| The evolution of a homogeneous, chemically reactive system with ns species forms a dynamical system in chemical state-space. Under suitable constraints, unique and stable equilibrium exists and can be interpreted as zeroth-dimensional (point like) attractors in this ns-dimensional space. At these equilibrium compositions, the rates of all reversible reactions vanish and can, in fact, be determined from thermodynamics independent of chemical kinetics.; Generalizing this concept, an m-dimensional Intrinsic Low Dimensional Manifold (ILDM) represents an m-dimensional subspace in chemical state-space where all but the m-slowest aggregate reactions are in equilibrium, and these aggregate reactions are determined by eigenvalue considerations of the chemical kinetics. In this context, a certain composition is said to be m-dimensional if it is on an m-, but not an (m − 1)-, dimensional ILDM.; Two new algorithms are proposed that allow the dimensionality of chemical compositions be determined simply. The first method is based on recasting the Maas and Pope algorithm. The second, and more efficient, method is inspired by the mathematical structure of the Maas and Pope algorithm and makes use of the technique known as arc-length reparameterization . In addition, a new algorithm for the construction of ILDM, and the application of these ideas to detonation simulations, is discussed.; In the second part of the thesis, numerical simulations of detonation waves initiated by hypervelocity projectiles are presented. Using detailed kinetics, only the shock-induced combustion regime is realized as simulating the conditions required for a stabilized detonation is beyond the reach of our current computational resources. Resorting to a one-step irreversible reaction model, the transition from shock-induced combustion to stabilized oblique detonation is observed, and an analysis of this transition based on the critical decay-rate model of Kaneshige (1999) is presented. |
