Thermochemical non-equilibrium effects on turbulent boundary layers

Abstract

This investigation employs direct numerical simulations (DNS) of high-Mach-number turbulent boundary layers under three flow conditions: a low-enthalpy calorically perfect gas, and two high-temperature gas mixtures, one in chemical non-equilibrium state and the other in full thermochemical non-equilibrium state. The influences of the two-temperature model on turbulent statistics and the coupling among turbulence, chemistry, and vibrational energy are examined. It is found that while high-enthalpy effects leave the velocity statistics virtually unchanged, they dramatically modify the near-wall temperature field. A pronounced disparity between the translational-rotational temperature and the vibrational temperature arises in the near-wall region, rendering the conventional generalized Reynolds analogy (GRA) inaccurate for vibrational temperature. To remedy this, a novel composite GRA is proposed that blends a vibrational-temperature-based relation with the standard formulation, and it demonstrates excellent agreement with the DNS data. Thermal non-equilibrium effects also substantially alter near-wall chemical reactions: it suppresses O2 dissociation while promoting NO formation, leading to a corresponding decrease and increase in the mean concentrations of O and NO, respectively. Spectral analyses of the turbulence-chemistry and turbulence-vibrational relaxation interaction terms reveal that temperature fluctuations dominate these flow quantities at energy-containing scales. Integrating the resulting spectral functions, we evaluate subgrid-scale closure terms for large-eddy simulation. At small filtering scales, the magnitude of the cross-correlation term rivals or exceeds that of the temperature fluctuation term, whereas the temperature fluctuation term becomes dominant at larger filter scales.