Strain-Rate-Free Diffusion Flames: Initiation, Properties, and Quenching

Abstract

For convenient diagnostic probing and analysis of the fundamental properties of the laminar burning of initially separated fuel vapor and gaseous oxidizer, the counterflow affords the advantage of planar symmetry; the key dependent variables depend on a single Cartesian coordinate only. However, in the diffusion-flame limit, in which the most vigorous and spatially intense chemical conversion occurs, the counterflow becomes unstable. As the strain rate goes to zero, the residence time of the throughput increases, so that, in earth gravity, small disturbances grow to finite amplitude during transit of the counterflow burner, and the planar symmetry is disrupted. Accordingly, in previous work, we have explored the properties of a fully developed, strain-rate-free planar diffusion flame in microgravity, with emphasis on the realistic case of differing species diffusivities (unequal Lewis-Semenov numbers). However, previously we dealt only cursorily with how such a planar diffusion flame might be initiated within a finite impervious noncatalytic isothermal container, and how the flame interacts with the walls of the container. Here, we discuss the triple-flame-related phenomena associated with the rapid constant-speed withdrawal, by translation in its own plane, of a thin planar interface, initially separating the contents or a half volume containing fuel vapor (diluted with an inert gas) from the contents of a half volume containing gaseous oxidizer (diluted with another inert gas)We also address the thickness of, and temperature fields within, near-wall flame-quench layers, which complement the vigorous burning in the interior of the container (until depletion of fuel and/or oxidizer effects extinction in the interior). For these studies, we formulate and solve simplistic models that straightforwardly extend the classical Shvab-Zeldovich/Burke-Schumann treatment of vigorous burning in unpremixed gaseous reactants with equidiffusion for species (equal Lewis-Semenov numbers). Our solutions indicate that, owing to large compressional heating at early times, the temperature at the thin flame is nonmonotonic, even though the residual unreacted amount of fuel and oxygen in the sealed container is monotonically decreasing in time. Furthermore, because the planar diffusion flame eventually travels toward the isothermal, cold end wall of the half volume containing the initially stoichiometrically deficient reactant, at later time during the burn the peak temperature does not occur at the flame. The time to effectively total depletion of the stoichiometrically deficient reactant increases appreciably as the initial deficiency of that reactant is chosen to be smaller. Also, to obtain a plausible description of phenomena in the thickening thermal boundary layer on each side wall ( a wall perpendicular to the plane of the diffusion flame in the core of the container), we must account explicitly for diffusion in direction both parallel to, and perpendicular to, the side wall.