Numerical Modeling of Combustion and Detonation in Aqueous Foams

Combustible aqueous foams and foamed emulsions represent prospective energy carriers. This paper is devoted to the overview of model assumptions required for numerical simulations of combustion and detonation processes in aqueous foams. The basic mathematical model is proposed and used for the analysis of the combustion development in the wet aqueous foam containing bubbles filled with reactive gas. The numerical results agree with the recent experimental data on combustion and detonation in aqueous foams containing premixed hydrogen–oxygen. The obtained results allowed for distinguishing the mechanisms of flame acceleration, transition to detonation, detonation propagation, and decay.

An Elementary Model for a Self-Accelerating Outward Propagating Flame Subject to the Rayleigh–Taylor Instability: Transition to Detonation

Within the Boussinesq approximation, an elementary model for the deflagration-to-detonation transition triggered by self-acceleration of an expanding flame is formulated and explored. The self-acceleration is sustained by the intrinsic Rayleigh–Taylor instability until the Deshaies–Joulin deflagrability threshold is reached, followed by an abrupt transition to detonation. Emergence of the threshold is caused by positive feedback between the accelerating flame and the flame-driven pressure shock that results in the thermal runaway when the flame speed reaches a critical level. The model offers a simple mechanism that may be responsible for the transition to detonation in thermonuclear supernovae.