A comprehensive understanding of the fundamental physics underlying combustion and detonations in turbulent and high-speed flows is crucial to the design of robust ramjet, scramjet, and detonation engines. This work uses high-fidelity, multidimensional numerical simulations to investigate flame stability and deflagration-to-detonation transition (DDT) mechanisms in supersonic reactive flows. The study consists of four major sections.

The first section discusses the acceleration of a flame in a channel with obstacles and its transition from a laminar, expanding flame to a turbulent deflagration and eventual detonation. As the flame accelerates, a highly dynamic, shock-heated region forms ahead of the flame. Shock collisions and reflections focus energy in localized volumes of unburned gas at timescales that are small relative to the acoustic timescale of the unburned gas. The rapid deposition of energy causes the unburned gas to detonate through an energy-focusing mechanism that has elements of both direct initiation and detonation in a gradient of reactivity.

The second section describes how the blockage of a channel with regularly spaced obstacles, analogous to the igniter in a detonation engine, affects flame acceleration and turbulence in the region ahead of the accelerating flame. The rate of flame acceleration, time and distance to DDT, and detonation mechanism are compared for channels with high, medium, and low blockage ratios. Stochasticity and uncertainty in the numerical solutions are discussed.

In the third section, the stability of premixed flames at high supersonic speeds in a constant-area combustor is investigated. After autoignition of the fuel-oxidizer mixture in the boundary layer at the combustor walls, the flame front eventually becomes unstable due to a Rayleigh-Taylor (RT) instability at the interface between burned and unburned gas. The turbulent flame front transitions to a detonation through the energy-focusing mechanism when a shock passes through the flame and amplifies its energy release.

The final section discusses the effect of inflow Mach number in the supersonic combustor on ignition, flame stability, and transition to detonation of a premixed flame. Timescales for growth of the RT instability and detonation initiation increase rapidly with flow speed, but, qualitatively, flame evolution is independent of Mach number.