PULLED AND PUSHED TRAVELLING WAVES IN THE THEORY OF PREMIXED TURBULENT FLAMES
Paper in proceedings, 2015
We present theoretical results regarding the influence of countergradient transport (CGT) on the speed of a statistically stationary, planar, 1D premixed flame that propagates in frozen turbulence in a form of a traveling wave (TW). In order to extend a previous theoretical study by the present authors (Sabelnikov and Lipatnikov, 2013), we introduce a new one-parameter algebraic relation for the mean rate of product creation, which subsumes a number of available models. Depending on the magnitude of a parameter inherent in the reaction term, (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solutions occurs due to interplay of two nonlinear terms; the reaction term and the CGT term. Explicit pushed TW solutions are derived. Physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, are determined by seeking the TW solution characterized by the maximum decay rate at its leading edge.