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A computational study of the interactions of three adjacent burning shrubs subjected to wind
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A computational study of the interactions of three adjacent burning shrubs subjected to wind ⁎
Satyajeet Padhi, Babak Shotorban , Shankar Mahalingam Department of Mechanical & Aerospace Engineering The University of Alabama in Huntsville, Huntsville, AL 35899, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Wildfires CFD Flame interactions
A three-dimensional physics-based model was used to investigate the effect of shrub size, shrub separation distance and wind on the burnout times of shrubs. The shrub considered for this study was chamise. Two shrub sizes with different physical dimensions and initial masses with two wind speeds were considered. The study was performed for an array of three shrubs with separation distances ranging from zero to one shrub diameter. The shrubs were situated at the vertices of an equilateral triangle with two shrubs placed upwind (upstream shrubs) of the third shrub (downstream shrub). For a smaller shrub and a higher wind speed, the direction of fire front propagation within the shrub was found to be opposite to the direction of the wind, which resulted in a longer burning time for the shrub. For larger shrubs, a decrease in burning time was observed with an increase in wind speed. The burnout time for upstream shrubs increased with an increase in shrub separation distance for all shrub sizes and wind speeds considered. The burnout time for the downstream shrub was found to decrease with an increase in the separation distance, reach a minimum, and then increase with an increase in separation distance. The trends observed in burnout times for downstream shrub were attributed to the balance between heat feedback into the downstream shrub from the flames in upstream shrubs and availability of sufficient oxygen for combustion to take place.
1. Introduction Wildland fire propagation is impacted by several factors such as atmospheric conditions, vegetation density, moisture content of vegetation and presence of nearby fire sources. Two of the most important factors include the presence of nearby fire sources and the presence of ambient wind. When separate fires are placed in closed proximity to each other, they interact and converge in one location and ultimately behave like a single large or mass fire [1]. Under windy conditions, it is known that the rate of spread of fire increases compared to cases with no wind [2,3]. A theoretical analysis of flame interactions was performed by Thomas et al. [4] where they proposed a functional relationship between the length of merged flames, separation distance and characteristic dimensions of the burners. They theorized that when two flames are placed in close proximity, a pressure drop is created between the neighboring flames as a result of a restriction in air entrainment. The flames are thus deflected from the vertical, with the greatest deflection occurring in the region of maximum pressure drop. A functional relationship between merged flame height, dimensions of fire source, and the separation distance between the fire sources was
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proposed using Bernoulli's equation and assuming, that the rate of air entrainment is unaffected by pressure gradients induced due to flame merging. Theoretical predictions of flame height were compared with experimental measurements using 60 cm×30 cm and 30 cm×30 cm burners supplied with methane gas. Merged flame height measurements from experiments and theory were in good agreement when the separation distance between the burners was small. While, Thomas et al. [4] performed a theoretical analysis for two fuel beds, Baldwin [5] extended the theory to include a square matrix of n2 fires from data obtained through experiments with porous burners using natural gas as the fuel. The experimental approach consisted of square array configurations varying from two to sixteen burners and burner sizes of 1 ft. ×1 ft. and 2 ft. ×1 ft. The theoretically derived scaling law between merged flame heights and separation distances between fire sources predicted the onset of flame merging, i.e., an increase in flame heights, with appreciable accuracy, and were independent of the number of fires involved. Subsequently, numerous works have examined flame merging in either pool fires [6–9] or on flames over porous burners [10,11], finding a strong correlation between fuel spacing and burning rate of individual fires. They have reported that as the fuel spacing increased, the burning rate increased
Corresponding author. E-mail address: [email protected] (B. Shotorban).
http://dx.doi.org/10.1016/j.firesaf.2017.03.028 Received 8 February 2017; Accepted 15 March 2017 0379-7112/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Padhi, S., Fire Safety Journal (2017), http://dx.doi.org/10.1016/j.firesaf.2017.03.028
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Fig. 1. Schematic representation of computational domain. (a) Shrub arrangement; (b) Definition of shrub separation distance (s/D).
propagation, resulting in a ‘backing fire’, the flame will tilt away from the unburned fuel. Thus, the unburned surface fuel ahead of the fire front receives less radiation and convection heat from the flames leading to a decrease in burning rate and the overall rate of spread [17]. Although there has been extensive study on burning rate measurements due to flame interaction for various liquid fuel pools with different pool diameters and flames from porous gas burners, studies on burning rates in shrub fires is lacking. Wildland fuel is characterized by small, discrete particles, such as leaves, branches and other wood particles, which are discrete compared with pools of liquid fuel, and highly porous compared with porous burners. Thus, it is important to understand the effects of wind, fuel spacing and size of fuel matrix in vegetative fuels to perform safe and successful prescribed burns. Thus, the objective in this paper is to study the effect of shrub separation distance, size of shrub and wind on the burning time of shrubs. A physics-based continuum model [13] is used, wherein governing equations for the various thermo-physical phenomena involved in fire spread through vegetative fuels are solved numerically. The next section provides a description of the problem statement followed by a summary of the physics-based model used in this work.
to reach a maximum, and then decreased with a further increase in fuel spacing. In a series of papers, Liu et al. [7–9] investigated flame interaction and flame merging phenomena in square fire arrays. The experiments were performed with square fire arrays consisting of multiple equidistant fires from fuel pans of n-heptane. The various arrays considered ranged from 3×3 to 15×15, with the fire spacing ranging from 5 to 50 cm. They used burnout time for the individual fuel sources with respect to a global burnout time, and flame heights to quantify flame merging. Their analysis showed the presence of two competing fire interaction mechanisms: heat feedback enhancement and air entrainment restriction. When the distance between the fire sources was less than a critical separation distance, the effect of heat feedback enhancement dominated air entrainment restriction. When the fire spacing was increased air entrainment mechanism dominated the heat feedback mechanism. In the context of wildland fires, Dahale et al. [12] used a physicsbased model [13] to study fire interactions in chamise shrubs. They studied fire interactions in two- and three-shrub arrangements in the absence of crosswind. The shrub used in the study was 0.6 m in diameter and 1 m in height with an initial mass of approximately 0.6 kg. Fire behavior was described in terms of global parameters such as shrub mass loss rates and total heat release rates, as well as local parameters such as the temporal evolution of temperature at points of interest within the shrub. It was found that the maximum rate of consumption of shrub mass and fire spread along the shrub height decreased as shrub separation distance increased. Flame heights from three-shrub arrangements were reported to be significantly higher than two-shrub arrangement suggesting stronger fire interactions in the former. It is noted that previous works that used physics-based modeling to investigate shrub or shrub-like canopy crown fires are due to Overholt et al. [14,15] who modeled the burning of isolated little bluestem grass, and Dahale et al. [13] and Padhi et al. [16] who modeled the burning of isolated chamise shrubs. The presence of ambient wind results in higher fire spread rates compared to cases with no ambient wind. If the wind is in the direction of fire propagation, resulting in a ‘heading fire’, the flame tilt angle, measured from the vertical, between the fire front and the surface fuel can increase, resulting in an enhancement of radiation and convection heat transfer to the unburned surface fuel ahead of the fire front. The result is an increase in burning rate, higher flow velocities, increased flame heights, and increased rate of spread and higher burning intensity. If the wind is in a direction opposite to that of fire
2. Problem setup and computational methodology A schematic of the computational domain used in this work is shown in Fig. 1(a). The shrub arrangement was chosen such that each shrub is placed on the vertex of an equilateral triangle as shown in Fig. 1(b). The crown separation distance is defined as the distance between the inner edges of the shrubs, which is indicated by s, normalized by the maximum value of the shrub diameter D along its height. Five normalized separation distances, s/D =0.0, 0.25, 0.50, 0.75, and 1.00, two wind speeds U∞ =1 and 2 m/s, and two shrub sizes were considered. The smaller shrub is 1 m tall with a maximum diameter of 0.6 m and 0.57 kg in mass. The larger shrub is 1.2 m tall with a maximum diameter of 0.8 m along its height and 1.15 kg in mass. Also, the diameter of the base of shrubs is 0.1 m for smaller shrubs and 0.2 m for larger shrubs. In addition, simulations for burning of an isolated shrub with two shrub sizes and wind speeds mentioned above, were also performed to understand the impact of neighboring fires on the burning of individual shrubs. In each case, the crown fuel was chamise (Adenostoma fasciculatum). The crown was assumed as a porous medium comprising of two distinct components: branches and foliage, with a mass-based proportion fixed at 53% and 47%, respectively. This choice was guided by the 2
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of solid into various gas-phase species is modeled in the species transport equation. The transport equation for soot evolution includes terms to capture effects of production, oxidation and thermophoretic diffusion of soot. Thermal radiation was modeled using a radiation transport equation for a multiphase, emitting, absorbing and nonscattering media. The filtered reaction rate of species is estimated as the product of species consumption rate per unit surface area and filtered flame surface density which the flame surface area per unit volume [23]. This approach decouples the species chemistry problem from the turbulence-combustion interaction problem. A single-step global reaction mechanism is used where the pyrolysis gas is modeled as a mixture of CO, CH4, H2, and CO2 [24]. The size of the computational domain is 6.0 m×4.0 m ×4.0 m in the x, y, and z directions as shown in Fig. 1. The governing equations were solved in a rectangular domain with a resolution of 300×200×200 in the x, y, and z directions, respectively. An explicit third-order accurate scheme in space and time, QUICKEST was used to numerically integrate the governing equations [25]. A three-dimensional Discrete Ordinates Method (DOM) was used to calculate radiation heat transfer between gas and solid phase, including contributions from gas (CO2 and H2O), soot and solid phase. Open boundary conditions were imposed on all lateral boundaries, wherein gradients of flow variables normal to the boundary are set to zero allowing for inflow and outflow such that fluid can be entrained into the domain through the surface normal direction. A convective boundary condition was employed at the top boundary, where convection velocity is set equal to local normal velocity calculated at the cell adjacent to the boundary. The bottom boundary has been modeled with a free slip wall boundary condition so that no mass enters or exits across this boundary. The computational model has been tested and validated for an isolated shrub fire under no-wind conditions by Dahale et al. [13] against the experimental results of Li [19]. Parameters such as burning time, total mass consumed, spread rates and the time required to reach maximum mass loss rate were in good agreement with the experiments. All the simulations reported in this work were performed using message passing interface (MPI) protocol on 20 processors of High Performance Technical Computing (HPTC) cluster at the College of Engineering of The University of Alabama in Huntsville. A typical simulation of 100 s required a wall time of about 340 h and 24 GB of memory. Results obtained from the burning of the three shrubs were compared against those obtained from the burning of an isolated shrub to explore the impact of neighboring fires on the burning of individual shrubs.
actual measurements performed by Tachajapong et al. [18]. The shrub was assumed to be spatially homogeneous, i.e., local solid-phase properties are independent of position. The bulk density of the shrub was 3.8 kg/m3, which corresponds to the average value of bulk density in the shrub volume measured by Li [19,20]. The physical properties of foliage used were 500 kg/m3, 8000 m−1, 31.35 MJ/kg, 28.60% and 3.50% for the fuel particle density, surface-to-volume ratio, heat of char combustion, char content and ash content, respectively [18]. The corresponding properties used for branches were 600 kg/m3, 1800 m−1, 32.37 MJ/kg, 15.40% and 0.50%, respectively [18]. Since flame size decreases with an increase in moisture content of the shrub [13], to observe significant fire interactions, a relatively low moisture content of 10% was used. The influence of moisture on fire behavior is important and a subject of ongoing investigation. Each shrub has an individual ignition zone in the surface fuel, which is located below the crown fuel. This arrangement was motivated by the experiments of Li [19], wherein dry excelsior was used as surface fuel in the experiments. The surface fuel bed comprises of 0.025 kg of aspen (Populus tremuloides) excelsior, with dimensions of 0.2 m, 0.2 m, and 0.2 m in the x, y, and z directions. The moisture content of the surface fuel was set at 7% [21]. The physical properties of excelsior used were 400 kg/m3, 4500 m−1, 32.3 MJ/kg, 15.4% and 3.50% for the fuel particle density, surface-to-volume ratio, heat of char combustion, char content and ash content, respectively [18]. The surface fuel was used as the ignition zone by raising the gas phase temperature in the surface fuel to 1200 K. The choice of this ignition mechanism was to reduce its direct impact on the burning behavior of shrubs. The effect of external ignition mechanism was negligible on the simulation results discussed herein as the igniter was switched off early (≈10 s) into the simulation. 2.1. Computational methodology A detailed description of the three-dimensional physics-based model utilized in this work can be found in [13] and references therein. Only a summary is provided here. The burning of shrubs and the fireinduced flow results in a fluid flow that is turbulent in nature. The dynamic two-way coupling between fire and fire-induced turbulent flow field was modeled using large eddy simulation (LES). In LES, a filtering procedure is used to separate the large energy containing scales from the smaller dissipative scales of motion. The larger or resolved scales are solved explicitly, while the smaller dissipative scales, also known as subgrid (SGS) scales, are modeled using appropriate closure models. Based on the LES approach, a set of three-dimensional transport equations was solved for the conservation of mass, momentum, energy, chemical species and soot evolution in the gas phase. The unresolved SGS fluxes arising owing to filtering of the transport equations were modeled via an eddy viscosity model in which the eddy viscosity coefficient was computed dynamically using a dynamic Smagorinsky approach [22]. The solid fuel was modeled as a porous medium and consisted of branches and foliage. For simplicity, the solid phase was assumed to be fixed in space throughout the burning process. The equations for time evolution of solid mass are based on Arrhenius-type laws where solid mass degradation due to vaporization of moisture, pyrolysis, and char oxidation are considered. A solid-phase energy equation was solved that accounts for effects of energy transfer by convection, radiation and phase change. The coupling between the burning solid phase and the gas phase was accomplished through various source terms appearing in the gasphase transport equations. The conversion of solid mass into gas is modeled in the gas-phase continuity equation, the effect on gas-phase momentum due to the presence of solid particles is accounted via the drag force term in the gas-phase momentum equation, energy transfer between solid and gas phase due to convection, radiation and combustion heat release is modeled in the energy equation, and decomposition
3. Results 3.1. Flame front behavior The iso-surface of gas-phase temperature (Tg) at 800 K for larger shrubs at s/D = 0.5 and U∞ = 2 m/s at various times, along with the shrub bulk density of 3.8 kg/m3 (shown in green contours) is shown in Fig. 2. The choice of this gas-phase temperature to identify the flame front was guided by a recent LES study of statistically stationary flames from chamise shrubs. Therein, a mean flame temperature of 800 K was chosen to compute flame heights that followed the standard two-fifths power law with respect to the heat release rate [16]. The flames over the downstream shrub are formed at the flanks or edges of the shrub, where they interact with the tilted flames from the upstream shrubs. Such an interaction of the flames from the upstream shrubs and the downstream shrub results in an increased flame length compared to flame lengths observed for isolated shrub under similar conditions. For example, the merged flame length at 50 s for the threeshrub arrangement was computed to be 1.4 m, while for an isolated shrub under similar conditions, the flame length was computed to be 1.0 m. In each case, the flame length was computed from the top 3
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Fig. 2. Iso-surface of Tg =800 K for larger shrubs at U∞ = 2 m/s and s/D = 0.5 at various times. The fuel is shown in green by the isosurface of the bulk density of 3.8 kg/m3.
surface of shrub to the point where the mean flame tip temperature drops to 800 K [16]. The flame tilt angle, which is computed as the angle between the flame front and the vertical, was approximately 66° for an isolated shrub compared to 54° for the three-shrub arrangement, under similar conditions. The radiation feedback mechanism from flames associated with the upstream shrubs into the downstream shrub enhance the heat received by the downstream shrub, thus reducing the time required for downstream shrub to burn out. The iso-surface of gas-phase temperature at 800 K for the larger shrub case at U∞ = 2 m/s and s/D = 0.0, 0.5, and 1.0 at time t = 50 s, along with the shrub bulk density of 3.8 kg/m3 (shown in green contours) are shown in Fig. 3. For s/D = 0, maximum flame interaction was observed and the three shrubs burned as a single mass fire. As the separation distance increased, interactions between the flames from upstream and downstream shrubs reduces and interaction ceases completely at a separation distance of s/D = 1. The flame lengths observed were maximum for s/D = 0 at approximately 2.0 m and were significantly greater than the flame lengths observed for an isolated shrub at approximately 1.0 m, under similar conditions. Flame front propagation within the shrub for the various cases considered is shown in Fig. 4 in the case of an isolated shrub and in Fig. 5 within the downstream shrub in the three-shrub arrangement. For the cases with U∞ = 1 m/s, the flame front begins at the upstreambottom end of the shrub and traverses upwards at an inclination with respect to the horizontal. At the same time, an accompanying flame front is developed at the trailing edge of the shrub which travels upwards and towards the vertical axis of the shrub. The movement of the flame front from the leading edge is similar to a `heading-like fire', where it travels in the direction of the free-stream wind. The flame front developed at the trailing edge exhibits behavior similar to a `backing-like fire', where the flame front travels in a direction opposite to that of the free-stream wind. Since, the movement of the flame front is predominantly similar to a heading-like fire, the flame front from the leading edge of the shrub is identified as the primary flame front. In the case of smaller shrub at U∞ = 2 m/s, shown in Fig. 4(d-f), the primary flame front is developed at the trailing edge of the shrub, as seen in Fig. 4(d). The higher magnitude of the free-stream velocity results in a greater tilt of the flames from surface fuel bed.
Consequently, the trailing edge of the shrub is ignited instead of the bottom surface of the shrub. The flame front then propagates in a direction opposite to the direction of wind, producing a backing-like fire. Similar trends were observed for the downstream shrub in smaller shrub cases at both wind speeds, as shown in Fig. 5(a-f). For the larger shrub cases shown in Fig. 5(g-l), the behavior of flame front in the downstream shrub was found to be similar to that in the isolated shrub case. The primary flame front travels upwards at an inclination to the horizontal plane and in the direction of the freestream velocity for both wind speeds. The effect of backing-like fire diminished in the case of the larger shrubs. Note that the base of the larger shrubs has a larger diameter than the smaller shrubs. While the tilting flames from the fuel bed ignite the trailing edge of the smaller shrubs, they ignite the base of the larger shrubs, thus reducing the possibility of a backing fire to develop.
3.2. Temporal evolution of mass of shrubs The time taken for the consumption of 80% of initial mass of an individual shrub is defined as the burnout time. The dependence of burnout time in the three-shrub arrangement for various separation distances is shown in Fig. 6. The burnout time for an isolated shrub for the corresponding shrub size and wind speed is also shown. The burnout times for smaller shrubs for the two wind speeds are shown in Fig. 6(a) and (b), while Fig. 6(c) and (d) show the burnout times for larger shrubs. The burnout time for isolated shrub cases are 69.0 s and 70.5 s for smaller shrubs at U∞ = 1 m/s and U∞ = 2 m/s, respectively. The corresponding times are 86.8 s and 70.2 s for larger shrubs at U∞ = 1 m/s and U∞ = 2 m/s, respectively. A similar global behavior of two upstream shrubs is expected because of the symmetric placement of the upstream shrubs with respect to the mid-plane of the domain (xy-plane passing at z=2 m) and the direction of the wind. It was observed that the burnout time for the upstream shrubs for all separation distances is close to each other in all panels of Fig. 6 but for panel (b) and s/D = 1 of panel (d). Both of these panels are for a higher wind speed. For the upstream shrubs, the fastest burnout were observed for s/D = 0 at both wind speeds. The burnout time for the upstream shrubs was on average 5.3% lower than
Fig. 3. Iso-surface of Tg = 800 K for larger shrubs at U∞ = 2 m/s and s/D = 0.0, 0.5 and 1.0 at t=50 s. The fuel is shown by the isosurface of the bulk density of 3.8 kg/m3.
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Fig. 4. Solid-phase temperature (in K) (color contours) with solid fuel bulk density (line contours) at various time instants for the isolated shrub. (a-c) Smaller shrub at U∞ = 1 m/s; (df) Smaller shrub at U∞ = 2 m/s; (g-i) Larger shrub at U∞ =1 m/s; (j-l) Larger shrub at U∞ =2 m/s. Snapshots are taken on a xy-plane passing through z = 2.0 m. Arrows show the direction of flame front propagation. In all cases, mean wind is from left to right.
for separation distances with minimum burnout time for s/D = 0, 0.5, and 1 at U∞ = 2 m/s is shown in Fig. 7. Temporal evolution of shrub mass for the corresponding isolated shrub case is also shown for comparison. The overall difference between most of the curves in each panel of Fig. 7 seems to be small; however, there is an appreciable difference between downstream shrub and the rest of the shrubs in panels for s/D = 0 and 0.5. The evolution of mass for the two upstream shrubs is identical for s/D =0, similar for s/D = 0.5, and somewhat different for s/D = 1. For s/D = 0, even though the downstream shrub mass loss rate is higher than that for the upstream shrubs at t < 40 s, the upstream shrubs eventually burnout earlier than the downstream shrub because of faster mass loss rate after approximately 60 s. At nonzero separation distances, the mass loss rate of downstream shrub is faster compared to the upstream shrubs resulting in faster burnout times. A similar trend is observed in the case of smaller shrubs, where the burnout times for downstream shrubs are higher than that for upstream shrubs at s/D =0, and less compared to upstream shrubs for non-zero separation distances. The time history of mass of pyrolysis gas and char mass for the downstream shrub for the three separation distances considered is
that for the isolated shrub cases for all wind speeds and s/D = 0. As the separation distance increases, the burnout times for upstream shrubs increase and approach the burnout time for the isolated shrub cases. However, burnout times in the downstream shrub follow a different trend. For the downstream shrub, the fastest burnout times were observed for a non-zero separation distance. The burnout times for the downstream shrubs at U∞ = 2 m/s were less compared to that at U∞ = 1 m/s. A similar trend was observed in larger shrubs, where a higher magnitude of free-stream velocity resulted in faster burnout times. However, for smaller upstream shrubs, the burnout times at higher wind velocities were longer due to the development of backing-like fire effect. The flame front begins at the trailing edge and has to travel towards the leading edge taking a longer time to heat the solid fuel which is cooled by the incoming wind. In order to identify the factors governing the burning behavior of the downstream shrub in the presence of neighboring shrubs due to fire interactions and wind, three shrub separation distances were chosen: s/D = 0, s/D = 1 and the shrub separation distance with minimum burnout time for the downstream shrub. The temporal evolution of shrub mass in the case with larger shrubs
Fig. 5. Solid-phase temperature (in K) (color contours) with solid fuel bulk density (line contours) at various time instants for the downstream shrub in the three-shrub arrangement. (a-c) Smaller shrub at U∞ = 1 m/s and s/D = 0.5; (d-f) Smaller shrub at U∞ = 2 m/s and s/D = 0.5; (g-i) Larger shrub at U∞ = 1 m/s and s/D = 0.25; (j-l) Larger shrub at U∞ = 2 m/s and s/D = 0.25. Snapshots are taken on a xy-plane passing through z=2.0 m. Arrows show the direction of flame front propagation. In all cases, mean wind is from left to right.
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Fig. 6. Burnout time of individual shrubs for various separation distances. Smaller shrubs – (a) U∞ = 1 m/s, (b) U∞ = 2 m/s. Larger shrubs – (c) U∞ = 1 m/s, (d) U∞ = 2 m/s. Burnout time for isolated shrub case is also shown for comparison.
Fig. 7. Temporal evolution of mass in individual shrubs (in kg) for larger shrubs at U∞ = 2 m/s and separation distances (a) s/D = 0, (b) s/D = 0.5, (c) s/D = 1 (isolated shrub cases are also shown for comparison).
shown in Fig. 8(b), respectively. The time taken for consumption of mass is longest for s/D = 0 and shortest for s/D = 0.5. This is in accordance with the burnout times observed for the entire shrub. The
mass loss in the solid phase is initiated by the drying process, followed by mass loss due to pyrolysis and char oxidation. The loss in shrub mass due to pyrolysis is the fastest for s/D = 0.5. This rapid loss in 6
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Fig. 8. Time history of (a) pyrolysis gas mass, ms,pyr (in kg), (b) char mass, ms,char (in kg), and (c) oxygen mass fraction averaged over the shrub volume in the downstream shrub for larger shrubs at U∞ = 2 m/s.
time history of solid-phase temperature of the fuel particle due to accumulated heat absorbed (positive value) or released (negative value) through convective heat transfer Qconv,s between gas and solid and radiative heat transfer Qrad,s. Accumulated energy is calculated by integrating energy transfer rate over the burning time as Q(t) = t ∫0 q ̇ (t′) dt′, where q ̇ (t′) is the heat transfer rate between solid phase and gas phase due to convection or radiation. For s/D = 0.5, the pyrolysis gases are released at the probe point by t≈30 s. This is indicated by the increase in solid-phase temperature to 500 K in Fig. 9(a). The solid-phase temperature increases further due to the heat released by gas-phase combustion. The solid-phase temperature rises slowly from t≈30 s to t≈37 s. During this time, heat is absorbed by the solid fuel particle by radiation from the gaseous flames which is indicated by the positive values of Qrad,s shown in Fig. 9(b). As discussed above, the availability of sufficient oxygen allows the pyrolysis gases to undergo gas-phase combustion rapidly and the heat feedback from the gaseous flames thus formed increases the solidphase temperature rapidly for s/D = 0.5. When the temperature of the particle reaches 673 K, it undergoes char oxidation, releasing a large amount of energy in the form of radiation. This is seen in the rapid fall of Qrad,s in Fig. 9(b) and rapid rise in the value of Qmass,s at t≈37 s, since char oxidation is an exothermic process. Consequently, the solid-phase temperature increases dramatically due to heat release via char oxidation. Convective heat transfer (Qconv,s) remains negative which implies a cooling effect on the solid particle. This cooling effect results in a drop in solid-phase temperature after t≈37 s. The rise in solid-phase temperature of the solid particle for s/D = 1.0 takes longer than for s/D = 0.5. This is due to increased distance of the probe point from the flames originating in the upstream shrub. The accumulated heat due to radiation from the flames takes a longer time to reach its peak value to initiate heat release due to char oxidation. Thus, the time taken for burnout is higher as seen in Fig. 8(a). For s/D = 0, heat is absorbed by the solid particle mainly by convection, which is indicated by the positive values of Qconv,s in Fig. 9(b). This implies a
mass is due to the availability of oxygen, as shown in Fig. 8(c) for the pyrolysis gas to undergo gas-phase combustion and subsequently increase the solid phase temperature, allowing the solid fuel to undergo rapid thermal degradation. A similar trend was observed for the mass evolution of char, where the availability of sufficient oxygen leads to rapid oxidation of char leading to increased mass loss rate of the downstream shrub at s/D = 0.5. However, at s/D = 0, a lack of availability of oxygen was observed in the downstream shrub leading to slower mass loss rates. This lack of availability of oxygen is due to the presence of the upstream shrubs blocking the entrainment of air into the downstream shrub.
3.3. Heat feedback into shrubs The burnout time of a shrub is affected by how fast the solid fuel undergoes thermal decomposition. In order to undergo thermal decomposition, the solid fuel must lose moisture through evaporation, undergo pyrolysis when the solid-phase temperature reaches 460 K and subsequently undergo char oxidation at temperatures higher than 673 K [26]. The evolution of solid-phase temperature is controlled by the convective and radiation heat transfer rates between solid and gas phase. In order to understand the trends observed in burnout times for the downstream shrub, a detailed analysis of the factors affecting burnout times was performed. A solid particle located in the downstream shrub for the larger shrub case at U∞ = 2 m/s was selected and the time history of solid-phase temperature and heat transfer rates at this point was examined. The location of the point is such that it is closer to the upstream shrubs and situated within the flame interaction region. The flame interaction region is defined as the region where the edges of the three shrubs are closest to each other, increasing the possibility of flame merging. Three separation distances are considered for the analysis: s/D = 0, s/D = 0.5 (separation distance with minimum burnout time for downstream shrub) and s/D =1.0. Fig. 9(a) shows the 7
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Fig. 9. Time history of (a) solid-phase temperature, Ts (in K), and (b) accumulated heat – convective, Qconv,s and radiative, Qrad,s (in MJ/m3) at a probe point in the downstream shrub for larger shrubs at U∞ = 2 m/s. The probe point is located at (x,y,z) =(1.39 m, 1.0 m, 2.0 m) for s/D = 0, (1.74 m, 1.0 m, 2.0 m) for s/D = 0.5, and (2.08 m, 1.0 m, 2.0 m) for s/D = 1.
flames due to their proximity to one another. However, it was found that the burnout time for the downstream shrub reduced with an increase in separation distance to reach a minimum and then increased with further increase in separation distance. The burnout times of the downstream shrub was found to be higher than the upstream shrub at zero separation distance. This trend was observed for all wind speeds and shrub sizes investigated. The slower burnout time observed in the downstream shrub for zero separation distance was attributed to the lack of oxygen available for efficient combustion. This is due to the presence of upstream shrubs and their combustion products restricting the flow of oxygen into the downstream shrub. For the case with the minimum burnout time for the downstream shrub, the heat transfer into the downstream shrub and air supply are at the optimal level to facilitate faster burnout of the shrub. The heat feedback into the downstream shrub at this separation distance was dominated by radiation from the flames of the upstream shrubs. As the shrub separation distance increases, the heat feedback from the flames of upstream shrubs into the downstream shrub decreases, causing the burnout times to increase. Thus, the burnout time of a shrub placed downwind of two burning shrubs under the influence of wind depends on the balance of heat feedback into the shrub and the oxygen available for efficient combustion.
long heating period where the gas-phase temperature is higher than solid-phase temperature, as char oxidation has not taken place to release heat via radiation and result in rapid mass loss of the particle. Despite the continuous heating of the solid particle in shrub for zero shrub separation distance, a greater time for char oxidation results in higher burnout time for the downstream shrub. F or s/D = 1.0, although there is enough air supply to the downstream shrub due to its increased separation distance from the neighboring shrubs, the heat transfer takes longer to heat the solid fuel to its ignition temperature resulting in higher burnout times than for s/D = 0.5.
4. Conclusions and future work The effects of shrub size, shrub separation distance and wind on the burning behavior of multiple chamise shrubs were analyzed using a multiphase physics-based model. The shrub considered for this study was chamise. Two shrub sizes with different physical dimensions and initial mass, 0.6 m in diameter, 1 m in height and 0.57 kg; and 0.8 m in diameter, 1.2 m in height and 1.15 kg, were considered. Two wind speeds of 1 and 2 m/s were considered. The multiple shrub arrangement considered consisted of three identical shrubs placed at the vertices of an equilateral triangle, with two shrubs placed upwind of the third shrub. Five shrub separation distances were considered, with the shrub separation distance being defined in terms of the maximum diameter of the shrub. The shrubs were ignited simultaneously with the aid of separate surface fuel beds. The results from the three-shrub arrangement cases were compared with an isolated shrub burn. It was found that the size of the shrub has an impact on the flame front propagation within the crown fuel matrix. A backing-like fire was observed in the smaller shrubs for higher wind speed for both isolated shrubs and individual shrubs in the three-shrub arrangement for all separation distances considered. The backing-like fire was due to the larger flame tilt angles from the surface fuel at higher wind speeds which resulted in the flames igniting the downwind trailing edge of the smaller shrubs. As a result of the backing-like fire, longer burnout times were recorded in the smaller shrubs at higher wind speed. However, for larger shrubs, the surface fuel flames ignite the base of the shrub, as the base of the larger shrubs is larger in diameter than the smaller shrubs. This reduces the possibility of a backing fire in the larger shrubs. For the larger shrubs, it was observed that higher wind speed leads to faster burnout times. It must be noted that the observations reported may be strongly impacted by the nature of surface ignition. Both the mass of the surface fuel and its burnout time will have an influence on results especially at higher wind speeds. It was found that the burnout times of upstream shrubs increased with an increase in separation distance for all wind speeds and shrub sizes considered. The faster burnout times of upstream shrubs at zero separation distance was due to the increased heat feedback from the
Acknowledgements The work was supported in part by National Science Foundation (grant numbers CBET-1049560 and CBET-1603947) and the 2013 Individual Investigator Distinguished Research (IIDR) program at The University of Alabama in Huntsville. Computational resources were provided by the Alabama Supercomputer Center (ASC). References [1] C.M. Countryman, Mass fires and fire behavior, USDA Forest Service Research Paper, 1964. [2] Pitts, Wind effects on fires, Progress in Energy and Combustion Science, 17, 1991, pp. 83–134. [3] B. Porterie, D. Morvan, J.C. Loraud, M. Larini, Firespread through fuel beds: modelling of wind aided fires and induced hydrodynamics, Phys. Fluids 12 (2000) 1762–1782. [4] P.H. Thomas, R. Baldwin, A.J.M. Heselden, Buoyant diffusion flames: Some measurements of air entrainment, heat transfer, and flame merging, in: Proceedings of the Tenth Symposium (International) on Combustion, 10, 1965, pp. 983–996. [5] R. Baldwin, Flame merging in multiple fires, Combust. Flame 12 (1968) 318–324. [6] K.G. Huffman, J.R. Welker, C.M. Sliepcevich, Interaction effects of multiple pool fires, Fire Technol. 5 (1969) 225–232. [7] N. Liu, Q. Liu, Z. Deng, K. Satoh, J. Zhu, Burn-out time data analysis on interaction effects among multiple fires in fire arrays, Proc. Combust. Inst. 31 (2007) 2589–2597. [8] N. Liu, Q. Liu, J.S. Lozano, L. Shu, L. Zhang, J. Zhu, Z. Deng, K. Satoh, Global burning rate of square fire arrays: experimental correlation and interpretation, Proc. Combust. Inst. 32 (2009) 2519–2526.
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S. Padhi et al. [9] N. Liu, Q. Liu, J.S. Lozano, L. Zhang, Z. Deng, B. Yao, J. Zhu, K. Satoh, Multiple fire interactions: a further investigation by burning rate data of square fire arrays, Proc. Combust. Inst. 34 (2013) 2555–2564. [10] D. Kamikawa, W.G. Weng, K. Kagiya, Y. Fukuda, R. Mase, Y. Hasemi, Experimental study of merged flames from multifire sources in propane and wood crib burners, Combust. Flame 142 (2005) 17–23. [11] W. Weng, D. Kamikawa, Y. Fukuda, Y. Hasemi, K. Kagiya, Study on flame height of merged flame from multiple fire sources, Combust. Sci. Technol. 176 (2004) 2105–2123. [12] A. Dahale, B. Shotorban, S. Mahalingam, Interactions of fires of neighboring shrubs in two- and three-shrub arrangements, Int. J. Wildland Fire 24 (5) (2015) 624–639. [13] A. Dahale, S. Ferguson, B. Shotorban, S. Mahalingam, Effects of distribution of bulk density and moisture content on shrub fires, Int. J. Wildland Fire 22 (5) (2013) 625–641. [14] K.J. Overholt, J. Cabrera, A. Kurzawski, M. Koopersmith, O.A. Ezekoye, Characterization of fuel properties and fire spread rates for little bluestem grass, Fire Technol. 50 (1) (2014) 9–38. [15] K.J. Overholt, A.J. Kurzawski, J. Cabrera, M. Koopersmith, O.A. Ezekoye, Fire behavior and heat fluxes for lab-scale burning of little bluestem grass, Fire Saf. J. 67 (2014) 70–81. [16] S. Padhi, B. Shotorban, S. Mahalingam, Computational investigation of flame characteristics of a non-propagating shrub fire, Fire Saf. J. 81 (2016) 64–73.
[17] J.S. Lozano, An Investigation of Surface and Crown Fire Dynamics in Shrub Fuels (Ph.D. dissertation), University of California, Riverside, 2011. [18] W. Tachajapong, J. Lozano, S. Mahalingam, D.R. Weise, Effects of distribution of bulk density and moisture content on shrub fires, Int. J. Wildland Fire (2014) 451–462. [19] J. Li, Experimental Investigation of Bulk Density and its Role in Fire Behavior in Live Shrub Fuels, University of California Riverside, 2011. [20] J. Li, S. Mahalingam, D.R. Weise, Experimental investigation of fire propagation in single live shrubs, Int. J. Wildland Fire 26 (1) (2017) 58–70. [21] W. Tachajapong, Understanding Crown Fire Initiation via Experimental and Computational Modeling, University of California, Riverside, 2008. [22] M. Germano, U. Piomelli, P. Moin, W.H. Cabot, A dynamics subgrid-scale eddy viscosity model, Phys. Fluids 3 (7) (1991) 1760–1765. [23] X. Zhou, S. Mahalingam, A flame surface density based model for large eddy simulation of turbulent non-premixed combustion, Phys. Fluids 14 (11) (2002) 77–80. [24] X. Zhou, S. Mahalingam, Evaluation of reduced mechanism for modeling combustion of pyrolysis gas in wildland fire, Combust. Sci. Technol. 171 (2001) 39–70. [25] B.P. Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng. 19 (1979) 59–98. [26] D. Morvan, J.L. Dupuy, Modeling of fire spread through a forest fuel bed using a multiphase formulation, Combust. Flame 127 (2001) 1981–1994.
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Contents lists available at ScienceDirect
Fire Safety Journal journal homepage: www.elsevier.com/locate/firesaf
A computational study of the interactions of three adjacent burning shrubs subjected to wind ⁎
Satyajeet Padhi, Babak Shotorban , Shankar Mahalingam Department of Mechanical & Aerospace Engineering The University of Alabama in Huntsville, Huntsville, AL 35899, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Wildfires CFD Flame interactions
A three-dimensional physics-based model was used to investigate the effect of shrub size, shrub separation distance and wind on the burnout times of shrubs. The shrub considered for this study was chamise. Two shrub sizes with different physical dimensions and initial masses with two wind speeds were considered. The study was performed for an array of three shrubs with separation distances ranging from zero to one shrub diameter. The shrubs were situated at the vertices of an equilateral triangle with two shrubs placed upwind (upstream shrubs) of the third shrub (downstream shrub). For a smaller shrub and a higher wind speed, the direction of fire front propagation within the shrub was found to be opposite to the direction of the wind, which resulted in a longer burning time for the shrub. For larger shrubs, a decrease in burning time was observed with an increase in wind speed. The burnout time for upstream shrubs increased with an increase in shrub separation distance for all shrub sizes and wind speeds considered. The burnout time for the downstream shrub was found to decrease with an increase in the separation distance, reach a minimum, and then increase with an increase in separation distance. The trends observed in burnout times for downstream shrub were attributed to the balance between heat feedback into the downstream shrub from the flames in upstream shrubs and availability of sufficient oxygen for combustion to take place.
1. Introduction Wildland fire propagation is impacted by several factors such as atmospheric conditions, vegetation density, moisture content of vegetation and presence of nearby fire sources. Two of the most important factors include the presence of nearby fire sources and the presence of ambient wind. When separate fires are placed in closed proximity to each other, they interact and converge in one location and ultimately behave like a single large or mass fire [1]. Under windy conditions, it is known that the rate of spread of fire increases compared to cases with no wind [2,3]. A theoretical analysis of flame interactions was performed by Thomas et al. [4] where they proposed a functional relationship between the length of merged flames, separation distance and characteristic dimensions of the burners. They theorized that when two flames are placed in close proximity, a pressure drop is created between the neighboring flames as a result of a restriction in air entrainment. The flames are thus deflected from the vertical, with the greatest deflection occurring in the region of maximum pressure drop. A functional relationship between merged flame height, dimensions of fire source, and the separation distance between the fire sources was
⁎
proposed using Bernoulli's equation and assuming, that the rate of air entrainment is unaffected by pressure gradients induced due to flame merging. Theoretical predictions of flame height were compared with experimental measurements using 60 cm×30 cm and 30 cm×30 cm burners supplied with methane gas. Merged flame height measurements from experiments and theory were in good agreement when the separation distance between the burners was small. While, Thomas et al. [4] performed a theoretical analysis for two fuel beds, Baldwin [5] extended the theory to include a square matrix of n2 fires from data obtained through experiments with porous burners using natural gas as the fuel. The experimental approach consisted of square array configurations varying from two to sixteen burners and burner sizes of 1 ft. ×1 ft. and 2 ft. ×1 ft. The theoretically derived scaling law between merged flame heights and separation distances between fire sources predicted the onset of flame merging, i.e., an increase in flame heights, with appreciable accuracy, and were independent of the number of fires involved. Subsequently, numerous works have examined flame merging in either pool fires [6–9] or on flames over porous burners [10,11], finding a strong correlation between fuel spacing and burning rate of individual fires. They have reported that as the fuel spacing increased, the burning rate increased
Corresponding author. E-mail address: [email protected] (B. Shotorban).
http://dx.doi.org/10.1016/j.firesaf.2017.03.028 Received 8 February 2017; Accepted 15 March 2017 0379-7112/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Padhi, S., Fire Safety Journal (2017), http://dx.doi.org/10.1016/j.firesaf.2017.03.028
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Fig. 1. Schematic representation of computational domain. (a) Shrub arrangement; (b) Definition of shrub separation distance (s/D).
propagation, resulting in a ‘backing fire’, the flame will tilt away from the unburned fuel. Thus, the unburned surface fuel ahead of the fire front receives less radiation and convection heat from the flames leading to a decrease in burning rate and the overall rate of spread [17]. Although there has been extensive study on burning rate measurements due to flame interaction for various liquid fuel pools with different pool diameters and flames from porous gas burners, studies on burning rates in shrub fires is lacking. Wildland fuel is characterized by small, discrete particles, such as leaves, branches and other wood particles, which are discrete compared with pools of liquid fuel, and highly porous compared with porous burners. Thus, it is important to understand the effects of wind, fuel spacing and size of fuel matrix in vegetative fuels to perform safe and successful prescribed burns. Thus, the objective in this paper is to study the effect of shrub separation distance, size of shrub and wind on the burning time of shrubs. A physics-based continuum model [13] is used, wherein governing equations for the various thermo-physical phenomena involved in fire spread through vegetative fuels are solved numerically. The next section provides a description of the problem statement followed by a summary of the physics-based model used in this work.
to reach a maximum, and then decreased with a further increase in fuel spacing. In a series of papers, Liu et al. [7–9] investigated flame interaction and flame merging phenomena in square fire arrays. The experiments were performed with square fire arrays consisting of multiple equidistant fires from fuel pans of n-heptane. The various arrays considered ranged from 3×3 to 15×15, with the fire spacing ranging from 5 to 50 cm. They used burnout time for the individual fuel sources with respect to a global burnout time, and flame heights to quantify flame merging. Their analysis showed the presence of two competing fire interaction mechanisms: heat feedback enhancement and air entrainment restriction. When the distance between the fire sources was less than a critical separation distance, the effect of heat feedback enhancement dominated air entrainment restriction. When the fire spacing was increased air entrainment mechanism dominated the heat feedback mechanism. In the context of wildland fires, Dahale et al. [12] used a physicsbased model [13] to study fire interactions in chamise shrubs. They studied fire interactions in two- and three-shrub arrangements in the absence of crosswind. The shrub used in the study was 0.6 m in diameter and 1 m in height with an initial mass of approximately 0.6 kg. Fire behavior was described in terms of global parameters such as shrub mass loss rates and total heat release rates, as well as local parameters such as the temporal evolution of temperature at points of interest within the shrub. It was found that the maximum rate of consumption of shrub mass and fire spread along the shrub height decreased as shrub separation distance increased. Flame heights from three-shrub arrangements were reported to be significantly higher than two-shrub arrangement suggesting stronger fire interactions in the former. It is noted that previous works that used physics-based modeling to investigate shrub or shrub-like canopy crown fires are due to Overholt et al. [14,15] who modeled the burning of isolated little bluestem grass, and Dahale et al. [13] and Padhi et al. [16] who modeled the burning of isolated chamise shrubs. The presence of ambient wind results in higher fire spread rates compared to cases with no ambient wind. If the wind is in the direction of fire propagation, resulting in a ‘heading fire’, the flame tilt angle, measured from the vertical, between the fire front and the surface fuel can increase, resulting in an enhancement of radiation and convection heat transfer to the unburned surface fuel ahead of the fire front. The result is an increase in burning rate, higher flow velocities, increased flame heights, and increased rate of spread and higher burning intensity. If the wind is in a direction opposite to that of fire
2. Problem setup and computational methodology A schematic of the computational domain used in this work is shown in Fig. 1(a). The shrub arrangement was chosen such that each shrub is placed on the vertex of an equilateral triangle as shown in Fig. 1(b). The crown separation distance is defined as the distance between the inner edges of the shrubs, which is indicated by s, normalized by the maximum value of the shrub diameter D along its height. Five normalized separation distances, s/D =0.0, 0.25, 0.50, 0.75, and 1.00, two wind speeds U∞ =1 and 2 m/s, and two shrub sizes were considered. The smaller shrub is 1 m tall with a maximum diameter of 0.6 m and 0.57 kg in mass. The larger shrub is 1.2 m tall with a maximum diameter of 0.8 m along its height and 1.15 kg in mass. Also, the diameter of the base of shrubs is 0.1 m for smaller shrubs and 0.2 m for larger shrubs. In addition, simulations for burning of an isolated shrub with two shrub sizes and wind speeds mentioned above, were also performed to understand the impact of neighboring fires on the burning of individual shrubs. In each case, the crown fuel was chamise (Adenostoma fasciculatum). The crown was assumed as a porous medium comprising of two distinct components: branches and foliage, with a mass-based proportion fixed at 53% and 47%, respectively. This choice was guided by the 2
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of solid into various gas-phase species is modeled in the species transport equation. The transport equation for soot evolution includes terms to capture effects of production, oxidation and thermophoretic diffusion of soot. Thermal radiation was modeled using a radiation transport equation for a multiphase, emitting, absorbing and nonscattering media. The filtered reaction rate of species is estimated as the product of species consumption rate per unit surface area and filtered flame surface density which the flame surface area per unit volume [23]. This approach decouples the species chemistry problem from the turbulence-combustion interaction problem. A single-step global reaction mechanism is used where the pyrolysis gas is modeled as a mixture of CO, CH4, H2, and CO2 [24]. The size of the computational domain is 6.0 m×4.0 m ×4.0 m in the x, y, and z directions as shown in Fig. 1. The governing equations were solved in a rectangular domain with a resolution of 300×200×200 in the x, y, and z directions, respectively. An explicit third-order accurate scheme in space and time, QUICKEST was used to numerically integrate the governing equations [25]. A three-dimensional Discrete Ordinates Method (DOM) was used to calculate radiation heat transfer between gas and solid phase, including contributions from gas (CO2 and H2O), soot and solid phase. Open boundary conditions were imposed on all lateral boundaries, wherein gradients of flow variables normal to the boundary are set to zero allowing for inflow and outflow such that fluid can be entrained into the domain through the surface normal direction. A convective boundary condition was employed at the top boundary, where convection velocity is set equal to local normal velocity calculated at the cell adjacent to the boundary. The bottom boundary has been modeled with a free slip wall boundary condition so that no mass enters or exits across this boundary. The computational model has been tested and validated for an isolated shrub fire under no-wind conditions by Dahale et al. [13] against the experimental results of Li [19]. Parameters such as burning time, total mass consumed, spread rates and the time required to reach maximum mass loss rate were in good agreement with the experiments. All the simulations reported in this work were performed using message passing interface (MPI) protocol on 20 processors of High Performance Technical Computing (HPTC) cluster at the College of Engineering of The University of Alabama in Huntsville. A typical simulation of 100 s required a wall time of about 340 h and 24 GB of memory. Results obtained from the burning of the three shrubs were compared against those obtained from the burning of an isolated shrub to explore the impact of neighboring fires on the burning of individual shrubs.
actual measurements performed by Tachajapong et al. [18]. The shrub was assumed to be spatially homogeneous, i.e., local solid-phase properties are independent of position. The bulk density of the shrub was 3.8 kg/m3, which corresponds to the average value of bulk density in the shrub volume measured by Li [19,20]. The physical properties of foliage used were 500 kg/m3, 8000 m−1, 31.35 MJ/kg, 28.60% and 3.50% for the fuel particle density, surface-to-volume ratio, heat of char combustion, char content and ash content, respectively [18]. The corresponding properties used for branches were 600 kg/m3, 1800 m−1, 32.37 MJ/kg, 15.40% and 0.50%, respectively [18]. Since flame size decreases with an increase in moisture content of the shrub [13], to observe significant fire interactions, a relatively low moisture content of 10% was used. The influence of moisture on fire behavior is important and a subject of ongoing investigation. Each shrub has an individual ignition zone in the surface fuel, which is located below the crown fuel. This arrangement was motivated by the experiments of Li [19], wherein dry excelsior was used as surface fuel in the experiments. The surface fuel bed comprises of 0.025 kg of aspen (Populus tremuloides) excelsior, with dimensions of 0.2 m, 0.2 m, and 0.2 m in the x, y, and z directions. The moisture content of the surface fuel was set at 7% [21]. The physical properties of excelsior used were 400 kg/m3, 4500 m−1, 32.3 MJ/kg, 15.4% and 3.50% for the fuel particle density, surface-to-volume ratio, heat of char combustion, char content and ash content, respectively [18]. The surface fuel was used as the ignition zone by raising the gas phase temperature in the surface fuel to 1200 K. The choice of this ignition mechanism was to reduce its direct impact on the burning behavior of shrubs. The effect of external ignition mechanism was negligible on the simulation results discussed herein as the igniter was switched off early (≈10 s) into the simulation. 2.1. Computational methodology A detailed description of the three-dimensional physics-based model utilized in this work can be found in [13] and references therein. Only a summary is provided here. The burning of shrubs and the fireinduced flow results in a fluid flow that is turbulent in nature. The dynamic two-way coupling between fire and fire-induced turbulent flow field was modeled using large eddy simulation (LES). In LES, a filtering procedure is used to separate the large energy containing scales from the smaller dissipative scales of motion. The larger or resolved scales are solved explicitly, while the smaller dissipative scales, also known as subgrid (SGS) scales, are modeled using appropriate closure models. Based on the LES approach, a set of three-dimensional transport equations was solved for the conservation of mass, momentum, energy, chemical species and soot evolution in the gas phase. The unresolved SGS fluxes arising owing to filtering of the transport equations were modeled via an eddy viscosity model in which the eddy viscosity coefficient was computed dynamically using a dynamic Smagorinsky approach [22]. The solid fuel was modeled as a porous medium and consisted of branches and foliage. For simplicity, the solid phase was assumed to be fixed in space throughout the burning process. The equations for time evolution of solid mass are based on Arrhenius-type laws where solid mass degradation due to vaporization of moisture, pyrolysis, and char oxidation are considered. A solid-phase energy equation was solved that accounts for effects of energy transfer by convection, radiation and phase change. The coupling between the burning solid phase and the gas phase was accomplished through various source terms appearing in the gasphase transport equations. The conversion of solid mass into gas is modeled in the gas-phase continuity equation, the effect on gas-phase momentum due to the presence of solid particles is accounted via the drag force term in the gas-phase momentum equation, energy transfer between solid and gas phase due to convection, radiation and combustion heat release is modeled in the energy equation, and decomposition
3. Results 3.1. Flame front behavior The iso-surface of gas-phase temperature (Tg) at 800 K for larger shrubs at s/D = 0.5 and U∞ = 2 m/s at various times, along with the shrub bulk density of 3.8 kg/m3 (shown in green contours) is shown in Fig. 2. The choice of this gas-phase temperature to identify the flame front was guided by a recent LES study of statistically stationary flames from chamise shrubs. Therein, a mean flame temperature of 800 K was chosen to compute flame heights that followed the standard two-fifths power law with respect to the heat release rate [16]. The flames over the downstream shrub are formed at the flanks or edges of the shrub, where they interact with the tilted flames from the upstream shrubs. Such an interaction of the flames from the upstream shrubs and the downstream shrub results in an increased flame length compared to flame lengths observed for isolated shrub under similar conditions. For example, the merged flame length at 50 s for the threeshrub arrangement was computed to be 1.4 m, while for an isolated shrub under similar conditions, the flame length was computed to be 1.0 m. In each case, the flame length was computed from the top 3
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Fig. 2. Iso-surface of Tg =800 K for larger shrubs at U∞ = 2 m/s and s/D = 0.5 at various times. The fuel is shown in green by the isosurface of the bulk density of 3.8 kg/m3.
surface of shrub to the point where the mean flame tip temperature drops to 800 K [16]. The flame tilt angle, which is computed as the angle between the flame front and the vertical, was approximately 66° for an isolated shrub compared to 54° for the three-shrub arrangement, under similar conditions. The radiation feedback mechanism from flames associated with the upstream shrubs into the downstream shrub enhance the heat received by the downstream shrub, thus reducing the time required for downstream shrub to burn out. The iso-surface of gas-phase temperature at 800 K for the larger shrub case at U∞ = 2 m/s and s/D = 0.0, 0.5, and 1.0 at time t = 50 s, along with the shrub bulk density of 3.8 kg/m3 (shown in green contours) are shown in Fig. 3. For s/D = 0, maximum flame interaction was observed and the three shrubs burned as a single mass fire. As the separation distance increased, interactions between the flames from upstream and downstream shrubs reduces and interaction ceases completely at a separation distance of s/D = 1. The flame lengths observed were maximum for s/D = 0 at approximately 2.0 m and were significantly greater than the flame lengths observed for an isolated shrub at approximately 1.0 m, under similar conditions. Flame front propagation within the shrub for the various cases considered is shown in Fig. 4 in the case of an isolated shrub and in Fig. 5 within the downstream shrub in the three-shrub arrangement. For the cases with U∞ = 1 m/s, the flame front begins at the upstreambottom end of the shrub and traverses upwards at an inclination with respect to the horizontal. At the same time, an accompanying flame front is developed at the trailing edge of the shrub which travels upwards and towards the vertical axis of the shrub. The movement of the flame front from the leading edge is similar to a `heading-like fire', where it travels in the direction of the free-stream wind. The flame front developed at the trailing edge exhibits behavior similar to a `backing-like fire', where the flame front travels in a direction opposite to that of the free-stream wind. Since, the movement of the flame front is predominantly similar to a heading-like fire, the flame front from the leading edge of the shrub is identified as the primary flame front. In the case of smaller shrub at U∞ = 2 m/s, shown in Fig. 4(d-f), the primary flame front is developed at the trailing edge of the shrub, as seen in Fig. 4(d). The higher magnitude of the free-stream velocity results in a greater tilt of the flames from surface fuel bed.
Consequently, the trailing edge of the shrub is ignited instead of the bottom surface of the shrub. The flame front then propagates in a direction opposite to the direction of wind, producing a backing-like fire. Similar trends were observed for the downstream shrub in smaller shrub cases at both wind speeds, as shown in Fig. 5(a-f). For the larger shrub cases shown in Fig. 5(g-l), the behavior of flame front in the downstream shrub was found to be similar to that in the isolated shrub case. The primary flame front travels upwards at an inclination to the horizontal plane and in the direction of the freestream velocity for both wind speeds. The effect of backing-like fire diminished in the case of the larger shrubs. Note that the base of the larger shrubs has a larger diameter than the smaller shrubs. While the tilting flames from the fuel bed ignite the trailing edge of the smaller shrubs, they ignite the base of the larger shrubs, thus reducing the possibility of a backing fire to develop.
3.2. Temporal evolution of mass of shrubs The time taken for the consumption of 80% of initial mass of an individual shrub is defined as the burnout time. The dependence of burnout time in the three-shrub arrangement for various separation distances is shown in Fig. 6. The burnout time for an isolated shrub for the corresponding shrub size and wind speed is also shown. The burnout times for smaller shrubs for the two wind speeds are shown in Fig. 6(a) and (b), while Fig. 6(c) and (d) show the burnout times for larger shrubs. The burnout time for isolated shrub cases are 69.0 s and 70.5 s for smaller shrubs at U∞ = 1 m/s and U∞ = 2 m/s, respectively. The corresponding times are 86.8 s and 70.2 s for larger shrubs at U∞ = 1 m/s and U∞ = 2 m/s, respectively. A similar global behavior of two upstream shrubs is expected because of the symmetric placement of the upstream shrubs with respect to the mid-plane of the domain (xy-plane passing at z=2 m) and the direction of the wind. It was observed that the burnout time for the upstream shrubs for all separation distances is close to each other in all panels of Fig. 6 but for panel (b) and s/D = 1 of panel (d). Both of these panels are for a higher wind speed. For the upstream shrubs, the fastest burnout were observed for s/D = 0 at both wind speeds. The burnout time for the upstream shrubs was on average 5.3% lower than
Fig. 3. Iso-surface of Tg = 800 K for larger shrubs at U∞ = 2 m/s and s/D = 0.0, 0.5 and 1.0 at t=50 s. The fuel is shown by the isosurface of the bulk density of 3.8 kg/m3.
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Fig. 4. Solid-phase temperature (in K) (color contours) with solid fuel bulk density (line contours) at various time instants for the isolated shrub. (a-c) Smaller shrub at U∞ = 1 m/s; (df) Smaller shrub at U∞ = 2 m/s; (g-i) Larger shrub at U∞ =1 m/s; (j-l) Larger shrub at U∞ =2 m/s. Snapshots are taken on a xy-plane passing through z = 2.0 m. Arrows show the direction of flame front propagation. In all cases, mean wind is from left to right.
for separation distances with minimum burnout time for s/D = 0, 0.5, and 1 at U∞ = 2 m/s is shown in Fig. 7. Temporal evolution of shrub mass for the corresponding isolated shrub case is also shown for comparison. The overall difference between most of the curves in each panel of Fig. 7 seems to be small; however, there is an appreciable difference between downstream shrub and the rest of the shrubs in panels for s/D = 0 and 0.5. The evolution of mass for the two upstream shrubs is identical for s/D =0, similar for s/D = 0.5, and somewhat different for s/D = 1. For s/D = 0, even though the downstream shrub mass loss rate is higher than that for the upstream shrubs at t < 40 s, the upstream shrubs eventually burnout earlier than the downstream shrub because of faster mass loss rate after approximately 60 s. At nonzero separation distances, the mass loss rate of downstream shrub is faster compared to the upstream shrubs resulting in faster burnout times. A similar trend is observed in the case of smaller shrubs, where the burnout times for downstream shrubs are higher than that for upstream shrubs at s/D =0, and less compared to upstream shrubs for non-zero separation distances. The time history of mass of pyrolysis gas and char mass for the downstream shrub for the three separation distances considered is
that for the isolated shrub cases for all wind speeds and s/D = 0. As the separation distance increases, the burnout times for upstream shrubs increase and approach the burnout time for the isolated shrub cases. However, burnout times in the downstream shrub follow a different trend. For the downstream shrub, the fastest burnout times were observed for a non-zero separation distance. The burnout times for the downstream shrubs at U∞ = 2 m/s were less compared to that at U∞ = 1 m/s. A similar trend was observed in larger shrubs, where a higher magnitude of free-stream velocity resulted in faster burnout times. However, for smaller upstream shrubs, the burnout times at higher wind velocities were longer due to the development of backing-like fire effect. The flame front begins at the trailing edge and has to travel towards the leading edge taking a longer time to heat the solid fuel which is cooled by the incoming wind. In order to identify the factors governing the burning behavior of the downstream shrub in the presence of neighboring shrubs due to fire interactions and wind, three shrub separation distances were chosen: s/D = 0, s/D = 1 and the shrub separation distance with minimum burnout time for the downstream shrub. The temporal evolution of shrub mass in the case with larger shrubs
Fig. 5. Solid-phase temperature (in K) (color contours) with solid fuel bulk density (line contours) at various time instants for the downstream shrub in the three-shrub arrangement. (a-c) Smaller shrub at U∞ = 1 m/s and s/D = 0.5; (d-f) Smaller shrub at U∞ = 2 m/s and s/D = 0.5; (g-i) Larger shrub at U∞ = 1 m/s and s/D = 0.25; (j-l) Larger shrub at U∞ = 2 m/s and s/D = 0.25. Snapshots are taken on a xy-plane passing through z=2.0 m. Arrows show the direction of flame front propagation. In all cases, mean wind is from left to right.
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Fig. 6. Burnout time of individual shrubs for various separation distances. Smaller shrubs – (a) U∞ = 1 m/s, (b) U∞ = 2 m/s. Larger shrubs – (c) U∞ = 1 m/s, (d) U∞ = 2 m/s. Burnout time for isolated shrub case is also shown for comparison.
Fig. 7. Temporal evolution of mass in individual shrubs (in kg) for larger shrubs at U∞ = 2 m/s and separation distances (a) s/D = 0, (b) s/D = 0.5, (c) s/D = 1 (isolated shrub cases are also shown for comparison).
shown in Fig. 8(b), respectively. The time taken for consumption of mass is longest for s/D = 0 and shortest for s/D = 0.5. This is in accordance with the burnout times observed for the entire shrub. The
mass loss in the solid phase is initiated by the drying process, followed by mass loss due to pyrolysis and char oxidation. The loss in shrub mass due to pyrolysis is the fastest for s/D = 0.5. This rapid loss in 6
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Fig. 8. Time history of (a) pyrolysis gas mass, ms,pyr (in kg), (b) char mass, ms,char (in kg), and (c) oxygen mass fraction averaged over the shrub volume in the downstream shrub for larger shrubs at U∞ = 2 m/s.
time history of solid-phase temperature of the fuel particle due to accumulated heat absorbed (positive value) or released (negative value) through convective heat transfer Qconv,s between gas and solid and radiative heat transfer Qrad,s. Accumulated energy is calculated by integrating energy transfer rate over the burning time as Q(t) = t ∫0 q ̇ (t′) dt′, where q ̇ (t′) is the heat transfer rate between solid phase and gas phase due to convection or radiation. For s/D = 0.5, the pyrolysis gases are released at the probe point by t≈30 s. This is indicated by the increase in solid-phase temperature to 500 K in Fig. 9(a). The solid-phase temperature increases further due to the heat released by gas-phase combustion. The solid-phase temperature rises slowly from t≈30 s to t≈37 s. During this time, heat is absorbed by the solid fuel particle by radiation from the gaseous flames which is indicated by the positive values of Qrad,s shown in Fig. 9(b). As discussed above, the availability of sufficient oxygen allows the pyrolysis gases to undergo gas-phase combustion rapidly and the heat feedback from the gaseous flames thus formed increases the solidphase temperature rapidly for s/D = 0.5. When the temperature of the particle reaches 673 K, it undergoes char oxidation, releasing a large amount of energy in the form of radiation. This is seen in the rapid fall of Qrad,s in Fig. 9(b) and rapid rise in the value of Qmass,s at t≈37 s, since char oxidation is an exothermic process. Consequently, the solid-phase temperature increases dramatically due to heat release via char oxidation. Convective heat transfer (Qconv,s) remains negative which implies a cooling effect on the solid particle. This cooling effect results in a drop in solid-phase temperature after t≈37 s. The rise in solid-phase temperature of the solid particle for s/D = 1.0 takes longer than for s/D = 0.5. This is due to increased distance of the probe point from the flames originating in the upstream shrub. The accumulated heat due to radiation from the flames takes a longer time to reach its peak value to initiate heat release due to char oxidation. Thus, the time taken for burnout is higher as seen in Fig. 8(a). For s/D = 0, heat is absorbed by the solid particle mainly by convection, which is indicated by the positive values of Qconv,s in Fig. 9(b). This implies a
mass is due to the availability of oxygen, as shown in Fig. 8(c) for the pyrolysis gas to undergo gas-phase combustion and subsequently increase the solid phase temperature, allowing the solid fuel to undergo rapid thermal degradation. A similar trend was observed for the mass evolution of char, where the availability of sufficient oxygen leads to rapid oxidation of char leading to increased mass loss rate of the downstream shrub at s/D = 0.5. However, at s/D = 0, a lack of availability of oxygen was observed in the downstream shrub leading to slower mass loss rates. This lack of availability of oxygen is due to the presence of the upstream shrubs blocking the entrainment of air into the downstream shrub.
3.3. Heat feedback into shrubs The burnout time of a shrub is affected by how fast the solid fuel undergoes thermal decomposition. In order to undergo thermal decomposition, the solid fuel must lose moisture through evaporation, undergo pyrolysis when the solid-phase temperature reaches 460 K and subsequently undergo char oxidation at temperatures higher than 673 K [26]. The evolution of solid-phase temperature is controlled by the convective and radiation heat transfer rates between solid and gas phase. In order to understand the trends observed in burnout times for the downstream shrub, a detailed analysis of the factors affecting burnout times was performed. A solid particle located in the downstream shrub for the larger shrub case at U∞ = 2 m/s was selected and the time history of solid-phase temperature and heat transfer rates at this point was examined. The location of the point is such that it is closer to the upstream shrubs and situated within the flame interaction region. The flame interaction region is defined as the region where the edges of the three shrubs are closest to each other, increasing the possibility of flame merging. Three separation distances are considered for the analysis: s/D = 0, s/D = 0.5 (separation distance with minimum burnout time for downstream shrub) and s/D =1.0. Fig. 9(a) shows the 7
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Fig. 9. Time history of (a) solid-phase temperature, Ts (in K), and (b) accumulated heat – convective, Qconv,s and radiative, Qrad,s (in MJ/m3) at a probe point in the downstream shrub for larger shrubs at U∞ = 2 m/s. The probe point is located at (x,y,z) =(1.39 m, 1.0 m, 2.0 m) for s/D = 0, (1.74 m, 1.0 m, 2.0 m) for s/D = 0.5, and (2.08 m, 1.0 m, 2.0 m) for s/D = 1.
flames due to their proximity to one another. However, it was found that the burnout time for the downstream shrub reduced with an increase in separation distance to reach a minimum and then increased with further increase in separation distance. The burnout times of the downstream shrub was found to be higher than the upstream shrub at zero separation distance. This trend was observed for all wind speeds and shrub sizes investigated. The slower burnout time observed in the downstream shrub for zero separation distance was attributed to the lack of oxygen available for efficient combustion. This is due to the presence of upstream shrubs and their combustion products restricting the flow of oxygen into the downstream shrub. For the case with the minimum burnout time for the downstream shrub, the heat transfer into the downstream shrub and air supply are at the optimal level to facilitate faster burnout of the shrub. The heat feedback into the downstream shrub at this separation distance was dominated by radiation from the flames of the upstream shrubs. As the shrub separation distance increases, the heat feedback from the flames of upstream shrubs into the downstream shrub decreases, causing the burnout times to increase. Thus, the burnout time of a shrub placed downwind of two burning shrubs under the influence of wind depends on the balance of heat feedback into the shrub and the oxygen available for efficient combustion.
long heating period where the gas-phase temperature is higher than solid-phase temperature, as char oxidation has not taken place to release heat via radiation and result in rapid mass loss of the particle. Despite the continuous heating of the solid particle in shrub for zero shrub separation distance, a greater time for char oxidation results in higher burnout time for the downstream shrub. F or s/D = 1.0, although there is enough air supply to the downstream shrub due to its increased separation distance from the neighboring shrubs, the heat transfer takes longer to heat the solid fuel to its ignition temperature resulting in higher burnout times than for s/D = 0.5.
4. Conclusions and future work The effects of shrub size, shrub separation distance and wind on the burning behavior of multiple chamise shrubs were analyzed using a multiphase physics-based model. The shrub considered for this study was chamise. Two shrub sizes with different physical dimensions and initial mass, 0.6 m in diameter, 1 m in height and 0.57 kg; and 0.8 m in diameter, 1.2 m in height and 1.15 kg, were considered. Two wind speeds of 1 and 2 m/s were considered. The multiple shrub arrangement considered consisted of three identical shrubs placed at the vertices of an equilateral triangle, with two shrubs placed upwind of the third shrub. Five shrub separation distances were considered, with the shrub separation distance being defined in terms of the maximum diameter of the shrub. The shrubs were ignited simultaneously with the aid of separate surface fuel beds. The results from the three-shrub arrangement cases were compared with an isolated shrub burn. It was found that the size of the shrub has an impact on the flame front propagation within the crown fuel matrix. A backing-like fire was observed in the smaller shrubs for higher wind speed for both isolated shrubs and individual shrubs in the three-shrub arrangement for all separation distances considered. The backing-like fire was due to the larger flame tilt angles from the surface fuel at higher wind speeds which resulted in the flames igniting the downwind trailing edge of the smaller shrubs. As a result of the backing-like fire, longer burnout times were recorded in the smaller shrubs at higher wind speed. However, for larger shrubs, the surface fuel flames ignite the base of the shrub, as the base of the larger shrubs is larger in diameter than the smaller shrubs. This reduces the possibility of a backing fire in the larger shrubs. For the larger shrubs, it was observed that higher wind speed leads to faster burnout times. It must be noted that the observations reported may be strongly impacted by the nature of surface ignition. Both the mass of the surface fuel and its burnout time will have an influence on results especially at higher wind speeds. It was found that the burnout times of upstream shrubs increased with an increase in separation distance for all wind speeds and shrub sizes considered. The faster burnout times of upstream shrubs at zero separation distance was due to the increased heat feedback from the
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