Intra-bubble-combustion. premixed limit, stage I: dynamics of rapid premixed flame propagation inside a bubble

Abstract

The propagation of a spherically symmetric premixed thin flame inside an initially centrally ignited bubble in an unconfined viscous, incompressible liquid is theoretically analysed. This model focuses on the dynamical competition between the pressure increase produced by the chemical reaction and the pressure decrease induced by the bubble expansion (a consequence of radial momentum conservation). When a balance between these two processes is achieved an oscillatory response may be observed. The conditions leading to such a response are investigated. The effective inertia (the squared ratio between the characteristic liquid response time and the combustion time) is the main parameter governing this evolution. Two qualitatively different behaviours are encountered for large and small effective inertia-parameter. An approximate analytical solution is provided for each limiting case, as well as a correlation for the gaseous state at the end of the process, based on the former approximate solutions. While the system considered is deliberately highly idealized, some of these quantitative and qualitative results are expected to be helpful in the design of intra-bubble-combustion experiments (Rosner D E, Arias-Zugasti M and La Mantia B 2001 Combustion of individual bubbles and submerged gas jets 6th International Microgravity Combustion Workshop (Cleveland, OH, USA, 22–24 May); Rosner D E, Arias-Zugasti M and La Mantia B 2002 Combustion of individual bubbles and submerged gas jets (poster) 29th Symp. (International) on Combustion (Sapporo, Japan, 21–26 July); Rosner D E 1997 Combustion synthesis and material processing Chem. Eng. Edu (ASEE) 31 228) and, ultimately, bubble reactors.