Instabilities of reverse smolder waves

Abstract

We use numerical strategies to examine the stability of reverse smolder waves in the context of a model that can permit both fuel-rich and fuel-lean waves. The steady-state response for such waves, maximum temperature versus blowing rate, is characterized, for increasing blowing rate, by a fuel-rich branch of rising temperature followed by a fuel-lean branch of falling temperature, followed by quenching. The propagation speed at the quenching point is non-zero. For the parameters that we consider, the entire fuel-rich branch is unstable to two-dimensional disturbances, but the dynamic consequences are modest. An interval of the fuel-lean branch whose left boundary is at the point of stoichiometry is stable, but the remainder of the branch, all the way to the quenching point, is unstable. These instabilities are destructive, and the smolder wave becomes fragmented. Tribrachial fragments can emerge, analogous to the tribrachial or triple flames familiar from gaseous edge-flame studies. Their emergence is characterized by a sharp rise in the maximum temperature, a rise that could lead to a transition to flaming (gas-phase) combustion.