On the dynamics of transition from propagating flame to stationary flame ball

A theoretical and numerical study was conducted on expanding spherical flames in order to understand how stationary flame ball (SFB) can be attained. Numerical simulation of the full unsteady problem was first performed for mixtures with low Lewis numbers. Depending on the order of magnitude of the heat loss, three typical regimes were found: (i) when the heat loss is very small, the spherical flame expands outwardly and transforms asymptotically to a planar flame; (ii) when the heat loss is moderately large, the planar flame does not exist and the expanding flame quenches; and (iii) when the heat loss is large, the expanding spherical flame transforms to a stationary flame ball. A quasi-steady nonlinear relation between the instantaneous flame radius R and its velocity U was obtained via asymptotic analysis and numerical computations with constant density and one-step Arrhenius kinetics. It was found that there is a continuous variation of the flame velocity from zero to the planar flame velocity. When the heat loss is larger than a critical value, the velocity-radius relation exhibits a turning point which may correspond to either flame extinction or reversal of the direction of propagation.