Gas-phase radiative effects on the burning and extinction of a solid fuel

Abstract

Gas-phase radiative effects on the burning and extinction of a solid fuel in a stagnation-point flow geometry are investigated using a statistical narrow-band model with carbon dioxide and water vapor as the radiative participating media. The model, coupled to other flame conservation equations with a one-step overall gas-phase chemical reaction and Arrhenius solid pyrolysis relation, is solved numerically. Flame temperature, solid burning rate, and heat fluxes are examined as functions of stretch rate. Using ambient oxygen percentage and stretch rate as coordinates, A U-shaped extinction boundary is identified. The extinction behavior at low stretch rates is qualitatively similar to that predicted by earlier theory with only surface radiation loss. However, gas radiation introduces additional heat loss from the system and shrinks the solid flammable domain. In addition, gas radiation can cause a substantial decrease of flame temperature and constitutes a significant portion of the heat feedback to the solid at low stretch rates. In the second part of the paper, a computationally less intensive gray gas radiation model is tested. As with a number of earlier investigations, the use of Planck mean absorption coefficient is found to overpredict net emission and flame radiative loss. By multiplying a correction factor (less than 1) in front of the Planck mean absorption coefficient, it is possible to compute many global flame properties with reasonable accuracy. An empirically determined formula is given to find the value of this correction factor for a given flame. This is offered as an engineering approach for the flame radiation treatment.