Effect of acoustic coupling on power-law flame acceleration in spherical confinement

A model describing acoustically-generated parametric instability in a spherical chamber is developed for quasi-one-dimensional, low-Mach number flames. We demonstrate how sound waves generated by a centrally-ignited, outwardly-propagating accelerating flamefront can be incorporated into an existing theory of self-similar flame acceleration in free space [V. Akkerman, C. K. Law, and V. Bychkov, "Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering," Phys. Rev. E83, 026305 (2011)]10.1103/PhysRevE.83.026305. Being reflected from the chamber wall, flame-generated acoustics interact with the flamefront and the attendant hydrodynamic flamefront cellular instability. This in turn affects the subsequent flame morphology and propagation speed. It is shown that the acoustics modify the power-law flame acceleration, concomitantly facilitating or inhibiting the transition to detonation in confinement, which allows reconciliation of a discrepancy in experimental measurements of different groups.