Modeling of 2D self-drifting flame-balls in Hele-Shaw cells

The disintegration of near limit flames propagating through the gap of Hele-Shaw cells has recently become a subject of active research. In this paper, the flamelets resulting from the disintegration of the continuous front are interpreted in terms of the Zeldovich flame-balls stabilized by volumetric heat losses. A complicated free-boundary problem for 2D self-drifting near circular flamelets is reduced to a 1D model. The 1D formulation is then utilized to obtain the locus of the flamelet velocity, radius, heat losses and Lewis numbers at which the self-drifting flamelet exists. Novelty and significance statement: The existence and limits of self-propagating 2D flame-balls have been substantiated theoretically for the first time. They have been investigated analytically, displaying the crucial role of heat losses. The regime arises in praxis in thin enclosures such as Hele-Shaw cells. The design of flame arresters may well be influenced by these findings.