Forced-Convection Extinction of a Diffusion Flame Sustained by a Charring Body

Abstract

The subsonic isobaric forced-convective flow of air past a pyrolyzing, char-forming body outgassing combustible fuel vapor is examined; the goal is to seek a generalized approach toward establishing approximate criteria for extinction of burning. A Shvab-Zeldovich formulation (incorporating, inter alia, a one-step irreversible exothermic finite-rate chemical reaction) is adopted to describe the gas-phase burning of initially unmixed reactants. For specificity, a sublimation model is adopted to describe the endothermic gasification at the surface of the (isothermal) pristine body; a nonisothermal porous char layer (through which combustible vapor, from pyrolysis of the pristine-body surface, can diffuse to the surrounding air) envelops the pristine body. Important features of the steadily burning configuration can be obtained for any simple bluff body, and sequentially the question of flame stability can be addressed via exploitation of the well-studied counterflow-diffusion-flame two-point-boundary-value problem for describing extinction of unpremixed burning. Thus, known results for the minimum Damk6hler number (ratio of forced-convective-fiow time to chemical-reaction time) compatible with vigorous burning of large-activation-energy, large-heat-of-combustion, counterflow diffusion flames are applicable. The uncoupling of the analysis for the heat transfer-flow problem from the analysis of the gas-phase flame-extinction problem depends on the fact (associated with all analyses known to the authors, for parameter values of practical interest) that always, during vigorous burning, the oxygen concentration at the gas-solid interface is extremely small. This observation permits a formulation of the composite problem which defers the detailed flame analysis until after the kinematic field, the temperature field of the char, and the usual Shvab-Zeldovich passive scalar variables in the region outside of the char, have been deduced. One can then use the rather extensive results which are already available in the literature to dispose, in most cases, of the extinction part of the problem. Aside from its role in the foregoing balance, the importance of the presence of the char lies in its capacity to store heat, if combustion is absent temporarily due, for example, to an enhanced external flow velocity, the heat stored in the char can supply the energy for continued pyrolyzation. Then, upon the resumption of a flow condition which permits a steady vigorously burning configuration, spontaneous reignilion can occur, provided that the time interval of enhanced velocity has been short enough so that pyrolyzation has not yet ceased and provided that the surface of the char is not yet below the ignition criterion of the pyrolyzate-air combination.