The goal of this research is to develop a predictive capability for oblique detonation waves (ODWs). Planar wedge flows and axisymmetric conical flows are considered. The Rankine-Hugoniot solution is reviewed first, which yields necessary conditions for attached ODWs. But this solution is limited to inviscid flows over idealized geometries and infinite Damkohler number (Da), which is the ratio of fluid dynamical to chemical time scales. A multidimensional numerical model is developed, tested against theory, and is then used to investigate the influence of finite Da and viscous flows. Results demonstrate the role of the Damkohler number in bulk ignition. Refined grid results show that viscous (laminar) effects are confined to boundary layers and do not contribute to ODW formation. This conclusion corrects a previously held belief that was based on inadequately resolved simulations.; Results presented for underdriven oblique detonation waves are the first known for fuel-air mixtures of propulsion interest. Together with an explanatory model, these results suggest the existence of underdriven ODW's. Transient numerical solutions give clues to the wave's formation mechanisms, and perturbed solutions illustrate interesting properties of the wave once formed.
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