Multiplicity and Stability of Supercritical Combustion in a Nonadiabatic Tubular Reactor

Combustible mixtures under supercritical pressures and temperatures are capable of supporting a self-propagating flame under certain conditions. We consider the multiplicity and stability of such flames in a nonadiabatic tubular reactor as a function of inflow velocity, inlet and volumetric heat loss parameters, reactor length, and overall activation energy. We find that a steady, planar flame can only exist within certain parameter ranges, and that there are both high- and low-temperature solutions which correspond to a given flame position within the reactor. In addition, a linear stability analysis shows that for sufficiently large values of the overall activation energy, the high-temperature solution is unstable to disturbances which correspond to nonsteady, nonplanar supercritical flames. Consequently, we show that for typical values of this parameter, the basic solution branch representing high-temperature, steady combustion is stable when the flame lies well within the reactor, but it loses stability to spinning and/or pulsating modes of burning when the inflow velocity is varied so that the flame approaches either end of the reactor.