Theory of the transition from conductive to convective burning

Modelling of the transition from conductive to convective burning in porous energetic materials

“…Except for the proposed change in the energy equation other ingredients of the formulation are similar to those of [13]. Specifically, the gas and solid are assumed to be in thermal equilibrium, allowing utilisation of a single-temperature description for the two-phase medium (T = T s ).…”

“…Therefore in this paper, for brevity's sake some intermediate technical details are omitted, and one may consult [13] for additional information.…”

“…Although both conductive and convective modes have been well explored previously [8][9][10][11][12], understanding of the transition phenomenon and its dependence on material and chemical properties and physical influences is still incomplete. The first successful attempt to bridge conductive and convective modes was undertaken in [13]. It was shown that the abrupt transition from slow to fast burning is triggered by autoignition of the solid explosive resulting from the overpressure-induced preheating of the gas within its pores.…”

“…Yet, as has recently been realised, the model adopted in [13], while capturing the basic aspects of the phenomenon, does not meet the requirement for conservation of energy. The current paper repairs this flaw.…”

“…The current paper repairs this flaw. Specifically, based on the motivational example that follows, the non-divergent term φ(∂P /∂t) in the energy equation in [13] is replaced by the divergent term ∂(φP )/∂t, P and φ being the gas pressure and the solid's porosity.…”