Premixed Laminar Flames with General Rates of Strain

Abstract

The characteristics of planar premixed laminar flames are analyzed for general fields of rates of strain that include axisymmetric and two-dimensional counterflowing streams of reactants and products as special cases. Activation energy asymptotics are employed for a one-step Arrhenius reaction with small departures from adiabaticity and from unity values of the Lewis number. Density changes by heat release are fully taken into account. Low to moderate strain rates are considered intitially but high rates are subsequently treated. Attention is directed mainly to the influence on flame structure, extinction and ignition of a parameter ĉ determining the three-dimensional character of the rate of strain field. Axisymmetric flow corresponds to ĉ= 1, two-dimensional flow to ĉ= 0, while there is inflow along one of the coordinates parallel to the reaction sheet if − 1 ĉ≤0. Attention is devoted to the existence of multiple solutions and their features for − 1 ĉ≤0. The boundaries for extinction and ignition in terms of parameters measuring the deviations from adiabaticity and from unity Lewis number are found to be insensitive to ĉ but Damköhler numbers on these boundaries vary with ĉ. The significance of density variations for the special case of ĉ= − 1 is discussed.