  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 an 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 burned and unburned gas. 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.
