Transition from pulled to pushed premixed turbulent flames due to countergradient transport

Abstract

The influence of countergradient transport on the speed of a statistically stationary, planar, 1D premixed flame that propagates in frozen turbulence is studied theoretically and numerically by considering the normalised magnitude NB of the countergradient flux to be an input parameter. Spectra of admissible flame speeds are analytically determined and explicit travelling wave solutions are found for two algebraic relations widely used to close the mean rate of product creation. A problem of selecting the physically relevant solution that is approached for sufficiently steep initial conditions is addressed. It is argued that, if NB is larger than an analytically determined critical number NcrB, then the type of the physically relevant solution is drastically changed. If NB < NcrB, the physically relevant solution is of pulled wave type, i.e. its speed is controlled by processes localised to the leading edge of the flame brush and can be determined within the framework of a linear analysis at the leading edge. If NB > NcrB, the physically relevant solution is of pushed wave type, i.e. its speed is controlled by processes in the entire flame brush. Analytical expressions for the speed of the physically relevant solution as a function of NB and the density ratio are obtained. For NB > NcrB, the mean flame brush thickness and the spatial profile of the Favre-averaged combustion progress variable are also determined analytically. These results are validated by numerical simulations. Both analytical expressions and numerical data indicate that (i) both turbulent flame speed and thickness are decreased when NB is increased and (ii) the direction of total scalar flux (i.e. the sum of countergradient and gradient contributions) is strongly affected not only by NB, but also by the shape of the dependence of the mean rate of product creation on the mean combustion progress variable.