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Morvan D, Méradji S, Accary G. Fire Safety J. 2009; 44(1): 50-61. |
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(Copyright © 2009, Elsevier Publishing) |
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unavailable |
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Abstract |
aUniversité de la Méditerranée, UNIMECA Technopôle de Château Gombert, 60 rue Joliot Curie, 13453 Marseille cedex 13, France bLaboratoire de Modélisation et Simulation en Mécanique et Génie des Procédés (MSNM-GP) UMR CNRS 6181 IMT La Jetée 38 rue Joliot Curie 13451 Marseille cedex 13, France cUniversité Saint Esprit de Kaslik, BP 446, Jounieh, Lebanon The propagation of grassland fires is simulated using a fully physical based model, partially developed during the FIRESTAR European Union programme. This approach, based on a multiphase formulation, includes the calculation of the degradation of the vegetation (by dehydration and pyrolysis) and the turbulent/reactive flow resulting from the mixing between the ambient gas (wind flow) and the pyrolizate. The solid fuel is simulated as homogeneous distribution of solid particles forming a porous media, interacting with the gas flow using a continuous distribution of drag forces. Other source terms representing the interactions between the vegetation and the gas flow are also taken into account, such as the production of water vapour and gaseous fuel, the radiation of soot particles and ashes, and the convective exchange in the energy balance. The model was validated from preliminary calculations carried out at small scale, for a homogeneous fuel bed (pine needles, excelsior, sticks) and compared with experimental results obtained in a wind tunnel. Calculations are then extended to study the propagation of fires through a flat grassland, for various wind speed conditions. The numerical results are compared to empirical and semi-empirical predictions obtained in similar conditions. Keywords: Wildfire modelling; Fire propagation; Physical model To predict the behaviour of grassland fire, the forest service in Australia has preferred to use an empirical approach based on a statistical analysis carried out on large-scale experimental fires [8], [9], [10] and [11]. This kind of ecosystem is characterized by a homogeneous solid fuel, on a flat terrain, for which the conditions of propagation are quite reproducible. In these conditions, the ROS can be evaluated from 5 or 6 parameters: the wind speed (UW), the relative air humidity (RH), the air temperature (T), the curing index (mass fraction of dead fuel), the slope, the surface fuel load (this parameter is taken into account only in the MkV model). These formulae were included inside the operational tools “Grassland fire danger metre: MkIV and MkV”, currently used by many forest services around the world [12] and [13]. A large set of experimental line fires (487) performed in Australia through open grassland and woodland with a grassy understory constitutes a major contribution to study the effects of the wind velocity and the dead fuel moisture content (FMC) on the behaviour of grassland fires [9] and [10]. For these experiments, the wind velocity (measured 2 m above the ground level) ranged between 2 and 6 m/s. These results showed that the fire front, initially rectilinear, took a more curved shape (parabolic) during the propagation. This effect was caused by the fresh air flow aspirated on both sides of the fire front; the trajectory of the flames was deviated, reducing locally the flame length. On both sides, the fire front was no more perpendicular to the wind direction and the convective heat transfer along the main direction of propagation (parallel to the wind direction) was reduced. Consequently, the local ROS of the fire front was larger in the middle than on the sides. For line fires at larger scale, the behaviour of the fire was less affected by these border effects and the ROS reached an asymptotic value. To cover a larger range of parameters, and to improve the predictions of this empirical model in operational conditions, the database was completed using some observations collected for 20 wildfires occurring in grasslands in Australia [11]. The results highlighted the existence of two modes of propagation according to the wind speed intensity: for relatively moderated wind conditions the ROS varies linearly with the wind speed (ROSUW), for stronger wind conditions the ROS varies as a power law function with the wind speed (ROSUWp) with an exponent p<1. This result is in agreement with previous works which have shown the existence of two regimes of propagation for a line fire, the first one governed by the radiation heat transfer (backing fire or plume dominated fire) and the other one by convective heat transfer (heading fire or wind-driven fire) [14] and [15]. The experimental results also showed that the fire did not propagate without wind, and that the propagation could be erratic for moderate wind conditions. Consequently, it is more convenient to express the ROS from critical conditions: This problem can be analysed using the more fundamental combustion problem of a solid fuel heated from an impinging hot jet [17]. The experimental results obtained for this configuration showed that the ignition time was piloted by two opposite mechanisms: the pyrolysis of the solid fuel and the combustion in the gas phase. Increasing the hot gas flow in the jet, one induced a corresponding increase of the heat flux at the surface of the solid fuel and a reduction of the residence time of the flow along the surface. Consequently, the pyrolysis time decreased and the chemical induction time in the gas phase increased. Experimentally, one can demonstrate the existence of an optimal condition corresponding to a minimum value for the ignition time. The same phenomenon can be observed for wind-driven fires, the wind flow increases the heat transfer between the hot gases coming from the burning zone and the solid fuel and consequently supports the pyrolysis of the solid fuel, but at the same time it increases the induction time in the gas phase. To evaluate the behaviour of a wildfire for a larger range of ecosystems, the US Forest Service uses a semi-empirical approach based on a single energy balance equation (written in a reference frame attached to the fire front) between the energy necessary to pyrolyze the vegetation and a fraction of the energy released by the burning zone (and received by the vegetation). The coefficient of proportionality between these two terms was evaluated empirically from experimental fires performed in a wind tunnel [18] and [19]. The coupling between this model and a method to describe the vegetation (classified in 13 fuel models included short and tall grass) allowed to develop operational tools BEHAVE [20] and FARSITE [21], currently used in United States and other countries all around the world (see also www.fire.org). After a presentation of the physical equations solved in the present model (FIRESTAR), various numerical results carried out for surface fires propagating in a grassland are presented and compared with experimental data obtained for outdoor fires [9], [10] and [11]. To complete this work, we also add the predictions obtained in similar conditions, using the operational tools MkV and BEHAVE currently used by the forest services in Australia and in United States. 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 (αS), the fuel density (ρS), the moisture content (tH2O), the size of fuel particles, the fuel temperature (TS), and the fuel composition. Experimental measurements [22] of the residence time of fires, propagating through homogeneous fuel beds, showed that only small fuel particles (φ<6 mm, surface area to volume ratio σS>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 (φ<6 mm) was consumed in the flaming zone [23]. This threshold size represents also the limit separating the thermally thick and thermally thin particles, for which the inner temperature gradients can be neglected. During the decomposition of the vegetation, resulting from the fire-induced heat stress, we assume that the composition of each solid fuel element could be characterized as a mixture of water (moisture content), dry material (cellulose, hemicellulose, lignin), char, and ashe (mineral residue). Each of these elements are represented by field variables corresponding to the mass fraction of water , 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 summarized using the three following steps: The time evolution of the solid fuel composition is governed by the following mass balance equations [24] and [25] (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)): Adding these three contributions (+ the mass balance of ash), the global mass balance equation is 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: The evaporation process is represented using a one-step temperature transformation (if TS=373 K): 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 [24], [25] and [26]: The surface oxidation of char is also represented using a kinetic law of the form [25] The evolution of 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 RANS (Favre) formulation. In this case the filtered variables are governed by the following set of transport equations: Fi(S) denotes the ith component of the drag force resulting from the interaction between the gas flow and the vegetation: 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, αG and σG 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 [28]), T is the temperature of the gas, and σ is the Stefan–Boltzmann constant. 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 supplementary diffusion term (Eddy viscosity concept). For the momentum equations, the eddy diffusion coefficient is evaluated from two variables characterizing the turbulence: the turbulent kinetic energy K and its dissipation rate ε (well-known K–ε turbulence model) [29]: The following set of constants are introduced in the turbulence model [30]: P and W are respectively the terms contributing to the production of turbulence, due to shear and buoyancy effects, given as: The turbulent Prandtl PrT number is calculated from the following relation (αT=1/PrT): The values with the subscript T design the turbulent values (without subscript: molecular values: α=1/Pr, molecular Prandtl number). The terms including the drag coefficient CD in Eqs. (5a) and (5b), 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 ε comes from the Renormalization Group (RNG) theory adapted for turbulent flow modelling [29] and [30]. This new development of the K–ε 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 fμ defined using the turbulent Reynolds number (ratio between the transport due to the turbulent flow and the viscous term) ReT=ρK2/(με). Near the fire front, due to the presence of hot spot (hot gases, burning particles, etc.) the pyrolizate (mainly CO and CH4), resulting from the decomposition of the vegetation, reacts very rapidly with the ambient air, with a quasi infinite reaction rate. Therefore, we can 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) [31]: 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 [31] and [32]: 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 (<1000 K) [24]. The mixing time τmix is evaluated from the characteristics time defined for the turbulent flow (τmix=K/ε). The source term on the right-hand side of the energy balance equation (1) 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: The heat transfer coefficient hconv is approximated using an empirical correlation obtained for laminar or turbulent flow around a cylinder [33]: The term coming from the radiation heat transfer can be written using the following form: The first term (αSσS)/4 in this expression represents the coefficient of extinction attached to the solid fuel. As mentioned in several studies (see Ref. [14] for a review), radiation is one of the most important heat transfer mechanisms 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 [23]. The total irradiance J is calculated by integrating the radiation intensity in every direction (I): Including the contribution of the flames (soot particles) and the embers, the radiation transfer equation (RTE) can be written as follows: Even if we know that soot particles in a flame can agglomerate adopting very complex forms, we assume that soot particles are spherical (diameter φ=1 μm). 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. We neglect the contribution due to soot oxidation in the flame. Considering that this soot production rate represents the maximum value reached in the under-oxygenated region in the flaming zone, this source term is multiplied by the ratio , representing the deviation from the oxygen concentration at infinity (standard atmospheric conditions). The RTE is solved using a discrete ordinate method (DOM), consisting of 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) [34]. The set of transport equations in the gas phase are solved using an implicit finite Volume (FV) method. To avoid the introduction of false numerical diffusion, the Ultra-Sharp (Universal Limiter for Tight Resolution and Accuracy Resolution Program) has been adopted [35] and [36]. The set of ordinary differential equations governing the evolution of the solid fuel was solved using the Runge Kutta method. An extensive numerical study, concerning the propagation of a surface fire through a grassland, has been carried out. The calculations are conducted under conditions similar to the extensive campaign of experimental fires carried out in the Northern Territory, in Australia [9] and [10]. The fuel structure is quite homogeneous (see Fig. 1) and identical to a natural undisturbed grassland; the physical properties characterizing this eco-system are listed in Table 1. The effect of two physical parameters are tested: Before the presentation of the results obtained during the burning, the vertical profile of the average longitudinal component of the velocity vector and of the turbulent kinetic energy are shown in Fig. 2; the variables are reduced using the depth of the combustible layer (HFuel) and the 2 m open wind velocity (UW). These curves are in agreement with the data of the literature, for example, the present numerical model predicts correctly that the maximum value of the turbulent kinetic energy is located at the top of the solid fuel layer and the existence of an inflexion point characterizing the velocity profile is also located at the top of the fuel layer (see Fig. 2 on the left) [37]. The numerical results obtained during the burning phase are compared with the predictions obtained using empirical [11] and [12] (MK V) and semi-empirical (BEHAVE) models [20]. The calculations are performed in a 2D plane perpendicular to the fire front, assuming that the gradients of scalar variables (temperature, chemical species concentrations) and the velocity vectors governing the behaviour of the fire are mainly located in the plane perpendicular to the fire front. Experimentally, it was shown that the fire front did not maintain a rectilinear shape [9] and [10]. Border effects can affect the heat transfer on both sides of a fire line (initially rectilinear), and consequently the amplitude of the propagation of the fire front between the centre and the lateral sides. The present calculations constitute an approximation of the asymptotic situation reached when the initial length of the fire tends towards infinity. Experimental results obtained for grassland fires showed that some parameters characterizing the behaviour of the fire (such as the ROS) reached an asymptotic value for an ignition line length greater than 100–200 m [10]. Instantaneous views of the temperature field (gas phase) and velocity vectors calculated during the propagation of the surface fire are shown in Fig. 3, for four values of the wind speed velocity UW: 0.5, 3, 5 and 8 m/s. For the smaller value of the wind velocity (UW=0.5 m/s), the trajectory of the flame is not at all affected by the action of the wind flow. The trajectory of the flame is quasi vertical and fresh air is entrained ahead of the fire front (see Fig. 5, on top). In this case the fire front can be assimilated as an obstacle, and the wind flow is deflected vertically with the plume. More generally, for weak wind conditions (UW<3 m/s), the propagation of the fire can be erratic. This phenomenon is also observed for experimental fires [11]. For larger values of the wind speed (UW=5 and 8 m/s), the wind flow affects more significantly the trajectory of the flame, crossing the fire front and pushing the hot gases toward the unburned vegetation (see Fig. 3 on bottom). This is further illustrated in Fig. 5, Fig. 6 and Fig. 7, which show the vertical distribution of the horizontal component of the velocity vector for two points P1 and P2 located 10 m on both sides of the fire front (see Fig. 4). For a more convenient interpretation of the results, the longitudinal velocity UX and the vertical coordinate Z are non-dimensionalized using the 2 m open wind speed (UW) and the solid fuel depth (HFuel), respectively. These curves highlight the existence of two regimes of propagation: In the literature, the first regime is called “plume dominated fires” and the second is the “wind-driven fires” [14] and [15]. The corresponding time evolution of the heat transfer by radiation and convection between the flame and the vegetation is reported in Fig. 8, Fig. 9, Fig. 10 and Fig. 11, for the same values of the wind speed (UW=0.5, 3, 5 and 8 m/s). The three first curves (Fig. 8, Fig. 9 and Fig. 10) show clearly that for moderate wind conditions the heat transfer between the flame and the unburned fuel can be dominated by radiation (Fig. 8 and Fig. 10) or piloted both by radiation and convection, which are at the same level of magnitude (Fig. 10). The results show also (see Fig. 10) that an increase of the wind intensity induces a corresponding increase of the heat transfer by radiation (due to an extension of the flame surface). Then for a larger value of the wind speed (UW=8 m/s) (see Fig. 11), we notice that the convective heat transfer increases significantly and can represent the main physical mechanism governing the propagation of a fire under strong wind conditions (wind driven fires). In this case the wind flow pushes the hot gases coming from the burning zone toward the unburned vegetation and contributes to initiate the decomposition (dehydration and pyrolysis ) of the vegetation necessary to sustain the propagation of the fire. In Fig. 12, a typical representation of the temperature field (on the top) in the solid fuel and the corresponding distribution of the dry material density (on bottom) are reported for the same time. We can notice that the temperature gradient ahead of the fire front is quite sharp, the value is around 260 K/m. The thickness of the pyrolysis front (defined as the region inside which all the dry fuel is transformed into gaseous fuel and charcoal) is around 0.25 m; the order of magnitude of this value is comparable to the length scale characterizing the absorption property of the solid fuel layer 4/(αSσS)=05 m. This remark explains the necessity to represent the solid fuel layer using a mesh size smaller than the length scale characterizing the radiation heat transfer which constitutes one of the most important modes of heat transfer contributing in many situations to the propagation of the fire. The evolution of the ROS versus the 10 m open wind speed (U10) is represented in Fig. 13. The present numerical results (FIRESTAR) are compared with empirical (MK5) and semi-empirical (BEHAVE) predictions; these tools are currently used by fire fighters and foresters in Australia and in USA, respectively. We have also added direct measurements obtained on experimental fires and wildfires in Australia [11] and some numerical results obtained using the 3D code FIRETEC developed at the LANL. The comparison between numerical (FIRESTAR), empirical (MK5) and semi-empirical (BEHAVE) results is quite satisfactory; all predict that the ROS varies more or less linearly with the wind speed U10. The same good agreement can be noticed with the data collected on experimental fires as long the wind speed U10 remained lower than 8 m/s. For larger values of the wind speed (10 m/s), direct observations carried out on uncontrolled wildfire seem to indicate a modification of the regime of propagation of the fire characterized by a sharp increase of the ROS. Considering the results reported in Fig. 12, this modification of the regime of propagation of the fire seems to be due to the predominance of the convective heat transfer which governs the behaviour of the fire as the wind speed exceeds a threshold level. For safety reasons, the experimental fires (used to elaborate the empirical models MK5 and BEHAVE) cannot be conducted for wind speeds larger than 7–8 m/s. This remark can explain why these two models seem to under-evaluate the ROS as the wind speed exceeds this critical value. For strong wind conditions, experimental data are more dispersed, and the comparison is more difficult. Therefore, at this stage of this study, it is difficult to understand what is the physical mechanism inducing this rapid amplification of the effect of the wind speed upon the propagation of the fire. The evolution of the fire intensity (IF) as a function of the 10 m open wind speed U10 is shown in Fig. 14; the present numerical results are compared with the predictions obtained using the operational models MK5 and BEHAVE; we have also reported some evaluations extracted from direct observations of prescribed and wildland fires on the field [7]. For the MK5 and BEHAVE, IF (W/m) is evaluated from the Byram formula [38]: In operational conditions, the consumed fuel Wfc is evaluated from the fuel load (Wf) assuming an arbitrary combustion efficiency: Wfc=ηWf (η1). To avoid this uncertainty in the present study, the fire intensity is directly calculated from the homogeneous and heterogeneous combustion rate in the gas phase (WCO) and at the surface of the charcoal (WCHAR) integrated over the entire domain: All empirical, semi-empirical, and numerical results exhibit similar behaviour (see Fig. 13 and Fig. 14). The transition between a high and a very high fire danger index corresponds to a fire intensity IF equal to 6000 kW/m. All the results obtained using the present model are located above this threshold value, which means that, even if the wind speed remains quite moderate, and because the fuel moisture content is very low (5%), the fire can exhibit a very dangerous behaviour. The effect of the fuel moisture content (FMC ranged from 0 to 30%) upon the ROS is reported in Fig. 15, representing the ratio ROS/ROS(0) (ROS(0) designing the rate of spread obtained for a FMC=0%). This particular study is carried out under moderate wind conditions (UW=3 m/s). The results obtained using the present numerical model (FIRESTAR) are compared with MK5 and BEHAVE predictions. We have also added the prediction obtained using a simplified theory, assuming that the energy received by the unburned fuel is not modified by the FMC. Writing a simple energy balance in the solid fuel layer, with this assumption the ratio ROS/ROS(0) can be coarsely approximated as The results can be regrouped in two behaviours: These two behaviours are compatible with the experimental observation carried out for fire propagating through homogeneous fuel beds in a wind tunnel [39]. This experimental study showed also that the ratio ROS/ROS(0) can be written as follows: A detailed analysis of these experimental data seems to indicate that the damping coefficient A can be affected by the fuel bed packing ratio (solid fuel volume fraction) αS; for a regular excelsior (σS=7596 m−1), A can vary from 0.41 to–0.73 as the packing ratio αS decreases from 0.02 to 0.005. Therefore, for a sparse solid fuel layer (in a grassland αS=0.002), we cannot exclude that the exponential damping can be negligible. We have also to mention that the semi-empirical model (BEHAVE) has been elaborated in a relatively dense fuel layer (the order of magnitude for the packing ratio was 10−2), and the effects of the fuel moisture content were calibrated for a free propagation of a surface fire, without the contribution of a wind flow. The effect of the FMC can also be considerably reduced by the action of the wind flow upon the trajectory of the flame, as shown in Fig. 16 and Fig. 17. Even if the increase of the FMC contributes to reduce the intensity of the fire (see Fig. 16 and Fig. 17 on the top), the wind flow pushes the flame front toward the unburned solid fuel (enhancing the heat transfer between the flame and the vegetation). Finally, these contradictory mechanisms contribute to maintain the energy received by convection and radiation approximately at the same level (see Fig. 17 on the bottom). The same calculation was carried out using UW=0.5 m/s and FMC=30%; in this case we observed a rapid extinction of the line fire. This additional result confirms that the intensity of the wind flow (encouraging the heat transfer between the flame and the unburned fuel) affects the threshold FMC beyond which the fire cannot spread. A numerical model based on a fully physical approach is proposed to study the behaviour of grassland fires. The mathematical model is based on the resolution of the set of conservation equations (mass, momentum, energy) governing the time evolution of the coupled system formed by the vegetation and the surrounding gas medium. We observe a relatively good agreement between the present numerical results and empirical predictions extracted from experimental grassland fires. The present numerical results confirm also that a wind-aided line fire in a very dry (FMC=5%) grassland can exhibit a large ROS (>5 m/s) and a very high intensity level (>30,000 kW/m), representing extreme danger and the capacity of great injuries, during a suppression or a prescribed burning operation. These results have also confirmed the difficulty in extrapolating an empirical formula established at small scale to understand the behaviour of large-scale fires. This remark confirms the necessity to carry out new experiments at large scale; when such experiments cannot be conducted (for safety reasons, for example), a numerical approach such as the physical modelling proposed in this study, represents an alternative tool to improve the knowledge concerning the behaviour of wildfires, especially when the dynamic of the fire is submitted to a rapid evolution resulting from the action of wind gusts, of a sharp slope, a discontinuity of the fuel layer. However, the present “fully” physical model cannot describe all physics present during the development of a wildfire. Compared to the great complexity of the real problem, it must be considered as a simplification. Many features characterizing a wildfire are not taken into account for this time: the 3D nature of the flow field, the turbulence/radiation interaction, and the soot production model are very crude. Therefore, we continue to improve this approach with a constant necessity to compare numerical results with experimental data as often as possible. The authors thank the two anonymous reviewers who greatly contributed to improve the present article. This study has been partially funded by the European Commission in the frame of the FIRE PARADOX research programme (6th Framework R&D Programme of the European Union, 2006–10). |