Flame Spread Analysis Using a Variable B-Number

Abstract

Flame spread over solid materials is commonly described in the literature by a two-dimensional reactive boundary layer solution first formulated by Emmons (1956). In the recent past, experimental measurements associated with material flammability testing (e.g. NASA-STD-6001) are compared with the Emmons solution, as modified by Pagni and Shih, and found in disagreement. In the classical solution the B-number (Spalding mass transfer number) appears as one of the boundary conditions, and has been traditionally assumed a constant for mathematical simplicity. However, experimental results show that the B- number is not a constant, but varies with time and space. A simple modification to the standard measurement procedure is described, which allows calculation of the B- number from the flame stand-off distance. Measurements of flame spread on solid fuels are performed to determine the flame and pyrolysis front spread rates, as a function of time, and the flame stand-off distance as a function of space and time. The classical combustion problem is revisited to model flame spread over a combustible surface, including three-dimensional effects. An experimentally- obtained B-number, variable in time and space, is used to model flame propagation, showing good agreement with current and previous experimental data obtained from the literature