Accurate Estimates of Fine Scale Reaction Zone Thicknesses in Hydrocarbon Detonations

Fully resolved predictions of steady, one-dimensional detonations near the ChapmanJouguet state in mixtures of methane-air and methane-oxygen-argon are presented. The model is restricted to inviscid continuum mixtures of calorically imperfect ideal gases described by detailed Arrhenius kinetics. Consistent with estimates from an underlying molecular collision theory, an eigenvalue analysis of locally linearized equations reveals that the continuum theory predicts evolution of species mass fractions on scales as fine as 10 cm, the mean free path length scale. In that such scales are orders of magnitude smaller than most discretization scales employed in simulations of combustion in engineering devices, it is suggested that one potential explanation for existing discrepancies between numerical prediction and observed data is that the calculations are highly under-resolved.