High order effects in one step reaction sheet jump conditions for premixed flames

The differences need to be understood between the leading order jump conditions, often assumed at a flame sheet in combustion theory, and the actual effect of a one step chemical reaction governed by Arrhenius kinetics. These differences are higher order in terms of a large activation temperature analysis and can be estimated using an asymptotic approach. This paper derives one order of asymptotic correction to the leading order jump conditions that are normally used for describing premixed laminar combustion, providing additional contributions that are due to curvature, flow through the flame sheet and the temperature gradient into the burnt gas. As well as offering more accurate asymptotic results, these can be used to estimate the errors that are inherent in adopting only the leading order version and they can point towards major qualitative changes that can occur at finite activation temperatures in some cases. Applied to steady non-adiabatic flame balls it is found that the effect of a non-zero temperature gradient in the burnt gas provokes the most serious deficiency in the asymptotic approach.