NUMERICAL MODELING OF HEAT-TRANSFER AND RELAXATION IN NONEQUILIBRIUM AIR AT HYPERSONIC SPEEDS

Kinetic theory is used to deduce a consistent model of molecular transport - in particular the transport of molecular energy - in thermal nonequilibrium flows, The first approximation of the Chapman-Enskog-theory is applied to determine the transport properties, Diatomic molecules are treated as harmonic oscillators with a finite number of internal energy levels. Rotational relaxation times are calculated by a modified Parker-type equation. Thivet's model is used to describe the vibrational relaxation. The transport of internal energies is then determined following the methods of Mason-Monchick and Brun-Pascal. The model was employed using the ONERA 2D Navier-Stokes code CELHYO for laminar hypersonic flows in chemical and thermal nonequilibrium. Five chemical species (N-2, O-2, NO, N, O) are considered. N-2 and O-2 are each characterized by their proper vibrational temperature while NO is assumed to be in thermodynamic equilibrium with the translational temperature. Nevertheless the vibrational-translational (V-T) and the non-resonant vibrational (V-V) energy exchanges are extended to include the species NO. The presented results were obtained using the Lobb testcase, a sphere with bow shock at Mn-infinity = 15.3 and with r = 0.5 inch. The accumulated influence of the presented Eucken correction, of rotational relaxation and of mixture laws on the calculated thermal conductivity is significant. The V-V energy exchange with NO has an accelerating effect on the predicted vibrational relaxation, and therefore on the size of the nonequilibrium region behind the shock.