Study of the Cellular Detonation Dynamics at the Sub-Cell and Macro Scales

Abstract

This thesis, presented as a series of articles, aims to provide a deeper understanding of how small-scale dynamics, i.e., the cellular structure of the reaction zone, influence large-scale dynamics, i.e., the shape and dynamics of the wave globally, and to develop a rational model for predicting the detonation dynamics at these large scales. Previous studies on detonation propagation in curved channels and suddenly enlarging area have shown that, while the detonation front remains cellular, the geometry induces a global curvature that is integrated over many cells. The resulting detonation dynamics can be effectively described by a speed-curvature (𝐷 – 𝜅) relationship, where non-steady effects are negligible at this scale. However, both curvature and non-steady effects are very important when investigating the detonation behaviour at the cellular level. This thesis aims to elucidate these effects through experimental analyses and modelling of detonation dynamics and behaviour.

The first article, presented in Chapter 2, investigates the evolution of a multi-cellular, irregular detonation structure, predicting its behaviour based on the global response of the detonation front to geometric influences. We introduce new experiments on detonation diffraction in a 2D channel, focusing on the highly irregular cellular structure of detonations in stoichiometric mixtures of ethylene, ethane, and methane with oxygen as the oxidizer. The critical conditions for detonation diffraction and the critical channel height for each mixture are determined experimentally. Critical curvature data obtained from single-headed detonation experiments conducted in a separate study were found to provide a good prediction of critical diffraction in detonation diffraction experiments. This finding supports the view that the concept based on the (𝐷 – 𝜅) relationship is meaningful in predicting critical diffraction of irregular structure detonations. Chapter 3 examines whether incorporating the global effect of curvature is a relevant approach to understanding the weakly transient phenomenon of detonation initiation. A novel experimental technique is proposed to isolate detonation formation from the reflection of two decaying shocks. The test gases include a regular cellular structure mixture of 2H₂/O₂/2Ar and a highly irregular cellular structure of CH₄/2O₂. Through these experiments, we identified three distinct regimes: detonation formation, a Mach shock followed by a flame, and a case where no ignition occurs behind the Mach shock. The transition between detonation formation and ignition was found to follow the critical curvature theory of quasi-steady curved detonations closely. Moreover, the boundary between re-ignition and no re-ignition was accurately predicted by the critical decay rate theory.

In Chapter 4, we study the propagation of detonation waves in narrow channels which are subjected to boundary layer losses. The effect of boundary layer losses appears as the lateral divergence of the flow due to the increase in boundary layer displacement thickness. Two highly regular cellular structure mixtures of 2H₂/O₂/7Ar and 2H₂/O₂/7He are employed as test gases. Both diluents, argon and helium, have identical kinetics, Mach number, and specific heat ratio; however, their transport properties differ. The experiments showed variations in velocity deficits and cell sizes, despite being designed to maintain a constant induction zone length across the mixtures. These differences were explained by modelling the impact of global lateral flow divergence caused by boundary layer losses. Therefore, it appears that the large-scale dynamics are controlled by the long reaction zone thickness and are decoupled from the rapid dynamics of the front.

In Chapter 5, we use the same experimental setup—a narrow channel—to investigate the hydrodynamic thickness of detonations in the regular mixture of 2H₂/O₂/7Ar and irregular mixture of CH₄/2O₂ cellular structures. We experimentally measure the mean pressure evolution within a detonation cell as well as the pressure changes resulting from the head-on reflection of the detonation wave. Our experiments show that, on a global scale, the hydrodynamic thickness corresponds to the length of one cell in both mixtures. Furthermore, we confirm that the overall pressure evolution of the detonation wave and its reflection can be accurately reconstructed using the one-dimensional ZND model for the regular mixture. For the irregular mixture, we introduce a simplified one-step model tailored to the global structure of the reaction zone. Building on the work presented in Chapter 4, we further confirm that in narrow channel experiments, the large-scale dynamics, in mixtures characterized by the extended reaction zone, can be decoupled from the fast dynamics of the front. These findings suggest that a physically accurate model of the reaction zone is adequate to capture the detonation dynamics.

In Chapter 6, we take the next step toward developing a sub-cellular model within a cell. While transient effects are crucial within a detonation cell, the onset of the reaction occurs much faster initially than its decay rate. Therefore, this work focuses on predicting detonation dynamics within a single cell, specifically determining the shock strength at the start of the cell based on its strength at the end. To achieve this, we reformulate the triple-point reflection model, assuming that the Mach shock is reactive. The objective is to predict the strength of the lead shock following the triple-point collision. The model’s predictions are then compared to experimental data from detonations propagating in narrow channels with an enlarged cell structure, with high-speed schlieren imaging capturing the reflection dynamics. Despite experimental uncertainties, the model demonstrates a strong agreement with the observed results.