Chapman-Jouguet Deflagrations and Their Transition to Detonations
Creators: name: Rakotoarison, Willstrong
Publisher: name: Université d'Ottawa / University of Ottawa
Year: 2023
Subjects: Deflagration
Detonation
Deflagration to detonation transition
High-speed flames
Explosions
Shock waves

description: This thesis by articles addresses the role played by Chapman-Jouguet (CJ) deflagrations in deflagration to detonation transition (DDT) events. By definition, CJ deflagrations are flames propagating with a sonic flow in the burned gases, and are theoretically the fastest subsonic combustion waves able to propagate steadily, predicted using conservation of mass, momentum and energy. DDT is difficult to describe, as many complex phenomena and their interaction take place, including flame instabilities, turbulent combustion, and combustion in compressible medium, among others. Recent experiments and numerical simulations however showed that, prior to transition to detonations, deflagrations plateau at the CJ regime before rapid acceleration. In the present thesis, multiple aspects of the last stages of DDT are studied, and are each presented in published articles or articles in preparation. The two articles presented in Chapter 2 focus on experiments performed on the transition of a shock-flame complex to a detonation downstream of a single obstacle, in a stoichiometric propane-oxygen mixture at low pressure, mimicking the common configuration found at the last stages of DDT in experiments and numerical simulations performed in a channel filled with obstacles. The relative large size of the obstacle and the low gas initial pressure permitted to visualize the details of the initiation of the detonation around the obstacle. Transition to detonation was found to occur in a similar fashion for variously shaped obstacles, after flame acceleration due to the interaction with reflected shocks. This acceleration process was found to occur rapidly in the case where the incident flame propagated with a burning rate close to the Chapman-Jouguet value. The third article presented in Chapter 3 describes a model aimed to predict the properties of shocks followed by a CJ deflagration, in experimental configurations where the burned gases can be vented. The formulation is similar to the double discontinuity problem adapted from the work of Chue (1993), extended to cases where the burned gases are not confined by a rear wall anymore, but can be vented through an opening of known dimensions. The properties of the shock / CJ-deflagration complex could then be predicted and compared to flame measurements done prior the initiation of detonations, obtained on a selection of large scale DDT experiments. The good agreement suggests that DDT occurs when deflagrations reach the CJ regime, corroborating with observations done in shock tubes. The article presented in Chapter 4 is aimed to present a consistent method for calculating the structure of flames propagating at arbitrary burning velocities, from the low-Mach case (isobaric) up to the CJ deflagration regime. The method uses a dynamical system approach to calculate the steady wave structure, described by ordinary differential equations. A stability analysis near the burned and unburned gases permitted to develop a numerical shooting technique, which was used to obtain the flame structure and burning rate eigenvalue. Chapter 5 is a numerical study of the deflagration to detonation transition problem in one-dimension. By linearly increasing the burning rate eigenvalue to increase the flame burning velocity, the flame first reached the CJ condition. Subsequent increase in the burning rate leads to the self-organization of the flame into a CJ deflagration - shock complex. This self-organization triggers a pulsating gasdynamic instability leading to the transition of the flame to detonation.