Diffusion-flame burning of fuel-vapor pockets in oxidizer for general Lewis numbers

We formulate, and then solve via numerical integration by the method of lines, the unsteady, diffusively limited burnup of initially unmixed fuel vapor and gaseous oxidizer. We study a simple geometry with spherical symmetry: an initially uniform fuel-vapor sphere is enveloped by a finite shell of gaseous oxidizer. The gaseous oxidizer, in turn, is confined by a concentric impervious noncatalytic spherical container, either adiabatic or isothermal. We treat the contents of the container as ideal gases, and we account for the rise of pressure in time during the exothermic burn (which ends when the stoichiometrically deficient reactant is fully depleted). primary results include the diffusion-flame locus in time, and the time interval for the exhaustion of the deficient reactant (burnup time), presented as functions of the fuel-to-oxidizer stoichiometry, the ratio of the container radius to the initial-fuel-sphere radius, etc. We also treat the case of differing diffusivities for fuel vapor, oxidizer, and sensible heat (nonunity Lewis numbers); that is, we undertake an explicit Stefan problem, in which the diffusion-flame locus is the moving boundary. Finally, we discuss the feasibility of related experiments in a microgravity environment.