Dynamic response of strained premixed flames to equivalence ratio gradients

Abstract

Premixed flames encounter gradients of mixture equivalence ratio in stratified charge engines, lean premixed gas-turbine engines, and a variety of other applications. In cases for which the scales—spatial or temporal—of fuel concentration gradients in the reactants are comparable to flame scales, changes in burning rate, flammability limits, and flame structure have been observed. This paper uses an unsteady strained flame in the stagnation point configuration to examine the effect of temporal gradients on combustion in a premixed methane/air mixture. An inexact Newton backtracking method, coupled with a preconditioned Krylov subspace iterative solver, was used to improve the efficiency of the numerical solution and expand its domain of convergence in the presence of detailed chemistry. Results indicate that equivalence ratio variations with timescales lower than 10 ms have significant effects on the burning process, including reaction zone broadening, burning rate enhancement, and extension of the flammability limit toward learner mixtures. While the temperature of a flame processing a stoichiometric-to-lean equivalence ratio gradient decreased slightly within the front side of the reaction zone, radical concentrations remained elevated over the entire flame structure. These characteristics are linked to a feature reminiscent of “back-supported” flames—flames in which a stream of products resulting from burning at higher equivalence ratio is continuously supplied to lower equivalence ratio reactants. The relevant feature is the establishment of a positive temperature gradient on the products side of the flame which maintains the temperature high enough and the radical concentration sufficient to sustain combustion there. Unsteadiness in equivalence ratio produces similar gradients within the flame structure, thus compensating for the change in temperature at the leading edge of the reaction zone and accounting for an observed “flame inertia”. For sufficiently large equivalence ratio gradients, a flame starting in a stoichiometric mixture can burn through a very lean one by taking advantage of this mechanism.