Flame acceleration associated with the Darrieus-Landau instability

Abstract

Flame acceleration associated with the Darrieus-Landau hydrodynamic instability is investigated computationally using an analytical model of premixed-flame structure valid in the limit of large-chemical-activation energies and weak flame stretch. A level-set formulation is used to track the evolution of the premixed flame and the Euler equations are used to describe the flow field. Coupling between the flame and flow-field dynamics resulting from order-unity gas expansion within the flame is found to result in growth of the average radius of outwardly propagating flames in proportion with the 3/2 power of time, consistent with experiment. Influences of the flame thickness, relative to the length scale of the hydrodynamic flow, and of the density ratio across the flame on the critical Reynolds numbers associated with the onset of wrinkled-flame propagation and self-similar acceleration are described also.