PULLED AND PUSHED TRAVELLING WAVES IN THE THEORY OF PREMIXED TURBULENT FLAMES
Paper i proceeding, 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.