Modeling Of Detonations Using Scenarios With Hydrogen As A Fuel

The goal of this dissertation was to obtain greater insights into detonation scenarios involving hydrogen-air/oxygen mixtures using computer simulations. A primary goal was to use coarse meshes to study detonations for realistic geometries and scales in a computationally efficient manner. We identified the chemistry model, kinetics model, and turbulence model that helped us during our investigation. We further studied the influence of equivalence ratio, viscosity and radiation on various detonation scenarios. In the first chapter, we begin by introducing the pertinent experimental and theoretical background of detonations. This section serves the purpose of preparing the reader on the main ideas in the research area. In addition to this, we list our contributions to the research area. In chapter 2, the impact of viscous and radiative losses and the point source approximation on detonation hydrodynamics were studied using a hydrocode and a computational fluid dynamics (CFD) framework for hydrogen-air mixtures. The hydrocode solved for the hydrodynamics using the non-reacting TNT equivalency method as well as the inviscid (Euler) equations and the JWL equation of state. For the CFD framework, we solved the hydrodynamics using the SRK equation of state, Large Eddy Simulations (LES) as well as the spectrally-averaged mean absorption coefficient for radiative properties. In addition, the CFD framework employed a 21-step detailed chemistry mechanism utilizing a hydrogen-air mixture After validating our simulation methodology by comparing it to transient pressure profile measurements from a small-scale explosion study, the settings in the validation were then utilized to solve for a detonation in a larger domain. The study on the impact of equivalence ratio showed that rich and lean flames strengthened the acceleration and strength of the wave. While viscous losses were shown to weaken the detonation, the impact of radiation wasnât appreciable due to the difference in the magnitude of the radiative source and chemical heat release term. In Chapter 3, we report our findings on the feasibility of a coarse mesh (cell size ~ 2mm) finite volume solver to reproduce experimental research on hydrogen-air mixture detonations. The solver utilized: Large Eddy Simulation (LES) to model the turbulence, a 21-step detailed mechanism to model the combustion, estimated transport properties (binary diffusion coefficients) using kinetic theory and employs the Soave-Redlich-Kwong equation of state to account for compressibility effects associated with the high-pressure detonation wave. Our solution methodology was first validated by comparing numerical predictions against experimental measurements of the interaction of a non-reacting shock wave against the walls of a cavity. We then carried numerical predictions of detonation at different blockage ratios (BR), BR = 0.3 and BR = 0, and equivalence ratios (0.5, 0.75, 1.0, 1.25 and 1.5). Using our approach, we showed that the trends of the detonation velocities with blockage ratios and equivalence ratios followed experimental trends. The methodology can therefore be extended to other detonation scenarios that have large dimensions or complex geometry and that require coarse computational cells (~2mm). Finally, we finish the dissertation by discussing our contributions to the research and some thoughts on future wor

A stability index for detonation waves in Majda's model for reacting flow

Using Evans function techniques, we develop a stability index for weak and strong detonation waves analogous to that developed for shock waves in [GZ,BSZ], yielding useful necessary conditions for stability. Here, we carry out the analysis in the context of the Majda model, a simplified model for reacting flow; the method is extended to the full Navier-Stokes equations of reacting flow in [Ly,LyZ]. The resulting stability condition is satisfied for all nondegenerate, i.e., spatially exponentially decaying, weak and strong detonations of the Majda model in agreement with numerical experiments of [CMR] and analytical results of [Sz,LY] for a related model of Majda and Rosales. We discuss also the role in the ZND limit of degenerate, subalgebraically decaying weak detonation and (for a modified, ``bump-type'' ignition function) deflagration profiles, as discussed in [GS.1-2] for the full equations.Comment: 36 pages, 3 figure

Steady non-ideal detonations in cylindrical sticks of expolsives

Numerical simulations of detonations in cylindrical rate-sticks of highly non-ideal explosives are performed, using a simple model with a weakly pressure dependent rate law and a pseudo-polytropic equation of state. Some numerical issues with such simulations are investigated, and it is shown that very high resolution (hundreds of points in the reaction zone) are required for highly accurate (converged) solutions. High resolution simulations are then used to investigate the qualitative dependences of the detonation driving zone structure on the diameter and degree of confinement of the explosive charge. The simulation results are used to show that, given the radius of curvature of the shock at the charge axis, the steady detonation speed and the axial solution are accurately predicted by a quasi-one-dimensional theory, even for cases where the detonation propagates at speeds significantly below the Chapman-Jouguet speed. Given reaction rate and equation of state models, this quasi-one-dimensional theory offers a significant improvement to Wood-Kirkwood theories currently used in industry

Theory of weakly nonlinear self sustained detonations

We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced, unsteady, small disturbance, transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multi- dimensional detonations