Generalized flame balls

We consider generalized flame balls which correspond to stationary spherical flames with a flow of hot inert gas, either a source or a sink, at the origin. Depending on the flow, these flames can have positive, zero, or negative burning speeds, with zero speeds characterizing the Zeldovich flame balls. A full analytical description of these structures and their stability to radial perturbations is provided, using a large activation energy asymptotic approach and a thermo-diffusive approximation. The results are also complemented by a numerical study. The number and stability of the generalized flame balls are identified in various regions of the l-M-h0 space, where l is the (reduced) Lewis number, and M and h0 the flow rate and its enthalpy at the origin, respectively. It is typically found that, when the flow is a source, there is a maximum value of the flow rate Mmax depending on l and h0, above which no stationary solutions exist, and below which there are two solutions characterizing a small stable flame ball and a large unstable flame ball; the implications of these results to the problem of ignition by a hot inert gas stream are discussed. When the flow is a sink, however, there is typically a single unstable solution, except for sufficiently large values of the Lewis number and large negative values of M , where three flame balls exist, the medium one being stable. Finally, the relation between the flame speed, positive or negative, and the flame curvature, small or large, is discussed.