Modelling of Quasi Steady Detonations with Inert Confinement

Abstract

In this thesis, we address the problem of steady propagation of a gaseous detonation weakly confined by an inert gas. The effect of the lateral divergence is modelled using Watt’s Straight Streamline Approximation and a newly derived simpler nozzle model in a hydrodynamic average description. The prediction of the models was compared against the detonation velocity data obtained numerically by Mi et al and Reynaud et al. Very good agreement is found for weakly stable detonations at low activation energy with all models. These models, however, fail to capture the dynamics of unstable gaseous detonations characterized by delayed energy release, long induction lengths and higher activation energies. This inconsistency is treated by different models for the macroscopic kinetics: the underlying chemical kinetics model applicable for a laminar formulation, an effective kinetic rate adjustment to account for the detonation thickening owing to the cellular instability and a new ignition delay distribution model conditioned on the distribution of shock temperatures at the shock. The study illustrates that the reaction zone thickening of detonation waves and the delayed energy release are responsible for its limits. Future work should be extended to incorporate more accurate sub-cellular models to capture other effects, such as the ignition of gases via turbulent mixing in very irregular detonations.