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

Modelling of heat transfer in non-equilibrium reacting gas flows is very important and promising for many up-to-date practical applications. Thus, calculation of heat fluxes is needed to solve the problem of heat protection for the surfaces of space vehicles entering into planet atmospheres. In high-temperature and hypersonic flows of gas mixtures, the energy exchange between translational and internal degrees of freedom, chemical reactions, ionization and radiation result in violation of thermodynamic equilibrium. Therefore the non-equilibrium effects become of importance for a correct prediction of gas flow parameters and transport properties. The first attempt to take into account the excitation of internal degrees of freedom in calculations for the transport coefficients was made in 1913 by E. Eucken Eucken (1913), who introduced a phenomenological correction into the formula for the thermal conductivity coefficient. Later on, stricter analysis for the influence of the excitation of internal degrees of freedom of molecules on heat and mass transfer was based on the kinetic theory of gases. Originally, in the papers concerning kinetic theory models for transport properties, mainly minor deviations from the local thermal equilibrium were considered for non-reacting gases Ferziger & Kaper (1972); Wang Chang & Uhlenbeck (1951) and for mixtures with chemical reactions Ern & Giovangigli (1994). In this approach non-equilibrium effects were taken into account in transport equations by introducing supplementary kinetic coefficients: the coefficient of volume viscosity in the expression for the pressure tensor and corrections to the thermal conductivity coefficient in the equation for the total energy flux. Such a description of the real gas effects becomes insufficient under the conditions of finite (not weak) deviations from the equilibrium, in which the energy exchange between some degrees of freedom and some part of chemical reactions proceed simultaneously with the variation of gas-dynamic parameters. In this case characteristic times for gas-dynamic and relaxation processes become comparable, and therefore the equations for macroscopic parameters of the flow should be coupled to the equations of physical-chemical kinetics. The transport coefficients, heat fluxes, diffusion velocities directly depend on non-equilibriumdistributions, whichmay differ substantially from the Boltzmann thermal equilibrium distribution. In this situation, the estimate for the impact of non-equilibrium kinetics on gas-dynamic parameters of a flow 21