Exact solutions to reaction-diffusion equation and the direction of turbulent scalar flux in a premixed turbulent flame and its leading edge

Paper in proceeding, 2012

A statistically stationary, planar, one-dimensional premixed turbulent flame is theoretically studied and exact analytical solutions to the problem are obtained using two sets of widely used closure relations. The solutions show that, contrary to widespread belief, the gradient behavior of scalar transport at the leading edge of a premixed turbulent flame brush is not a necessary condition in order for the flame to propagate. The above theoretical results are confirmed by a numerical study of the development of one-dimensional, planar flames initiated by a localized step in combustion progress variable profile. Numerical simulations also indicate that the dependence of the mean rate of product creation on the Favre-averaged combustion progress variable affects significantly the direction of turbulent scalar flux in a premixed flame.