, laminar and turbulent natural convection, forced convection, and 191 neutrally stratified flow within and above a sparse forest canopy

, FireStar3D shares many similitudes with WFDS but it also 194 presents important differences. In FireStar3D, as in WFDS, the flow solver is based on a 195 low Mach number formulation, a real calculation of the turbulent combustion in the flame 196 (using Eddy Dissipation Concept model), which is not the case in FIRETEC [30]. From a 197 numerical point of view, FireStar3D is fully implicit whereas the solver in WFDS is 198 explicit. One of the main differences at the modeling level with WFDS is related to the 199 estimation of the radiation heat transfer from the flame. In WFDS, the radiative heat 200 transfer is calculated but a minimum threshold value is fixed as a minimum radiative ratio 201 from the energy released from homogeneous combustion

, Grassland Fire Configuration

, numerically the spread of a fire through grassland. A perspective view of the 208 domain is shown in Fig. 1; the computational domain was 120 m long, 140 m wide, and 209 40 m high. The homogeneous vegetation layer, of height ? = 0.7 m, is 100 m long and 100 210 m wide, and it is located at 20 m from the domain inlet and at 20 m from the domain 211 lateral boundaries

, The 214 shape of the fuel particles is used for the description of their regression law and for the 215 estimation of the heat transfer coefficient. For the solid phase, a uniform grid with (?x, 216 ?y, ?z) = (0.25 m, 0.25 m, 0.035 m) was used matching the vegetation zone, while a non-217 uniform grid of 224?248?90 cells was used for the fluid phase covering the whole 218 computational domain. Within the vegetation zone, the fluid-phase grid was uniform with 219 (?x, ?y, ?z) = (0.5 m, 0.5 m, 0.07 m) and then it was coarsened gradually toward the open 220 boundaries according to a geometric progression with common ratio 1.05. Both the solid-221 phase and the fluid-phase grids were characterized by cells sizes below the extinction 222 length scale [14] within the vegetation given by 4/?? and equal to 0.5 m in our case, The heat yield of the fuel is 18000 kJ/kg, the solid fuel particles are assumed to 213 behave as a black body, and a vegetation family of cylindrical shape was considered

. Furthermore, the 226 choice of the mesh size at the vicinity of solid bottom wall is strongly related to the quality 227 of the obtained solution, the context of using a high Reynolds number turbulence model, vol.417, p.418

, -6 ) colored by 420 the temperature of the gas (in yellow) and one isovalue surface of the water mass fraction 421 (10 -3 ) (in grey with 50% of transparency) for U 10 = 1 m/s (top) and U 10 = 10 m/s (bottom), 422 showing the effect of, 3D View of one isovalue surface of the soot volume fraction

, For moderate wind conditions, 427 we notice that the fresh air is sucked from the vicinity of the fire front supplying the 428 thermal plume; the streamlines in Fig. 10 (top) show clearly the existence of aspiration 429 regions ahead the fire front. In the literature, this regime is often referred to as ''plume 430 dominated fires''. As indicated previously, these results highlight the capability of the 431 code to reproduce the backflow generated by the fire front on the leeward direction, These phenomena are further illustrated by Fig. 10 showing cuts of the temperature and 426 the flow fields (streamline) in the vertical median plane, vol.10

, Byram's convective number is an indicator of the fire propagation regime. Large values 605 of Byram's number are normally obtained in fires governed by plumes (plume dominated 606 fires), with a heat transfer between the flame and the vegetation dominated by radiation

, Whereas small values of Byram's number are obtained in fires piloted by inertial effects 608 (wind driven fire)

, 610 A comparison between the two methods of calculation of the fireline intensity (I BYR 611 obtained from Eq. 4 and I obtained successively from Eqs. 5 and 6) is presented in Tab, vol.2

, We can notice that the deviation between these two approaches increases with the wind 613 speed: for U 10 = 1 m/s, the relative variation ?I/I is equal to 26%

, ?I/I is equal to 101%. Two factors can explain these differences: (1) in the calculation of

, where the ROS was 616 maximum) and averaged over the propagation time of the fire; and (2) it was assumed 617 that all the solid fuel had burned. Both these effects result in an overestimation of the 618 quantity of fuel consumed by the fire and are therefore responsible for the 619 overestimation of I BYR (as seen in Tab. 2). Furthermore, these effects become more 620 pronounced as the wind speed increases, I BYR the rate of spread was evaluated at the center of the front line

, Fireline intensity evaluated using two approaches: (1) from the average rate of 624 spread and assuming that the initial fuel load had fully burned (I BYR , Eq. 4) and (2) from 625 the rate of total mass-loss of solid fuel (I

, To illustrate the relation between Byram's convection number and the fire regime, we 628 notice for example that for a 10-m open wind speed U 10 = 1 m/s, Byram's number N C , 629 estimated from Eq. 7 using the value of the ROS from Fig. 14 and the value of I from Tab

, We can conclude that the 631 situation observed for U 10 = 1 m/s was clearly a plume dominated fire, and that for U 10 = 632 10 m/s the situation was closer to a wind driven fire. The ratio ROS/U 10 versus the 633 inverse of Byram's convective number N C (calculated from Eq. 7) is shown in Fig. 16, 634 where the numerical results are compared to experimental data collected from the 635 various experimental campaigns carried out in Australia, vol.2

, That means that for fires dominated by inertial forces (wind driven fires) 642 the ROS converges toward a linear relationship with the wind speed. This behavior has 643 been reported by many experimental studies, in various ecosystems (surface fires in 644 grassland, shrubland ?) [62]. The relatively high values observed for the two branches of 645 the curve (comparable to the values observed on the field), can be interpreted as a 646 consequence of the low value of the fuel moisture content (M = 5%) that contributes 647 significantly to promote the propagation of the fire, and therefore to obtain high rates of operational empirical models (such as MK5 and BEHAVE), and with 660 the numerical results of other 3D physical models (FIRETEC and WFDS), ROS/U 10 (equal to 0.7 in our case) is obtained for fires dominated by buoyancy (plume 639 dominated fires), and thus for small values of the ratio 1/N C . On the other side of the curve 640 (i.e. for large values of 1/N C ), the ratio ROS/U 10 tends towards a constant value

, Consequently, it seems that the non-uniform fire-ignition of the grassland properties (heterogeneity, discontinuity ?) or to simulate some operational 694 situations

, This work was granted access to the HPC resources of Aix-Marseille Université funded by 699 the project Equip@Meso (ANR-10-EQPX-29-01) of the program "Investissements 700 d'Avenir" supervised by the "Agence Nationale pour la Recherche". The authors thank the 701 anonymous reviewers for the quality of their analysis

R. J. Whelan, The ecology of fire, Cambridge studies in ecology, 1995.

S. J. Pyne, P. L. Andrews, and R. D. Laven, Introduction To Wildland Fire, 1996.

W. T. Sommers, S. G. Coloff, and S. G. Conard, Synthesis of Knowledge: Fire History and 709 Climate Change, JFSP Synth. Reports. Pap, vol.19, p.190, 2011.

M. G. Cruz, A. L. Sullivan, J. S. Gould, N. C. Sims, A. J. Bannister et al., 711 Anatomy of a catastrophic wildfire: The Black Saturday Kilmore East, p.712

A. Victoria, For. Ecol. Manage, vol.284, pp.269-285, 2012.

V. Parliament-of, Victorian Bushfires Royal Commission, 2009.

K. G. Tolhurst, B. Shields, and D. M. Chong, Phoenix: Development and Application of a 716 Bushfire Risk Management Tool, Aust. J. Emerg. Manag, vol.23, p.47, 2008.

M. A. Finney, FIRESITE: Fire Area Simulator-Model Development and Evaluation, vol.718, p.47, 1998.

A. G. Mcarthur, Weather and Grassland Fire Behaviour, Canberra 720 Aust. For. Timber Bur, issue.100, p.23, 1966.

A. G. Mcarthur, Fire behaviour in eucalypt forests, Leaflet No. 107, For. Res. 722 Institute, 1967.

R. C. Rothermel, A mathematical model for predicting fire spread in wildland fuels, 724 USDA For. Serv. Res. Pap. INT USA, p.40, 1972.

H. P. Hanson, M. M. Bradley, J. E. Bossert, R. R. Linn, and L. W. Younker, The potential and 726 promise of physics-based wildfire simulation, Environ. Sci. Policy, vol.3, pp.161-727, 2000.

A. L. Sullivan, Wildland surface fire spread modelling, 1990-2007. 1: Physical and 729 quasi-physical models, Int. J. Wildl. Fire, vol.18, pp.349-368, 2009.

A. M. Grishin, Mathematical modeling of forest fires and new methods of fighting 731 them, p.732

. Russia, , 1997.

D. Morvan, Physical Phenomena and Length Scales Governing the Behaviour of 734 Wildfires: A Case for Physical Modelling, Fire Technol, vol.47, pp.437-460, 2011.

W. Mell, M. A. Jenkins, J. Gould, and P. Cheney, A physics-based approach to modelling 736 grassland fires, Int. J. Wildl. Fire, vol.16, pp.1-22, 2007.

R. R. Linn and P. Cunningham, Numerical simulations of grass fires using a coupled 738 atmosphere-fire model: Basic fire behavior and dependence on wind speed

, Geophys. Res, vol.110, p.13107, 2005.

D. Morvan, S. Meradji, and G. Accary, Wildfire behavior study in a mediterranean pine 741 stand using a physically based model, Combust. Sci. Technol, vol.180, pp.230-248, 2008.

D. Morvan and J. L. Dupuy, Modeling the propagation of a wildfire through a 743 Mediterranean shrub using a multiphase formulation, Combust. Flame, vol.138, pp.744-199, 2004.

D. Morvan, Numerical study of the behaviour of a surface fire propagating through 746 a firebreak built in a Mediterranean shrub layer, Fire Saf, J, vol.71, pp.34-48, 2015.

D. Morvan, S. Meradji, and W. Mell, Interaction between head fire and backfire in 748 grasslands, Fire Saf, J, vol.58, pp.195-203, 2013.

W. Mell, S. Manzello, and A. Maranghides, The Wildland-Urban Interface Problem -750 Current Approaches and Research Needs, Int. J. Wildl. Fire, vol.19, p.238, 2010.

E. Koo, R. R. Linn, P. J. Pagni, and C. B. Edminster, Modelling firebrand transport in 752 wildfires using HIGRAD/FIRETEC, Int. J. Wildl. Fire, vol.21, pp.396-417, 2012.

G. Accary, S. Meradji, D. Morvan, and D. Fougère, FireStar3D-3D finite volume model for 754 the prediction of wildfires behavior, Advances in Forest Fire Research, pp.251-261, 2014.

G. Accary, S. Meradji, D. Morvan, and D. Fougère, Towards a numerical benchmark for 757 3D mixed-convection low Mach number flows in a rectangular channel heated from 758 below, Fluid Dyn. Mater. Process, vol.141, pp.1-7, 2008.

K. Gavrilov, G. Accary, D. Morvan, D. Lyubimov, S. Méradji et al., Numerical 760 simulation of coherent structures over plant canopy, Flow, Turbul. Combust, vol.86, pp.89-111, 2011.

K. Gavrilov, D. Morvan, G. Accary, D. Lyubimov, and S. Meradji, Numerical simulation of 763 coherent turbulent structures and of passive scalar dispersion in a canopy sub-764 layer, Comput. Fluids, vol.78, pp.54-62, 2013.

N. P. Cheney, J. S. Gould, and W. R. Catchpole, The influence of fuel., weather and fire 766 shpae variables on fire-dpread in grasslands, Int. J. Wildl. Fire, vol.3, pp.31-44, 1993.

N. P. Cheney and J. S. Gould, Fire growth in grassland fuels, Int. J. Wildl. Fire, vol.5, pp.768-237, 1995.

N. P. Cheney, J. S. Gould, and W. R. Catchpole, Prediction of fire spread in grasslands, Int. 770, J. Wildl. Fire, vol.8, pp.1-13, 1998.

D. Morvan, S. Méradji, and G. Accary, Physical modelling of fire spread in Grasslands, 772 Fire Saf, J, vol.44, pp.50-61, 2009.

A. Favre, L. S. Kovasznay, R. Dumas, J. Gaviglio, and M. Coantic, La turbulence en 774 mecanique des fluides, 1976.

G. Cox, Combustion fundamentals of fire, 1995.

V. Yakhot and L. M. Smith, The renormalization group, the epsilon-expansion and 777 derivation of turbulence models, J. Sci. Comput, vol.7, pp.35-61, 1992.

S. A. Orszag, I. Staroselsky, W. S. Flannery, and Y. Zhang, Introduction to renormalization 779 group modeling of turbulence, Simul. Model. Turbul. 780 Flows, pp.155-183, 1996.

R. J. Kee, F. M. Rupley, and J. A. Miller, The Chemkin Thermodynamic Data Based, Sandia 782 Natl. Lab, 1992.

B. F. Magnussen and B. H. Mjertager, On mathematical modeling of turbulent 784 combustion, Combust. Sci. Technol, vol.140, pp.93-122, 1998.

K. J. Syed, C. D. Stewart, and J. B. Moss, Modelling soot formation and thermal radiation in 786 buoyant turbulent diffusion flames, 23rd Symposium (International) on 787 combustion, vol.23, pp.1533-1541, 1991.

J. B. Moss, Turbulent Diffusion Flames, vol.789, 1990.

J. Nagle and R. F. Strickland-constable, Oxidation of Carbon Between, 1000.

, Proc. Fifth Conf. Carbon, pp.154-164, 1962.

F. P. Incropera and D. P. Dewitt, Fundamentals of Heat and Mass Transfer, 1996.

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer. Hemisphere Publishing 795 Corporation, 1992.

S. V. Patankar, Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing, 797, 1980.

Y. Li and M. Rudman, Assessment of higher-order upwind schemes incorporating FCT 799 for convection-dominated problems, Numer. Heat Transf. Part B Fundam, vol.27, pp.1-21, 1995.

H. K. , M. Versteeg, and W. , An introduction to Computational Fluid Dynamics, The 802 Finite Volume Method, 2007.

J. H. Ferziger, M. Peric, and A. Leonard, Computational Methods for Fluid Dynamics, vol.804, 2002.

M. F. Modest, , 2003.

C. R. Kaplan, S. W. Bek, E. S. Oran, and L. Ellzeyj, Dynamics of a Strongly Radiating Insteady, vol.807

, Ethylene Jet Diffusion Flame, Combust. Flame, vol.96, pp.1-21, 1994.

G. Accary, O. Bessonov, and D. Foug, Optimized Parallel Approach for 3D Modelling of 809

, PaCT 2007, vol.810, pp.96-102, 2007.

G. Accary, O. Bessonov, and D. Foug, Efficient Parallelization of the Preconditioned, vol.812

V. E. Conjugate-gradient-method and . Malyshkin, PaCT 2009, p.813

. Heidelb, , vol.5968, pp.60-72, 2009.

A. Khalifeh, G. Accary, S. Meradji, G. Scarella, D. Morvan et al., Three-815 dimensional numerical simulation of the interaction between natural convection 816 and radiation in a differentially heated cavity in the low Mach number 817 approximation using the discrete ordinates method, Proc. Fourth Int. Conf

, Therm. Eng. Theory Appl. Abu Dhabi, 2009.

A. G. Mcarthur, Grassland Fire Danger Meter MkV. CSIRO Division of Forest, Annual, vol.820, 1977.

R. E. Burgan and R. C. Rothermel, Behave: Fire Behavior Prediction and Fuel Modeling 822 System -FUEL Subsystem, Behave. Intermount, 1984.

W. Mell, J. Charney, and M. Jenkins, Numerical simulations of grassland fire behavior 824 from the LANL-FIRETEC and NIST-WFDS models, p.825

V. A. Fairfax, EastFIRE Conf, pp.1-10, 2005.

T. Beer, The interaction of wind and fire, Boundary-Layer Meteorol, vol.54, pp.287-827, 1991.

J. C. Hunt, A. A. Wray, and P. Moin, Eddies, streams, and convergence zones in turbulent 829 flows, Stud. Turbul. Using Numer. Simul. Databases, 2. Proc, Summer Progr. 1, vol.830, pp.193-208, 1988.

M. A. Finney, J. D. Cohen, J. M. Forthofer, S. S. Mcallister, M. J. Gollner et al., , p.832

N. K. Saito, B. A. Akafuah, J. D. Adam, and . English, Role of buoyant flame dynamics in 833 wildfire spread, Proc. Natl. Acad. Sci, pp.9833-9838, 2015.

R. R. Linn, J. M. Canfield, P. Cunningham, C. Edminster, J. L. Dupuy et al., Using 835 periodic line fires to gain a new perspective on multi-dimensional aspects of 836 forward fire spread, Agric. For. Meteorol, vol.157, pp.60-76, 2012.

D. Morvan, Wind effects, unsteady behaviors, and regimes of propagation of surface 838 fires in open field, Combust. Sci. Technol, vol.186, pp.869-888, 2014.

R. M. Nelson, Re-analysis of wind and slope effects on flame characteristics of 840 Mediterranean shrub fires, Int. J. Wildl. Fire, vol.24, pp.1001-1007, 2015.

G. M. Byram, Forest Fire Control and Use in, 1959.

P. Cheney and A. Sullivan, Grassfires : Fuel, Weather and Fire Behaviour, Behaviour, vol.844, pp.0-16, 2008.

A. L. Sullivan, Convective Froude number and Byram's energy criterion of 846 Australian experimental grassland fires, Proc. Combust. Inst, vol.31, pp.2557-847, 2007.

, ? Numerical simulations of grassland fire ? Detailed physical fire model ? Plume dominated fire, wind driven fire ? Byram's convective number