In this paper, the structure of the relaxation zone behind shock waves in hypersonic air flows is studied taking into account state-to-state non-equilibrium vibrational and chemical kinetics [1]. Along with the traditional case of thermally equilibrium free stream before a shock, we consider the conditions when a shock wave appears in a vibrationally excited air flow. It occurs as a result of different kinds of vibrational energy pumping in the free stream: in the ground test facilities (see Ref. [2]), in the flows near bodies of complicated form or may be important for the problem of conducting by chemical reactions in a shock heated gas. Propagation of shock waves in a non-equilibrium gas is discussed in Refs. [3], [4], the air flow parameters behind a shock wave occurring in non-equilibrium free stream are studied in [5].
In the present paper we use the model proposed in [5] for a non-viscous 1-D flow of five-component air mixture N2/O2/NO/N/O with different vibrational energy transitions, dissociation, recombination and two Zeldovich exchange reactions of NO formation. Vibrational energies of air molecules are simulated by the anharmonic oscillator model. 83 equations for vibrational level populations of molecular species and atomic number densities are coupled to the conservation equations of momentum and total energy and solved numerically under the conditions typical for the flow near a space craft re-entering to the Earth atmosphere. Mach numbers M0=10, 15 and flight altitudes 48 km in the free stream are considered. Different test cases with equilibrium and non-equilibrium vibrational distributions of nitrogen and oxygen molecules before the shock front are studied. In the equilibrium case, vibrational level populations before a shock have the form of the Boltzmann distributions with the gas temperature T0. In non-equilibrium cases, N2 and O2 molecules in the free stream are supposed to be vibrationally excited and level populations are described by the non-equilibrium Boltzmann distributions with vibrational temperatures TvN2, TvO2 which are higher than the gas temperature T0.
The evolution of the gas temperature, velocity, mixture composition and vibrational level populations along the relaxation zone is studied for the considered conditions. The results show the influence of Mach numbers and vibrational distributions in the free stream on flow parameters and populations of various vibrational levels of oxygen and nitrogen molecules behind a shock. It is found that the character of variation of the gas temperature and mixture composition in the relaxation zone changes dramatically in the case of vibrationally excited free stream molecules. This effect is particularly pronounced if, just behind a shock, the gas temperature occurs lower than the vibrational temperatures. It happens when free stream Mach numbers are not so high whereas a strong vibrational energy pumping before a shock front takes place.
Acknowledgements
This work was partially supported by the Russian Foundation for Basic Research (grant 12-08-00826).
References
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3. A.I. Osipov, A.V. Uvarov, Physics-Uspekhi 35 (11) (1992) 903-923, in Russian.
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5. O.V. Kunova, E.A. Nagnibeda, Chem. Phys. 441 (2014) 66-76.
