Efficient calculation of multicomponent diffusion fluxes based on kinetic theory

Abstract

The calculation of the diffusion matrix in mixtures of dilute gases with large numbers (N) of components is revisited. An extremely simple relation providing the multicomponent diffusion matrix as a power series in terms of the N−1 independent mole fractions in the mixture is analytically derived from the kinetic theory of gases. This power series provides a convergent scheme with high convergence rate in the case of a gas mixture with one major component in which the remaining N−1 species are diluted. However, the convergence rate of this power series is lower if a certain number (M) of these species are far from the dilute limit. In that case we show that a straightforward modification of the former scheme leads to a relation providing the diffusion matrix as a power series in terms of a subset of N−1−M mole fractions, which are assumed to be dilute, keeping full dependence on the mole fractions of the remaining 1+Mmajor species. This relation takes full advantage of the usual situation found in combustion, where there is a relatively small number of major species (here 1+M), with the remaining N−1−M chemical components (often radicals) being in trace amounts. The error found in the diffusion fluxes with each one of these new methods in a typical combustion scenario is analyzed as a function of the number of terms included in the expansion. It is found that the second method (based on a power series in terms of the dilute species), truncated at the linear term, produces relative errors less than 1% in all the cases considered—including cases far from the dilute limit. Hence, this method provides an efficient tool for the accurate calculation of multicomponent diffusion fluxes in combustion.