We investigate iterative methods for solving linear systems arising from the kinetic theory and providing transport coefficients of dilute polyatomic gas mixtures. These linear systems are obtained in their naturally constrained, singular, and symmetric form, using the formalism of Waldmann and Trübenbacher. The transport coefficients associated with the systems obtained by Monchick, Yun, and Mason are also recovered, if two misprints are corrected in the work of these authors. Using the recent theory of Ern and Giovangigli, all the transport coefficients are expressed as convergent series. By truncating these series, new, accurate, approximate expressions are obtained for all the transport coefficients. Finally, the computational efficiency of the present transport algorithms in multicomponent flow applications is illustrated with several numerical experiments.

Conclusions derived from the solution of premixed laminar flames in a stagnation point flow are important in the determination of chemically controlled extinction limits and in the ability to characterize the combustion processes occurring in turbulent reacting flows. In the neighborhood of the stagnation point produced in these flames, a chemically reacting boundary layer is established. For a given equivalence ratio, the input flow velocity can be varied and solutions can be determined for increasing values of the strain rate. As the strain rate increases, the flame nears extinction. Recent experimental, computational and theoretical work has shown that extinction of these flames can be achieved by either flame stretch or by a combination of flame stretch and incomplete chemical reaction. Extinction by flame stretch is possible when the Lewis number of the deficient reactant is greater than a critical value and extinction resulting from both flame stretch and incomplete chemical reaction is possible when the Lewis number of the deficient reactant is less than this value. In this paper we study the extinction process computationally. We model the governing conservation equations with complex transport and detailed kinetics. By employing adaptive boundary value solution methods with numerical bifurcation techniques, we generate detailed extinction curves for hydrogen-air and methane-air flames in a counterflow geometry.

The influence of thermal diffusion on the structure of hydrogen-air and methane-air flames is investigated numerically using complex chemistry and detailed transport models. All the transport coefficients in the mixture, including thermal diffusion coefficients, are evaluated using new algorithms which provide, at moderate computational costs, accurate approximations derived rigorously from the kinetic theory of gases. Our numerical results show that thermal diffusion is important for an accurate prediction of flame structure. Combustion models used in the study of pollutant formation, ignition processes and chemically controlled extinction limits combine complex chemical kinetics with detailed transport phenomena. One such transport phenomenon, often neglected in numerical flame models, is thermal diffusion which gives rise to the Soret and Dufour effects. In the governing equations of multicomponent reactive flows, both effects are expressed in terms of the same transport coefficients, namely the thermal diffusion coefficients. This originates from the self-adjointness of the linearized Boltzmann collision operator or also from the reciprocal relations in Onsager's theory. The Soret effect corresponds to an additional term in the species diffusion velocities which is proportional to the temperature gradient. On the other hand, the Dufour effect is accounted for by an additional term in the heat flux vector. From a qualitative viewpoint, it is well known that the Soret effect tends to drive light molecules towards hot regions and heavy molecules towards cold regions of the flow. It is thus particularly important in the presence of strong temperature gradients such as those found in flame fronts and chemical reactors where the wall temperature differs significantly from that of the surrounding gases. In particular, hydrogen, atomic or molecular, is a species which is likely to be strongly influenced by thermal diffusion. The influence of thermal diffusion on flame structure was first studied numerically for laminar one-dimensional hydrogen-nitrogen-oxygen flames (1-3). In (1), it was found that the laminar flame speed was slightly lower when thermal diffusion was taken into account. This result was obtained for both lean and rich flames, but thermal diffusion was modelled using semi-empirical expressions and only for the diffusion flux of atomic and molecular hydrogen. For rich flames, discrepancies in the thermal diffusion coefficients with respect to the values predicted by the kinetic theory were observed (1). On the other hand, it was

Freely propagating and counterflow laminar premixed steady hydrogen/air and methane/air flames are investigated numerically using complex chemistry and detailed transport models. All the transport coefficients in the mixture, including thermal diffusion coefficients, are evaluated using cost-effective, accurate algorithms derived recently by the authors from the kinetic theory of gases. Our numerical results provide a quantitative assessment of the impact of thermal diffusion on planar flame speed as a function of equivalence ratio and on extinction limits of counterflow flames as a function of either strain rate or equivalence ratio. In some cases, such as rich hydrogen/air flames, the effect of thermal diffusion is actually opposite to the one expected from a qualitative viewpoint or obtained with empirical models. In addition, we observe relevant effects of thermal diffusion on extinction of methane/air counterflow flames