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RESEARCH ARTICLE
Contents Vol 19(2)

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 B
+ Author Affiliations
- Author Affiliations

A 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.


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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)

  • fcell, 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)

  • Tgas, average gas temperature (K)

  • THC, temperature of reacting, combustible, hydrocarbon-like gas (K)

  • WF07116_IE3.gif, specific volume of reacting air (m3 kg–1)

  • Vair,r, volume of reacting air (m3)

  • WF07116_IE4.gif, 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)

  • WF07116_IE5.gif, bulk density of vegetation (kg m–3)

  • WF07116_IE6.gif, 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)

  • WF07116_IE7.gif, mean bulk density of oxygen in the gas phase (kg m–3)

  • WF07116_IE8.gif, mean bulk density of primary mass in the gas phase (kg m–3)

  • ρref, reference density, 1 kg m–3 (kg m–3)

  • WF07116_IE9.gif, 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