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Project no. FP6-018505 Project Acronym FIRE PARADOX Project Title FIRE PARADOX: An Innovative Approach of Integrated Wildland Fire Management Regulating the Wildfire Problem by the Wise Use of Fire: Solving the Fire Paradox Instrument Integrated Project (IP) Thematic Priority Sustainable development, global change and ecosystems D2.4-1 Simulations of wildfire behaviour: 2D results Due date of deliverable: Month 18 Actual submission date: Month 21 Start date of project: 1st March 2006 Duration: 48months Organisation name of lead contractor for this deliverable: Univ. de la Méditerranée Revision (1000) Project co-funded by the European Commission within the Sixth Framework Programme (2002-2006) Dissemination Level PU Public PP Restricted to other programme participants (including the Commission Services) RE Restricted to a group specified by the consortium (including the Commission Services) CO Confidential, only for members of the consortium (including the Commission Services) X TABLE OF CONTENTS 1. Introduction .............................................................................................................. 3 2. Physical model .......................................................................................................... 5 Solid fuel modelling ................................................................................................... 5 Gas Flow Modelling .................................................................................................... 7 Turbulence and combustion modelling......................................................................... 8 Convection and radiation heat transfer ...................................................................... 11 3. Numerical results and discussion ............................................................................... 13 Surface fire propagating through an heterogeneous fuel (shrubland) ........................... 19 4. Conclusions ............................................................................................................ 25 5. References ............................................................................................................. 26 D2.4-1-18-1000-1 Page 2 of 28 This work is carried out within the context of the European integrated project “FIRE PARADOX”, aiming to obtain a fully physical three-dimensional model of forest fire behaviour. The development of this 3D code constitutes an extension of the 2D fire behaviour model FIRESTAR developed during a previous European project (EVG1-CT-2001). In this preliminary task, some physical sub-models have been modified, such as the turbulence and the combustion modelling, to improve the capability of this tool to reproduce the main characteristics observed during the propagation of a surface fire through a solid fuel layer. After a short introduction and a brief presentation of the set of equations constituting the physical model, some numerical results obtained in 2D for a surface fire propagating through an homogeneous (grassland) and an heterogeneous (shrubland) fuel layer, are analysed and compared with experimental and empirical data from the literature. 1. Introduction Considering that semi-empirical models, such as BEHAVE (Rothermel 1972), did not produce good predictions concerning the behaviour of wildfires in particular situations, such as for heterogeneous vegetations, for crown fires or when slope and wind effects are combined (Hanson & al 2000), a new fully physical approach has been developed this last decade (Clark & al 1996, Linn & al 2002, Mell & al 2005, Morvan & al 2004). Wildfire behaviour modelling is a very complex problem, it involves strong interactions between non linear phenomena in the gaseous phase, such as the turbulence in the lower part of the atmospheric boundary layer, chemical reactions and radiation heat transfer in the flaming zone. In addition, the description of the degradation of the solid fuel layer representing the vegetation, including the drying and the pyrolysis of the vegetation and the surface oxidation of the char coal, contributes also to increase the complexity of the problem. From a more theoretical point of view, some physical mechanisms, such as the turbulence, the coupling between the combustion and the turbulence, the turbulence/radiation interaction …, governing the behaviour of fires are not completely understood, and are considered as currently in progress by the physician community. Therefore, even if this new approach is based on the resolution of well known balance equations (mass, momentum, energy), governing the evolution of the state of the vegetation and of the surrounding atmosphere, due to the coupling between these non-linear phenomena, the development of such model remains very complex and the numerical results need to be validate using numerous comparisons with experimental data. At this time no physical model can be considered as “fully” physical, more or less all the models introduce some approximations to represent a part of the physical processes governing the behaviour of wildfires. It is very important to keep in mind this introductive remark, if we plan in the future to use this kind of tool in operational conditions, especially if the safety of fire fighters or foresters must be guarantee. Nevertheless, this approach is considered by the scientific community as very promising, taking into account the difficulties to collect experimental data, it constitutes an interesting alternative (or complementary) tool to improve the knowledge concerning the physical mechanisms governing the behaviour of fires at various stages of its evolution (ignition, propagation, extinction), or during some particular situations such as a prescribed burning or a suppression fire. One of the objectives of the work summarized in this deliverable, is to present the physical bases used in the FIRESTAR computer code and to illustrate the possibility of this approach, D2.4-1-18-1000-1 Page 3 of 28 in presenting some numerical simulations carried out for surface fires propagation in grassland and shrubland, compared to experimental data from the literature (Cheney & al 1993, 1995, 1998, Fernandes & al 2000, Catchpole & al 1999). D2.4-1-18-1000-1 Page 4 of 28 2. Physical model The approach used in this study is based on a multi-phase formulation describing the behaviour of the coupled system formed by the vegetation and the surrounding atmosphere (Grishin 1997). The model includes two sub-models: the first one to describe the evolution of the state of the vegetation subjected to the intense heat flux coming from the flaming zone the second one to calculate the turbulent-reactive flow resulting from the mixture between the pyrolysis products and the ambient air. Solid fuel modelling To specify the conditions of propagation of a fire, the state of the vegetation must be characterized using the following set of physical variables: the fuel volume fraction (S), the fuel density (S), the moisture content (tH2O), the size of fuel particles (or the Surface Area to Volume fraction SA/V, S), the fuel temperature (TS), and the fuel composition. Experimental measurements (Burrows 2001) of the residence time of fires, propagating through homogeneous fuel beds, showed that only small fuel particles (<6 mm, Surface Area to Volume ration S>600 m-1) can contribute actively to the dynamics of a wildfire. This result was confirmed by wildfire observations, showing that a high fraction (90%) of thin fuel particles (<6 mm) was consumed in the flaming zone (Cheney & al 1981). This threshold size represents also the limit separating the thermally thin and the thermally thick particles heat transfer regime, for which the inner temperature gradients can be or not neglected. During the decomposition of the vegetation, resulting from the heat stress induced by the fire, we assume that the composition of each solid fuel element can be characterized as a mixture of water (moisture content), dry material (cellulose, hemi-cellulose, lignin), char, and ashes (mineral residue). Each of these elements are represented by field variables corresponding to the mass fraction of water YH2O(S) , dry material YI(S), and char YCHAR(S). Under the action of the intense heat flux coming from the flaming zone, the decomposition of the vegetation can be summarised using the three following steps: Drying (rate of mass loss = WVAP), Pyrolysis (rate of mass loss = WPYR), Surface oxidation (rate of mass loss = WCHAR), The time evolution of the solid fuel composition is governed by the following mass balance equations (Grishin 1997, Morvan & al 2001) (neglecting the oscillatory motions of the vegetation, due to the wind and the heat transfer by conduction inside the vegetation, the formulation of the problem was reduced to a set of ordinary differential equations (ODE)): d S S YH( S2)O WVAP (1.a) dt d S S YI( S ) WPYR (1.b) dt D2.4-1-18-1000-1 Page 5 of 28 (S ) d S S YCHAR CHAR SOOT WPYR ASH 1WCHAR (1.c) dt CHAR (1.a): mass balance of moisture content (drying) (1.b): mass balance of dry material (pyrolysis) (1.c): mass balance of char (production, soot formation, oxidation, ash formation) Adding these three contributions (+ the mass balance of ash), the global mass balance equation is: d S S 1 CHAR SOOT WPYR WCHAR WVAP M ( S ) (1.d) dt where M(S) represents the mass transfer of a chemical species between the solid phase and the gas phase. Assuming that, during the drying and the pyrolysis processes, the variations of volume are negligible compared to that during the surface combustion of charcoal, the evolution of the volume fraction is governed by the following equation: d S 1 WCHAR (1.e) dt S Since thermal equilibrium is not assumed between the solid fuel particles and the gaseous phase, the temperature in the solid phase (S) can be written as follows: S S C PS dTS Q( S/ ) hVAPWVAP hPYRWPYR hCHARWCHAR (1.f) dt where Q+/-(S) represents the energy balance exchanged by convection and radiation with the gaseous phase, hVAP , hPYR , hCHAR the heat of vaporisation, pyrolysis and char combustion: hVAP=2.25 x 103 kJ/kghPYR=418 kJ/kg, hCHAR= - 12 x 103 kJ/kg (exothermic reaction, assuming that 50% of the heterogeneous combustion takes place at the surface of the solid phase, we fixed ) The evaporation process is represented using a one step temperature transformation (if TS = 373 K): WVAP 0 T 373 K Q( S/ ) T 373 K h VAP D2.4-1-18-1000-1 (2.a) Page 6 of 28 Experimental investigations on the pyrolytic behaviour of some wood species, showed that if a fuel sample received a heat flux larger than 40 kW/m2 (condition verified ahead of a fire front), the pyrolysis process can be represented using a one step first order Arrhénius kinetics law (Grishin 1997, Morvan & al 2001, Di Blasi & al 2001) E WPYR S S YI( S ) K PYR exp PYR (2.b) RTS KPYR: pre-exponential factor (= 3.64 103 s-1) EPYR / R: temperature of activation (= 7250 K) The surface oxidation of char is also represented using a kinetic law of the form (Grishin 1997): WCHAR E S S g g YO 2 K CHAR exp CHAR (S ) O2 RTS (2.c) KCHAR=430 m s-1, ECHAR/R = 9000 K g , g represent the volume fraction and the average density of the gaseous phase, S is the surface area to volume ratio (SA/V) of solid fuel particles. Gas Flow Modelling The evolution of the gaseous phase is governed by a set of transport equations representing the balance equations for mass, momentum and energy. As previously mentioned, the flow regime can be considered as fully unsteady or turbulent. Consequently, the equations are filtered using a weighted average TRANS (Favre) formulation. In this case the filtered variables are governed by the following set of transport equations: D M (S ) (3.a) Dt ( G ij ) D u~i (u j ' ' u i ' ') g i Fi ( S ) (3.b) Dt x j x j ~ D h (q j ) (S ) (u j ' ' h' ') QCONV G G J 4T 4 (3.c) Dt x j x j ~ D Y Dt x j ~ D Y x j D2.4-1-18-1000-1 (u j ' ' Y ' ') W M ( S ) (3.d) x j Page 7 of 28 where all transported variables (density , velocity component ui , enthalpy h, and mass fraction of chemical species Y are decomposed as a sum of two contributions (Favre ~ average + fluctuation '' ). The differential operator D/Dt is defined as: ~ D u j (3.e) Dt t x j Fi(S) denotes the i-component of the drag force resulting from the interaction between the gas flow and the vegetation: Fi ( S ) C D S S ~ ~ U u i (3.f) 2 where CD is the drag coefficient of fuel particles (defined using the half specific surface of fuel particles), QCONV(S) is the energy exchange by convection between the gas and the solid fuel particles, qj is the heat transfer by conduction, J is the total irradiance, G and G are the volume fraction of the gas phase and the extinction coefficient of the gas + soot mixture (including the absorption due to the presence of CO, CO2, H2O and soot particles in the flame and along the plume (Kaplan & al 1996)), T is the temperature of the gas, and Stefan-Boltzmann constant. Even if the gas density cannot be considered as constant in a fire, the high temperature gradients, and the gas mixing in the vicinity of the flame, induce a significant dilatation phenomena above the burning zone, the flow in the flaming zone and in the plume remains largely subsonic and no significant fully compressible phenomena (wave propagation) (excepted the noise generated by the fire front) are observed near such fires. From a hydrodynamics point of view, the gas flow can be assimilated as quasi-isobar and weakly compressible (dilatable). This case constitutes a very good example for the introduction of the low Mach number approximation. Turbulence and combustion modelling The turbulence model introduced in the FIRESTAR system is based on the eddy viscosity concept, assuming that the turbulent motion can be approximated as a additional diffusion term (Eddy viscosity concept). For the momentum equations, the eddy diffusion coefficient is evaluated from two variables characterising the turbulence: the turbulent kinetic energy K and its dissipation rate (well known K- D K Dt x j eff K Pr x j T D Dt x j eff 3 ~3 ~ C 1 P C 3 W (C 2 R) C D S S U 6U (4.b) Pr x T T T 2 2 K j T D2.4-1-18-1000-1 P W C D S S U~ 3 4U~K (4.a) 2 Page 8 of 28 T C K2 f (4.c) f exp 2.5 d) 10.02ReT where T=max( T ) is the maximum value between the turbulence time scale ) and a value proportional (CT=6) to the Kolmogorov time scale where eff represents the effective viscosity i.e. the sum of the molecular and the turbulent contribution. The following set of constants is introduced in the turbulence model (Yakhot & al 1992): C1=1.42, C2=1.68, C3=1.5, C=0.085 P and W are respectively the terms contributing to the production of turbulence, due to shear and buoyancy effects, given as: P ui'' u 'j' u~i x j W T ~p 2 x j x j (4.e) The turbulent Prandtl PrT number is calculated from the following relation (T= 1/PrT): T 1.3929 1.3929 0.6321 T 2.3929 2.3929 0.3679 (4.f) T The values with the subscript T design the turbulent values (without subscript: molecular values: = 1/Pr, molecular Prandtl number) The terms including the drag coefficient CD in the equations (5.a) (5.b), represent the contribution of the drag force, induced by the vegetation, to the turbulent kinetic energy budget, including both production and dissipation terms. The additional source term R in the transport equation for comes from the Renormalization Group (RNG) theory adapted for turbulent flow modelling (Pope 2000, Yakhot & al 1992). This new development of the K- turbulence model has extended the domain of validity of this model to weak turbulent flow regions, i.e. near a wall or inside a wake, where the turbulence is far from isotropic and homogeneous conditions. In the previous expression, the eddy viscosity is damped in the weak turbulent regions by introducing a function f defined using the turbulent Reynolds number (ratio between the transport due to the turbulent flow and the viscous term) ReT = Near the fire front, due to the presence of hot spot (hot gases, burning particles …) the pyrolizate (mainly CO and CH4) resulting from the decomposition of the vegetation reacts very quickly with the ambient air with a quasi infinite reaction rate. Therefore, we can D2.4-1-18-1000-1 Page 9 of 28 postulate that the reaction rate is not limited by chemical kinetics, but by the time necessary for the mixing between the gaseous fuel and the oxygen. This mixing, is mainly assured by the turbulent structures (eddies) located in the flaming zone. If the conditions are fully turbulent, the reaction rate can be written as a function of the local mass of fuel available for burning divided by the integral turbulent time scale (Eddy Dissipation Combustion Concept) (Magnussen & al 1979): EDC WFuel YOxy min YFuel , CA mix (4.g) where YFuel and YOxy denote the mass fraction of Fuel and Oxygen, respectively, is the stoichiometric ratio of the combustion reaction, and CA is a function of the turbulent Reynolds number (Magnussen & al 1978): CA 23.6 (4.h) 1/ 4 ReT 1 * Where the fraction occupied by the reaction zone inside these small structures, defined as following: YPr o (1 ) YFuel YPr o (1 ) 2.13 (4.i) 3/ 4 ReT YPro: mass fraction of combustion products. To take into consideration the regions where the turbulence is not fully developed, the average rate of reaction is pondered using the reaction rate calculated from an Arrhenius kinetics law (Magnussen & al 1978, Li & al 2003): EDC Ar WFuel min WFuel ,WFuel E Ar WFuel 2 YFuel YOxy K Ar exp Ar RT (4.j) Where the pre-exponential factor (KAr ) and the activation energy (EAr) are: KAr = 7 104 m3/kg.s, EAr = 6.651 104 J/mol In FIRESTAR system, it is assumed that the composition of pyrolysis products is mainly a mixture of CO and CO2 (+H2O coming from the dehydration of plants). This assumption is confirmed by experimental measurements performed using Thermo-Gravimetric Analysis (TGA) at low temperature (<1000K) (Grishin 1997). The mixing time mix is evaluated from the characteristics time defined for the turbulent flow (mix = K/). D2.4-1-18-1000-1 Page 10 of 28 Convection and radiation heat transfer The source term Q+/-(S) on the right hand side of the energy balance equation (1.f) for the solid fuel, includes mainly two contributions, resulting from the radiation and the convection heat transfer, between the hot gases, the flame and the unburned solid fuel. The term representing the contribution due to the convection heat transfer Qconv(S) can be written as follows: (S ) Qconv hconv S S T TS (5.a) The heat transfer coefficient hconv is approximated using an empirical correlation obtained for laminar or turbulent flow around a cylinder (Incropera & DeWitt 1996, Morvan & al 2004). The term coming from the radiation heat transfer can be written using the following form: (S ) Qrad S S 4 J 4T (5.b) The first term 4 S S S 4 the solid fuel. As mentioned in several studies (see reference (Pitts 1991) for a review), radiation is one of the most important heat transfer mechanism contributing to the propagation of a fire. Even if it is not always the dominant factor (in many situations the fire is piloted by convection heat transfer), it usually represents at least 30% of the energy received by the vegetation located ahead of the fire front (Cheney 1981)). The total irradiance J is calculated by integrating the radiation intensity in every direction (I): 4 J Id (5.c) 0 Including the contribution of the flames (soot particles) and the embers, the radiation transfer equation (RTE) can be written as follows: T 4 d G I S S TS4 I G G I (5.d) ds 4 Even if we know that soot particles in a flame can agglomerate adopting very complex forms, we assumed that soot particles are spherical; we assumed that the diameter of soot particles (agglomerated soot) was equal to m, corresponding to the average value observed experimentally inside a forest fire plume (Banta & al 1992). The soot field is calculated solving a transport equation for the soot volume fraction, assuming that the rate of production of soot particles in the flaming zone represented 5% (in mass) of the rate of degradation of the solid fuel by pyrolysis. Considering that the soot production rate represents the maximum value reached in the under-oxygenated region in the flaming zone, D2.4-1-18-1000-1 Page 11 of 28 this source term is multiplied by the ratio YO2 YO 2 , representing the deviation from the YO2 oxygen concentration at infinity (standard atmospheric conditions). We have neglected the contribution due to soot oxidation in the flame. The RTE is solved using a discrete ordinate method (DOM), consisting in the decomposition of the radiation intensity I in a finite number of directions. Then, to calculate the irradiance J, this set of discrete contributions are integrated using a numerical Gaussian quadrature (for the present calculation in 2D, we used a S8 method, the radiation field is rebuilt using 40 directions) (Siegel & al 1992). D2.4-1-18-1000-1 Page 12 of 28 3. Numerical results and discussion To illustrate the possibility of the present code FIRESTAR-2D, we have performed numerical simulations for two types of surface fuel (homogeneous and heterogeneous): grassland and Mediterranean shrubland (garrigue). Even if grasslands do not represent a typical landscape of Mediterranean regions, due to the large amount of experimental data (especially those collected on experimental fire in Australia), this ecosystem represents now the base on which all physical models of wildland fire are tested. Recent compilations of experimental data collected in Portugal, Spain, Australia and New Zeeland (Fernandes & al 2003) showed that, even if the species characterizing the shrublands in these four countries present differences, the behaviour of surface fire through this kind of ecosystem presented some similarities. It is for this reason that we have decided to choose a typical shrubland (Quercus coccifera) characteristics of the region around Marseille, for the second set of simulations. All the simulations are performed using two grids: One for the vegetation, with an uniform mesh size One for the gas phase, using an Adaptive Mesh Refinement (AMR) algorithm near the fire front. To capture correctly the heat transfer by radiation, the size of the grids (in the vegetation and in the gas phase) along the streamwise and the vertical direction must be smaller than the length scale characterizing the radiation heat transfer inside the solid fuel layer, defined as following: R S S 1 4 Taken into account the specific properties characterizing the two selected landscapes, we used the following set of grid sizes in the vegetation and in the gas phase: Grassland Shrubland R (m) 0.5 0.34 X (m) (solid fuel grid) 0.25 0.2 Z (m) (solid fuel grid) 0.02 0.025 X (m) (gas grid) 0.5 0.34 Z (m) (gas grid) 0.25 0.17 D2.4-1-18-1000-1 Page 13 of 28 Surface fire propagating through an homogeneous fuel (grassland) A first set of numerical simulations has been realized to study the behaviour of a surface fire propagating through grassland. The characteristics of the fuel layer have been chosen to reproduce similar conditions as those observed on the field in northern Australia (see Figure 1) where various experimental campaigns were carried out (Cheney & al 1993, 1995, 1998): Fuel depth (m) 0.7 Fuel load (t/ha) 7 Solid fuel density (kg/m3) 500 Surface Area to Volume ratio (m-1) 4000 Fuel moisture content (%) 5 For all the calculations the vertical wind profile has been fixed at the inlet (above a nude ground) of the computational domain, using a logarithmic distribution. The value of the velocity (UW) is fixed at a defined height Z=ZH (for grassland ZH = 2 m). The curves shown in Figure 2 are the vertical distributions of the normalized turbulent kinetic energy and the normalized longitudinal velocity component calculated above the grass before the ignition of the fuel. To facilitate the comparison with other data from the literature (Finnigan 2000), the variables are reduced using the 2m open wind velocity (UW) and the fuel depth (HFuel). From a qualitative point of view, the present numerical results are in agreement with the knowledges concerning this type of boundary layer flow (Brunet & al 1994, Finnigan 2000, Katul & al 2004): The velocity profile exhibits an inflexion point for Z/HFuel =1, The production rate of turbulent kinetic energy resulting from the shear between the wind flow and the vegetation, and the maximum value for this variable is located just above the fuel layer for Z/HFuel =1 D2.4-1-18-1000-1 Page 14 of 28 As shown by the linear stability theory, this flow structure constitutes favourable conditions to promote a Kelvin-Helmholtz instability, which represents the mechanism for the early development of the turbulence (Bailly & Comte-Bellot 2003). A typical view of the fields of dry fuel volume fraction (on the top) and solid fuel temperature (on bottom), obtained after the ignition during the quasi-steady state phase of a surface fire are shown in Figure 3. This simulation was carried out for a 2m open wind speed UW = 3 m/s. These results show clearly that the depth of the pyrolysis front (inside which the dry fuel fraction decreases from 1 to 0) is much thinner than the thermally affected zone. We can also notice on this view (Figure 3 on top) that the typical value for this length scale is much smaller than the optical length scale characterizing the fuel layer (defined as the inverse of the extinction coefficient, for the present simulations this value is equal to 0.5 m). If the radiation heat transfer represents a significant mode of propagation of the fire, the mesh size used to discretize the solid fuel layer must be smaller than the grid size in the gaseous phase, and both must be at least smaller than the optical length scale. Figure 1: Typical view of a grassland in northern Australia where experimental fire campaigns were carried out (Cheney & al 1993, 1995, 1998). D2.4-1-18-1000-1 Page 15 of 28 Figure 2: Normalized turbulent kinetic energy (on the left) and wind velocity profiles (on the right). Figure 3: Typical dry fuel volume fraction (on the top) and fuel temperature (on bottom), calculated during the propagation of a grassland fire. The temperature field (for the gaseous phase) and the velocity vectors calculated for three values of the 2m open wind speed UW =3, 5 and 8 m/s are shown in Figure 4. The results obtained for UW = 3 and 8 m/s, are a good illustration of the two modes of fire propagation previously identified in the literature (Pagni and Peterson 1973). The result obtained for UW = 3 m/s, highlights that the fire affects significantly the gas flow in the region located just ahead of the fire front. The flame and the hot plume form a sort of barrier, preventing the wind flow to cross the fire front. In this case some fresh gases are aspirated ahead of the burning zone, contributing to the oxygen supply of the fire, and the propagation of the fire is D2.4-1-18-1000-1 Page 16 of 28 partially sustained by the radiation heat transfer between the flame and the unburned vegetation. The result obtained for UW = 8 m/s, shows an other mechanism of propagation, in this case the hot gases released during the combustion reaction, are pushed toward the unburned vegetation, increasing the heat transfer by convection with the unburned fuel and consequently enhancing the conditions of propagation of the fire through the fuel layer. This result is a confirmation that a great part of the behaviour of a surface fire, on a flat ground, depends strongly from the balance between two forces (Pagni and Peterson 1973, Morvan and Dupuy 2004): The buoyancy resulting from the gradient of density between the plume and the ambient gas, contributing to the vertical development of the flame The wind flow inducing a deviation of the flame toward the unburned vegetation D2.4-1-18-1000-1 Page 17 of 28 Figure 4: Temperature field and velocity vectors during the propagation of a grassland fire calculated for three values of the wind velocity UW = 3, 5 and 8 m/s. The evolution of the rate of spread (ROS) and the fire line intensity (I) as a function of the 10m open wind speed are shown in Figure 5, the present numerical results are compared with experimental data and observations collected on grassland fires (Cheney & al 1993, 1995, 1998, Alexander 2002). Even if some approximations do not represent completely the reality (the present calculations are only 2D) and taking into account the strong non linear character of the phenomena governing the behaviour of the fire (the turbulence flow and the combustion in the gaseous phase, the decomposition by pyrolysis of the vegetation, the radiation heat transfer …), the present numerical results are quite comparable with the experimental observations. To complete the comparison, we also added the predictions proposed by two operational tool used in USA (BEHAVE) and in Australia (MKV) for this kind of fire. Concerning the results obtained for the ROS, we have introduced the results obtained with another physical model (FIRETEC) developed at the Los Alamos National Laboratory (LANL). We know from experimental observations (Cheney & al 1993, 1995, 1998) that, even if the conditions are homogeneous, grassland fires exhibit 3D behaviour, inducing a deformation of the fire front. This behaviour results from border effects, due to the reduction of the heat transfer between the flame and the unburned vegetation on both side of the line fire. The amplitude of such deformation depends of the initial length of the line fire. The 3D simulations using FIRETEC (shown in Figure 5, on the left) were carried out for a short (16m) and a long (100m) line fire. All the approaches (2D and 3D physical model, empirical or semiempirical model) gives satisfactory results as long as the wind conditions remains moderate (<8 m/s), for stronger wind conditions it is more difficult to conclude. Direct observations of uncontrolled grassland fires indicate a sharp increase of the ROS (see Figure 5 on the left), which is not observed in the physical model (both in 2D and 3D) and in the predictions obtained using the empirical models. For the empirical models, this lack of accuracy for stronger wind conditions is not surprising, because all these models have been elaborated using experimental data obtained for weak wind conditions (for experimental fires outdoor or in a wind tunnel). Because of the high complexity of the physical phenomena governing the behaviour of wildfires, we are sure that all the physics cannot be correctly represented in the physical models. Some important phenomenon are not presently taken into account, such as the turbulent bursts (or gusts) in the wind flow, the turbulence/radiation interaction … which D2.4-1-18-1000-1 Page 18 of 28 can partially explain the discrepancies between the numerical results and the experimental observations. Figure 5: Rate of spread (on the left) and fireline intensity (on the right) as a function of the 10m open wind velocity (the present FIRESTAR results are compared with numerical, empirical and experimental data from the literature). Surface fire propagating through an heterogeneous fuel (shrubland) To simulate the behaviour of surface fires through fuel complex such in shrublands, it is necessary to define what is the good level of description to represent correctly an heterogeneous vegetation. Previous experimental fires carried out for a large number of homogeneous solid fuels, showed that the fire residence time varied inversely proportionally to the Surface Area to Volume ratio (SA/V) (Burrows 2001). It is well known (it is in fact a consequence of the previous result) that only finer solid fuel particles (typical size less than 6 mm) can effectively contribute to the propagation of a fire. Consequently, to represent a characteristic shrubland of Mediterranean regions (such as represented in Figure 6), only 4 families of solid fuel particles were necessary: one for the leaves, two for the twigs (including two classes of diameter: 0-2 mm and 2-6 mm) and one for the grass: SA/V (m-1) FMC (%) Coverage (%) Density (kg/m3) Leaves 5920 70 100 810 Twigs (0-2 mm) 2700 70 100 900 Twigs (2-6 mm) 1000 70 100 930 Grass 10 30 440 D2.4-1-18-1000-1 20 000 Page 19 of 28 Figure 6: Typical view of a Mediterranean shrubland near Marseille (France) and corresponding vertical solid fuel density distribution. The depth of the fuel layer, used for the present calculations, was equal to 0.75 m and the vertical distribution of fuel particles was piecewise linear (see Figure 6 on the right) reproducing the fuel samples collected on the field. D2.4-1-18-1000-1 Page 20 of 28 Figure 7: Temperature field calculated in the gaseous phase, in the leaves, in the thinner twigs and in the grass (top to bottom) during the propagation of a shrubland fire (wind velocity UW = 5 m/s). To illustrate the interaction between the gaseous phase and each family of solid fuel particles, the temperature fields calculated at the same time in the gas, in the leaves, in the thinner twigs and in the grass are shown in Figure 7. This simulation was carried out for a 10m open wind speed UW equal to 5m/s. As indicated previously, the stiffness of the thermal problem is more severe in the solid phase than in the gaseous phase. In many part of the domain, the temperature of the gas is greater than in the vegetation, indicating that in this case, the convection heat transfer could contribute actively to the propagation of the fire. Because each solid fuel family is characterized by its own set of physical properties, each one does not react identically compared to another one, as illustrated by the differences between the temperature fields shown in Figure 7. D2.4-1-18-1000-1 Page 21 of 28 Figure 8: Temperature field and velocity vectors during the propagation of a shrubland fire calculated for three values of the wind velocity UW = 5, 7 and 10 m/s. The temperature fields (in the gaseous phase) obtained for three values of the 10m open wind speed UW = 5, 7 and 10 m/s, show that the increase of the intensity of the wind contributes to extend the hot gases released by the burning zone, toward the unburned vegetation located ahead of the fire front, with a consequence to increase the relative contribution of the convective heat transfer in the energy balance equation governing the propagation of the fire. The evolution of the ROS as a function of the 2m open wind velocity U2 is represented in Figure 9, the present numerical results (FIRESTAR) are compared with three empirical correlation elaborated from experimental fires carried out in shrublands in Portugal and in Australia (Catchpole & al 1999, Fernandes & al 2000, 2003). Despite the fact that the characteristics of the vegetation is described using only one parameter (the depth of the fuel layer) and sometimes one or two additional parameters for the fuel moisture content (dead and living fuel), the differences between the predictions produced using these different empirical models are not so important, three of them (Fernandes 2003 and Catchpole 1999), exhibit a quasi-linear relationship between the ROS and the wind speed, indicating that the propagation of the fire could be mainly governed by the convection heat transfer between the hot gases and the unburned vegetation (as indicated previously). This result is confirmed by the evaluation of the various contributions (by convection and radiation) calculated using the present physical model. The numerical results produced using FIRESTAR compare very well with the experimental correlations (see Figure 9). D2.4-1-18-1000-1 Page 22 of 28 Figure 9: Evolution of the rate of spread (ROS) of a shrubland fire, as a function of the 2m open wind velocity U2. We must notice that this kind of comparison is not so easy to do, especially if the wind speed for the experimental data is specified near the ground (a lot of measurements are made at a height of 2m). There is an ambiguity concerning the state of the ground above which the velocity measurement is performed: is it nude or is it covered by the initial unburned vegetation (in FIRESTAR the wind speed is specified above a nude ground, at the inlet of the computational domain)? Preliminary numerical results, obtained for a boundary layer above the same kind of vegetation showed that the roughness induced by the presence of the vegetation can affect the velocity profile along a vertical distance equal to 5 times the depth of the fuel layer. The two points (1) and (2) reported in Figure 10, are located 2m and 10m above the ground level, respectively. We notice that the velocity magnitudes evaluated 10m (point 2) above a shrubs layer and above a nude ground do not differed, which is not the case for the velocities evaluated 2m (point 1) above the ground level (see Figure 10). Therefore, to avoid this ambiguity, in the future, during experimental campaigns, it will be preferable to measure the wind speed, at a height at least 5 times equal to the depth of the fuel layer. D2.4-1-18-1000-1 Page 23 of 28 Figure 10: Normalized velocity profile calculated above the nude ground (at the inlet) and above the shrubs. We noticed also that a small variation of grass FMC (fuel moisture content) ranged between 10 and 20% does not affect significantly the conditions of propagation (see Figure 9). We can interpreted this result as following: with a surface ratio equal to 30%, the grass do not represent a great part of the fuel load, it can contribute to the ignition (as a precursor) of the shrub fuel, but this particular fuel layer is not sufficiently continuous to sustain an autonomous fire front. As shown in Figure 7, the characteristics of the fire front (the Rate of Spread for example) are more affected by the structure of the shrubs than the properties of the grass. D2.4-1-18-1000-1 Page 24 of 28 4. Conclusions We have presented in detail the theoretical base of the physical model presently used by the FIRESTAR-2D model, which will also constitute the base from which, the 3D FIREPARADOX model will be developed. Despite the fact that all the complexity of the problem cannot be directly resolved (as indicated in the introduction), the physical approach used in this model seems to correctly reproduce the main tendencies observed experimentally for the surface fires on a flat ground. Nevertheless, we are conscious of the limitation introduced using a 2D approximation, and the development of a 3D modelling is completely necessary to simulate some situations such as: the crown fires dynamics, the interaction between two fire fronts, the effects of the heterogeneity of the fuel on surface fire dynamics, the slope effects … D2.4-1-18-1000-1 Page 25 of 28 5. References Alexander ME, Fogarty LG, A pocket card for predicting fire behaviour in grasslands under severe burning conditions, Fire Technology Transfer Note 25, 2002. Andrews PL, Bevins CD, In Proceedings 2nd Int. Congress on Wildland Fire Ecology & Fire Management 5th Symposium on Fire & Forest Meteorology , 2003. Mc Arthur AG, Common Aust. 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