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Model of Transport of Fuel Gases in a Charring Solid and Its Application to Opposed-Flow Flame Spread.

Model of Transport of Fuel Gases in a Charring Solid and
Its Application to Opposed-Flow Flame Spread.
(377 K)

Baum, H. R.; Atreya, A.

Volume 31; Part 2;

Combustion Institute, Symposium (International) on
Combustion, 31st. Proceedings. Volume 31. Part 2.
August 5-11, 2006, Heidelberg, Germany, Combustion
Institute, Pittsburgh, PA, Barlow, R. S.; Sick, V.;
Glarborg, P.; Yetter, R. A., Editor(s)(s), 2633-2641 pp,
2007.

### Keywords:

combustion; fire research; flame spread; fuels;
mathematical models; charring; solids; degradation;
char; pressure differential; equations; mass transfer

### Abstract:

*
This paper outlines the development of a mathematical
model for the transport of gases through the char matrix
of a burning solid. Two basic assumptions are made.
First, the gases evolved by the degradation of the
virgin material are transported by pressure differences
through a network of narrow passageways created in the
char by the conversion of material from the solid to the
gas phase. This process is treated as flow through a
porous medium, with the mass flux related to the
pressure gradient by Darcy's law. Second, the gas
temperature is the same as the local char temperature.
This model is first used to study the time-dependent
thermal degradation of a semi-infinite charring solid
heated above the charring temperature. Then, the opposed
flow flame spread treated by Atreya and Baum is
revisited. It was found that the solution to the
condensed phase flame spread problem is identical to the
initial transient problem. Weak dependence of the
solution on the accumulation parameter ss validates the
assumption made in and completes the flame spread
solution. Fuel mass flux follows the heat flux lines and
is normal to the isobars. Calculations using
representative values for wood show that the pressure
generation at the char-virgin material interface is
considerable and equal to 13.27 kPa. Finally, in view of
the fact that the nonlinear pressure equation poses
considerable numerical difficulties, this analytical
solution may help in determining the stability and
accuracy of the numerical scheme used for more
complicated problems.
*