On the simplified state-to-state transport coefficients

Role of State-to-State Kinetics in Determining Transport Coefficients for Hypersonic Flow Simulations

“…The evolution of these distribution functions, based on kinetic theory, can be expressed as [1,7,[11][12][13] …”

“…This limitation is overcome in the approach given in the works of [1,[11][12][13] that includes the vibrational energy states in the collision operator of the transport equation, thus providing state to state transport coefficients for calculation of the transport properties in a gas flow. A justification for this more general state kinetic approach for transport coefficients for given sets of flow conditions was provided in earlier work, see for example [14,15].…”

“…In the present study, a quantitative assessment is made of the relative differences in transport coefficients calculated from Blottner curve fits [4] and the VHS model [6] in air mixture of a high temperature hypersonic flow. Then, using the state kinetic approach of Kustova [1], the role of binary and self diffusion is identified in a gas mixture.…”

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

“…Solving transport linear systems for multi-component mixtures in the state-to-state approximation is a very complicated technical problem because a great number of equations should be considered. A simplified technique for the calculation of the transport coefficients keeping the main advantages of the state-to-state approach, is suggested in Kustova (2001). The assumptions proposed in this paper made it possible to noticeably reduce the number of multi-component diffusion and thermal diffusion coefficients and simplify the expressions for the diffusion velocity and heat flux:…”

Heat flux and diffusion velocities behind shock wave: state-to-state approach

“…Unfortunately, the practical implementation of the state-to-state approach for viscous reacting mixtures occurs extremely computationally consuming since a large number of equations for vibrational distributions should be solved; moreover, at each time and space step of numerical simulation, the state-dependent transport coe©cients have to be computed solving the high-rank transport linear systems containing equations for each chemical component and vibration level. A simpli¦ed algorithm for the transport coe©cients calculation which reduces noticeably the number of equations has been proposed in [7]. Nevertheless, direct implementation of state-to-state transport algorithms is still complicated.…”