# Physics-Based Simulations of Flow and Fire Development Downstream of a Canopy

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## Abstract

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## 1. Introduction

## 2. Problem Description and Methodology

#### 2.1. Problem Description and Approach

_{S}σ

_{S}, where α

_{S}is the volume fraction of the solid particles and σ

_{S}is their surface-to-volume ratio. σ

_{S}was set to 4000 m

^{−1}and the required distribution of the LAD was obtained from a variable space-distribution of α

_{S}. The distribution of the LAD in the vertical z-direction is given by Equation (1), which is representative of Australian pine canopies [5]:

_{max}was determined in order to obtain the desired leaf-area-index (LAI), equal to the integral of LAD with respect to z over the canopy height H [15]. As shown by Figure 2, three values of LAI (0.5, 2, and 8) were considered in the first phase of the study. These values of LAI were chosen because they cover the transition of the flow over a canopy from a boundary-layer-like flow to a mixing-layer-like one, as shown by Nepf et al. [16]. This transition occurs for C

_{D}× LAI ≈ 0.1 [16], where C

_{D}is the drag coefficient of the canopy, equal to 0.15 [5] in this case.

_{10}at the top of the canopy. The value of the pressure gradient tends asymptotically to zero once a statistically-steady flow is obtained. For each of the three values of the LAI reported in this study, five different values of U

_{10}were considered: 1, 3, 5, 8, and 12 m/s. Thus, a total of 15 simulations were carried out until a statistically-steady flow was obtained in each case. The development of the turbulent flow during this precursory phase was examined by considering the average profiles of turbulence statistics [14]. The steady state was considered to be reached when the average profiles of turbulence statistics and the mean stream-wise velocity at the top of the canopy were constant in time.

_{S}= 0.002, surface-to-volume ratio σ

_{S}= 4000 m

^{−1}, dry-material density ρ

_{S}= 500 kg/m

^{3}, moisture content M = 5%, solid-fuel particles were assumed to have cylindrical shape and to behave as a black body. The second-phase simulations were carried out for a canopy LAI = 2 only (for reasons explained in the result section) and for the five values of U

_{10}considered in phase 1, i.e., U

_{10}= 1, 3, 5, 8, and 12 m/s.

^{3}). When the burner was activated, the average velocity of CO injection was at its maximum (equal to 0.1 m/s), and then it was decreased linearly with the consumed mass of solid-fuel. This procedure avoids destabilizing the flame front by abruptly ceasing the CO injection and avoids any excessive external energy input. More details about the ignition procedure are given in [18,20].

#### 2.2. Mathematical Model

_{2}, N

_{2}, CO, CO

_{2}, and H

_{2}O) filtered in space using a LES approach, with a Favre-average formulation [25]. The closure of the filtered conservation equations is based on the eddy viscosity concept [26]. An LES high-order sub-grid scale stresses model was used [27]. The temperature dependence of the gas-mixture enthalpy is based on CHEMKIN thermodynamic tables [28]. A combustion model based on the Eddy Dissipation Concept (EDC) was used to evaluate the combustion rate occurring in the gaseous phase [26,29]. The soot volume-fraction in the gas mixture is calculated by solving a transport equation including a thermophoretic contribution in the convective term and taking into consideration soot oxidation [30,31,32].

#### 2.3. Numerical Method

_{2}and H

_{2}O), on the gas mixture temperature, and of the soot volume fraction [40]. The set of ordinary differential equations describing the time evolution of solid-fuel state (mass, temperature, and composition) are solved separately using a fourth order Runge–Kutta method. From an implementation point of view, the computation code is parallelized using OpenMP directives [41] and optimized [42,43]. Finally, the hydrodynamic module of the code has been extensively validated on several benchmarks of laminar and turbulent natural-convection, forced convection, and neutrally-stratified flow within and above a sparse forest-canopy [14,15,44,45]. The predictive potential of FIRESTAR3D model has been estimated at small scale in the case of litter fires in well-controlled experimental conditions (fire propagation through a homogeneous fuel-bed in a wind tunnel) [18,21] and at a larger scale for grassland fires (experimental campaign carried out in Australia) [13].

^{−4}in normalized form [21]. As a rough estimation of the computational cost in phase 2 (much higher than in phase 1), the simulation of 1s of fire propagation required about 7 h of CPU time on a 24-core node.

## 3. Results and Discussion

#### 3.1. Phase 1: ABL Flow Over a Tree Canopy

_{10}= 5 m/s and LAI = 2. The Kelvin-Helmholtz rolls come in pair in shear flows, where the vortices rotate around each other and eventually merge, due to the velocity induction mechanism: each vortex tends to lead the other non-rotational motions, causing the vortices to roll up around each other as shown in Figure 4b. Consequently, the outer part of each vortex turns more slowly than the inner part, and each vortex develops a tail leading to the development of so-called horseshoe vortices; some of these structures can be seen in Figure 4b. Then, longitudinal-hairpin vortices form by the stretching, by the ambient deformation field at the canopy-top level, of the weak vorticity that exists initially in the stagnation region between the Kelvin–Helmholtz rolls; the hairpin structures are also visible in Figure 4b. Finally, the fully-developed turbulent flow shown in Figure 4c is characterized by a dominance of streamwise vortices that are located at the top of the canopy. The progression shown in Figure 4 is in qualitative agreement with the mechanisms discussed by Finnigan [46]. Notice that in the case of Figure 4, C

_{D}× LAI = 0.3 is three times the threshold value of 0.1 characterizing the transition of the flow over a canopy from a boundary-layer-like flow to a mixing-layer-like one [16]. Even though the explored flow contains characteristics of both flow types [14], the analogy with the mixing-layer flow is stronger: the presence of Kelvin–Helmholtz rolls pairing, three-dimensional helical pairing, and hairpin vortices suggests more similarity with a mixing-layer flow transition.

_{10}= 1 m/s and 12 m/s velocity cases. The u-velocity oscillates around a constant mean, showing the flow is well developed, and we noticed that the wind speed increases the frequency of fluctuation of the velocity. Interesting analyses may be conducted for the ABL flow over a tree canopy, such as characterizing the wavelength and the frequency contents of the velocity field, but this would be tangential to the main objective of the paper, which is to study the spread of a grassland fire downstream of a canopy.

#### 3.2. Phase 2: Grassland Fire Spread Downstream of a Tree Canopy

#### 3.2.1. Flow Redevelopment

#### 3.2.2. Fire Spread

_{10}= 3, 5, 8, and 12 m/s with a canopy, and 139, 58, 14, and 5, respectively, for the cases without a canopy. The Nc was evaluated after the fire reached a quasi-equilibrium spread rate using averaged RoS and intensity.

_{10}= 1 m/s and U

_{10}= 12 m/s are shown in Figure 9. The U

_{10}= 1 m/s case is likely buoyancy dominated with a characteristically vertical flame, whereas the U

_{10}= 12 m/s case is likely wind dominated with a horizontal and attached flame. Figure 10 shows streamlines in vertical median and xy (z = 2h) planes around the flame for three cases: U

_{10}= 1, 3, and 12 m/s. The U

_{10}= 1 m/s case shows the flame entraining fluid from both sides and the U

_{10}= 12 m/s case shows the flame entraining from only upstream, confirming that these cases are buoyancy and wind dominated, respectively, despite the low intermediate N

_{c}values. The U

_{10}= 5 m/s is more complicated and can be considered as a hybrid between these two regimes. The flame appears be attached but there is a complicated flow structure in front of the flame. The streamlines in the horizontal plane suggest that the flow is predominantly from left to the right of the domain, even though there is a plume present. The entrainment of fresh air into the plume is therefore on the upstream side only. This suggests that this fire is a more wind-dominated fire than a buoyancy-dominated fire. The U

_{10}= 5 m/s case streamlines can be contrasted with those of the U

_{10}= 1 m/s case, which clearly shows entrainment on both sides of the flame. In the U

_{10}= 1 m/s case there is a large vortex structure generated by the plume; however, it is not a canopy-induced recirculation region as observed by Cassiani et al. [5]. Canopy induced recirculation regions occur directly behind the canopy and extend from the ground to the canopy top. The horizontal plane z = 2h images in Figure 10 also show differences in the flame structure. For the U

_{10}= 1 m/s case, the flame depth (the distance in the x-direction between the two edges of the burning region) is very small and the burning region is largely continuous in the spanwise directions. However, small interruptions to the flaming zone are present at the edges and center of the domain. Small vortex-pair structures can be seen at the edges of the individual flaming regions (e.g., at approximately (x,y) = (65,10) m). In the U

_{10}= 5 m/s case, the flame structure is considerably different: long streak-like structures are visible and the flame depth is approximately 25 m (at z = 2h). In the U

_{10}= 12 m/s case, the flame structure at z = 2h is patchier. The front is considerably deeper, approximately 50 m than the other two cases. Both of these observations are consistent with a more inclined and attached flame.

_{10}= 1 m/s case extinguishes at approximately 15 m downstream of the ignition location. The wind velocity at flame height is very low (see Figure 8b) and is likely insufficient to sustain a propagating fire in this particular fuel bed. All other cases propagate to the end of the domain in an approximately quasi-equilibrium manner, as indicated by the approximately-linear behavior of frontal location with time. All of the average-frontal positions as a function of time shown in Figure 12 are slightly nonlinear, indicating that the fires are slowly accelerating.

_{vap}, ω

_{pyr}, ω

_{char}, ω

_{CO}, and ω

_{soot}are, respectively, the total mass rates of water evaporation, pyrolysis, char combustion, combustion of CO in the gas mixture, and soot combustion, and ΔH

_{vap}, ΔH

_{pyr}, ΔH

_{char}, ΔH

_{CO}, and ΔH

_{soot}are the corresponding specific heats. Note that ΔH

_{char}is not constant; it depends on the proportion of CO to CO

_{2}produced during charcoal combustion [21], and it varies between 9 MJ/kg (for incomplete combustion) and 30 MJ/kg (for complete combustion).

_{10}= 1 m/s case shows a brief period (between approximately 10 and 20 s) of quasi-equilibrium intensity, consistent with the period of linear growth in frontal location (Figure 12), before the intensity decays to zero as the fire extinguishes. The other cases grow towards a quasi-equilibrium intensity; however, with the exception of the U

_{10}= 12 m/s case, the intensity still grows very slowly throughout the simulation. The U

_{10}= 3, 5, and 8 m/s cases tend towards intensities of 8, 14, and 20 MW/m, respectively. The amplitude of the variance in intensity also increases with time. The U

_{10}= 12 m/s behaves differently; the intensity peaks at around 60 s before decaying and re-intensifying between 60–80 s. This is suggestive of surge-stall behavior [54], which is consistent with the step-like changes in the frontal location that emerge at approximately 50 s after ignition. The variation of the intensity also increases with wind speed across all cases. The U

_{10}= 10 m/s case also exhibits step-like behavior in the frontal location, and some regular bursting in the intensity occurs at 55, 65, and 75 s after ignition. However, further investigation is required to completely characterize the fire behavior over this regime.

_{10}= 1 m/s case does not extinguish, suggesting that the sheltered wind speed downstream of the canopy is insufficient to sustain the fire when a canopy is present. The canopy does reduce the average RoS; however, the effect is minor. The largest difference of approximately 15% occurs in the U

_{10}= 8 m/s case (Figure 14a). The average intensity is also systematically lower downstream of a canopy than in the open by approximately 10% (Figure 14b). On the other hand, the average RoS and fire intensity obtained at steady state of fire spread are in agreement with experimental data [56] and with predictions of other numerical studies [18,57] and empirical models [3,58].

_{10}= 3 m/s and U

_{10}= 12 m/s. The fires in open grassland are significantly further, approximately 50 m for t > 30 s in the U

_{10}= 12 m/s case, ahead of the fires where a canopy is present. The distance systematically increases with wind speed, as shown in Figure 15b, although the rate of growth decreases with increasing wind speed. The U

_{10}= 12 m/s case frontal locations differ by 52 m. The intensity development shown in Figure 16 exhibits a similar delay. The U

_{10}= 3 m/s case recovers to the open intensity at approximately 70 s after ignition, and the U

_{10}= 12 m/s case recovers after approximately 50 s after ignition. The critical point between the two parts of the curve (sharp at the beginning and flatter at the end) seems to occur at U

_{10}= 8 m/s, which also corresponds to the beginning of the fully wind-driven regime for the fire propagating through the canopy free region. In fact, it is for this value of the wind speed that the Byram convective number reaches a value nearly equal to 11 (> 10 i.e., the beginning of the fully wind-driven fire regime). In analyzing the fire intensity history in Figure 13 and in considering the sudden increase of fluctuations highlighted for U

_{10}= 8 and 12 m/s, compared to the results obtained for lower values of the wind speed, we could conclude that for safety reasons, prescribed burning would be more suitable (in this configuration) for wind speed at least smaller than 5 m/s.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ABL | Atmospheric Boundary Layer |

C_{D} | Drag coefficient |

h | Grassland height, m |

H | Canopy height, m |

HRR | Heat Release Rate, W |

LAD | Leaf Area Density, m^{−1} |

LAI | Leaf Area Index |

LES | Large Eddy Simulation |

M | Grass moisture content, % |

N_{C} | Byram convection number |

Q | 2nd invariant of the velocity tensor gradient, s^{−2} |

RoS | Rate of Spread, m·s^{−1} |

t | time, s |

u, v, w | Flow velocity components, m·s^{−1} |

U_{10} | 10-m wind speed, m·s^{−1} |

WRF | Wind Reduction Factor |

x, y, z | Space coordinates, m |

α_{S} | Fuel volume fraction |

ΔH | Reaction heat, J.kg^{−1} |

ρ_{S} | Fuel density, kg·m^{−3} |

σ_{S} | Fuel surface-to-volume ratio, m^{−1} |

ω | Reaction rate, kg·s^{−1} |

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**Figure 1.**Two-dimensional (2D) view of the computational domain and boundary conditions used for phase 1. Domain width was 50 m in the y-direction with periodic boundary conditions.

**Figure 2.**Distribution of the canopy leaf-area-density (LAD) in the vertical z-direction obtained from Equation (1), corresponding to a leaf-area-index (LAI) = 0.5, 2, and 8.

**Figure 3.**2D view of the computational domain and boundary conditions used for phase 2. Domain width is 50 m in the y-direction with periodic boundary conditions.

**Figure 4.**Iso-surface Q = 2 s

^{−2}of the Q-criterion, colored by the vertical velocity component, obtained in phase 1 for U

_{10}= 5m/s and LAI = 2. (

**a**) t = 15 s, (

**b**) t = 20 s, (

**c**) t = 1500 s (steady state).

**Figure 5.**Effect of the wind speed (

**a**) and the canopy LAI (

**b**) on the normalized velocity profile u(z) (averaged in the x and the y directions and in time between t = 1200 s and t = 1500 s) obtained at steady state.

**Figure 6.**Time evolution of stream-wise velocity component u obtained at steady state (t = 1300 s) at point (x = 100 m, z = H) for LAI = 2 and for U

_{10}= 1 m/s (

**a**) and 12 m/s (

**b**).

**Figure 7.**Vertical cross section of the stream-wise velocity field obtained at t = 1000 s, for canopy LAI = 2 and U

_{10}= 5 m/s, at y = 25 m.

**Figure 8.**Variation in the x-direction of the averaged stream-wise velocity component u obtained (

**a**) at the canopy-top surface (z = H) and (

**b**) at the grassland-top surface (z = h), for canopy LAI = 2 and for different wind speeds. u(x) was time-averaged between t = 800 s and t = 1000 s as well as in the y-direction.

**Figure 9.**Three-dimensional (3D) views of grassland fire spread downstream of a canopy obtained for U

_{10}= 1 m/s (

**a**) and U

_{10}= 12 m/s (

**b**), 20 s and 30 s, respectively, after ignition. Fire is visualized by an isovalue surface of the soot volume fraction (10

^{−6}) colored by the gas temperature and by an isovalue surface of the water mass-fraction (0.00075) in grey shades with 75% transparency.

**Figure 10.**Cuts in the vertical-median plane y = 25 m (

**a**,

**c**,

**e**) and in the horizontal plan z = 2h (

**b**,

**d**,

**f**) of the temperature field with streamlines obtained for U

_{10}= 1 m/s (

**a**,

**b**), 5 m/s (

**c**,

**d**), and 12 m/s (

**e**,

**f**).

**Figure 11.**Distribution of the fuel composition at the grassland surface (z = h), obtained 45 s after ignition (t

_{Ignition}= 1000 s in phase 2) in the case of U

_{10}= 5 m/s, showing the position of the fire front.

**Figure 12.**Time evolution of the average position of the fire front at the grassland surface obtained for different wind speeds. The rate of spread (RoS) is the slope of the curve at steady fire propagation.

**Figure 13.**Time evolution the total heat release rate per unit length of fire line obtained for different wind speeds from Equation (2).

**Figure 14.**(

**a**) Rates of fire spread obtained at steady state for different wind speeds in the presence of a canopy compared to those obtained for the same simulation conditions but without a canopy. (

**b**) Average heat release rates obtained at steady state for different wind speeds in the presence of a canopy compared to those obtained for the same simulation conditions but without a canopy.

**Figure 15.**(

**a**) Time evolution of the average position of the fire front at the grassland surface obtained for U

_{10}= 3 m/s and 12 m/s in the case of fire spread downstream of a canopy, compared to the case of fire spread obtained for the same simulation conditions but without a canopy. (

**b**) Distance between the fire position obtained at steady state with and without the presence of a canopy upstream the grassland for all cases except the U

_{10}= 1 m/s case.

**Figure 16.**Time evolution of the heat release rate obtained from Equation (2) for U

_{10}= 3 m/s and 12 m/s in the case of fire spread downstream of a canopy, compared to the case of fire spread obtained for the same simulation conditions but without a canopy.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Accary, G.; Sutherland, D.; Frangieh, N.; Moinuddin, K.; Shamseddine, I.; Meradji, S.; Morvan, D.
Physics-Based Simulations of Flow and Fire Development Downstream of a Canopy. *Atmosphere* **2020**, *11*, 683.
https://doi.org/10.3390/atmos11070683

**AMA Style**

Accary G, Sutherland D, Frangieh N, Moinuddin K, Shamseddine I, Meradji S, Morvan D.
Physics-Based Simulations of Flow and Fire Development Downstream of a Canopy. *Atmosphere*. 2020; 11(7):683.
https://doi.org/10.3390/atmos11070683

**Chicago/Turabian Style**

Accary, Gilbert, Duncan Sutherland, Nicolas Frangieh, Khalid Moinuddin, Ibrahim Shamseddine, Sofiane Meradji, and Dominique Morvan.
2020. "Physics-Based Simulations of Flow and Fire Development Downstream of a Canopy" *Atmosphere* 11, no. 7: 683.
https://doi.org/10.3390/atmos11070683