Analysis of mixture stratification effects on unstrained laminar flames

Abstract

Detailed one-dimensional computations of unsteady unstrained laminar flames subjected to sinusoidal equivalence ratio perturbations are presented. The responses of the flame thickness, flame speeds, species concentrations and the species reaction rates to equivalence ratio variations are investigated. The effect of stratification is quantified by comparing the structure of a stratified flame to that of an equivalent homogeneous mixture flame at an equivalence ratio that the stratified flame experiences. The difference between a flame burning into a leaner mixture or a richer mixture yields hysteresis for consumption speed and flame thickness in the equivalence ratio space, which becomes more prominent with stronger stratification, especially when the flame propagates towards a negative equivalence ratio gradient under fuel-lean conditions. The displacement speed and its components are analysed, with the diffusion, reaction rate and cross-dissipation components all showing a strong hysteresis, but with different signs, partially cancelling each other. The phase space responses of the scalars are compared and the different phase shifts are evaluated. Interestingly, these observations were not affected by the choice of the reaction mechanism. The effects of equal and mixture-average diffusivity assumptions on the results are tested, where the latter caused two times stronger hysteresis effects: the thermo-diffusive effects of heat and products behind the flame were found to play a significant role for laminar flame propagation in stratified mixtures, even for unstrained flames. The stratified flame shows significant alteration in the species concentrations and reaction rates, especially for the minor and product species. The response of the sinusoidal oscillations is compared against cases with linear mixture stratification. Even with the absence of the compressible strain, it is demonstrated that the stratification effects heavily influence the flame properties and the treatment of thermo-physical transport properties has been demonstrated to be pivotal to the accurate prediction of this behaviour.