Multidimensional numerical simulations of a homogeneous, chemically reactive gas were used to study ignition, flame stability, and deflagration-to-detonation transition (DDT) in a supersonic combustor. The configuration studied was a rectangular channel with a supersonic inflow of stoichiometric ethylene-oxygen and a transimissive outflow boundary. The calculation is initialized with a velocity in the computational domain equal to that of the inflow, which is held constant for the duration of the calculation. The compressible reactive Navier-Stokes equations were solved by a high-order numerical algorithm on a locally adapting mesh. This paper describes two calculations, one with a Mach 3 inflow and one with Mach 5.25. In the Mach 3 case, the fuel-oxidizer mixture does not ignite and the flow reaches a steady-state oblique shock train structure. In the Mach 5.25 case, ignition occurs in the boundary layers and the flame front becomes unstable due to a Rayleigh-Taylor instability at the interface between the reactant and products. Growth of the reaction front and expansion of the burned gas compress and preheat the unburned gas. DDT occurs in several locations, initiating both at the flame front and in the unburned gas, due to an energy-focusing mechanism. The growth of the flame instability that leads to DDT is analyzed using the Atwood number parameter.
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