Extinction of the Stagnation Point Diffusion Flame: Effect of Conductive Heat Loss into Solid Interior
The flammability boundary of a solid is U-shaped with the ordinate as ambient oxygen percentage (or total pressure) and the abscissa represents flow velocity, gravity level, stretch rate, etc. The left side of the flammability boundary is the quenching branch, and the right side is the blow-off branch. Quenching is due to a weak flame whose heat release from combustion cannot overcome the excessive heat losses from, for example, radiation. Blow-off is due to a short gas residence time that is smaller than the chemical reaction time (traditionally referred to as the small Damköhler number effect). For thick solids, the heat conduction into the solid interior has a long transient after ignition before the solid temperature reaches the steady state. During this slow transient, there is excessive (i.e. more than that at the steady state) gas phase heat conduction into the solid interior. From the viewpoint of the quasi-static gaseous flame, this is an additional heat loss that will affect the gas flame's flammability. In this work, a previously developed one-dimensional axisymmetric stagnation-point diffusion flame model is extended to account for the excessive heat loss into the solid beyond the steady burning state. A non-dimensional excessive conductive heat loss parameter Ψ is defined in the paper to account for the transient solid effect. For each Ψ, the gas phase is considered reaching a quasi-steady state. Extensive numerical computations have been performed to determine the extinction boundary and the characteristics of near-limit flames. The U-shaped flammability boundary is now a series of boundaries with Ψ as a parameter. Flame structures under the same environment condition but with different Ψ are compared. For a given oxygen ambient, the extinction boundary Ψ vs stretch rate is an inverted U-shape. The boundary consists of a blowoff branch and a radiative quenching branch. Extensive computed data including flame and pyrolysis temperatures, burning rate, flame standoff distance, species concentration, and reaction rate are presented along the extinction boundaries. Heat balance analysis is performed for both the gas phase and the gas-solid interface. Along the extinction boundary, the relative importance of conduction, convection, radiation, and chemical reaction are analyzed in detail.