Detonation waves are supersonic combustion waves that have a complex three-dimensional cellular structure. There is growing experimental evidence that the cellular structure of detonations promotes their propagation in the presence of losses. In spite of that, the conventional model for the detonation structure, known as the Zeldovich - Von Neumann - Doring (ZND) model, neglects the existence of cellular structure for detonations and assumes the wave to consist of a strong leading planar shock coupled with trailing chemical reactions. Therefore, the influence of cellular structure on the dynamics and extinction limits of detonation waves has been of particular interest. Previous studies have investigated the influence of cellular structure on the dynamics of detonations with mass divergence in the framework of narrow tubes, porous-walled tubes and weak confinement. However, precise quantification of the loss mechanism in these frameworks has been associated with some difficulties. Complex flow in the boundary layers, inherent in thin tubes, or attenuation of the transverse waves in the porous-walled tubes has made the evaluation of the loss mechanism more difficult in such geometries. In this thesis, a novel well-posed problem is formulated for detonations with mass divergence. It is shown that detonations propagating in a channel with a cross-section area increasing exponentially have a constant mass divergence. The detonations were found to propagate at a quasi-steady speed below the ideal Chapman-Jouguet velocity. This permitted to make meaningful comparison with the theoretical models and simulations. The experiments were performed in two mixtures, one displaying characteristic weakly unstable detonations (2C2H2 + 5O2 + 21Ar), and the other displaying highly unstable detonations (C3H8 + 5O2). The dependence of the velocity deficits and limits on the amount of mass divergence for the two mixtures were compared with the predictions of the quasi-one-dimensional ZND model with lateral mass divergence. Since the ZND model neglects the cellular structure of the detonations, such comparison permitted to asses the influence of cellular structure on the dynamics of detonations with mass divergence. Comparisons were also made with the results of simulations of inviscid cellular detonations. These comparisons showed that the velocity deficits and critical rate of mass divergence in the weakly unstable mixture were reasonably well predicted by the quasi-one-dimensional model. For smaller values of mass divergence rate, a good agreement between the experiments and the predictions of the two-dimensional cellular simulations was observed for the weakly unstable mixture. For the highly unstable detonations, the quasi-one-dimensional model significantly over-predicted the effect of mass divergence.Detonations were observed for rates of mass divergence 93% higher than the critical predicted value, displaying more substantial velocity deficits than predicted. Such observations show conclusively that the ZND model cannot capture the dynamics of highly unstable detonations on large scales.

Detonations in gases usually propagate with lateral strain rates, in either weakly confined or varying-cross-section or curved or even small-sized geometries. Lateral strain rates have been generally known to significantly impact the detonation dynamics, i.e., decreasing the propagation speeds lower than the theoretical Chapman-Jouguet (CJ) velocities, increasing the propagation limit pressures as well as cell sizes. Since the detonation-based engines require the reliable control of the accurate ignition and stable propagation of a detonation wave, it is desirable to have the predictive capability of the response of detonation dynamics to lateral strain rates, for achieving the practical purposes of detonation applications. Therefore, the present thesis aims to provide such predictability, by quantifying the effect of lateral strain rates on detonation dynamics from both the experimental and numerical modelling perspectives. Experimentally, this study extended the exponential horn technique of Radulescu and Borzou (2018) to a range of characteristic mixtures with varied detonation instability levels, i.e., from the weakly unstable system of 2H₂/O₂/7Ar to the highly unstable one of CH₄/2O₂. Steady detonation waves were obtained at the macro-scale, with the very regular H₂/O₂/Ar detonation cellular structures characterized by reactive transverse waves while the unstable hydrocarbon-oxygen detonation reaction zone structures in the presence of significant unreacted gas pockets. The meaningful D-K curves characterizing the relationships between the detonation mean propagation speeds and lateral strain rates were directly obtained from experiments. Comprehensive comparisons were then made between experiments and predictions from the generalized ZND model with lateral strain rates. Excellent agreement was found for the stable H₂/O₂/Ar detonations due to the much longer thermally insensitive reaction zone lengths compared to the characteristic induction zone lengths, while substantial departures exist for the highly unstable CH₄/2O₂ detonations. The degree of departure was found to correlate well with the detonation instability. As compared to the laminar ZND wave, the more unstable hydrocarbon-oxygen detonations manifested themselves in the significantly enhanced global rates of energy release with the notably suppressed thermal character of ignition. Implications of such a globally enhanced burning mechanism highlight the important role of diffusive processes involved in turbulent burning of the unreacted gas pockets. Finally, empirical global reaction rate laws were developed for effectively capturing the dynamics of unstable detonations. Numerically, this work proposed a novel model for evaluating the effect of boundary layer losses on cellular structures of 2D detonations in narrow channels. The boundary-layer-induced lateral strain rate was evaluated using the negative boundary layer displacement of Mirels' theory. With the theoretical Mirels' constant KM reduced by a factor of 2, the experimentally obtained 2H₂/O₂/7Ar detonations can be very well reproduced by simulations using the resulting quasi-2D formulation. It was further found out that detonation cellular cycle dynamics can be modified by the presence of boundary layer losses, yielding larger velocity fluctuations and more rapid decay rates of the lead shock. The exponential sensitivity of detonation cell sizes to velocity deficits, controlled by the global activation energy, highlights the importance of providing the detonation speed when reporting experimentally measured cell sizes.