Numerical investigation of the effect of wind, slope and fuel moisture on the radiative and convective heating of excelsior fuels
M. S. Sadeghi A * , Maryam Ghodrat
A * , Duncan Sutherland B , Albert Simeoni C , Jason Sharples B and Harald Kleine A
A
B
C
Abstract
Wind, slope angle and moisture content are the three major parameters that affect fire rate of spread and heat transfer in propagating bushfires.
This study investigates the effect of the slope angle (0°–40°), wind speed (0–3 m s−1) and fuel moisture content (FMC, 4–12%) on convective heat transfer (cooling and heating) and radiative heat transfer of burning excelsior fuel particles at different locations downstream of a spreading fire.
The simulations were conducted using Fire Dynamics Simulator (FDS). The zone located downstream of the fire front was divided into two regions: the flame-induced region and the natural convection region.
For uplifted flames, there is convective cooling of particles downstream of the flame region. However, when the flame attaches to the unburnt fuel, flame depth and fire line intensity both increase, and there is convective heating of the particles ahead of the flames. Radiative heating of the particles also decreases consistently as the distance from the flame increases.
The results of this analysis reveal the mechanism of local convective and radiative heat transfer to downstream vegetation. Although heat transfer mechanisms are identified from this numerical analysis, these need to be verified through experimental work.
Keywords: convective cooling, convective heating, excelsior, FDS, Fire Dynamics Simulator, flame length, fuel moisture content, Large Eddy Simulation, LES, radiative heat transfer, upslope fire.
Introduction
Analysis of the relative importance of different heat transfer mechanisms during the preheating of fuel particles is vital in developing a comprehensive understanding of bushfire spread. Three modes of heat transfer play a dominant role in fire propagation: the first mode is radiation, the second is convection (Morvan and Frangieh 2018) and the third is direct flame contact. The ignition of fuel particles downstream of the burning zone happens when sufficient convective and/or radiative heat required for pyrolysis or ignition is transferred to them (Finney et al. 2015), or fuels downwind can be ignited by firebrands and embers. For the latter case, heat transfer from burning vegetation or structural materials can occur through conduction or direct contact (Suzuki and Manzello 2021a, 2021b). There is still a debate in the fire science community about which of these three modes of heat transfer dominates in different scenarios of fire propagation. Many of the works in the literature consider radiation as the main source of heat transfer in wildland fires (Pagni and Peterson 1973 (for their no-wind cases); Apte et al. 1991; Chen et al. 2018); however, recent works reveal that convection is as effective as radiation in fire propagation in porous wildland fuels (Silvani and Morandini 2009; Anderson et al. 2010; Morandini and Silvani 2010; Dupuy and Maréchal 2011; Finney et al. 2012; Clements and Seto 2015) and even the dominant mode of heat transfer (Finney et al. 2015). In their work, Pagni and Peterson (1973) showed that convection influences the flow entrainment of hot gases and products of pyrolysis toward the flame in their wind-driven cases. Vogel and Willimas (1970) explored the effect of convective heat transfer as the primary mechanism in the ignition process of uniform, linear vertical matchsticks. In some research, the preheating effect of convection is of interest (Dold and Zinoviev 2009; Sharples et al. 2010; Dupuy et al. 2011; Pimont et al. 2012; Silvani et al. 2012; Miller et al. 2015). However, there are other works focusing on the remarkable effect of convective cooling on preheating of the vegetation ahead of the fire front and fire spread (Liu et al. 2014, 2015; Finney et al. 2015).
There are multiple factors affecting the amount of convective heat transfer to vegetation downstream of a fire. One of these factors is the slope angle, which affects the fire front shape (Dupuy et al. 2011), convective heat transfer (Silvani et al. 2012) and rate of fire spread (Finney and McAllister 2011). Based on the experiments performed by Dupuy and Maréchal (2011) on pine needle fuel beds, the dominant mode of heat transfer for slope angles 0°–20° is radiative heat transfer whereas for higher angles, convective heat transfer becomes the dominant mode. The other important factors affecting fire behaviour and convective heat transfer are wind speed and the profile of the driving wind. Zhang et al. (2020) investigated the coupled effect of tree canopy characteristics (as this modifies the driving wind profile) and the Byram convective number (which compares the speed of the external driving wind and the vertical flow speed in the plume region) to characterise the fire regime as plume-dominated, in which radiation is considered the dominant heat transfer mode, or wind-driven, in which convection is considered the main source of heat transfer (Morvan and Frangieh 2018). Another parameter significantly affecting fire rate of spread (ROS) and heat transfer is the fuel moisture content (FMC) determined on a dry weight basis (Xie et al. 2017). Various empirical models for fire spread rate and intensity consider the FMC as one of the main parameters influencing fire (Sullivan 2009). In their experiments, Mendes-Lopes et al. (2003) demonstrated that increasing the FMC from 10 to 18% reduces the mean rate of spread by 20–60% for different slope angles and wind speeds for Pinus pinaster needles and their specific experimental case. They also demonstrated that increasing the FMC reduces both the flame height and flame angle (above the horizontal plane) for the mentioned cases, though they did not study the effect that varying FMC has on the transfer of radiative and convective heat to the fuel particles. Butler et al. (2007) considered the range 5–8% FMC for their experiments on excelsior particles. However, they did not report the effect of varying moisture on fire behaviour. Moinuddin et al. (2021) studied the effect of fuel moisture on simulated grass fire propagation using the Wildfire–urban Fire Dynamics Simulator (WFDS). They varied moisture contents from 3.55 to 12.5%, and their results revealed that fire frontal fluxes, heat release rate and ROS were significantly affected by FMC. Innocent et al. (2023) used WFDS to study the effect of wind (0–12.5 m s−1) and slope angle (−30° to 30°) on the fire ROS and heat transfer at field scales. However, they did not study the effect of convective cooling.
The specific impact of convective cooling during fire spread is not generally considered by researchers (Morvan and Dupuy 2001). Albini (1985) and De Mestre et al. (1989) added a convective cooling term into their model and demonstrated good agreement between simulated fire spread and that observed in experiments. Liu et al. (2023) studied the effect of slope angle on linear fires burning in pine needle beds. In their experiments, they used thermocouples, two Pitot tubes and heat flux gauges to capture the temperature, velocity and radiative and convective heat flux data. They recorded natural and flame-induced convective cooling downstream of the fire and on the unburnt fuel. They defined natural convective cooling as the convection due to the temperature difference between unburnt fuel and the ambient air, and flame-induced convective cooling as the convection of induced inflow from the flame, which produces a pressure difference between the flame and the ambient air (a more detailed description of natural convection and flame-induced regions is given by Liu et al. (2014)). Their results revealed that steeper slope angles were associated with higher levels of flame-induced convection compared with natural convection.
The literature records many attempts to measure convective and radiative heat transfer downstream of a fire. Most of these attempts are experimental (Finney et al. 2022; He et al. 2022). Cohen and Finney (2023) studied convection and radiation heat transfer in spreading fire. They considered wood particles in a wind tunnel with two different sizes (1 and 12 mm) and captured the heat flux and temperature data using thermocouples and heat flux gauges at different locations downstream of the fire. They concluded that for particles with 1 mm diameter, convective cooling offset radiative heating, and the main mechanism for preheating of the particles was intermittent impingement of hot gases from the flame front region (i.e. convective heating). The effect of flame intermittency on fire spread and heat transfer has also been investigated in the literature (Viegas and Simeoni 2011; Finney et al. 2015; Singh et al. 2021). Finney et al. (2015) studied the effect of buoyancy inertia-driven instabilities on the convective heat transfer needed for fire spread. They mentioned convective cooling to be an offset for heating by radiation until the time convective heating occurred owing to the flame arrival, and when the unburnt fuels were intermittently bathed in hot gases.
We used Fire Dynamics Simulator (FDS) in our analysis, which is a physics-based modelling platform that facilitates solution of the governing equations for gas phase, solid phase, heat and mass transfer turbulence and combustion (McGrattan et al. 2013a). McGrattan (2017) conducted a sensitivity analysis of FDS with prescribed burns on grasslands in Australia. Two cases of CSIRO controlled burns, C064 and F19 (McGrattan 2017), were modelled using FDS, and the effect of wind speed, moisture, pyrolysis temperature and other parameters were studied on the fire ROS. The results of McGrattan’s work revealed that fire ROS is most sensitive to changes in wind speed and pyrolysis temperature. There is extensive literature validating versions of FDS, including the specific wildfire version WFDS. This literature includes the aforementioned works by McGrattan (2017), Morvan et al. (2013), Sánchez-Monroy et al. (2019) and Sutherland et al. (2020). Given the extensive body of literature on similar fire simulations in FDS, we can be confident in the simulation results that FDS provides.
The review of the literature presented suggests that important insights into fire propagation can be gained from numerical investigation of the combined effects of wind, slope angle and moisture content on heat transfer. As such, the present analyses consider the effect of these factors on the convective heating and cooling and radiant heating of excelsior particles at various locations downstream of a fire. The novelty of this work is that it studies the combined effect of wind, slope and FMC on the heat transfer mechanisms, analysed using the flame-induced and natural convection framework.
In particular, we seek to answer the following questions:
How do wind, slope angle and FMC alter convective and radiative heat transfer?
Where does convective cooling appear and become important?
Where do the flame-induced and natural convection regimes become dominant?
When is radiation or convection the dominant mode of heat transfer?
Addressing these research questions provides detailed insights into how fire propagates and will inform the development of reduced models of fire behaviour in the future.
Methodology
The zone located downstream of the fire front was divided into two regions: the flame-induced region (where a flame-induced inflow is present and produces a pressure difference between the ambient fluid and the flame) and the natural convection region (where there is natural convection between the unburned fuel and the ambient fluid).
Overview of physics-based model
We used FDS, which is a Large Eddy Simulation (LES) model with solid pyrolysis and combustion. It is a Computational Fluid Dynamics (CFD) model, specifically designed for fire-driven flows (McGrattan et al. 2013b). The model solves the Navier–Stokes equations for thermally driven flows at low Mach numbers. The Finite Difference method is used in the model to approximate the partial derivatives of the conservation equations of mass, momentum and energy. The Finite Volume method is used to calculate thermal radiation, and fuel is modelled as Lagrangian particles. This approach helps to solve the governing equations and radiation absorption for solid particles that cannot be resolved in a numerical grid but are still larger than gas particles (for more detail, see McGrattan et al. (2013b)). For heat transfer (Bergman 2011) and drag coefficients (Schlichting 1979; Crowe et al. 1998), empirical sub-models are used. Particles are considered as cylinders with a constant drag coefficient of 2.8. Details of the theoretical framework are described by McGrattan et al. (2013b). For the present work, it is important to understand the heat transfer into (and out of) fuel particles, which is given by the energy balance on an excelsior particle (Sánchez-Monroy et al. 2019):
The term on the left-hand side is the rate of change of internal energy of the solid phase – ρ is density, cp is the specific heat capacity, T is temperature and subscript s stands for solid fuel – and the terms on the right-hand-side of Eqn 1 are the endothermic pyrolysis (ΔhpyrRpyr), endothermic generation of water vapour (ΔhvapRH2O), exothermic char oxidation (αcharΔhcharRchar), convective and radiative heat transfer , respectively. The subscript pyr stands for pyrolysis, vap stands for vaporisation and vb is the volume of the computational grid cell. Convective heat transfer for each particle is calculated based on the following formulae, modelled as a combination of forced and natural convection (McGrattan et al. 2013a):
Here, Tg is the gas temperature, Tw is the surface temperature, Nufree is the Nusselt number for free convection, Nuforced is the Nusselt number for forced convection, L is the characteristic length (which is considered as the excelsior particle diameter, 1.5 mm) and K is the thermal conductivity of the gas. Nufree is defined as:
where Ra is the Rayleigh number:
with kinematic viscosity υ and thermal diffusivity α. The Nusselt number for forced convection is:
The coefficients C1 = 0, C2 = 0.037, n = 0.8 and m = 0.33 are selected for cylindrical particles, based on McGrattan et al. (2013a). Pr is the Prandtl number, Re the Reynolds number, u is the velocity, ρ is the density and μ is the dynamic viscosity.
Finally, the radiation heat flux is calculated based on a grey gas model and is as follows (McGrattan et al. 2013b):
where κ(x) is the radiation absorption coefficient, Ib(x) is the source term for radiation emission, and U (W m–2) is total irradiance (McGrattan et al. 2013b). The term Ib(x) depends on the fourth power of the local temperature. Accordingly, this term requires special treatment owing to its high sensitivity to changes in temperature (Mell et al. 2009). In the flame region, there is a limitation in the computational grid capturing the effects of the sub-grid flame temperature. To resolve this issue, the source term is computed based on the following equation:
The constant C is calculated for each time step and σ is the Stefan-Boltzmann constant. The criterion is that the volume integral of Eqn 6 over the entire flaming region would approximately be equal to the volume integral of χrq̇‴ over the same region. χr is also the global fraction of the energy emitted as thermal radiation (1/3 for sooty fires) (McGrattan et al. 2013b).
There are multiple numerical parameters required for the simulation. Most parameters, like fuel properties, can be obtained from the literature, or in the case of the time step, are automatically constrained by numerical stability requirements. The simulation domain size and grid size must be evaluated.
Simulation domain
The simulation domain is 5 m long, 2.5 m wide and 2.5 m high. The test bed length is 1.8 m long and 1 m wide. These dimensions were selected to match those of our experimental set-up for future tests; as such, the simulation results will help inform experimental design and complement the experimental results. A schematic of the domain is shown in Fig. 1. The black dots show the position of the thermocouples, and the dimensions of the domain and test bed location are illustrated. The inlet is defined as the atmospheric boundary layer (ABL) with a power law profile (Morvan et al. 2013). The synthetic eddy method (Jarrin 2008; McGrattan et al. 2013a) is applied to add a turbulence intensity to the driving wind. The number of eddies (71), their characteristic length (0.04 m) and the root mean square velocity fluctuations (0.1 m s−1) are parameters to be specified (these numbers are subject to change based on the dimensions of the inlet domain and the cell sizes chosen at the inlet). The range of parameters mentioned is selected in a way that we have 10% turbulence intensity (Sullivan et al. 2013). The sides of the domain, ceiling and outlet are all set to be open boundaries (constant pressure surfaces; McGrattan et al. 2013b). To add the effect of the slope angle, the ramp is defined as a series of solid obstacles below the simulated fuel bed following Sánchez-Monroy et al. (2019). Using this ramp, we can simulate air entrainment from the sides of the test bed. The air entrainment is at various angles with respect to the horizon, which closely emulates real scenarios. Radiative heat flux devices oriented towards the incoming fire are used through the centreline of the test bed.
Fuel properties
The Particle Model (PM) is applied to simulate the fuel and therefore the fire behaviour. In this model, the solid fuel is introduced as a collection of Lagrangian particles (McGrattan et al. 2013a). The cylindrical particles, with a density of 398 kg m−3, diameter of 1.5 mm and length of 80 mm use thermophysical and chemical parameters based on excelsior, with the same properties as used by Sánchez-Monroy et al. (2019). The fuel bed section is modelled as steel with a thickness of 1 cm and a conductivity of 45.9 W m−1 K−1 Again, this was chosen in anticipation of the properties of an experimental set-up to measure the convective and radiative heat transfer on a test bed. Steel has one of the lowest thermal conductivity values among metals, making it an ideal material for use in high-temperature environments. The thermophysical, combustion and pyrolysis parameters of the fuel and fuel bed are presented in Table 1 (EXSC96 is one of the experiments done by Catchpole et al. (1998)).
| Input parameters | Values used | Source and reason | |
|---|---|---|---|
| Gas phase combustion parameters | |||
| Heat of combustion | 17260 kJ kg−1 | Catchpole et al. (1998) | |
| Soot yield | 0.02 kg kg−1 | McGrattan et al. (2013b) – EXSC96 | |
| Vegetation parameters | |||
| Vegetation drag coefficient | 2.8 | McGrattan et al. (2013b) – EXSC96 | |
| Vegetation load | 0.3184 kg m−2 | ||
| Vegetation depth | 0.08 m | Sánchez-Monroy et al. (2019) | |
| Vegetation moisture content | 0.04–0.012 | Assumption | |
| Surface-to-volume ratio of vegetation | 3092 | Catchpole et al. (1998) | |
| Vegetation char fraction | 0.154 | McGrattan et al. (2013b) – EXSC96 | |
| Vegetation bulk density | 398 kg m−3 | Catchpole et al. (1998) | |
| Ambient temperature | 32°C | Assumption – Moinuddin et al. (2018) | |
| Vegetation heat of pyrolysis | 711 kJ kg−1 | Catchpole et al. (1998) | |
| Fuel packing ratio | 0.01 | Sánchez-Monroy et al. (2019) | |
| Steel under vegetation | |||
| Emissivity | 0.95 | McGrattan et al. (2013b) – EXSC96 | |
| Specific heat | 0.46 kJ kg−1 K−1 | McGrattan et al. (2013b) – EXSC96 | |
| Conductivity | 45.8 W m−1 K−1 | McGrattan et al. (2013b) – EXSC96 | |
| Density | 7850 kg m−3 | McGrattan et al. (2013b) – EXSC96 | |
Grid convergence and domain sensitivity
Mesh independence analysis is conducted to find the optimal mesh size for capturing the fire behaviour characteristics, particularly the flame and heat transfer behaviour. The results of this analysis, namely the heat release rate at different spatial resolutions, are shown in Fig. 2. Refining the mesh further to 1.5 cm does not significantly affect the results obtained (2.69% difference in the total heat release rate compared with the 2 cm mesh size) (Fig. 2b). Owing to the turbulent fluctuations in the flame and sensitivity to the initial conditions, it is not possible to exactly fit the graphs for two different mesh sizes. However, the variation in heat release rate between the 2 cm and the 1.5 cm cube grid is negligibly small. Therefore, a mesh size of 2 cm was deemed most appropriate for subsequent analyses. Domain size is studied to ensure that any effects of the boundaries on the fire behaviour are avoided (Fig. 3). A domain size of 5 × 2.5 × 2.5 m is the most suitable option for the present work (0.82% difference in total heat release rate compared with a larger domain) because it can capture the heat release rate in the plume region and is also computationally time-effective compared with a larger domain.
Validation
The simulations are validated by comparing our simulations with the experimental results of Butler et al. (2007) and Sánchez-Monroy et al. (2019). Test scenarios no. 1 and no. 4 of table 1 in Sánchez-Monroy et al. (2019) were selected (because they derived the fire ROS graphs for these two cases) for the validations. As mentioned by Sánchez-Monroy et al. (2019), for the first case with a fuel depth (δ) of 7.62 cm, packing ratio of 0.01 and mean moisture 7.85%, the simulated fire extinguishes after ~30 s, which highlights the point that there is a need for developing better drag models for excelsior in FDS (Mell et al. 2009, Sánchez-Monroy et al. 2019). Comparison of the present analysis with the mentioned works is depicted in Fig. 4. The method of Liu et al. (2015) is used here to find the rate of fire spread. In this method, different (simulated) thermocouples are installed every 0.2 m from the beginning of the fuel bed to the end. Then, a threshold of 300°C is selected as the criterion for flame arrival at each thermocouple. The position of the thermocouples is 2.5 cm above the fuel bed. The rate of fire spread to the end of the domain is calculated using linear regression (Liu et al. 2015). As Sánchez-Monroy et al. (2019) demonstrated in their numerical work, the zero-slope case in Fig. 4a extinguishes after ~30 s. For the other cases in Fig. 4a, b, the results are in good agreement with the experiments of Butler et al. (2007) and Sánchez-Monroy et al. (2019).
Validation of the numerical simulation with experiments done in literature for: (a) δ = 7.62 cm, and for (b) δ = 15.24 cm.
One of the sources of the difference between the present simulation and the mentioned experiments is the small fuel depth difference used in the present work and the experiments due to the limitations in the mesh size (for the present simulation, δ = 8 cm, and for the experiments of Sánchez-Monroy et al. (2019), δ = 7.62 cm). To see the effect of fuel depth, the ROS for the case with a slope angle of 16° was tested for both 8 and 6 cm fuel depths, and shows a 15% higher ROS for a fuel depth of 8 cm. For our simulations, the side walls’ depth was assumed to be 20 cm. However, based on other experiments reported in the literature (e.g. Xie et al. (2017)), the side wall aspect ratio has a considerable effect on flame attachment length and heat transfer to the downstream vegetation. It is beyond the scope of this work, but in future, we aim to study the effect of the side wall aspect ratio on convective and radiative heat transfer to see the effects of the air indraught on the mentioned quantities.
Results
To gain an understanding of the typical dynamics of the fire, the global behaviour of the fire is investigated. First, the effect of three main parameters – wind, slope angle and FMC – on the fire front location is depicted in Fig. 5. This is done by looking at the location of the flame from the beginning of the test bed to the end and for all time steps. The consistent gradient shows that flame advance is fairly consistent during the fire spread.
Flame front position versus time under: (a) wind effect (no slope, 8% FMC), (b) slope effect (no wind, 8% FMC), and (c) FMC effect (no wind, 10° slope).
As the wind speed increases, less time is needed for the flame front to reach to the end of the domain (Fig. 5a). For slope angles less than 20°, the flame front motion is very close to linear, and has uplifted sustainable propagating fire in which the flames are detached from the fuel bed for the whole spread. If the angle is above 20°, there are jumps in the graphs of the fire front position that are representative of instances of flame attachment to the downstream vegetation. FMC has a negative impact on the fire front movement, and increasing the FMC from 4 to 12% reduces the fire ROS and increases the time of arrival at the end of the domain. For the 12% FMC case, the fire self-extinguishes after 60 s for the no-wind and zero slope case.
The contours of temperature and U-velocity for the 10°, 15° and 20° slope angles and for the 20 s time step are shown in Fig. 6. The flame length, plume region and flame tilt angle can be estimated from the contours of Fig. 6. The first noteworthy point is that at the 20° slope angle, the start of flame attachment is consistent with the literature (Liu et al. 2014), but the flame becomes detached after 40 s (there is an ignitor effect for the first 11 s). This attachment increases rapidly for the 25° slope angle. The ignitor size and ignition duration are also effective parameters in early attachment of the flame. The main reason that we did not show the contours for higher slope angles is that the heat transfer mechanisms on the downstream side would be difficult to analyse. In the velocity contours, negative velocities are observed: these represent the incoming air that enters the flame region in the opposite direction to the flame propagation. These negative velocities are produced by the pressure difference between the hot air around the flame region and the surrounding air. This entrainment of ambient air occurs on both sides of the flame region. As the slope angle increases and before flame attachment, there is stronger air entrainment in the proximity of the flame. For attached flames (20° slope angle), the air entrainment is postponed but is larger, resulting from a higher pressure difference caused by a flame region with a greater flame depth and a plume that tends to attach to the sloped surface. For the 20° slope angle, the reverse flow of ambient air occurs on only one side of the flame (in the flame-induced region). However, for the other two slope angles, there is a reverse flow from both sides of the flame that makes the flame detach from the fuel surface.
The contours of temperature (°c) for: (a) 10° slope angle, (b) 15° slope angle, (c) 20° slope angle; contours of velocity (m s−1) for: (d) 10° slope angle, (e) 15° slope angle, and (f) 20° slope angle; and plots of velocity along the centreline, at Z = 30 cm, and for: (g) 10° slope angle, (h) 15° slope angle, and (i) 20° slope angle (X = 0 is the start of the simulation domain, the red lines are schematics of the fuel bed, and the data are derived at time step 20 s).
In order to quantify air entrainment, the area around the flame region is of interest. Fig. 6g–i shows the U-velocity along the centreline at the height z = 30 cm and time step 20 s and for 10°, 15° and 20° slope angles, respectively. The back face of the domain is an open boundary. For the 10° slope angle, the flame is uplifted, and the effect of the flame on the pressure difference in the air happens within a short spatial distance. The negative peaks show the entrained air coming into the flame region owing to this pressure difference generated by the flame. For the 15° slope angle, there is more interaction between cold and hot air (positive and negative velocities downstream of the flame) but again, interaction of the air entrainment and hot gases from the flame is detected and measured (we still have an uplifted flame). The flame region becomes larger with the onset of flame attachment (here for the 20° slope angle case) and a strong flow hot air from the flame in the form of large eddies travels far downstream.
The location of the flame from the beginning to the end of the test bed over the simulation time was examined to provide a clear understanding of whether flame behaviour is consistent across the simulation and to identify how much heat is released from the flame to the surroundings. Figs 7 and 8 show this behaviour under different wind speeds. When the wind velocity is 1 m s−1, the plume is uplifted (the flames remain detached from the unburned fuel) and there is no reattachment of the flame to the downstream surface for all the time steps except for a moment at approximately t = 25 s, as indicated by Fig. 7a – the 25 s case. There are two convective cooling zones for this case, at t = 25 s, which shows the reattachment of the flame to the downstream vegetation (see the two local minima at x = 0.7 m and 0.9 m in Fig. 7a). After this time, the fire again becomes uplifted, with only one convective cooling zone for each time step. The flame-induced convection region is always visible close to the head of the fire, in every case at every time observed. The absorption and emission of radiation by particles in different regions can be seen in the radiation graphs (Fig. 7b, d and f). At time step 15 s in Fig. 7b, there is absorption of the radiative heat flux by excelsior particles (at the top of the fuel surface) between x = 0.2 m and 0.4 m. This absorption is shown by the positive amount of radiative heat transfer (from 0 to ~30 kW m−2). Inside the flaming zone, there is emission of the radiative heat flux (from 0.4 to 0.5 m in Fig. 7b) with negative heat flux observed (i.e. the flame radiates heat). There is also a negative local minimum for each time step, which shows flame arrival and the ignition of unburnt excelsior particles. When the wind increases from 1 to 2 m s−1, there is a steep increase in the fire ROS. The total heat flux data, which are the sum of the convective and radiative heat flux, are depicted in Fig. 8. This set of graphs also show that for the 3 m s−1 case (Fig. 8c), the fire reaches the end of the test bed in 35 s.
Convective heat flux over fuel bed length for 8% FMC, no slope and for the cases: (a) 1 m s−1 wind, (c) 2 m s−1 wind, (e) 3 m s−1 wind, and radiative heat flux over fuel bed length for the cases: (b) 1 m s−1 wind, (d) 2 m s−1 wind, and (f) 3 m s−1 wind.
Total heat flux over fuel bed length for 8% FMC, no slope and for the cases: (a) 1 m s−1 wind, (b) 2 m s−1 wind, and (c) 3 m s−1 wind.
The effect of the slope angle on heat transfer to the particles at the surface and the centreline (y = 0.5 m) of the fuel bed over the simulation time is depicted in Fig. 9. The wind speed and FMC are kept constant (no wind and 8% FMC) to study the sole effect of slope angle variation on the convective, radiative and total heat flux.
Convective heat flux over fuel bed length for no wind, 8% FMC and for the cases: (a) 10° slope angle, (c) 15° slope angle, (e) 20° slope angle, and radiative heat flux over fuel bed length for the cases: (b) 10° slope angle, (d) 15° slope angle, (f) 20° slope angle. Note that the data are given only for 1.4 m in the X-direction because the downstream fuel is unaffected past this distance.
The graphs of convection (Fig. 9a, c and e) again show both cooling and heating effects on the particles. In the flaming zone, there is negative convection during the burning of the particles. The maximum convective heat release rate reaches ~500 kW m−2. In the convective heating zone, the heat flux has a maximum of 50 kW m−2. This heating is due to the presence of the flame and its effect on the particles in the flame-induced region. This range can be a threshold for the maximum heating of the downstream particles (in both flame-induced and natural convection regions) received from the flame. The flame-induced region length increases with slope angle. Convective heating has a greater spatial extent for a 15° slope angle (Fig. 9c) compared with a slope angle of 10° (Fig. 9a). This also applies for the slope angle 20° (Fig. 9e) compared with the 15° slope angle (Fig. 9c). This means that the flame-induced region length increases with the slope angle. The thermal effect of flame downstream for the 40 s time step increases from 0.7 to 1.3 m as the slope angle increases from a 10° to a 20° slope angle, which means the flame front is deeper for higher slope angles.
For the case with the 20° slope (Fig. 9e), there are a number of points where the flame reattaches on the downstream vegetation and non-steady convective heating and cooling happen. These reattachments are shown by large fluctuations in the convective cooling zone and small fluctuations in the convective heating zone and at the selected times. The fluctuations clearly show the tendency of the fire to accelerate. For example, in Fig. 9e, at the 20 s time step, there are four local negative peaks in the convective cooling zone (from x = 0.5 to 0.7 m) and three local positive peaks in the convective heating zone (from x = 0.7 to 0.8 m). Towards the end of the burn (from time step 35 s), the fire becomes stable, but the observed intermittency is because the slope is close to the critical angle, typically thought to be ~25° for continuous flame attachment (Liu et al. 2015).
For the radiative heat flux data (Fig. 9b, d, f), there is both absorption and transmission of the radiation by the fuel. For each time step, first, the fuel particles at the surface absorb radiative heat flux. The spatial length and the amount of absorption increase with slope angle for most of the time steps. There is steady behaviour of the flame for the 10° slope angle (Fig. 9b) with the same flame arrival behaviour, and the same peak in radiation. This behaviour changes to become non-steady as slope angle increases, when the intermittency in convective heat flux becomes more pronounced. The corresponding total heat flux data are shown in Fig. 10.
Total heat flux over fuel bed length for no wind, 8% FMC and for the cases: (a) 10° slope angle, (b) 15° slope angle, (c) 20° slope angle. Note that the data are demonstrated only for 1.4 m in the X-direction because there were no informative data after this limit.
The effect of the FMC on the convective, radiative and total heat fluxes over time and distribution along the centreline is shown in Fig. 11. This parameter has the least effect on the overall behaviour of the flame and heat transfer in the domain, compared with the wind speed and slope angle effects (see the following sensitivity analysis section). The range of FMC from 4 to 12% was selected to reflect typical fuel conditions that support fire (Innocent et al. 2023). The first notable effect of increasing the moisture content is a slight reduction in the ROS (from 9.92 cm s−1 for 4% FMC to 7.78 cm s−1 for 8% FMC) as shown by location of the flame arrival (light blue peaks) after 40 s in Fig. 11. For example, the location of the last peak in convection graphs decreases from x = 0.63 m (Fig. 11a) to x = 0.57 m (Fig. 11e). This is because wet fuel particles are less likely to ignite compared with dry ones and moisture postpones the burning of each fuel particle. The case with 4% FMC has slightly greater convective heating for each time step (Fig. 11a, c and e). As FMC increases, the fire heat release rate (HRR) will decrease because more energy is needed for moisture evaporation. This reduction in HRR means less heat is released into the surroundings, which produces weaker buoyant forces. These forces are responsible for cold air entrainment. Lower air entrainment means less oxygen is pulled into the flame, and with lower HRR, one has lower convective heating of the surroundings. This finding indicates that downstream fuel near the flame receives more convection compared with radiation heat transfer.
Convective heat flux over fuel bed length for 10° slope angle, no wind and for the cases: (a) 4% FMC, (c) 8% FMC, (e) 12% FMC, and radiative heat flux over fuel bed length for the cases: (b) 4% FMC, (d) 8% FMC, (f) 12% FMC. Note that the data are demonstrated only for 1.0 m in the X-direction because there were no informative data after this limit.
The same trend is observed for the radiative heat flux (Fig. 11b, d, f). Convective heating dominates over radiative heating in the positive peaks where the particles receive heating. The absorption of radiative heat flux by the fuel in the flame-induced region decreases with increasing FMC content. This reduction is very small compared with the changes with the wind and slope angle. For example, the absorption of radiation maximum for time step 15 s is 24.28 kW m−2 for 4% FMC (Fig. 11b), which decreases to 20.11 kW m−2 for 12% FMC (Fig. 11f), corresponding to a 17% reduction. The x-location for the peak transmission of the radiative heat flux for the case 40 s (x = 0.6 m) also reveals that a 4% FMC has a higher ROS (3.05 cm s−1) compared with the other cases (ROS = 2.73 cm s−1 for 8% FMC and ROS = 2.22 cm s−1 for 12% FMC). This means that increasing the moisture content (from 4% to 12% FMC) of the fuel reduces the ROS by 27%. The corresponding total heat flux data are shown in Fig. 12.
Sensitivity analysis
The effect of wind, slope and FMC on the heat transfer and ROS of the fuel was studied in the previous section. However, it is important to find a way to compare the relative importance of these parameters. To investigate which parameter has the dominant effect on ROS, a sensitivity analysis was conducted following the procedure outlined by McGrattan (2017). The relative importance of each parameter on the ROS is assessed by the condition number, c, defined as follows (McGrattan 2017):
which gives the relative effect of parameter xi on the fire ROS (R). The values of c for the effect of the wind, slope angle and FMC are listed in Table 2. Based on the results of Table 2, one can see that slope angle has the greatest effect on the fire ROS, then wind speed and finally FMC. The negative value of c for FMC means increasing this parameter causes a reduction in the fire ROS; however, the magnitude of c suggests FMC has the weakest effect on the ROS.
Flame-induced and natural convection regions
As we are interested in the convective and radiative heat fluxes transferred to the downstream excelsior fuel during flame arrival, this section focuses on the heat fluxes received by each particle located ahead of the flame region. The virtual thermocouples are placed every 20 cm on the centreline and at the top of the fuel bed. These thermocouples are defined in FDS by considering the temperature lag compared with the real temperature owing to the bead size of the thermocouple, emissivity of the thermocouple and the bead convective heat transfer coefficient. The formulae for calculating the thermocouple temperature can be found in McGrattan et al. (2013a), eqn 22.26. Using these simulated thermocouples will allow us to conduct future comparisons with experimental test data.
When the fire front passes the third thermocouple (at x = 0.7 m) and the temperature reaches 300°C, the data ahead of the flame to the end of the fuel bed are captured. These data relate to the amount of convection and radiation flux that each excelsior particle at the top of the fuel bed receives and are gathered along the centreline of the fuel bed (y = 0.5 m).
The results of varying the FMC on the convective and radiative heat fluxes of the particle are shown in Fig. 13. The zigzag behaviour over the length is an artifact caused by a step-like fuel bed representation in the FDS domain to give the inclined fuel bed at the slope angle of 10°. There are two main regions with different fire behaviours. The first region is called the flame-induced convection region (Liu et al. 2014) (from 0.7 m to ~1.0 m) and the second is the natural convection region (from ~1.0 m to the end of the fuel bed). In the flame-induced region, increasing the FMC causes an increase in the convective cooling of particles that are close to the head fire (from 0.7 to 1 m). As the FMC increases, water evaporation increases, which in turn reduces the fuel temperature. This is a result of the latent heat for the phase change of water from liquid to gas being drawn from the fuel surface. However, there is a higher radiation effect (Fig. 13b) for higher FMC due to the high absorption coefficient of water (κw = 1578) (McGrattan et al. 2013b). The latter effect is dominant, and as a result, the fuel surface temperature increases with increasing FMC in the flame-induced region, and accordingly there is more convective cooling. As the distance from the head fire increases in this region, there is less convective cooling and less radiative heating. First, the particles heat up by radiation and their temperature increases compared with the surrounding air and hot gases. If the particle temperature is greater than that of the surrounding air, then convective cooling occurs, leading to a negative value, as seen in the graphs (Figs 13a, 14a, 15a). In the natural convection region, there is less convective cooling and less radiative heating. The fluctuations in the flame-induced region are because of the intermittency of the head fire and the backward and forward movement of the flames in this region.
Total heat flux over fuel bed length for 10° slope angle, no wind and for the cases: (a) 4% FMC, (b) 8% FMC, (c) 12% FMC. Note that the data are demonstrated only for 1.0 m in the X-direction because there were no informative data after this limit.
The effect of FMC on the downstream region: (a) convective heat flux (10° slope angle, no wind), and (b) radiative heat flux (10° slope angle, no wind). The flame front is located at 0.7 m. Note the different scales of the vertical axes.
The effect of slope angle on the downstream region: (a) convective heat flux (no wind, 8% FMC), and (b) radiative heat flux (no wind, 8% FMC). The flame front is located at 0.7 m.
The effect of wind speed on the downstream region: (a) convective heat flux (8% FMC, no slope), and (b) radiative heat flux (8% FMC, no slope). The flame front is located at 0.7 m.
Fig. 14 shows the effects of the slope angle on convective and radiative heat transfer to the downstream particles. The reason for selecting 10°, 15° and 20° slope angles is that these cases have a detached flame at the third thermocouple, which makes it possible to distinguish a slope angle effect. In the flame-induced region, the first case with a 10° slope angle has no convective heating because of the detached flame. The flame is detached with a flame length of 30.41 cm and tilt angle of 9.45° (the tilt angle is the angle between the vertical line and the flame). For the 15° slope angle, the flame length is 42.19 cm (39% increase), and the flame tilt is 31.34° (27% increase) for the time step at which the flame reaches the third thermocouple. For the 20° slope, the flame is nearly attached for the first 20 s and then becomes detached, which shows that this angle is near the critical angle at which the mode changes from buoyant flame to attached flame. The 20° slope angle is also the starting angle for convective heating in the flame-induced region, which means that the hot plumes of air coming from the head fire add a heating effect to the particles due to attachment of the flame. For the other two cases, there is a cooling effect in the flame-induced region.
There is also convective heating for the particles very close to the head fire in the 15° slope angle case. This means that there is little tendency for the flame to attach to the fuel bed at this angle and at the third station. For the natural convection region, the 20° slope angle has a convective heating effect towards the end of the fuel bed, which means hot plumes of air move through the particles at the top surface of the fuel bed and their temperature increases. It also shows that the wind velocity vectors are in the direction of the fire ROS. The 10° and 15° slope angle cases have a cooling effect on the downstream particles, and the direction of the induced flow is opposite to the fire ROS. This difference is one reason for the higher rate of spread for the 20° slope angle because both radiation and convection have a positive impact on the particle temperature downstream of the flame location.
The effect of wind speed on convective and radiative heat transfer in flame-induced and natural convection regions was also investigated (see Fig. 15). For all the three cases, attachment of the flame to downstream excelsior particles occurs, and there are significant fluctuations in both the convective and radiative heat transfer in the flame-induced region. The 1 m s−1 wind shows that there is both convective cooling and heating in the flame-induced region, which implies that this is the initiation of flame attachment. When a flame attachment occurs, then convective heating of the fire is the prominent heating effect on the downstream unburnt fuel. The 1 m s−1 wind also produces longer flames (58.1 cm for this specific station of the head fire), which provide higher values of radiative heat flux compared with the other two cases. For 2 and 3 m s−1 wind, there is consistent flame attachment and convective heating on the downstream excelsior particles. The overall trend and effect of the wind are displayed in Fig. 7, which shows that increasing the wind speed causes an increase in both radiative and convective heat transferred to the fuel and consequently an increase in the ROS.
Discussion
The present numerical work addresses the following the four questions raised in the introduction regarding the mechanism of heat transfer in fire propagation in wildland fuels, which, to the best of our knowledge, have not yet been fully examined in the literature.
Addressing these questions helps to reveal the mechanism of heat transfer in terms of convective heating, convective cooling and radiation under various conditions in bushfires.
Convective cooling of fuel particles in wildland fire fuels has not been extensively examined in the literature. The purpose of our study is to capture this cooling effect for the various scenarios defined in our work. Our findings show that convective cooling appears downstream of the flame in both flame-induced and natural convection regions. The cooling effect in the natural convection region is negligible compared with the flame-induced region. The amount of convective cooling is slightly lower than the radiative heating to the unburned fuel. This cooling occurs because of the higher temperature of the excelsior particles compared with the ambient air around them. For attached flames, there is only the heating effect of convection on the downstream particles. However, for detached flames, there is a cooling effect of convection on the downstream particles and for critical cases (close to the attached flame), there is both heating and cooling convection on downstream particles.
More than 90% of convective and radiative heat transfer downstream happens in the flame-induced regions for all the cases, and the length of the flame-induced region (assumed to be the location at which convection is less than 0.1 kW m−2) is approximately equal to the flame length calculated based on the flame height (the height at which the flame temperature drops below 300°C) (Table 3) and flame tilt angle. The natural convection region length is defined as extending from the end of flame-induced region to the end of the fuel bed (more than 1 m for all the cases studied). Maximum radiative heat flux to the downstream particles happens for the cases close to flame attachment owing to the higher flame angle and flame length. When flame attachment is observed, the radiative heat flux decreases compared with the detached cases.
| Flame length (cm) | Flame tilt angle (°) | Flame-induced length (cm) | ||
|---|---|---|---|---|
| 4% FMC | 32.56 | 10.61 | 35 | |
| 8% FMC | 30.41 | 9.45 | 35 | |
| 12% FMC | 32.97 | 14.02 | 35 | |
| 10° slope angle | 30.41 | 9.45 | 35 | |
| 15° slope angle | 42.19 | 31.34 | 45 | |
| 20° slope angle | 49.74 | 59.55 | 55 | |
| 1 m s−1 wind | 57.31 | 60.82 | 55 | |
| 2 m s−1 wind | 91.08 | 78.57 | 70 | |
| 3 m s−1 wind | 130.84 | 83.93 | 120 |
We considered different regions of interest to see whether radiation or convection is the dominant mode of heat transfer. In our simulations, convective and radiative heat transfer become comparable in the burning zone, with radiation being slightly higher. There is one region in which convective heating becomes dominant compared with radiation, and this happens for all the cases studied here. This region includes the particles that are in the flame zone but not yet burned. This behaviour agrees with the results of Finney et al. (2015), namely that convection is the main trigger for ignition of the fuel.
The flame-induced distance increases with slope angle and wind. This is consistent with experiments done by Li et al. (2021). The cooling effect of convection in the flame-induced region for slope angles less than 20° and heating effect for higher slope angles is also consistent with the literature (Anderson et al. 2010; Dupuy and Maréchal 2011; Li et al. 2021). The contribution of radiation to the heat transfer over unburnt excelsior in the plume-dominated cases is higher than convection (Morvan and Frangieh 2018); however, convection is dominant in the cases with flame attachment.
The findings above are derived from the data for individual surface excelsior particles at the surface of the fuel bed and through the centreline for specific time steps. There is a need for more analysis to consider more time steps and different locations other than the centreline downstream of the flame. Internal heat transfer should also be investigated in future works to validate these findings.
In addition to the parameters studied here (wind, slope angle and FMC), the fuel structure can also greatly influence flame spread behaviour and controlling mechanisms. FDS assumes excelsior particles are oriented vertically and present in each cell. This is a bit different from the arrangement of grass in real bushfire experiments in which the fuel particles have different orientations. This area of research needs further analysis to make the comparison between simulations and experiments more valid.
Conclusion
We numerically investigated the effect of the three parameters wind, slope and FMC on the thermal behaviour of excelsior particles in a fuel bed using FDS. Our findings show that increasing the wind velocity from 1 to 3 m s−1 increases the number of reattachments of the flame and convective heating to the unburned fuel. Increasing the slope angle is a trigger for increasing both convective and radiative heat transfer to the unburned fuel. Reducing the FMC causes a slight increase in both radiative and convective heat transfer to the unburned fuel. The maximum convective cooling effect on the natural convection region of downstream particles occurs for the case with 15° slope angle, no wind and 8% FMC. Based on our sensitivity analysis for the broader range of the parameters (0.3 to 3 m s−1 wind, 10° to 40° slope angle, and 4% to 12% FMC), the fire ROS is more sensitive to slope angle than to the other two factors. The influence of wind velocity on the fire ROS is slightly lower than that of the slope angle but the FMC sensitivity is low. Our results of wind speed and FMC impacting the ROS are consistent with the observations made by McGrattan (2017). Our results contrast with the results of Mendes-Lopes et al. (2003) for the sensitivity of fire ROS to slope angle. One reason could be that the results of Mendes-Lopes et al. (2003) are based on experiments for slope angles below 15° for which there is no flame attachment.
Future work
Future work includes an experimental study that will be done with a fuel bed of excelsior particles under the same conditions as this numerical study in order to compare the present numerical results with experimental fires. A larger range of the present variables will be considered to study flame behaviour at different time steps. The other effective parameter that affects results could be the depth of the side walls, which are not mentioned in the experiments of Butler et al. (2007) and Sánchez-Monroy et al. (2019). We will focus on this parameter in our future work.
Supplementary material
For Fig. 6, additional resources can be found at: Developed wind field-Wind 1 m s−1, Slope Angle 00, FMC 8%.mp4, Fig.6a.mp4, Fig.6b.mp4, Fig.6c.mp4, Fig.6d.mp4, Fig.6e.mp4, Fig.6f.mp4. For Figs 7 and 8, additional resources can be found at: Wind1, Slope0, FMC8%.mp4, Wind2, Slope0, FMC8%.mp4, Wind3, Slope0, FMC8%.mp4. For Figs 9 and 10, additional resources can be found at: Slope10, Wind0, FMC8%.mp4, Slope15, Wind0, FMC8%.mp4, Slope20, Wind0, FMC8%.mp4. For Figs 11 and 12, additional resources can be found at: Slope10, Wind0, FMC8%.mp4, FMC12%, Slope10, Wind0.mp4, FMC4%, Slope10, Wind0.mp4. Supplementary material is available online.
Data availability
The data that support this study will be shared on reasonable request to the corresponding author.
Conflicts of interest
Albert Simeoni is associate editor of International Journal of Wildland Fire but was not involved in the peer review or any decision-making process for this paper. The authors declare no other conflicts of interest.
Acknowledgements
The current work was conducted with the assistance of resources provided by the National Computational Infrastructure (NCI) National Facility at the Australian National University through the National Computational Merit Allocation Scheme supported by the Australian Government.
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