Multitemperature kinetic model for heat transfer in reacting gas mixture flows

Abstract

Heat transfer in a high temperature reacting gas flow is investigated taking into account the influence of strong vibrational and chemical nonequilibrium. Rapid and slow vibrational energy exchanges in a mixture of molecular gases with realistic molecular spectra are taken into account and the deviation from the Boltzmann distribution over vibrational levels is studied. A kinetic theory approach is developed for the modeling of transport properties of a reacting mixture of polyatomic gases and a generalized multitemperature model is given. This theoretical model is applied for the analysis of the heat transfer and diffusion behind a strong shock wave propagating in air. The heat conductivity, diffusion coefficients, and heat flux are calculated on the basis of this model and compared to the one-temperature approach. The influence of anharmonicity of molecular vibrations is evaluated.

Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

“…Most of the kinetic literature, however, is still restricted to the simplified case of mono-atomic particles, which, in spite of its limitation, reproduces interesting results with good agreement with reality and expectation [5][6][7]. On the other hand it is clear that gases involved in practical applications are typically made up by polyatomic molecules, not su ciently described by the motion of their center of mass, and that the situation becomes even more complicated when chemical interactions with additional exchange of mass among species may take place [8][9][10][11]. Usually, in kinetic approaches, the non-translational degrees of freedom are accounted for by a suitable internal energy variable in a sort of semi-classical scheme [12], and such a variable may be either continuously ranging on the real line, or discrete, in correspondence to an internal structure of energy levels [13].…”

Different Approaches for Modelling of Heat Transfer in Non-Equilibrium Reacting Gas Flows

“…Then the obtained non-equilibrium distributions were used to calculate the transport coefficients, diffusion velocities, and heat fluxes on the basis of the accurate formulae of the kinetic theory. This approach was used for the evaluation of transport properties in the flows of non-equilibrium reacting mixtures of air components behind shock waves Chikhaoui et al (2000); , in the nozzle expansion Capitelli et al (2002); Kustova, Nagnibeda, Alexandrova & Chikhaoui (2002), in the hypersonic boundary layer Armenise et al (2006;; Kustova, Nagnibeda, Armenise & Capitelli (2002) (see also ). Below, we present some results of these applications concerning heat transfer in particular flows studied using the state-to-state, multi-temperature and one-temperature models.…”

“…Among up-to-date analytical models for vibration transition probabilities we can recommend the forced harmonic oscillator model Adamovich & Rich (1998) and generalizations of the SSH model Armenise et al (1996); Gordietz & Zhdanok (1986). The proposed multi-temperature model was applied in Chikhaoui et al (2000) for the simulation of gas-dynamic parameters, transport coefficients and heat fluxes in non-equilibrium reacting flows of 5-component air mixture behind shock waves. The flows of binary mixtures of air components behind shock waves are studied in and in nozzles in Kustova, Nagnibeda, Alexandrova & Chikhaoui (2002).…”

“…The closed set of governing equations for the macroscopic parameters n c (r, t), v(r, t), T(r, t), and T c 1 (r, t) were derived in Chikhaoui et al (2000;, it includes conservation equations for the momentum and the total energy, equations for species number densities and additional relaxation equations for the specific numbers of vibrational quanta W c in each molecular species c:…”

Vibrational and Chemical Kinetics in Non-Equilibrium Gas Flows

“…The closed set of governing equations for the macroscopic parameters n c (r, t), v(r, t), T(r, t), and T c 1 (r, t) derived in Chikhaoui et al (2000; includes the equations of the multi-temperature chemical kinetics for the species number densities…”