The Structure and Stability of Flame Balls: A Near-Equidiffusional Flame Analysis

Source abstract

The structure and stability of flame balls is examined in the context of an asymptotic analysis in which $\theta \to \infty ,\, ( {{\text{1 - Le}}} ) = O( 1/\theta )$, where $\theta$ is the activation energy and Le the Lewis number. The heat-loss mechanism necessary for stable solutions is radiation from the burnt gas. For heat losses less than the quenching value there are two stationary solutions, but the one with the smaller radius is always unstable to one-dimensional disturbances. When ${\text{Le}} = 1$ the large solution is also unstable, but for ${\text{Le}} < {\text{Le}}_c < 1$, where ${\text{Le}}_c$ is a critical value, a portion of the large-solution branch is stable. Sufficiently large solutions are always unstable to three-dimensional disturbances, independent of Le. These results imply that flame balls can only be generated if Le is sufficiently small, and are consistent with previous results which suggest that the three-dimensional instability is not a Turing instability but is instead a creature of the near-field heat losses.