A COMPARISON OF NUMERICAL AND ANALYTICAL SOLUTION OF THE CREEPING FLAME SPREAD OVER THERMALLY THIN MATERIAL

A numerical solution of the well known de Ris (Twelfth Symposium [International] on Combustion, 1969, pp. 241-252) problem of flame spread over thin condensed fuel in opposed-flow environment is presented. The problem is reformulated in terms of four nondimensional parameters, retaining all the assumptions of the original theory. For a particular baseline case extensive testing has been performed to check the accuracy of the solution, the grid independence and domain-size independence. The results of this numerical analysis indicate that the flame, downstream of the leading edge, is lifted despite the linearization of the mass-flux at the vaporizing surface. The non-dimensional flame stand-off distance varies with the controlling parameters in a way similar to the behavior exhibited by one-dimensional diffusion flames. While the de Ris theory hypothesizes that the location of the leading edge and the location of the onset of vaporization, the eigen-location, are identical, the present analysis treats the leading edge as part of the solution. The most important finding of this work is that the location of the flame leading edge is usually upstream of the eigen-location. This has significant bearings on the spread rate formula. The value of A in the de Ris formula, V(f) = Axg(T(f) - T(upsilon))/zrho(s)c(T(upsilon) - rho(infinity)), is found, approximately, to be about unity in the present work rather than, pi/4, suggested by Delichatsios [Combust. Sci. Technol. 44:257-267 (1986)]. However, it is sensitive to the vaporization parameter, beta4 = L(upsilon)o/CT(infinity), and to some extent to the stoichiometric parameter, beta1 = m(O,infinity)/s. These parameters affect the location of the flame leading edge the most. The functional dependence of spread rate on beta4 does not appear to be adequately captured by the Delichatsios solution.