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Flame balls stabilized by suspension in fluid with a steady linear ambient velocity distribution

The ignition of lean H2/air mixtures under microgravity (μg) conditions can lead to the formation of spherical premixed flames (flame balls) with small Péclet number (Pe). A central question concerning these structures is the existence of appropriate stationary stable solutions of the combustion equations. In this paper we examine an individual flame ball that is suspended in a fluid whose velocity far from the flame is steady and varies linearly in space. Detailed results are obtained for simple shear flows and simple straining flows, both axisymmetric and plane. Convection enhances the flux of heat from the flame and the flux of mixture to the flame, but because the Lewis number (Le) is less than unity the relative impact on the former is greater than on the latter. Consequently, there is a net loss of energy from the flame to the far field, and if large enough this will quench the flame. For values of shear or strain less than the quenching value there are two possible stationary solutions, but one of these is unstable to spherically symmetric disturbances of the flame ball. The radius of the other solution is unbounded as Pe goes to zero. Examination of a class of three-dimensional disturbances reveals no additional instability when the energy losses are due only to convection, but sufficiently large flame balls are unstable when volumetric heat losses from radiation are accounted for. This last result is in agreement with previous results that have been obtained for zero Pe, albeit with inadequate accounting for the flow field generated by the perturbations.