A reduced model for a self-accelerating expanding flame subjected to the Darrieus-Landau and Rayleigh-Taylor instabilities: Transition to detonation

• Published in: Combustion and flame Vol. 245; p. 112333
• Main Authors: Kagan, Leonid, Gordon, Peter V., Sivashinsky, Gregory
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.11.2022
• Subjects: Darrieus-Landau and Rayleigh-Taylor instabilities in flames; Deflagration-to-detonation transition; Self-accelerating flames; Supernovae explosions; Deflagration-to-detonation transition; Supernovae explosions; Self-accelerating flames; Darrieus-Landau and Rayleigh-Taylor instabilities in flames
• ISSN: 0010-2180; 1556-2921
• DOI: 10.1016/j.combustflame.2022.112333

A weakly nonlinear model for a self-accelerating outward propagating corrugated flame is formulated and explored. The self-acceleration is sustained by the intrinsic Darrieus-Landau and Rayleigh-Taylor instabilities 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.