Burning Rate and Flow Resistance Through Porous Fuel Beds: Axisymmetric Versus Line Fires

ABSTRACT

The burning rate of wildland fuels is a poorly understood yet key fire behavior metric. Previous work has utilized wood cribs; however, it has not yet been addressed whether the burning behavior of a crib, an axisymmetric fire, can be representative of a line fire, a typical configuration in wildfires. In this study, airflow into two sides of the crib was physically blocked and the resulting burning rate was noted. Six crib designs with a range stick thicknesses and porosities were tested both on the ground and with a gap underneath. For most cases, blocking the sides had only a modest effect on the burning rate (up to 22% reduction). In these cases, axisymmetric fire sources may give an acceptable approximation for the burning rate of a segment of a line fire. However, for the cribs built with thinner sticks placed directly on the ground, the reduction was more dramatic (up to 45%) and the use of axisymmetric and line fire sources requires further consideration. Resistances to flow in both the horizontal and vertical directions within the crib were used to understand these trends and to provide a better qualitative picture of how flows govern the burning of cribs in general.

KEYWORDS:

• Burning rate
• wildland fire
• axisymmetric fire
• line fire
• airflow

Nomenclature

A	=	cross-sectional flow area (general) [cm2]
As	=	exposed stick surface area [cm2]
Aside	=	horizontal flow area [cm2]
Av	=	area of vertical vents (vertical flow area) [cm2]
b	=	stick thickness [cm]
D	=	characteristic diameter [cm]
Dhorizontal	=	characteristic diameter for horizontal flow [cm]
dP	=	pressure drop (general) [Pa]
dPhorizontal	=	pressure drop through width of crib [Pa]
dPvertical	=	pressure drop through height of crib [Pa]
f	=	Darcy friction factor []
g	=	acceleration due to gravity [m/s2]
h	=	height of crib [cm]
ℓ	=	stick length [cm]
L	=	pipe length (general) [cm]
$\dot{m}$	=	mass flow rate (general) [g/s]
${\dot{m}}_{air}$	=	flow rate of air [g/s]
${\dot{m}}_b$	=	burning rate [g/s]
$\overline{{\dot{m}}_b}$	=	normalized burning rate []
n	=	number of sticks per layer []
N	=	number of layers []
Q*	=	non-dimensional heat release rate []
r	=	stoichiometric air to fuel ratio []
Re	=	Reynolds number (general) []
Rehorizonal	=	Reynolds number for horizonal flow []
Revertical	=	Reynolds number for vertical flow []
s	=	spacing between sticks [cm]
V	=	flow velocity [cm/s]
μ	=	dynamic viscosity [Pa-s]
ρ	=	density [g/cm3]
φ	=	crib porosity [cm]
Ωh	=	horizontal flow resistance [g/(m3s)]
Ωv	=	vertical flow resistance [g/(m3s)]

Acknowledgments

The author wants to thank Chelsea Phillips and Sophia Vernholm for building the many cribs and help performing the experiments; Torben Grumstrup the many discussions and preliminary review of the manuscript; Mark Finney and Jason Forthofer for helping to brainstorm this idea; Randy Pryhorocki and Josh Deering for building the apparatus; and Cyle Wold for setting up the data acquisition system and keeping the load cells calibrated.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was funded by the National Fire Decision Support Center.