A simplified theory for de ris flame over thick and thin fuel beds

Abstract

The creeping flame spread problem in an opposed-flow environment over a flat fuel, called here de Ris flame, is revisited. Although the exact solution for the spread rates is well known (de Ris 1969; Delichatsios 1986), very little is definitively known about the flame structure, although a number of analytical and numerical studies have addressed this topic. None of the numerical studies have reproduced the exact solutions for the spread rates to date. The thick-fuel problem is reformulated in terms of five non-dimensional governing parameters retaining all the assumptions of the original theory; the thin fuel formulation is obtained as a limiting case. Direct numerical solution is presented first. The exact solution for the spread rate for thick fuel is reproduced for widely different sets of the controlling parameters. For thin fuel, however, the exact solution can be reproduced only when the flame hang-distance, the distance between the flame leading edge and the pyrolysis front, approaches zero. A finite hang-distance is found to cause an increase in spread rate by as high as 60%. This deviation from the exact formula is expressed in terms of a correction factor which is correlated with the hang-distance, which in turn is correlated with the known governing parameters. The thick-fuel flame is found to hug the surface in contrast to a lifted flame over a thin fuel. A simplified theory is proposed to predict the flame structure in the downstream region. The closed-form solutions for the conserved scalars reproduce the downstream flame structure for both the thick and thin fuel with remarkable accuracy and provide insight into the mechanism of flame spread.