UNSTEADY PLANAR DIFFUSION FLAMES: IGNITION, TRAVEL, BURNOUT

ABSTRACT

The interior of a squat rectangular solid, with isothermal noncatalytic impervious walls, is subdivided into two equal half volumes by a thin plastic film. One half-volume is filled with hydrogen, diluted with argon; the other, with oxygen, diluted with helium; the density, temperature, pressure, and (hence) “effective molecular weight” of the two half volumes are initially equal. At time zero, the film is broken to permit, briefly, interpenetration of the initially segregrated reactants, and ignition quickly follows. Except for quenching near cold walls, a diffusion flame results; it remains planar in microgravity. The subsequent position and temperature of the diffusion flame may be predicted, facilely, within a (Shvab-Zeldovich) formulation which adopts a direct one-step irreversible reaction. Specifically, we generalize the (Burke-Schumann) limit of diffusion-controlled, combustion to encompass: (1) a travelling flame (a moving boundary between fuel and oxidizer), and (2) differing diffusivities for fuel, oxidizer, and heat. Furthermore, we derive a sufficient condition for the extinction of burning by asymptotic analysis of a finite-rate, Arrhenius-type model of the one-step reaction. The conjunction of a numerical solution of the diffusion-controlled (Stefan-type) formulation, and an asymptotic solution of the finite-rate formulation, readily permits prediction of an upper bound on the time until extinction. An extended microgravity-testing interval, available during Shuttle flight, permits comparison of these predictions with experimental observations.

Key Words:

• Diffusion flame
• microgravity combustion
• mixing-limited combustion
• moving-boundary problem
• Stefan problem