the mean and fluctuating specific heat and enthalpy for the BC condition are larger than those for the UI condition. An inverted trend is observed for the temperature and dissociation degree. Compared with the UI condition, the near–wall streaks for the BC condition are arranged in a more spanwise manner, owing mainly to the increase in anisotropy ratios. The large–scale structures become small, sharp, and chaotic for the BC condition.
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