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Physics based modelling of tree fires and fires
transitioning from the forest floor to the canopy
K. A. M Moinuddin a,c and D. Sutherland a,b,c
aCentre for Environmental Safety and Risk Engineering, Victoria University, Victoria
b Department of Mechanical Engineering, University of Melbourne,
c Bushfire and Natural Hazards Cooperative Research Centre.
Email: khalid.moinuddina@vu.edu.au
Abstract: Wildland fires or bushfires can be a surface fire such as a grassfire or an elevated crown fire.
Crown fires are often supposed to originate from surface fires spreading either along the bark of the tree trunks
or direct flame contact to low branches with leaves and needles. In a previous study, surface fire (grassfire)
spread simulation was successfully conducted using a physics based model, Wildland Urban Interface Fire
Dynamics Simulator (WFDS). The base open-source code of WFDS was developed by the National Institute
of Standard and Technology (NIST), USA from its original building fire model Fire Dynamics Simulator
(FDS); but it is being further developed by other researchers. It is important that the capabilities of WFDS for
modelling tree and forest canopy fire are explored to develop rate of spread equations for crown fires.
In this study, we have first quantitatively studied a burning single tree and then semi-quantitatively studied
forest floor fire transitioning to a crown fire. For tree burning simulations, Douglas fir experiments conducted
at NIST are considered, where mass was measured and mass loss rate (MLR) was calculated taking into
consideration the moisture content in the samples. We have used two thermal degradation sub-models within
the physics-based model to simulate the tree burning experiments the linear and Arrhenius models.
The aim of the first part is twofold: one we seek numerically converged results, which were elusive with the
previous version of the model; and secondly we appraise two thermal degradation sub-models. Comparison of
MLR results from the simulations shows that grid convergence is not elusive and convergence is deemed to be
obtained with 50 mm grid for both thermal degradation sub-models. The grid converged solution agrees well
with the experimental result involving burning of a Douglas fir tree.
Then a fire in a hypothetical forest of Douglas Fir trees sitting on a grassland, which can be thought of as a
model of a plantation, is simulated using the linear thermal degradation sub-model due to its simpler
parameterization requirement. A sensitivity of the domain height and space downstream of the forest is carried
out. Final results are obtained with a narrow simulation domain of 124 m long, 8 m wide and 25 m high, which
is not sensitive to domain size variation. The result, firstly, shows that the WFDS model is capable of
qualitatively predicting propagation of surface fire to this forest canopy. It is also found that upon transitioning
to a crown fire, after an adjustment period, a fire propagating with a quasi-steady rate of spread is established.
We can therefore be confident that crown fire simulations and studying detailed crown fire dynamics are
possible with the physics-based model.
Analysis of the heat release rate (HRR) data shows that the surface fire propagates underneath the crown fire
and therefore the fire observed here is a supported crown fire. That is, the surface fire puts energy into the
crowns to sustain the burning of the crown material. Overall many features are qualitatively in agreement with
other crown fire studies.
By changing the properties and configuration of the fuel material, simulation of native Australian vegetation
can be attempted. In the future, similar simulations will lead to greater understanding of the transition of surface
fires to crown fires. With further refinement, simulations could be used to construct threshold models of crown
fire transition. The largest drawback of physics based simulations remains the large computational time due to
the extremely fine grid sizes required. However, a simple linear parameterisation of thermal degradation model
along with simple turbulence model can be used to reduce some of the computational effort.
Keywords: Physics based modelling, Crown fire, Tree fire, Fire transition, Rate of spread
Moinuddin et al., Physics based modelling of tree fires and fires transitioning from forest floor canopies
1. INTRODUCTION
Wildland fires can have devastating effects on the community, economy and infrastructure. The fires can also
impact on the viability of the surrounding areas. This includes disruption in water supplies due to erosion and
contaminants caused by the fires. The incidence of fires attracts much public concern and fires are given
considerable attention by the media due to their devastating effects. This is exemplified by the cases of Black
Saturday (2009) and Ash Wednesday (1983) in Australia and the 2009 bushfires in Athens and Los Angeles.
Therefore it is important to conduct studies on the behaviour of fire spread, although this proves extremely
difficult since the sizes and rate of spread depends on numerous factors.
In a previous study Moinuddin et al. (2017), grassfire spread simulation was successfully conducted using
physics based model, Wildland Urban Interface Fire Dynamics Simulator (WFDS). It is important to explore
the extension of previous studies to tree and forest canopy fire. In this study, we have first studied a single tree
burning quantitatively, following Mell et al. (2009). Then we have semi-quantitatively studied forest floor fire
transitioning to a crown fire and the forward advancing behaviour of the crown fire.
For the tree burning simulations, the experiments of Douglas fir burning conducted at National Institute of
Standard and Technology (NIST) are considered (Mell et al., 2009). During these experiments, 2.25m high
trees were mounted on custom stands and allowed to dry. The 2.25m trees were separated into two groups with
average moisture content by mass of 14% and 49%. Trees were ignited using a circular natural gas burner with
a specific heat release rate of 30 kW. The mass of the sample tree was measured and the mass loss rate
calculated taking into consideration the moisture content in the samples. In our simulations we have used two
thermal degradation sub-models to simulate tree burning – WFDS (linear) (Mell et al, 2007, Mell et al, 2009)
and Fire Dynamics Simulator, FDS (simplified Arrhenius) (McGrattan et al. 2008). FDS is the original building
fire model developed by NIST. Both models have the same fluid flow, turbulence, continuity, pressure, energy,
radiative heat transfer and combustion models. They also simulate the fuel distribution in a similar, but not
identical, manner. The main difference is in thermal degradation sub-model which will be discussed in the next
section.
After replicating experiments of Douglas fir burning using two models, we aim to model fire behaviour with
the more suitable model in a forest of Douglas Fir trees sitting on a grassland – a hypothetical scenario which
can be thought of a plantation. The behaviours include transition from surface fire to crown fire, forward
advancing of both crown fire and surface fire etc.
2. MODEL OVERVIEW AND ITS INPUT PARAMETERS
WFDS and FDS use a Computational Fluid Dynamics (CFD) methodology to solve the governing equations
for buoyant flow, heat transfer, combustion, and the thermal degradation of vegetative fuels and Large Eddy
Simulation (LES) techniques are used to account for turbulence (Mell et al. 2007). The model aims to include
fire spread through vegetative fuels. Vegetative fuels can include those characteristic of bushlands i.e. trees,
grasses, understory growth, and ground litter as well as those purchased at nurseries for home or community
landscaping purposes such as trees, mulch, grasses, and decorative plants.
2.1. Fuel (vegetation) model
The models have two ways of modelling vegetative fuels, namely (i) the fuel element (FE) model for vegetation
that occupies a specified volume such as trees (for example, Douglas fir trees are modelled as cones (Mell et
al. 2009)) and (ii) the boundary fuel (BF) model for surface fuels such as grasslands (Moinuddin et al. 2017).
With the FE model, trees can be modelled with various shapes: cone, frustum, cylinder and rectangle. Table 1
gives other physical parameters needed for the tree fire simulation. In the FE model, there is no distinction
between solid phase and gas phase grid. The grid resolution is the same for both phases. The fuel distribution
within the tree (ie the leaves and twigs) is modelled as a cloud of burnable particles with the specified
properties.
The BF model treats fuel as a flat bed and above this the domain is used for gas phase. Within the fuel bed a
sufficiently high spatial resolution is used to capture the vertical radiant heat transfer. However, the horizontal
grid is the same as the gas phase and the accuracy of convective heat transfer will be heavily influenced by the
gas phase grid resolution. The assumptions leading to the BF model are most consistent with large fires for
which the majority of the heat release (and, therefore, radiant emission) occurs above the fuel bed (resulting in
predominantly vertical radiant heat transfer in the thermally degrading fuel bed).
Moinuddin et al., Physics based modelling of tree fires and fires transitioning from forest floor canopies
Table 1. Physical parameters used in WFDS
Parameters
Values
Units
Description
Needles
0-3mm
3-6mm
6-10mm
Mass fraction
63%
13%
10%
14%
TREE
Text
.TRUE. for vegetation particles.
VEG_SV
3940
2667
889
500
m-1
Surface to volume ratio of the vegetation element
VEG_MOISTURE
0.14
Moisture fraction (mass of moisture in vegetation/dry
mass of vegetation)
VEG_CHAR_FRACTION
0.25
Fraction of char that develops from virgin dry virgin
vegetation
VEG_DRAG_COEFFICIENT
0.375
Non-dimensional multiplicative factor used to model
drag
VEG_DENSITY
514
kg/m3
Vegetative fuel’s density
VEG_BULK_DENSITY
1.66
0.34
0.26
0.37
kg/m3
Density of the bulk vegetation; mass of dry vegetation
divided by the bulk volume that is containing the
vegetation
VEG_REMOVED_CHAR
Text
.TRUE. or .FALSE.; whether the fuel element is
removed or kept once the thermal degradation has
converted the vegetation to pure char. Selected as
.TRUE.
FUEL_GEOM
Cone
Shape of bulk volume that contains vegetation:
RECTANGULAR, CYLINDER, CONE, FRUSTUM
CROWN_WIDTH
1.65
m
Diameter, measured in meters relative to XYZ of the
top of the bulk vegetation if the shape is cone, cylinder
or frustum.
CROWN_BASE_HEIGHT
0.3
m
Height, measured in meters relative to XYZ of the base
or bottom of the bulk vegetation if the shape is cone,
cylinder or frustum.
TREE_HEIGHT
2.25
m
Height, measured in meters relative to XYZ of the top
of the bulk vegetation if t
he shape is cone, cylinder or
frustum
While BF model is the same in WFDS and FDS- the FE model is slightly different in FDS. In this study, the
Douglas Fir tree crown is approximated as being cone shaped with four different sizes of particles in both
models. In WFDS needles, 0-3mm branch, 3-
6 mm branch and 6-10 mm branch are used
and their properties are given in Table 1.
Each component differs by surface to volume
ratio and vegetation bulk density. On the
other hand, in FDS we used: foliage (length
0.05m and thickness 0.0005 m), small
roundwood (length 0.1m and thickness 0.001
m), medium roundwood (length 0.1m and
thickness 0.002 m) and large roundwood
(length 0.1m and thickness 0.003 m) and all
with cylindrical shapes. There are 100,000
particles of each type per unit volume and
bulk densities are 2.0, 0.4, 0.3 and 0.5
kg/m3 , respectively.
2.2. Thermal degradation model
There are two models for thermal
degradation: ‘linear’ and ‘Arrhenius’.
Both are based on empirical studies.
The linear degradation model assumes
a two-stage endothermic thermal
decomposition (water evaporation and
then solid fuel pyrolysis). For water
evaporation, Eq 1 is used:
If Ts=373 K, =
…(1)
Table 3. Thermal parameters used in FDS
Parameters
Moisture
Vegetation
Char
Thermal conductivity (W/m.K)
2.0
2.0
2.0
Specific heat (kJ/kg.K)
4.184
1.2
1.2
Density (kg/m3)
1000
514
300
REFERENCE_TEMPERATURE (oC)
100
200
350
REFERENCE_RATE
0.002
.0005
0.0002
HEATING_RATE (oC/min)
1.6
1.6
1.6
HEAT OF PYROLYSIS (kJ/kg)
2500
418
418
MASS FRACTION
0.123
0.649
0.228
Table 2. Thermal parameters used in WFDS
Variable
Values
Units
HEAT_OF_COMBUSTION
17,770
kJ/kg
SOOT_YIELD
0.015
kg/kg
VEG_INITIAL_TEMPERATURE
20
oC
HEAT_OF_VAPORIZATION
2259
kJ/kg
HEAT_OF_PYROLYSIS
416
kJ/kg
SPECIFIC_HEAT_CAPACITY
1.11 + 0.0037 Ts
kJ/kg/C
VEGETATION_BURNING_RATE_MAX
0.4
kg/(m3s1)
Moinuddin et al., Physics based modelling of tree fires and fires transitioning from forest floor canopies
where, Ts is the vegetation surface temperature, is the evaporation rate, is the net energy (convection
plus radiation) on the fuel surface and is the latent heat of evaporation. It uses the temperature-dependent
mass loss rate expression of Morvan and Dupuy (2004) (presented as Eq 2) to model the solid fuel degradation
and assumes that pyrolysis begins at 400 K.
If 400 K ≤Ts≤500 K, =
(2)
where, is the pyrolysis rate and is the heat of pyrolysis (also known as the heat of reaction). With
the Linear model, ignition and sustained burning occurs more ‘easily’ (i.e., at lower gas phase temperatures)
because pyrolysis occurs over a lower temperature range. Because of this, coarser gas phase grid resolutions
may be sufficient but requires that the user supply a boundary on the maximum mass loss rate per unit area or
volume in the form of FIRELINE_MLR_MAX (kg/s/m2), VEGETATION_BURNING_RATE_MAX
(kg/s/m3) or VEGETATION_DEHYDRATION_RATE_MAX (kg/s/m3 ).
The ‘Arrhenius’ model used in WFDS/ FDS is described in (McGrattan et al. 2008) which employs a kinetic
triplet to model thermal degradation. However FDS also has a simplified Arrhenius model which uses
alternative parameters REFERENCE_TEMPERATURE, REFERENCE_RATE and HEATING_RATE. We
have termed this here as “simplified Arrhenius” model and used for simulation using FDS version 6.2.0.
The required parameters to solve submodels in WFDS are presented in Tables 1 and 2. Thermo-physical
parameters used in FDS simulation is presented in Table 3.
3. RESULTS AND ANALYSIS
3.1. Douglas Fir tree fire –quantitative analysis
The choice of the size of the grid (cell) in a mesh is one of the first and most important decisions one must
make when conducting a quantitative simulation. The choice of grid size can affect the results. In conducting
physics-based analysis it is essential to undertake a grid convergence study.
(a) WFDS_9977
(b) FDS 6.2.0
Figure 1: Comparison of Mass loss rate (MLR) results for 2.25 m Douglas fir tree simulations for grid sizes:
75 mm, 50 mm and 37.5mm
The first step in a grid convergence study is to compare the Mass Loss Rate (MLR) or Heat Release Rate
(HRR) results of similar simulations but with finer grid sizes. We conducted a similar study with WFDS’s
version 4 (Moinuddin et al. 2010) in terms of HRR
and we found that grid convergence was elusive.
However, the developers of FDS/WFDS claim that
the current version (version 6) is less grid sensitive
due to the use of an alternative LES model, a new
near-wall model, a new combustion model, along
with some bug-fixing. We have selected 75 mm, 50
mm and 37.5 mm grid cells for WFDS_9977 version
and 100 mm, 50 mm and 37.5 mm grid cells for FDS
6.2.0 version.
The MLR results are compared for the three
simulations of the 2.25m Douglas fir tree with
WFDS_9977 and FDS 6.2.0 in Figure 1. For both
versions of the physics based model, the results from
Figure 2
.
MLR results comparison with experimental data
(Mell
et al, 2009) –
both numerical results are shifted by 1.5
sec.
Moinuddin et al., Physics based modelling of tree fires and fires transitioning from forest floor canopies
50mm grid and 37.5 mm converge. So convergence is deemed to have obtained with 50 mm grid. Grid
convergence is also observed in the HRR data from both FDS and WFDS simulations at 50 mm grid. However
the trends are different: in WFDS only the peak appears to be sensitive whilst in FDS the as the grid is reduced
from 100mm to 50mm the peak is delayed with a lower, but much longer duration of peak burning rate.
The MLR results from grid converged simulations (where 50 mm grid cells are used) of the 2.25m Douglas fir
tree with the experimental data in Figure 2. The simulation results are shifted towards the left by 1.5 sec to
roughly match the peak. It can be observed that the area under the curve is roughly the same. The averaged
total mass loss from nine experiments was 3.62 kg. The mass loss rate is exactly the same for FDS 6.2.0
simulation. However it is roughly 12% less while the simulation is conducted with WFDS_9977. The
discrepancy may be due to the fact that different fuel representation are used for WFDS simulation.
Figure 3 shows snapshots of simulations of a 2.25 m tall tree using WFDS’ companion graphical output
software Smokeview (Forney, 2008). Figures represent temperature slices to show the gas-phase temperature
at various instances of time after ignition.
(a) 4.9 sec
(b) 11.9 sec
(b) 14.9 sec
(d) 19.9 sec
Figure 3: Graphical representation of Douglas fir tree burns simulation. The results from the WFDS simulation
is depicted to show the gas-phase temperature at various instances of time after ignition.
3.2. Forest floor and canopy fire- semi-quantitative
With successful quantitative simulation of the burning 2.25m Douglas Fir tree along with achieving numerical
convergence, we now attempt to model a scenario where forest floor fire interacts with tree canopy. We have
used WFDS due to its lesser computational resource requirement. As FDS needs 100,000 particles of each type
of vegetation parts per unit volume, it needs enormous computational resources to model a number of trees.
We have modelled a forest of 2.25m Douglas Fir trees sitting on a grassland. Therefore the forest canopy height
(CH) is 2.25 m. This is absolutely a hypothetical scenario (may not be practical, though possibly it can be a
model of a plantation) to assess whether fire progression from the surface to the crown can be simulated. The
simulation is conducted with a narrow domain. The validity of such simulation approach was demonstrated by
Linn et al (2012). The simulation domain is 124 m long, 8 m wide as shown in Figure 4. The inlet is prescribed
as power law (1/7) model of the atmospheric boundary layer (ABL) with a wind speed of 3 m/s at 2 m. The
two lateral edges are modelled as periodic, that is the left and right boundaries are constrained to be equal.
Therefore the simulation can be thought of as an infinite side-by-side tiling of similar domains. The outlet and
top of the domain are modelled as lines of constant pressure. The burnable grass plot (37 m long) starts 45 m
(in the longitudinal direction) from the inlet. Four longitudinal columns of Douglas Fir trees are modelled. The
crown was approximated as cones and the trunk as cylinders. For simplicity the crowns are modelled only as
needles with 2.2 kg/m3 bulk density. Alternate columns had 16 and 17 trees in a staggered fashion. The columns
are 2m apart and within the column, the trees are
also 2m apart. Moinuddin et al. (2016) showed that
for grassfire, 250 mm grid provides grid
convergence rate of spread. As 50mm grid for
forest fire simulation is extremely expensive, in
this study 100mm grid is used. A sensitivity study
is conducted with shorter forest length and domain
size with 50mm grid. It is found that while the size
(HRR) of the forest fire are roughly the same, the
transition from the surface fire to crown fire occurs ~13 sec earlier.
Figure
4. Graphical representation of surface fire
-
crown interaction simulation
.
Moinuddin et al., Physics based modelling of tree fires and fires transitioning from forest floor canopies
Prior to actual simulation of fire line spread, a precursor simulation was carried out to generate an initial wind
field within the simulation domain. Upon establishment of a steady state wind field, a lateral line fire of 1m
width is ignited with 500 kW/m2 heat release rate per unit area (Fig 4).
The domain size was tested in relation two ways:
• Domain length – especially downstream of the forest space with 24 m and 42 m
• Domain height (H)– with 10 m, 15m, 20m and 25m height
HRR vs time results (Fig 5) of four simulations
shows that the results are not affected by 24 m and
42 m space downstream of the forest indicated by
the same surface to forest fire transitions and
similar growth rate. However domain height does
have a significant effect shown by the HRR values
40 secs after ignition. However no significant
difference is observed between 20m and 25m
domain height cases (representing ~9 and 11 H/CH
ratio). This indicates that a domain height roughly
8 times of the crown height may be sufficient. The
results below presented are from 25m domain
height case.
In Fig 6, fire front location and HRR as a function
of time are presented. A fire front is determined
based on HRR data. The definition of the
instantaneous centreline flame front is the xz-location of the point at which 90% of the total HRR is obtained.
In Fig 6(a) the red line is a least-squares regression fit to the surface fire behaviour and the blue line is a fit to
the crown fire data. Surface fire and transition to crown propagation is clearly visible between 30 to 40 sec.
Deciding when the fire has completely reached a crown phase
is ambiguous. HRR vs time data in Fig 6(b) shows that
roughly 53 sec after the ignition of line fire a quasi-steady
period emerges which corresponds well with Fig 6(a).
Visual representation of flames impacting on the crown and
during quasi-steady period is shown in Fig 7. From the
isosurfaces of HRR at 200 kW/m3 (eg Fig 7) it appears as if
the surface fire transitions up to the crown, then transitions
back down again at some later time. The surface fire, as
measured by large HRR at the surface, appears to propagate
fairly uniformly. The isosurfaces of heat release rate
associated with surface burning are probably difficult to
visually distinguish from the isosurfaces of heat release rate
associated with crown material burning. Because the surface
fire continues underneath the crown fire, this is a supported
crown fire. That is, the surface fire puts energy into the crowns
to sustain the burning of the crown material. (Dupuy and
Figure
5. HRR vs time results from sensitivity analysis
.
0
50
100
150
200
250
300
350
010 20 30 40 50 60
HRR (MW)
TIME (SEC)
Domain Sensitivity
Downstream 24 m; Height 10m
Downstream 42 m; Height 15m
Downstream 42 m; Height 20m
Downstream 42 m; Height 25m
(a) Flame upon impacting the crown
(b) Quasi-steady flame propagation
Figure 7
.
Visual representation flame
propagation
(a) Fire front location
(b) HRR
Figure 6: Finding quasi-steady rate of spread of crown fire
Moinuddin et al., Physics based modelling of tree fires and fires transitioning from forest floor canopies
Morvan, 2005). Overall many features are qualitatively in agreement with other crown fire studies (eg
experiments of Cruz et al, 2013). We can therefore be confident that crown fire simulations are possible with
the physics-based model.
4. CONCLUSIONS
This study is an initial step into understanding the capabilities of physics-based models FDS and WFDS
establishing its capability of producing grid-converged results for fuel element models. A 2.25 m Douglas fir
tree burning experiment conducted at NIST has been used to benchmark models’ capability. Both models
produced grid converged results of both mass loss rate and heat release rate which is a large step forward from
its version 4. In the second step of the study a scenario where forest floor fire interacts with tree canopy is
modelled using WFDS. In this forest floor fire is modelled using boundary fuel model whilst the forest is
modelled as fuel elements. The simulation shows that WFDS can qualitatively predict propagation of surface
fire to the forest canopy. From the analysis of simulation data, it appears that the surface fire continues
underneath the crown fire. Other researchers also reported this kind of supported crown fire. After
establishment of a crown fire, a quasi-steady propagation is observed. Therefore there is potential that the rate
of spread of crown fire could be determined using a physics based model. Future work will consider changing
the properties of fuels so that simulation of native Australian vegetation can be conducted.
We stress that these simulation results are for a very particular set of parameters and the numerical results may
be sensitive to parameters not varied in this study. Obviously further studies and validation against observed
crown fires are required before any operational correlations can be constructed. Such a validation study would
need to compare simulations of extreme fire scenarios to field observations of wild fires. Eventually it is hoped
that this work may lead to the determination of rate of spread for crown fire as a function of fuel and
atmospheric characteristics.
The largest drawback of physics based simulations remains the large computational time due to the extremely
fine grid sizes required. However, instead of LES turbulence model, simpler one-equation model and a simple
linear parameterisation of thermal degradation model can be used to reduce some of the computational effort.
ACKNOWLEDGMENTS
We wish to acknowledge the financial support given by Bushfire and Natural Hazard Cooperative Research
Centre (BNHCRC), Melbourne, Australia. The authors wish to thank Dr William Mell from US Forest
Department for helpful discussion and making necessary changes in the WFDS source code.
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