Download 3. Numerical results and discussion

yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Fire ecology wikipedia , lookup

Control of fire by early humans wikipedia , lookup

Greek fire wikipedia , lookup

Firestorm wikipedia , lookup

Fire wikipedia , lookup

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
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
Dissemination Level
Restricted to other programme participants (including the Commission Services)
Restricted to a group specified by the consortium (including the Commission Services)
Confidential, only for members of the consortium (including the Commission Services)
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
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,
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).
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)
d  S  S YI( S )
 WPYR (1.b)
Page 5 of 28
 
(S )
d  S  S YCHAR
  CHAR  SOOT WPYR   ASH  1WCHAR (1.c)
  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)
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
  WCHAR (1.e)
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
 Q( S/ )  hVAPWVAP  hPYRWPYR   hCHARWCHAR (1.f)
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/kghPYR=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):
0 T  373 K
  Q( S/ )
T  373 K
 h
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
 E
 S S
 g  g YO 2 K CHAR  exp  CHAR 
(S )
 O2
 RTS 
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:
  M (S ) (3.a)
( G ij )
D u~i
(u j ' ' u i ' ')   g i  Fi ( S ) (3.b)
x j
x j
D h (q j )
(S )
(u j ' ' h' ')  QCONV
  G G J  4T 4 (3.c)
x j
x j
D Y
x j
 D Y
x j
 
(u j ' ' Y ' ')  W  M ( S ) (3.d)
 x
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 
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)
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
x j
  eff K
 Pr x
 T
D 
x j
  eff  
  3  ~3
~ 
  C 1 P  C 3 W   (C 2  R)
 C D S S 
U  6U  (4.b)
 Pr x 
2 2 K
j 
 T
  P  W    C D  S  S U~ 3  4U~K (4.a)
Page 8 of 28
 T  C 
 f  (4.c)
f  exp  2.5  d)
 10.02ReT 
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
The following set of constants is introduced in the turbulence model (Yakhot & al 1992):
C1=1.42, C2=1.68, C3=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'
x j
W 
T  ~p
 2 x j x j
The turbulent Prandtl PrT number is calculated from the following relation (T= 1/PrT):
 T  1.3929
  1.3929
 T  2.3929
  2.3929
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
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):
 min  YFuel ,
 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 
1/ 4
1   *
Where 
 the fraction
occupied by the reaction zone inside these small structures, defined as following:
YPr o (1   )
  YFuel  YPr o (1   )
 
3/ 4
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):
WFuel   min WFuel
 E 
  2  YFuel  YOxy  K Ar  exp   Ar 
 RT 
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/).
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
(S )
 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 )
 S S
J  4T  (5.b)
The first term
 S S
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):
J   Id (5.c)
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)
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,
Page 11 of 28
this source term is multiplied by the ratio
YO2  YO 2
, representing the deviation from the
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).
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
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:
R (m)
X (m) (solid fuel grid)
Z (m) (solid fuel grid)
X (m) (gas grid)
Z (m) (gas grid)
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)
Fuel load (t/ha)
Solid fuel density (kg/m3)
Surface Area to Volume ratio (m-1)
Fuel moisture content (%)
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
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).
Page 15 of 28
Figure 2: Normalized turbulent kinetic energy (on the left) and wind velocity profiles (on the
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
Page 16 of 28
partially sustained by the radiation heat transfer between the flame and the unburned
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
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
Page 18 of 28
can partially explain the discrepancies between the numerical results and the experimental
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)
Twigs (0-2 mm) 2700
Twigs (2-6 mm) 1000
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.
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.
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).
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.
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.
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 …
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. For. Timb. Bur., 100 p. Camberra, 1966.
Mc Arthur AG, “Grassland fire danger meter MkIV” Forest Research Institute, Forestry and
timber bureau, Canberra, 1973.
Mc Arthur AG, “Grassland fire danger meter MkV” CSIRO Division of Forest Annual Report
1976-1977 p.58, 1977.
Bailly C, Comte-Bellot G, Turbulence, CNRS Editions, 2003.
Banta RM, Olivier LD, Holloway ET, Kropfli RA, Bartram BW, Cupp RE, Post MJ, Smoke
Column Observations from Two Forest Fires Using Doppler Lidar and Doppler Radar. J. Appl.
Meteor., 31, 1328-1349, 1992 .
Brunet Y, Finnigan JJ, Raupach MR, A wind tunnel study of air flow in waving wheat: singlepoint velocity statistics, Boundary-Layer Meteorology, 1994, 70: 95-132.
Burrows ND, Flame residence times and rates of weight loss of eucalypt. forest fuel particles,
Int. J. of Wildland Fire 2001, 10 137-143.
Catchpole WR, Catchpole EA, Butler BW, Rothermel RC, Morris GA, Latham DJ, Rate of
spread of free-burning fires in woody fuels in a wind tunnel. Combust. Science Tech. 131
(1998) 1-37.
Catchpole WR, Bradstock RA, Choate J, Fogarty LG, Gellie N, McCarthy GJ, McCaw WL,
Marsden-Smedley JB, Pearce G, Cooperative development of prediction equations for fire
behaviour in heathlands and shrublands, Australian Bushfire Conference, 1999.
Clark TL, Jenkins MA, Coen J, Packham D, A Coupled Atmospheric-Fire Model: Convective
Froude number and Dynamic Fingering. Int. J. Wildland Fire 1996, 6:177-190.
Cheney NP, in: R.H. Gill, R.H. Groves, I.R. Noble (Eds.), Fire and the Australian biota,
Autralian Academy of Science, Canberra, 1981, p. 151.
Cheney NP, Gould JS, Catchpole WR, The influence of fuel, weather and fire shape variables
on fire spread in grasslands. Int. J. Wildland Fire 1993, 3(1):31-44.
Cheney NP, Gould JS, Fire growth in grasslands. Int. J. Wildland Fire 1995, 5(4):237-247.
Cheney NP, Gould JS, Catchpole WR, Prediction of fire spread in grasslands. Int. J. Wildland
Fire 1998, 8(1):1-13.
Page 26 of 28
Di Blasi C, Branca C, Santoro A., Hernandez EG, Pyrolytic behaviour and products of some
wood varieties, Combust. Flame 2001 ,124:165-177.
Fernandes PM, Catchpole WR, Rego FC, Shrubland fire behaviour modelling with microplot
data, Can. J. For. Res., 2000, 30:889-899.
Fernandes PM, Vega JA, Cuinãs P, Fontùbel T, Catchpole W, Empirical analysis of fire
behaviour in Europe: state of the art and current work, EuFireLab meeting, 2003, Firenze.
Fernandez-Pello AC, in: G. Cox (Ed.), Combustion fundamentals of fire, Academic Press,
1995, p. 31.
Finnigan J, Turbulence in plant canopies, Annu. Rev. Fluid Mech., 2000, 32:519-571.
Fogarty LG, Alexander ME, A field guide for predicting grassland fire potential: derivation and
use, Fire Technology Transfer Note, 1999, 20.
Frandsen WH, Fire spread through porous fuels from the conservation of energy, Combust.
Flame 1971, 16:9-16.
Grishin AM, in: F. Albini (Ed.) A mathematical modelling of forest fires and new methods of
fighting them, Publishing House of the Tomsk University, Tomsk, Russia, 1997.
Hanson HP, Bradley MM, Bossert JE, Linn RR, Younker LW, The potential and promise of
physics-based wildfire simulation. Environment Science Policy 2000, 3 :161-172.
Incropera FP, DeWitt DP, Fundamentals of heat and mass transfer, Wiley 5th Edition,
Chichester UK, 1996.
Kaplan CR, Shaddix CR, Smith KC, Computations of enhanced soot production in time-varying
CH4/air diffusion flames, Combust. Flame, 106 (1996) 392-405.
Katul GG, Mahrt L, Poggi D, Sanz C, One-and two-equation models for canopy turbulence,
Boundary-Layer Meteorology, 2004, 113:81-109.
Li ZQ, Wei F, Jin Y, Numerical simulation of pulverized coal combustion and NO formation,
Chemical Engineering Science, 58(2003) 5161-5171.
Linn RR, Reisner J, Colman JJ, Winterkamp J, Studying wildfire behavior using FIRETEC. Int.
J. Wildland Fire 2002, 11:233-246.
Magnussen BF, Hjertager BH, Olsen JG, Bhaduri D, Effects of turbulent structure and local
concentrations on soot formation and combustion in C2H2 diffusion flames. 17th Symposium
(Int) on Combustion, The Combustion Institute, 1979, 1383-1393.
Mell W, Charney JJ, Jenkins MA, Cheney NP, Gould J, Numerical simulations of grassland fire
behavior from the LANL-FIRETEC and NIST-WFDS models. In Proceedings EastFIRE
Conference, May 11-13, Fairfax (VA), 10 pp., 2005.
Page 27 of 28
Morvan D, Dupuy JL, Modelling of fire spread through a forest fuel bed using a multiphase
formulation, Combust. Flame 2001,127:1981-1994.
Morvan D, Dupuy JL, Modeling the propagation of a wildfire through a Mediterranean shrub
using a multiphase formulation. Combust. and Flame 2004, 138:199-210.
Noble IR, Bary GAV, Gill AM, McArthur's fire-danger meters expressed as equations. Aust. J.
of Ecol. 1980, 5:201-203.
Pagni PJ, Peterson TG, Flame spread through. porous fuels, 14th Symposium (Int) on
Combustion, The Combustion Institute, 1973, 14 1099-1107.
Pitts WM, Wind effects on fires. Prog. Energy Combust. Sci. 1991, 17:83-134.
Pope SB, Turbulent Flows, Cambridge University Press 2000.
Rothermel RC, A mathematical model for predicting fire spread in wildland fuels, USDA Forest
Service Research Paper INT-115, 1972.
Siegel R, Howell JR, Thermal radiation heat transfer, 3rd Edition, Hemisphere Publishing
Corporation, 1992.
Wilson CC, Sorenson JC, Publication NA-GR-8, 31 pp., USDA Forest Service, Broomall,
Pennsylvania, 1978.
Yakhot V, Orszag SA, Thangam S, Gatski TB, Speziale CG, Development of turbulence models
for shear flows by a double expansion technique, Phys. Fluids A4(7) (1992) 1510-1520.
Page 28 of 28