A sub-grid, mixture–fraction-based thermodynamic equilibrium model for gas phase combustion in FIRETEC: development and results
Michael M. Clark A B C , Thomas H. Fletcher A and Rodman R. Linn BA Department of Chemical Engineering, Brigham Young University, Provo, UT 84602, USA.
B Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
C Corresponding author. Email: mmclark@byu.net
International Journal of Wildland Fire 19(2) 202-212 https://doi.org/10.1071/WF07116
Submitted: 2 August 2007 Accepted: 9 September 2008 Published: 31 March 2010
Abstract
The chemical processes of gas phase combustion in wildland fires are complex and occur at length-scales that are not resolved in computational fluid dynamics (CFD) models of landscape-scale wildland fire. A new approach for modelling fire chemistry in HIGRAD/FIRETEC (a landscape-scale CFD wildfire model) applies a mixture–fraction model relying on thermodynamic chemical equilibrium to predict combustion flame temperatures and product species compositions. The mixture–fraction approach is common in combustor modelling applications. However, since individual flame sheets are not resolved in HIGRAD/FIRETEC, application of the mixture–fraction approach requires the development of a sub-grid model, which is based on the two assumptions (i) that combustible gases are concentrated into distinct pockets surrounded by air and combustion products and (ii) that reaction is limited by the mixing of the surrounding air with combustible gases from these pockets. The pocket radius and the thickness of the mixing zone are key parameters used in this model to characterise the sub-grid region where reaction occurs. The development of this sub-grid gas phase model is presented along with simulation results for various types of vegetation, including grass, California chaparral and ponderosa pine.
Acknowledgements
This work was performed using the computing resources of the Los Alamos National Laboratory Institutional Computing Program at Los Alamos National Laboratory and the Fulton Supercomputing Laboratory at Brigham Young University. Financial support from the LANL Institute for Geophysics and Planetary Physics and the USDA Forest Service is also gratefully acknowledged.
Cheney NP, Gould JS , Catchpole WR (1998) Prediction of fire spread in grasslands. International Journal of Wildland Fire 8, 1–13.
| Crossref | GoogleScholarGoogle Scholar |
Clark TL, Coen J , Latham D (2004) Description of a coupled atmosphere–fire model. International Journal of Wildland Fire 13, 49–63.
| Crossref | GoogleScholarGoogle Scholar |
Cunningham P , Linn RR (2007) Numerical simulations of grass fires using a coupled atmosphere–fire model: dynamics of fire spread. Journal of Geophysical Research 112, D05108.
| Crossref | GoogleScholarGoogle Scholar |
Hajaligol MR, Howard JB, Longwell JP , Peters WA (1982) Product compositions and kinetics for rapid pyrolysis of cellulose. Industrial & Engineering Chemistry Process Design and Development 21, 457–465.
| Crossref | GoogleScholarGoogle Scholar | CAS |
Linn RR , Cunningham P (2005) Numerical simulations of grass fires using a coupled atmospheric–fire model: basic fire behavior and dependence on wind speed. Journal of Geophysical Research 110, D13107.
| Crossref | GoogleScholarGoogle Scholar |
Mell W, Jenkins MA, Gould J , Cheney P (2007) A physics-based approach to modelling grassland fires. International Journal of Wildland Fire 16, 1–22.
| Crossref | GoogleScholarGoogle Scholar |
Pitsch H (2006) Large-eddy simulation of turbulent combustion. Annual Review of Fluid Mechanics 38, 453–482.
| Crossref | GoogleScholarGoogle Scholar |
Zhou XY , Pereira JCF (2000) Multidimensional model for simulating vegetation fire spread using a porous media sub-model. Fire and Materials 24, 37–43.
| Crossref | GoogleScholarGoogle Scholar | CAS |
Zhou X, Mahalingam S , Weise D (2005a) Modeling of marginal burning state of fire spread in live chaparral shrub fuel bed. Combustion and Flame 143, 183–198.
| Crossref | GoogleScholarGoogle Scholar | CAS |
Zhou X, Weise D , Mahalingam S (2005b) Experimental measurements and numerical modeling of marginal burning in live chaparral fuel beds. Proceedings of the Combustion Institute 30, 2287–2294.
| Crossref | GoogleScholarGoogle Scholar |
Appendix
Nomenclature used in this paper
-
a, flame-sheet thickness ratio
-
cF, FIRETEC reaction rate coefficient
-
cp, heat capacity (J kg–1 K–1)
-
F, combined solid–gas reaction rate in FIRETEC (kg m–3 s–1)
-
fair, mixture–fraction of air in a computational cell (excludes unreacted, combustible, hydrocarbon-like gas)
-
f cell, mean mixture–fraction in a computational cell -
Fgas, gas reaction rate in FIRETEC (kg m–3 s–1)
-
fHCpocket, mixture–fraction of spherical pockets composed of pure, unreacted, combustible, hydrocarbon-like gas; by definition equal to 1
-
fr, mixture–fraction of reacting mixture
-
Fsolid, solid reaction rate in FIRETEC (kg m–3 s–1)
-
ΔHrxn, heat of reaction (J kg–1)
-
ΔHsensible, change in sensible heat (J kg–1)
-
l, flame-sheet thickness parameter (m)
-
Mair, molecular weight of air (kg mol–1)
-
MHC, molecular weight of combustible, hydrocarbon-like gas (kg mol–1)
-
NHC, mass ratio of reactive gas that reacts with oxygen
-
No, mass ratio of oxygen that reacts with a reactive gas
-
P, pressure (atm)
-
r, radius of a spherical pocket of combustible, hydrocarbon-like gas (m)
-
R, gas constant (m3 atm K–1 mol–1)
-
sx, turbulent length scale (m)
-
Tair, temperature of reacting air (K)
-
Tflame, flame temperature predicted by chemical equilibrium (K)
-
T gas, average gas temperature (K) -
THC, temperature of reacting, combustible, hydrocarbon-like gas (K)
-
, specific volume of reacting air (m3 kg–1)
-
Vair,r, volume of reacting air (m3)
-
, specific volume of reacting, combustible, hydrocarbon-like gas (m3 kg–1)
-
VHC,r, volume of reacting combustible, hydrocarbon-like gas (m3)
Greek symbols
-
λof, stoichiometric coefficient
-
π, mathematical constant
-
ρ , total gas density (kg m–3) -
ρair,r, bulk density of reacting air (kg m–3)
-
, bulk density of vegetation (kg m–3)
-
, mean bulk density of combustible hydrocarbon-like vapours in the gas phase (kg m–3)
-
ρHC,r, bulk density of reacting, combustible, hydrocarbon-like gas (kg m–3)
-
, mean bulk density of oxygen in the gas phase (kg m–3)
-
, mean bulk density of primary mass in the gas phase (kg m–3)
-
ρref, reference density, 1 kg m–3 (kg m–3)
-
, mean bulk density of secondary mass in the gas phase (kg m–3)
-
σcm, turbulent mixing term (m2 s–1)
-
φr, volume fraction of reacting gas
-
χ, fraction of reacting mixture that consists of pure, combustible, hydrocarbon-like gas
-
Ψs, fraction of solid fuel that is above Tcrit
-
Ψg, fraction of gaseous fuel that is above Tcrit