Resonance of oscillations in reaction products and initial mixture as a reason for the deflagration-to-detonation transition

Qualitative transformation of a low-velocity laminar flow to a turbulent state (owing to natural or artificial instability) and formation of compression waves passing ahead have been studied in much detail. A disputable issue is the nature of the emergence of a reaction site in the region between the bow compression wave and the flame front moving at a certain distance behind this wave, as well as the dynamics of interaction of this site with the main structural elements. It is the type of this site (slow or explosive combustion) that defines its subsequent interaction with the compression wave front: shockless or shock-induced expansion capable of forming a detonation wave. As a method of transforming the reaction site to an explosion site, its amplification owing to the resonance of streamwise acoustic oscillations of hot reaction products with the initial combustible mixture induced by flame propagation is discussed. It is the resonance with its multiple enhancement of the amplitude of gas-dynamic parameters that can effectively initiate the deflagration-to-detonation transition. Various stages of this transition are discussed; the corresponding estimates are made and are found to be consistent with experiments.