Stability of a spherical flame ball in a porous medium

High order effects in one step reaction sheet jump conditions for premixed flames

“…As an illustration of their utility, the improved jump conditions are applied to a model for steady, non-adiabatic flame balls [7][8][9][10]. It is found that the higher order jump conditions successfully predict a qualitative disagreement with the leading order results at moderate values of the Zeldovich number, as has been observed numerically [10].…”

“…Stability analyses, leading for example to the Sivashinsky equation [6], or describing the stability of flame balls [7][8][9][10], often involve a dispersion relation that covers two orders of magnitude in a perturbation parameter. Both orders are generated by the leading order jump conditions at a flame sheet, because of their extreme sensitivity to temperature changes at the sheet.…”

“…The activation temperature used in any one numerical simulation must also then be fixed and, necessarily, finite. Unexpectedly large differences can then arise between leading order asymptotic predictions for large activation temperature, based on using jump conditions, and numerical observations at finite activation temperatures [10]. Higher order corrections to the jump conditions can be used to estimate these differences.…”

“…It is informative to examine these higher order effects in the context of a model for non-adiabatic, spherically symmetric flame balls (as studied in [7][8][9][10], for example).…”

Near limit premixed flamelets in Hele-Shaw cells

“…The squeezed flamelet will take a pie shape in the narrow channel, and therefore thermal interactions between the flame and the channel walls are expected to play a significant role in the stabilization of the premixed flamelet. In this connection, the configuration under consideration is to some extent similar to that described by Shah et al [18] , where the structure and stabilization of flame balls in porous media were explored. However, it should be pointed out that, in their work the heat conductivity of the porous media has been neglected, so that the porous media merely behaves as a heat sink and has no contribution to heat redistribution.…”