Accurate heat (Fourier) and mass (Fick and thermodiffusion) multicomponent transport at similar cost as mixture-averaged approximation

Abstract

An “extended 1 + M model” for Fick diffusion and thermodiffusion is proposed as a combination of both the efficient 1 + M model for Fick diffusion by Naud and Arias-Zugasti (2020), and an extension of the recent efficient multicomponent thermodiffusion formulation of Córdoba and Arias-Zugasti (2022). This new accurate and efficient model is mainly based on two ideas: proper re-scaling, enabling accurate and efficient inversion formulae based on Neumann series, and problem size reduction based on local identification of “main species”. Calculations of steady and unsteady 1D counterflow flames prove the excellent accuracy of the model. Considering the evaluation of Fick and thermal diffusion coefficients and thermal conductivity, together with the efficient approximation for molecular viscosity, the model appears to have a similar cost as the standard mixture-averaged approximation, being even cheaper for large numbers of species. Compared to the complete multicomponent formulation, the cost is reduced by an order of magnitude with a 58-species mechanism and by two orders of magnitude with 202-species and 300-species mechanisms.