Numerical and analytical studies of the dynamics of gaseous detonations

Abstract

This thesis examines two dynamic parameters of gaseous detonations, critical energy and cell size. The first part is concerned with the direct initiation of gaseous detonations by a blast wave and the associated critical energy. Numerical simulations of the spherically symmetric direct initiation event with a simple chemical reaction model are presented. Local analysis of the computed unsteady reaction zone structure identities a competition between heat release rate, front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the shock front. On this basis, simplifying assumptions are applied to the governing equations, permitting solution of an analytical model for the critical shock decay rate. The local analysis is validated by integration of reaction zone structure equations with detailed chemical kinetics and prescribed unsteadiness. The model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models, this equation is not dependent on other experimentally determined parameters. For different fuel-oxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude. The second part of the thesis is concerned with the development of improved reaction models for accurate quantitative simulations of detonation cell size and cellular structure. The mechanism reduction method of Intrinsic Low-Dimensional Manifolds, originally developed for flame calculations, is shown to be a viable option for detonation simulations when coupled with a separate model in the induction zone. The agreement with detailed chemistry calculations of constant volume reactions and one-dimensional steady detonations is almost perfect, a substantial improvement on previous models. The method is applied to a two-dimensional simulation of a cellular detonation in hydrogen-oxygen-argon. The results agree well with an earlier detailed chemistry calculation and experimental data. The computational time is reduced by a factor of 15 compared with a detailed chemistry simulation.