Model of Opposed-Flow Flame Spread Over Charring Materials.
Model of Opposed-Flow Flame Spread Over Charring
Atreya, A.; Baum, H. R.
Combustion Institute, Symposium (International) on
Combustion, 29th. Proceedings. Volume 29. Part 1.
July 21-25, 2002, Sapporo, Japan, Combustion Institute,
Pittsburgh, PA, Chen, J. H.; Colket, M. D.,
Editor(s)(s), 227-236 pp, 2002.
Sponsor:National Institute of Standards and Technology,
combustion; flame spread; charring; diffusion flames;
solids; formulations; equations; flame spread rate;
This paper presents a theoretical description of a
diffusion flame spreading against the wind on a
semiinfinite charring solid. It extends the previous
flame spread models on "vaporizing" solids to charring
materials like wood and provides a realistic description
of the gas phase. To make the problem analytically
tractable, a mixture fraction approach is used in the
gas phase and the no-slip boundary condition is
satisfied only for x > 0. In the solid phase, the
charring solid is assumed to decompose abruptly
(endothermically or exothermically) into char and fuel
gases at a specified pyrolysis temperature. The
steady-state coupled elliptic equations for conservation
of energy, mixture fraction, and momentum in the gas
phase and conservation of energy in the char and the
pristine solid are solved by using orthogonal parabolic
coordinates. A general analytical solution is presented
that reduces to deRis's flame spread formula in the
limit of zero char thickness and with similar
assumptions. The growing char layer in the solid phase
has considerable influence on the flame spread rate. It
is seen that formation of a thicker char layer
significantly retards the spread rate. Unique
steady-state solutions for the parabolic char-material
interface were found to exist only for Stefan number >
-1. For Stefan number = -1 (i.e., exothermic), two
solutions were found. One of these solutions corresponds
to the location of the char-solid interface at infinity,
indicating the likelihood of a thermal runaway. This
happens regardless of the property values.