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Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire
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Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire Xiaodong Xie a, Naian Liu a,∗, Jiao Lei a, Yanlong Shan b, Linhe Zhang a, Haixiang Chen a, Xieshang Yuan a, Han Li a a State
Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, PR China b Forestry College, Beihua University, 132013 Jilin City, Jilin, PR China Received 4 December 2015; accepted 24 July 2016 Available online xxx
Abstract Eruptive fire is a typical extreme fire behavior in wildland fuels, characterized by a sudden acceleration of fire spread over confined slopes in trench-like terrain (e.g. in a deep canyon). However, wildfire spread acceleration in trench configuration has received little study. This paper presents a systematic experimental study on the fire spread over a pine needle fuel bed in an inclined trench. The effects of aspect ratio (ratio of the trench side wall height to the trench width) and slope angle on the fire spread behaviors are investigated. It is indicated that flame attachment toward the fuel bed surface is induced by the combined effects of the slope and the air entrainment restriction due to the trench configuration. The flame attachment occurring at higher slopes with higher aspect ratios induces an acceleration of fire spread, causing the fire spread to undergo a rapid transition from a steady phase with lower rate of spread (ROS) to quick spread phase with much higher ROS. The fire spread acceleration induced by the flame attachment leads to remarkable enhancement of burning intensity, as verified by long flame depth and high mass loss rate during fire spread. The fuel consumption efficiency decreases almost linearly with increasing slope angle. Under higher slope angles (higher than 20◦ in this work) the flame tilting induces hot gas flow ahead of the flame front, which enhances the convective heating. When flame attachment occurs, the spatial influence range of convective heating increases sharply. It is concluded that for eruptive fire, radiative heating and convective heating play a comparable role in fuel preheating. Experimental data suggest that when flame attachment occurs the convective heating is greatly enhanced and becomes an important mechanism of fuel preheating. This is inferred to be a major potential mechanism for eruptive fire in trench configuration. © 2016 by The Combustion Institute. Published by Elsevier Inc. Keywords: Eruptive fire; Flame attachment; Trench configuration; Slope; Rate of fire spread
1. Introduction ∗
Corresponding author. Fax: +86 551 63601669. E-mail address: [email protected] (N. Liu).
Eruptive fire, also referred as blow-up in literature, is a typical extreme fire behavior characterized by a sudden change of the rate of fire spread (ROS)
http://dx.doi.org/10.1016/j.proci.2016.07.091 1540-7489 © 2016 by The Combustion Institute. Published by Elsevier Inc.
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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even when there is no change of fuel properties, meteorological or topographical conditions [1]. A great percentage of fatal accidents produced during wildland fires are ascribed to eruptive fires [2], however there have been very few systematic studies on this topic. Brown and Davis [3] defined blow-up as the transition from a low-energy to a high-energy fire, and suggested that such a transition is seldom a gradual process. In literature there are diverse interpretations on the mechanism of fire acceleration associated with fire eruption. One interpretation is based on the general flame spread theory that states that under specific conditions there is no steady state solution and flame spread can be self-acceleratory [4]. Such a self-acceleration was observed in the fire spread over a small-scale fuel bed of inclined paper [5]. However as pointed out by Viegas and Simeoni [1], the assumption that the preheat length is proportional to the flame length, which is in turn proportional to the length of the pyrolysis area, is difficult to be verified in large-scale wildfires. Viegas and Simeoni [1] indicated that eruptive fire behavior can occur in wind induced fires. Korobeinichev [6] also suggested that fire spread may undergo acceleration when the wind speed is beyond a certain critical value. Nevertheless, it is recognized that eruptive fires are more likely to occur in steep slopes and especially in deep narrow canyons [2]. One explanation is on the gas accumulation, which assumes the existence of an accumulation of unburnt products [7] or the production of Volatile Organic Compounds (VOC) [1] in deep canyons. However it is difficult to validate this assumption for wildfires occurring in open spaces. In recent years, the group of J. W. Dold proposed that flow attachment to the vegetation surface in confined slopes at and immediately ahead of the fireline is a potential cause of eruptive fire [8,9]. In their preliminary tests, an inclined fuel bed was used and two vertical walls 60 cm apart were erected along the lateral sides of the fuel bed to prevent lateral air flow [9]. This inclined fuel bed in trench configuration can be regarded as an analog of confined slopes in deep canyons. The authors estimated the positions of the front and rear of the overall visible flame from video images, and the results suggested that fire acceleration can occur under higher slope angles. The air flow ahead of the flame front was simply observed by injecting a stream of soap bubbles into the air. However, no quantitative measurements were conducted to investigate the physical association of eruptive behavior with the flow attachment. In fact the trench configuration used by Dold and Zinoviev [9] was also used by the group of D. D. Drysdale and others for the investigation of the King’s Cross Fire in 1987 in London. That fire occurred in an escalator and the exclusion of lateral entrainment was considered as the essential cause [10]. Experiments of scale models of the escalator
trench were carried out to elucidate the mechanism of fire evolution [11]. CFD simulations indicated that the critical angle for flow/flame attachment decreases with increasing aspect ratio (defined as the ratio of the height of trench side walls to the trench width) [12]. The experimental works [13,14] mainly used gas burners to investigate the flame attachment in trench configuration. To the knowledge of the authors, there has been no systematic experimental work addressing the fire spread acceleration over wildland fuel bed with trench configuration. This study fills in this gap. In this work, we performed the experiments of fire spread over a pine needle fuel bed in an inclined trench, and the impacts of aspect ratio and slope angle on the fire spread behaviors are examined. By analyzing the experimental data, the acceleration in fire spread associated with the flame attachment is investigated, and a potential mechanism of eruptive fire is inferred. 2. Experimental All the experiments were conducted in a closed experimental hall (height: 16 m, horizontal dimensions: 9.4 m × 9.4 m) in still air. The experimental bench (Fig. 1) had a size of 6.0 m (length) × 1.8 m (width), with a fuel bed area of 6.0 m (length) × 1.0 m (width). The bench was installed on a steel supporting frame and designed to be motor-driven, so that the slope angle (α) of the bench could be adjusted from 0 to 40◦ . In each experiment two strips of metal sheeting with the same height were fixed along each side of the fuel bed, and the sheeting was painted in gray to avoid reflection of flame radiation. Four heights of the sheeting of 10 cm, 20 cm, 30 cm and 40 cm were used to generate trench configurations with different aspect ratios (A) of 0.1, 0.2, 0.3 and 0.4. For each aspect ratio A, slope angles of 0◦ , 10◦ , 20◦ , 25◦ and 30◦ were used. There were five square openings (42 cm × 42 cm) at the bottom of the fuel bed along the centerline of the fuel bed with a spacing of 1 m. Five separate fireproof boards were inlaid in the openings, and one load cell was installed beneath each board to measure the mass loss. The output signal of each load cell was calibrated under different slope angles. The dead pine needles (Pinus elliotti) were used as fuels, with a uniform fuel load of 0.6 kgm − 2 of dry basis. The fuel bed was 6 cm in depth. In tests the fuel bed length was 580 cm for α ≥ 10◦ , while it was 380 cm for α = 0◦ to avoid unnecessarily long fire durations. The fuel moisture contents (measured just before ignition) were 8.6 ± 2.2%, and the temperature and relative humidity were 28.3 ± 1.3°C and 75.4 ± 7.3% respectively. The fire spread was initiated from a line ignition at the bottom edge of the fuel bed using a cotton line soaked in alcohol. For each experiment a separate
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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Fig. 1. Schematic of the experimental measurement.
reference test was conducted at the same time on a small table with a size of 1.0 m × 1.0 m under zero-slope condition with no restriction of lateral air entrainment. The type K (chromel-alumel) thermocouples (with a bead diameter of 0.5 mm and a wire diameter of 80 μm) were used to measure the gas temperatures over the fuel bed. All the thermocouples were installed just over the fuel bed, along its central axis, with a spacing of nearly 20 cm. Five calibrated bi-directional Pitot tubes (series 160S produced by Dwyer Instruments, Inc.) were positioned just above the fuel bed, to measure the flow speed along the fuel bed. A total heat flux meter (64-5-18 by Medtherm Inc., range: 0– 50 kWm − 2 , sensitivity: 0.1662 mVkW − 1 m − 2 , view angle: 180°) and a radiative heat flux meter (64p5-22 by Medtherm Inc., range: 0–50 kWm − 2 , sensitivity: 0.2878 mVkW − 1 m − 2 , view angle: 150°) of water-cooled type were positioned 10 cm past the fuel bed end. The sensors were calibrated by the manufacturer. The top surfaces of both heat flux sensors, facing upwards, were positioned flush with the top surface of the fuel bed. A NI SCXI-1600 data logger was used for data recording, with a data acquisition frequency of 100 Hz. Two DV cameras were used to monitor the side and top views of fire spread.
3. Results and discussion 3.1. Fire spread acceleration
Fig. 2. Data of flame front position versus time (t = 0 denotes the moment when the flame front reaches the first thermocouple).
The rate of spread (R, cm s − 1 ) was obtained from the derivative of the curve of ‘flame front position v. time’. The flame front position was determined by identifying the moment when the temperature measured by the thermocouples reached 300 °C (an estimation of the ignition temperature). For A = 0.1, our previous work [15] indicated that the fire spread was steady under different slope angles, which is consistent with the data of this work. However for higher aspect ratios (A = 0.2, 0.3, 0.4), the data in this work reveal sudden change of ROS under higher slope angles. An example of A = 0.3 is presented in Fig. 2(a). As shown, when
α ≤ 20◦ , the linear regression on the data of ‘flame front position v. time’ achieves fairly high correlation coefficients (R2 > 0.99), which suggests that the fire spread is in steady state. When α = 25◦ , the square of correlation coefficient slightly decreases to 0.961. When α = 30◦ , however, the square of correlation coefficient sharply decreases to 0.732. This suggests that within α = 25 − −30◦ there is significant change of burning behavior for the spreading flame front, and the fire spread becomes unsteady. Figure 2(b) presents the data of ‘flame front position v. time’ for α = 30◦ under three aspect
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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Fig. 4. Typical experimental photos for A = 0.2.
Fig. 3. Rate of fire spread under different aspect ratios and different slope angles.
ratios of A ≥ 0.2. The case of A = 0.1 is not shown because the fire spread was steady in global sense and the time period was much larger than other cases. The data indicate that for α = 30◦ and A ≥ 0.2 the fire spread process involves two phases: a development phase with relatively low ROS, and the subsequent quick spread phase. The transition periods between the two phases are very short. Significant fluctuation of flame front was observed in the second phase. Such a sudden acceleration of fire spread denotes that eruptive fire occurs under conditions of α = 30◦ and A ≥ 0.2. Figure 3 presents the ROS with different aspect ratios and slope angles, in which the data of α = 30◦ and A ≥ 0.2 are calculated by the linear regressions on the curves of ‘flame front position v. time’ corresponding to the quick spread phase. When A = 0.1, the ROS increases slowly with increasing slope angle, however when A ≥ 0.2, there is a sudden increase of ROS between α = 25◦ and α = 30◦ . When the slope angle α ≤ 25◦ , the ROS data under different aspect ratios differ little from each other, which suggests that the aspect ratio has minor effect on the ROS. However when α = 30◦ , the ROS significantly depends on the aspect ratio, and especially the ROS for A = 0.1 is much lower than the ROS under higher aspect ratios (A ≥ 0.2). An important result is that under α = 30◦ the ROS shows nonmonotonic variation with the aspect ratio, which potentially suggests that the trench configuration has a nonlinear effect on the restriction of the lateral air entrainment and fire spread behavior. The results of ROS are consistent with the experimental observation of flame depth. Figure 4 presents some typical experimental photos for A = 0.2 under different slope angles. As shown, the flame front was linear due to the restriction of lateral air entrainment. The flame depth is observed to increase slowly within α = 0−25◦ , while it shows a remarkable increase when α = 30◦ . Figure 5 shows the flame depth calculated by the flame residence
Fig. 5. Calculated flame depth and some typical photos of the flame fronts.
time (33.70 ± 3.80 s in all tests, evaluated as the time periods when the measured temperature exceeded 300 °C) multiplied by ROS, for which the value for α=30◦ refers to the quick spread phase. As shown, the variation of the flame depth with slope is similar with that of ROS shown in Fig. 3. It can be suggested that the fire spread acceleration under higher aspect ratios and higher slope angles is closely associated with flame attachment to the fuel surface at and immediately ahead of the fireline. Figure 5 presents some typical photos of flame fronts which show the flame tilting under non-zero slope angles. The fuel bed surface is parallel to the horizontal plane for all photos. For A = 0.1, the flame front was almost vertical for α = 0◦ , and then with increase of slope angle up to α = 30◦ , the flame gradually tilted toward the fuel bed. Note for all the slope angles the flame front did not attach the fuel bed under A = 0.1. Comparatively, flame attachment was observed for α = 30◦ and A = 0.2 or higher aspect ratios. By contrast between Fig. 3 and Fig. 5, it can be inferred that flame attachment plays a key role in the sudden increases of ROS and flame depth under higher aspect ratios and higher slope angles.
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suggests marked convective heating ahead of the flame front. Remarkable convective heating is also found for α = 30◦ with A = 0.2 or A = 0.4. Comparatively, for α = 30◦ and A = 0.1, the total and radiative heat fluxes differ little from each other. It is indicated from the heat flux data that for steady fire spread, radiation is the dominant mechanism for fuel preheating, however when there is fire spread acceleration associated with eruptive fire (α = 30◦ , A ≥ 0.2), the radiative heating and convective heating play a comparable effect on fuel preheating. As shown in Fig. 7, for α = 30◦ and A = 0.3, the peak of convective heat flux is 11.8kWm − 2 , which is comparative to the peak of radiative heat flux of 11.3kWm − 2 . Fig. 6. Mass loss rate and fuel consumption efficiency in fire spread.
3.4. Flow speed 3.2. Mass loss −1
The mass loss rate (m’, gs ) was obtained from the mass loss data during the periods when the flame front passed the weighing boards. The data of m’ for α = 30◦ and A ≥ 0.2 were obtained from the mass loss data in the quick spread phase. As shown in Fig. 6, when α ≤ 25◦ , the mass loss rates under different aspect ratios show minor differences, and normally the mass loss rate slowly increases with increasing slope angle. It is of importance to see that when α = 30◦ , the flame attachment for A ≥ 0.2 is accompanied by significant increase of mass loss rate, which suggests that flame attachment induces significant enhancement of burning intensity. For A ≥ 0.2, the mass loss rate increases with increasing aspect ratio. The fuel consumption efficiency (η) shown in Fig. 6 denotes the fraction of the fuel mass consumed in the period when the flame front passes the weighing boards. All the values of η decrease almost linearly with increasing slope angle, and it is interesting to note that such a variation trend is not influenced by the flame attachment under α = 30◦ and A ≥ 0.2. 3.3. Heat flux The results in the above sections clearly indicate that the fire spread acceleration is closely related to the flame attachment under higher aspect ratios and higher slope angles. The fire spread acceleration implies that the heat transfer from the flame front to the unburnt fuels is significantly enhanced. This point can be verified from the heat fluxes measured by the total and radiative heat flux meters located 10 cm past the end of the fuel bed. Figure 7 presents the heat flux data under A = 0.3. As shown, for slope angle α ≤ 25◦ , the total and radiative heat fluxes differ slightly from each other. When α = 30◦ , the radiative heat flux is only slightly higher than the value for α = 25◦ , however, the peak of total heat flux is much higher than that of α = 25◦ , which
The effect of flame attachment on fire spread acceleration can also be derived from the flow speed measurements. Under non-zero slope conditions, the flame fronts deviate from the vertical direction and tilt toward the fuel bed, caused by the asymmetric upslope and downslope inflows around the flame front. In general, the flame tilting naturally promotes the radiant heat transfer from the flame to the fuel surface and enhances the flame burning. If the fuel bed is in an inclined trench with higher aspect ratio, the flame attachment will further significantly enhance the hot gas flow ahead of the flame front. Figure 8 presents the flow speed (U, ms − 1 ) above the fuel bed for A = 0.2 measured by the fourth Pitot tube (see Fig. 1), for which the fire spread for α = 30◦ was in the quick spread phase. Air density change is considered by the temperatures measured using thermocouples combined with the pitot tubes. The speed data are smoothed by an algorithm of 20-point FastFourier-Transform (FFT). Positive values represent the gas flow in the forward direction of fire spread (upslope direction). The flame front reaches and leaves the Pitot tube respectively on the moments of t1 and t2 , which are extracted from the temperature data, and the corresponding flow speeds are denoted as U1 and U2 . For α = 0◦ , the speed decreases with time to negative values before the arrival of the flame front. The negative value of U1 and positive value of U2 suggest normal air entrainment around the flame front. For α = 20◦ , the speed U1 becomes to be positive, which suggests that hot gases flow from the flame front toward the upslope direction. This may be associated with flame puffing at the top of the fuel bed [16]. In this case, air entrainment mainly exists behind the flame front. For α = 30◦ , both speeds U1 and U2 are positive, which suggests significant gas flow induced by the flame attachment. Figure 8 also presents the measured speed U1 under different aspect ratios and slope angles, which shows that for
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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Fig. 7. Measured total heat flux and radiative heat flux in tests.
Fig. 8. Measured flow speed in tests.
each aspect ratio, the speed U1 increases almost linearly with increasing slope angle. The convective heating effect can be examined by the flow speed ahead of the flame front. In Fig. 9, we present the measured flow speed 10 cm ahead of the flame front. For α ≤ 20◦ , the speed U is negative, which suggests convective cooling, while the speed U sharply increases to positive values when α ≥ 25◦ . Recall that the heat flux meters were located 10 cm away from the end of the fuel bed, while the total heat flux is slightly higher than the radia-
tive heat flux when α ≤ 20◦ . The inconsistency between the speed data and the heat flux data is considered to be caused by the difference of the view angles of the two heat flux meters (150° for radiative heat flux meter and 180° for total heat flux meter). What is of most importance is the fact that speed U undergoes sharp increases of for α ≥ 25◦ , which clearly suggests significant convective heating under higher slope angles for all the aspect ratios. This is consistent with the findings from heat flux data as suggested in Fig. 7.
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Fig. 9. Measured flow speed at 10 cm ahead of the flame front in tests.
Fig. 11. Relationship between R’ − 1 and U’.
Fig. 10. Calculated convective heating range v. slope.
the dominant mechanism for fuel preheating, while heat convection becomes more significant with increasing slope. For eruptive fire, the fuel preheating is controlled by both radiative and convective heating, and especially when flame attachment occurs, the convective heating is greatly enhanced and has a comparable effect with radiative heating. The speed U1 represents the speed of the flow immediately ahead of the flame fronts, and thus the corresponding flow can be regarded as the local ambient wind around the flame front. An empirical relationship between ROS and wind speed was developed by Viegas [17] in the form of R = 1 + a1U b1 , here R’ and U’ denote the non-dimensional ROS and wind speed respectively. The coefficients a1 and b1 depend on the fuel properties. In this work, the non-dimensional ROS is calculated as R = R/R0 , here R0 is the ROS of the linear flame front under zero-slope condition with no lateral air entrainment restriction. The non-dimensional wind speed U = U1 /U0 , here U0 = 1ms − 1 . As shown in Fig. 11, for each aspect ratio, a fairly good linear regression is achieved between ln (R’ − 1) and U’. Further, from Fig. 8 it is shown that the speed U1 approximately depends on the slope angle α linearly. Therefore the R’ also varies exponentially with α. The exponential relationship between ROS and U1 is induced by the forward gas flow with greatly enhanced convective heating. This suggests that when dealing with canyon-shaped fire, firefighters should pay attention to the forward gas flow ahead of the flame front. If this flow exists, it could be a very dangerous signal for acceleration of fire spread.
3.5. Convective heating spatial range The convective heating takes effect within a certain spatial range ahead of the flame front, and this spatial range can be calculated by the time period with positive values of the speed U multiplied by ROS. Figure 10 presents the calculated convective heating spatial ranges for different aspect ratios under α ≥ 20◦ . Note convective heating was not observed for α ≤ 10◦ . The results indicate that the heating spatial range increases slightly within α = 20−25◦ , while when α = 30◦ , the heating spatial range increases sharply for A ≥ 0.2, which is much higher than that for A = 0.1. As indicated, the variation of heating spatial range shown in Fig. 10 is consistent with the variations of ROS (Fig. 3), flame depth (Fig. 5) and mass loss rate (Fig. 6). All the results reveal the difference of fuel preheating mechanism between normal steady fire spread and eruptive fire. For lower slopes with steady fire spread in global sense, heat radiation is
4. Conclusions This paper presents an experimental study on fire spread over a pine needle fuel bed in an inclined trench. The effects of aspect ratio and slope angle
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on the flame burning behaviors are investigated. The major results are summarized as follows. (1) For the fuel bed within trench configuration, flame attachment toward the fuel bed surface is induced by the combined effects of the slope and the air entrainment restriction. In this work, flame attachment occurs within angle slopes of 25−30◦ for aspect ratio higher than 0.2. Under lower slope angles, flame attachment does not occur and the fire spread is steady in global sense. When flame attachment occurs, an acceleration of fire spread will be induced, causing the fire spread to undergo a rapid transition from a steady spread phase with lower ROS to quick spread phase with much higher ROS. Such a sharp acceleration is associated with eruptive fire. (2) The fire spread acceleration by the flame attachment leads to remarkable enhancement of burning intensity, as verified by long flame depth and high mass loss rate in fire spread. The fuel consumption efficiency decreases almost linearly with increasing slope angle. Under higher slope angles (higher than 20◦ in this work) the flame tilting induces hot gas flow ahead of the flame front, which enhances the convective heating. When flame attachment occurs, the spatial influence range of convective heating increases sharply. (3) For lower slopes with steady fire spread, radiative heating is the dominant mechanism for fuel preheating, while convective heating becomes more significant with increasing slope. For eruptive fire, when flame attachment occurs the convective heating is greatly enhanced and becomes an important mechanism of fuel preheating, with a comparable effect with radiative heating. This is inferred to be a major potential mechanism for eruptive fire. Acknowledgments
(No. 51476156), National Science Foundation for Distinguished Young Scholars of China and the National Key Research and Development Plan (No. 2016YFC0800101). This work was also supported by the Fundamental Research Funds for the Central Universities (Nos. WK2320000036 and WK2320000037). Xiaodong Xie was supported by the China Postdoctoral Science Foundation (No. 2015M571945). References [1] D.X. Viegas, A. Simeoni, Fire Technol. 47 (2011) 303–320. [2] D.X. Viegas, L.P. Pita, Int. J. Wildland Fire 13 (2004) 253–274. [3] A.A. Brown, K.P. Davis, Forest Fire: Control and Use, second ed., Mcgraw-Hill, New York, 1973, p. 557. [4] J.G. Quintiere, et al., SFPE Handbook of Fire Protection Engineering, third ed., Society of Fire Protection Engineers, Maryland, 2002, pp. 2–246. [5] T. Hirano, S.E. Noreikis, T.E. Waterman, Combust. Flame 22 (1974) 353–363. [6] O.P. Korobeinichev, A.G. Tereshchenko, A.A. Paletsky, et al., in: 7th International Conference on Forest Fire Research, Coimbra, 2014. [7] J.W. Dold, R.O. Weber, M. Gill, R. McRae, N. Cooper, in: 5th Asia-Pacific Conference on Combustion, Adelaide, 2005. [8] J.W. Dold, in: 6th International Conference on Forest Fire Research, Coimbra, 2010. [9] J.W. Dold, A. Zinoviev, Combust. Theory Modell. 13 (2009) 763–793. [10] G. Cox, R. Chitty, S. Kumar, Fire Safety J. 15 (1989) 103–106. [11] D.D. Drysdale, A.J.R. Macmillan, D. Shilitto, Fire Safety J. 18 (1992) 75–82. [12] P.J. Woodburn, D.D. Drysdale, Fire Safety J. 31 (1998) 143–164. [13] G.T. Atkinson, D.D. Drysdale, Y. Wu, Fire Safety J. 25 (1995) 141–158. [14] D.A. Smith, Fire Safety J. 18 (1992) 231–244. [15] N.A. Liu, J.M. Wu, H.X. Chen, et al., Proc. Combust. Inst. 35 (2015) 2691–2698. [16] J.L. Dupuy, J. Maréchal, Int. J. Wildland Fire 20 (2011) 289–307. [17] D.X. Viegas, Int. J. Wildland Fire 15 (2006) 169–177.
This work was sponsored by the National Natural Science Foundation of China
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire Xiaodong Xie a, Naian Liu a,∗, Jiao Lei a, Yanlong Shan b, Linhe Zhang a, Haixiang Chen a, Xieshang Yuan a, Han Li a a State
Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, PR China b Forestry College, Beihua University, 132013 Jilin City, Jilin, PR China Received 4 December 2015; accepted 24 July 2016 Available online xxx
Abstract Eruptive fire is a typical extreme fire behavior in wildland fuels, characterized by a sudden acceleration of fire spread over confined slopes in trench-like terrain (e.g. in a deep canyon). However, wildfire spread acceleration in trench configuration has received little study. This paper presents a systematic experimental study on the fire spread over a pine needle fuel bed in an inclined trench. The effects of aspect ratio (ratio of the trench side wall height to the trench width) and slope angle on the fire spread behaviors are investigated. It is indicated that flame attachment toward the fuel bed surface is induced by the combined effects of the slope and the air entrainment restriction due to the trench configuration. The flame attachment occurring at higher slopes with higher aspect ratios induces an acceleration of fire spread, causing the fire spread to undergo a rapid transition from a steady phase with lower rate of spread (ROS) to quick spread phase with much higher ROS. The fire spread acceleration induced by the flame attachment leads to remarkable enhancement of burning intensity, as verified by long flame depth and high mass loss rate during fire spread. The fuel consumption efficiency decreases almost linearly with increasing slope angle. Under higher slope angles (higher than 20◦ in this work) the flame tilting induces hot gas flow ahead of the flame front, which enhances the convective heating. When flame attachment occurs, the spatial influence range of convective heating increases sharply. It is concluded that for eruptive fire, radiative heating and convective heating play a comparable role in fuel preheating. Experimental data suggest that when flame attachment occurs the convective heating is greatly enhanced and becomes an important mechanism of fuel preheating. This is inferred to be a major potential mechanism for eruptive fire in trench configuration. © 2016 by The Combustion Institute. Published by Elsevier Inc. Keywords: Eruptive fire; Flame attachment; Trench configuration; Slope; Rate of fire spread
1. Introduction ∗
Corresponding author. Fax: +86 551 63601669. E-mail address: [email protected] (N. Liu).
Eruptive fire, also referred as blow-up in literature, is a typical extreme fire behavior characterized by a sudden change of the rate of fire spread (ROS)
http://dx.doi.org/10.1016/j.proci.2016.07.091 1540-7489 © 2016 by The Combustion Institute. Published by Elsevier Inc.
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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even when there is no change of fuel properties, meteorological or topographical conditions [1]. A great percentage of fatal accidents produced during wildland fires are ascribed to eruptive fires [2], however there have been very few systematic studies on this topic. Brown and Davis [3] defined blow-up as the transition from a low-energy to a high-energy fire, and suggested that such a transition is seldom a gradual process. In literature there are diverse interpretations on the mechanism of fire acceleration associated with fire eruption. One interpretation is based on the general flame spread theory that states that under specific conditions there is no steady state solution and flame spread can be self-acceleratory [4]. Such a self-acceleration was observed in the fire spread over a small-scale fuel bed of inclined paper [5]. However as pointed out by Viegas and Simeoni [1], the assumption that the preheat length is proportional to the flame length, which is in turn proportional to the length of the pyrolysis area, is difficult to be verified in large-scale wildfires. Viegas and Simeoni [1] indicated that eruptive fire behavior can occur in wind induced fires. Korobeinichev [6] also suggested that fire spread may undergo acceleration when the wind speed is beyond a certain critical value. Nevertheless, it is recognized that eruptive fires are more likely to occur in steep slopes and especially in deep narrow canyons [2]. One explanation is on the gas accumulation, which assumes the existence of an accumulation of unburnt products [7] or the production of Volatile Organic Compounds (VOC) [1] in deep canyons. However it is difficult to validate this assumption for wildfires occurring in open spaces. In recent years, the group of J. W. Dold proposed that flow attachment to the vegetation surface in confined slopes at and immediately ahead of the fireline is a potential cause of eruptive fire [8,9]. In their preliminary tests, an inclined fuel bed was used and two vertical walls 60 cm apart were erected along the lateral sides of the fuel bed to prevent lateral air flow [9]. This inclined fuel bed in trench configuration can be regarded as an analog of confined slopes in deep canyons. The authors estimated the positions of the front and rear of the overall visible flame from video images, and the results suggested that fire acceleration can occur under higher slope angles. The air flow ahead of the flame front was simply observed by injecting a stream of soap bubbles into the air. However, no quantitative measurements were conducted to investigate the physical association of eruptive behavior with the flow attachment. In fact the trench configuration used by Dold and Zinoviev [9] was also used by the group of D. D. Drysdale and others for the investigation of the King’s Cross Fire in 1987 in London. That fire occurred in an escalator and the exclusion of lateral entrainment was considered as the essential cause [10]. Experiments of scale models of the escalator
trench were carried out to elucidate the mechanism of fire evolution [11]. CFD simulations indicated that the critical angle for flow/flame attachment decreases with increasing aspect ratio (defined as the ratio of the height of trench side walls to the trench width) [12]. The experimental works [13,14] mainly used gas burners to investigate the flame attachment in trench configuration. To the knowledge of the authors, there has been no systematic experimental work addressing the fire spread acceleration over wildland fuel bed with trench configuration. This study fills in this gap. In this work, we performed the experiments of fire spread over a pine needle fuel bed in an inclined trench, and the impacts of aspect ratio and slope angle on the fire spread behaviors are examined. By analyzing the experimental data, the acceleration in fire spread associated with the flame attachment is investigated, and a potential mechanism of eruptive fire is inferred. 2. Experimental All the experiments were conducted in a closed experimental hall (height: 16 m, horizontal dimensions: 9.4 m × 9.4 m) in still air. The experimental bench (Fig. 1) had a size of 6.0 m (length) × 1.8 m (width), with a fuel bed area of 6.0 m (length) × 1.0 m (width). The bench was installed on a steel supporting frame and designed to be motor-driven, so that the slope angle (α) of the bench could be adjusted from 0 to 40◦ . In each experiment two strips of metal sheeting with the same height were fixed along each side of the fuel bed, and the sheeting was painted in gray to avoid reflection of flame radiation. Four heights of the sheeting of 10 cm, 20 cm, 30 cm and 40 cm were used to generate trench configurations with different aspect ratios (A) of 0.1, 0.2, 0.3 and 0.4. For each aspect ratio A, slope angles of 0◦ , 10◦ , 20◦ , 25◦ and 30◦ were used. There were five square openings (42 cm × 42 cm) at the bottom of the fuel bed along the centerline of the fuel bed with a spacing of 1 m. Five separate fireproof boards were inlaid in the openings, and one load cell was installed beneath each board to measure the mass loss. The output signal of each load cell was calibrated under different slope angles. The dead pine needles (Pinus elliotti) were used as fuels, with a uniform fuel load of 0.6 kgm − 2 of dry basis. The fuel bed was 6 cm in depth. In tests the fuel bed length was 580 cm for α ≥ 10◦ , while it was 380 cm for α = 0◦ to avoid unnecessarily long fire durations. The fuel moisture contents (measured just before ignition) were 8.6 ± 2.2%, and the temperature and relative humidity were 28.3 ± 1.3°C and 75.4 ± 7.3% respectively. The fire spread was initiated from a line ignition at the bottom edge of the fuel bed using a cotton line soaked in alcohol. For each experiment a separate
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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Fig. 1. Schematic of the experimental measurement.
reference test was conducted at the same time on a small table with a size of 1.0 m × 1.0 m under zero-slope condition with no restriction of lateral air entrainment. The type K (chromel-alumel) thermocouples (with a bead diameter of 0.5 mm and a wire diameter of 80 μm) were used to measure the gas temperatures over the fuel bed. All the thermocouples were installed just over the fuel bed, along its central axis, with a spacing of nearly 20 cm. Five calibrated bi-directional Pitot tubes (series 160S produced by Dwyer Instruments, Inc.) were positioned just above the fuel bed, to measure the flow speed along the fuel bed. A total heat flux meter (64-5-18 by Medtherm Inc., range: 0– 50 kWm − 2 , sensitivity: 0.1662 mVkW − 1 m − 2 , view angle: 180°) and a radiative heat flux meter (64p5-22 by Medtherm Inc., range: 0–50 kWm − 2 , sensitivity: 0.2878 mVkW − 1 m − 2 , view angle: 150°) of water-cooled type were positioned 10 cm past the fuel bed end. The sensors were calibrated by the manufacturer. The top surfaces of both heat flux sensors, facing upwards, were positioned flush with the top surface of the fuel bed. A NI SCXI-1600 data logger was used for data recording, with a data acquisition frequency of 100 Hz. Two DV cameras were used to monitor the side and top views of fire spread.
3. Results and discussion 3.1. Fire spread acceleration
Fig. 2. Data of flame front position versus time (t = 0 denotes the moment when the flame front reaches the first thermocouple).
The rate of spread (R, cm s − 1 ) was obtained from the derivative of the curve of ‘flame front position v. time’. The flame front position was determined by identifying the moment when the temperature measured by the thermocouples reached 300 °C (an estimation of the ignition temperature). For A = 0.1, our previous work [15] indicated that the fire spread was steady under different slope angles, which is consistent with the data of this work. However for higher aspect ratios (A = 0.2, 0.3, 0.4), the data in this work reveal sudden change of ROS under higher slope angles. An example of A = 0.3 is presented in Fig. 2(a). As shown, when
α ≤ 20◦ , the linear regression on the data of ‘flame front position v. time’ achieves fairly high correlation coefficients (R2 > 0.99), which suggests that the fire spread is in steady state. When α = 25◦ , the square of correlation coefficient slightly decreases to 0.961. When α = 30◦ , however, the square of correlation coefficient sharply decreases to 0.732. This suggests that within α = 25 − −30◦ there is significant change of burning behavior for the spreading flame front, and the fire spread becomes unsteady. Figure 2(b) presents the data of ‘flame front position v. time’ for α = 30◦ under three aspect
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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Fig. 4. Typical experimental photos for A = 0.2.
Fig. 3. Rate of fire spread under different aspect ratios and different slope angles.
ratios of A ≥ 0.2. The case of A = 0.1 is not shown because the fire spread was steady in global sense and the time period was much larger than other cases. The data indicate that for α = 30◦ and A ≥ 0.2 the fire spread process involves two phases: a development phase with relatively low ROS, and the subsequent quick spread phase. The transition periods between the two phases are very short. Significant fluctuation of flame front was observed in the second phase. Such a sudden acceleration of fire spread denotes that eruptive fire occurs under conditions of α = 30◦ and A ≥ 0.2. Figure 3 presents the ROS with different aspect ratios and slope angles, in which the data of α = 30◦ and A ≥ 0.2 are calculated by the linear regressions on the curves of ‘flame front position v. time’ corresponding to the quick spread phase. When A = 0.1, the ROS increases slowly with increasing slope angle, however when A ≥ 0.2, there is a sudden increase of ROS between α = 25◦ and α = 30◦ . When the slope angle α ≤ 25◦ , the ROS data under different aspect ratios differ little from each other, which suggests that the aspect ratio has minor effect on the ROS. However when α = 30◦ , the ROS significantly depends on the aspect ratio, and especially the ROS for A = 0.1 is much lower than the ROS under higher aspect ratios (A ≥ 0.2). An important result is that under α = 30◦ the ROS shows nonmonotonic variation with the aspect ratio, which potentially suggests that the trench configuration has a nonlinear effect on the restriction of the lateral air entrainment and fire spread behavior. The results of ROS are consistent with the experimental observation of flame depth. Figure 4 presents some typical experimental photos for A = 0.2 under different slope angles. As shown, the flame front was linear due to the restriction of lateral air entrainment. The flame depth is observed to increase slowly within α = 0−25◦ , while it shows a remarkable increase when α = 30◦ . Figure 5 shows the flame depth calculated by the flame residence
Fig. 5. Calculated flame depth and some typical photos of the flame fronts.
time (33.70 ± 3.80 s in all tests, evaluated as the time periods when the measured temperature exceeded 300 °C) multiplied by ROS, for which the value for α=30◦ refers to the quick spread phase. As shown, the variation of the flame depth with slope is similar with that of ROS shown in Fig. 3. It can be suggested that the fire spread acceleration under higher aspect ratios and higher slope angles is closely associated with flame attachment to the fuel surface at and immediately ahead of the fireline. Figure 5 presents some typical photos of flame fronts which show the flame tilting under non-zero slope angles. The fuel bed surface is parallel to the horizontal plane for all photos. For A = 0.1, the flame front was almost vertical for α = 0◦ , and then with increase of slope angle up to α = 30◦ , the flame gradually tilted toward the fuel bed. Note for all the slope angles the flame front did not attach the fuel bed under A = 0.1. Comparatively, flame attachment was observed for α = 30◦ and A = 0.2 or higher aspect ratios. By contrast between Fig. 3 and Fig. 5, it can be inferred that flame attachment plays a key role in the sudden increases of ROS and flame depth under higher aspect ratios and higher slope angles.
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suggests marked convective heating ahead of the flame front. Remarkable convective heating is also found for α = 30◦ with A = 0.2 or A = 0.4. Comparatively, for α = 30◦ and A = 0.1, the total and radiative heat fluxes differ little from each other. It is indicated from the heat flux data that for steady fire spread, radiation is the dominant mechanism for fuel preheating, however when there is fire spread acceleration associated with eruptive fire (α = 30◦ , A ≥ 0.2), the radiative heating and convective heating play a comparable effect on fuel preheating. As shown in Fig. 7, for α = 30◦ and A = 0.3, the peak of convective heat flux is 11.8kWm − 2 , which is comparative to the peak of radiative heat flux of 11.3kWm − 2 . Fig. 6. Mass loss rate and fuel consumption efficiency in fire spread.
3.4. Flow speed 3.2. Mass loss −1
The mass loss rate (m’, gs ) was obtained from the mass loss data during the periods when the flame front passed the weighing boards. The data of m’ for α = 30◦ and A ≥ 0.2 were obtained from the mass loss data in the quick spread phase. As shown in Fig. 6, when α ≤ 25◦ , the mass loss rates under different aspect ratios show minor differences, and normally the mass loss rate slowly increases with increasing slope angle. It is of importance to see that when α = 30◦ , the flame attachment for A ≥ 0.2 is accompanied by significant increase of mass loss rate, which suggests that flame attachment induces significant enhancement of burning intensity. For A ≥ 0.2, the mass loss rate increases with increasing aspect ratio. The fuel consumption efficiency (η) shown in Fig. 6 denotes the fraction of the fuel mass consumed in the period when the flame front passes the weighing boards. All the values of η decrease almost linearly with increasing slope angle, and it is interesting to note that such a variation trend is not influenced by the flame attachment under α = 30◦ and A ≥ 0.2. 3.3. Heat flux The results in the above sections clearly indicate that the fire spread acceleration is closely related to the flame attachment under higher aspect ratios and higher slope angles. The fire spread acceleration implies that the heat transfer from the flame front to the unburnt fuels is significantly enhanced. This point can be verified from the heat fluxes measured by the total and radiative heat flux meters located 10 cm past the end of the fuel bed. Figure 7 presents the heat flux data under A = 0.3. As shown, for slope angle α ≤ 25◦ , the total and radiative heat fluxes differ slightly from each other. When α = 30◦ , the radiative heat flux is only slightly higher than the value for α = 25◦ , however, the peak of total heat flux is much higher than that of α = 25◦ , which
The effect of flame attachment on fire spread acceleration can also be derived from the flow speed measurements. Under non-zero slope conditions, the flame fronts deviate from the vertical direction and tilt toward the fuel bed, caused by the asymmetric upslope and downslope inflows around the flame front. In general, the flame tilting naturally promotes the radiant heat transfer from the flame to the fuel surface and enhances the flame burning. If the fuel bed is in an inclined trench with higher aspect ratio, the flame attachment will further significantly enhance the hot gas flow ahead of the flame front. Figure 8 presents the flow speed (U, ms − 1 ) above the fuel bed for A = 0.2 measured by the fourth Pitot tube (see Fig. 1), for which the fire spread for α = 30◦ was in the quick spread phase. Air density change is considered by the temperatures measured using thermocouples combined with the pitot tubes. The speed data are smoothed by an algorithm of 20-point FastFourier-Transform (FFT). Positive values represent the gas flow in the forward direction of fire spread (upslope direction). The flame front reaches and leaves the Pitot tube respectively on the moments of t1 and t2 , which are extracted from the temperature data, and the corresponding flow speeds are denoted as U1 and U2 . For α = 0◦ , the speed decreases with time to negative values before the arrival of the flame front. The negative value of U1 and positive value of U2 suggest normal air entrainment around the flame front. For α = 20◦ , the speed U1 becomes to be positive, which suggests that hot gases flow from the flame front toward the upslope direction. This may be associated with flame puffing at the top of the fuel bed [16]. In this case, air entrainment mainly exists behind the flame front. For α = 30◦ , both speeds U1 and U2 are positive, which suggests significant gas flow induced by the flame attachment. Figure 8 also presents the measured speed U1 under different aspect ratios and slope angles, which shows that for
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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Fig. 7. Measured total heat flux and radiative heat flux in tests.
Fig. 8. Measured flow speed in tests.
each aspect ratio, the speed U1 increases almost linearly with increasing slope angle. The convective heating effect can be examined by the flow speed ahead of the flame front. In Fig. 9, we present the measured flow speed 10 cm ahead of the flame front. For α ≤ 20◦ , the speed U is negative, which suggests convective cooling, while the speed U sharply increases to positive values when α ≥ 25◦ . Recall that the heat flux meters were located 10 cm away from the end of the fuel bed, while the total heat flux is slightly higher than the radia-
tive heat flux when α ≤ 20◦ . The inconsistency between the speed data and the heat flux data is considered to be caused by the difference of the view angles of the two heat flux meters (150° for radiative heat flux meter and 180° for total heat flux meter). What is of most importance is the fact that speed U undergoes sharp increases of for α ≥ 25◦ , which clearly suggests significant convective heating under higher slope angles for all the aspect ratios. This is consistent with the findings from heat flux data as suggested in Fig. 7.
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Fig. 9. Measured flow speed at 10 cm ahead of the flame front in tests.
Fig. 11. Relationship between R’ − 1 and U’.
Fig. 10. Calculated convective heating range v. slope.
the dominant mechanism for fuel preheating, while heat convection becomes more significant with increasing slope. For eruptive fire, the fuel preheating is controlled by both radiative and convective heating, and especially when flame attachment occurs, the convective heating is greatly enhanced and has a comparable effect with radiative heating. The speed U1 represents the speed of the flow immediately ahead of the flame fronts, and thus the corresponding flow can be regarded as the local ambient wind around the flame front. An empirical relationship between ROS and wind speed was developed by Viegas [17] in the form of R = 1 + a1U b1 , here R’ and U’ denote the non-dimensional ROS and wind speed respectively. The coefficients a1 and b1 depend on the fuel properties. In this work, the non-dimensional ROS is calculated as R = R/R0 , here R0 is the ROS of the linear flame front under zero-slope condition with no lateral air entrainment restriction. The non-dimensional wind speed U = U1 /U0 , here U0 = 1ms − 1 . As shown in Fig. 11, for each aspect ratio, a fairly good linear regression is achieved between ln (R’ − 1) and U’. Further, from Fig. 8 it is shown that the speed U1 approximately depends on the slope angle α linearly. Therefore the R’ also varies exponentially with α. The exponential relationship between ROS and U1 is induced by the forward gas flow with greatly enhanced convective heating. This suggests that when dealing with canyon-shaped fire, firefighters should pay attention to the forward gas flow ahead of the flame front. If this flow exists, it could be a very dangerous signal for acceleration of fire spread.
3.5. Convective heating spatial range The convective heating takes effect within a certain spatial range ahead of the flame front, and this spatial range can be calculated by the time period with positive values of the speed U multiplied by ROS. Figure 10 presents the calculated convective heating spatial ranges for different aspect ratios under α ≥ 20◦ . Note convective heating was not observed for α ≤ 10◦ . The results indicate that the heating spatial range increases slightly within α = 20−25◦ , while when α = 30◦ , the heating spatial range increases sharply for A ≥ 0.2, which is much higher than that for A = 0.1. As indicated, the variation of heating spatial range shown in Fig. 10 is consistent with the variations of ROS (Fig. 3), flame depth (Fig. 5) and mass loss rate (Fig. 6). All the results reveal the difference of fuel preheating mechanism between normal steady fire spread and eruptive fire. For lower slopes with steady fire spread in global sense, heat radiation is
4. Conclusions This paper presents an experimental study on fire spread over a pine needle fuel bed in an inclined trench. The effects of aspect ratio and slope angle
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091
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on the flame burning behaviors are investigated. The major results are summarized as follows. (1) For the fuel bed within trench configuration, flame attachment toward the fuel bed surface is induced by the combined effects of the slope and the air entrainment restriction. In this work, flame attachment occurs within angle slopes of 25−30◦ for aspect ratio higher than 0.2. Under lower slope angles, flame attachment does not occur and the fire spread is steady in global sense. When flame attachment occurs, an acceleration of fire spread will be induced, causing the fire spread to undergo a rapid transition from a steady spread phase with lower ROS to quick spread phase with much higher ROS. Such a sharp acceleration is associated with eruptive fire. (2) The fire spread acceleration by the flame attachment leads to remarkable enhancement of burning intensity, as verified by long flame depth and high mass loss rate in fire spread. The fuel consumption efficiency decreases almost linearly with increasing slope angle. Under higher slope angles (higher than 20◦ in this work) the flame tilting induces hot gas flow ahead of the flame front, which enhances the convective heating. When flame attachment occurs, the spatial influence range of convective heating increases sharply. (3) For lower slopes with steady fire spread, radiative heating is the dominant mechanism for fuel preheating, while convective heating becomes more significant with increasing slope. For eruptive fire, when flame attachment occurs the convective heating is greatly enhanced and becomes an important mechanism of fuel preheating, with a comparable effect with radiative heating. This is inferred to be a major potential mechanism for eruptive fire. Acknowledgments
(No. 51476156), National Science Foundation for Distinguished Young Scholars of China and the National Key Research and Development Plan (No. 2016YFC0800101). This work was also supported by the Fundamental Research Funds for the Central Universities (Nos. WK2320000036 and WK2320000037). Xiaodong Xie was supported by the China Postdoctoral Science Foundation (No. 2015M571945). References [1] D.X. Viegas, A. Simeoni, Fire Technol. 47 (2011) 303–320. [2] D.X. Viegas, L.P. Pita, Int. J. Wildland Fire 13 (2004) 253–274. [3] A.A. Brown, K.P. Davis, Forest Fire: Control and Use, second ed., Mcgraw-Hill, New York, 1973, p. 557. [4] J.G. Quintiere, et al., SFPE Handbook of Fire Protection Engineering, third ed., Society of Fire Protection Engineers, Maryland, 2002, pp. 2–246. [5] T. Hirano, S.E. Noreikis, T.E. Waterman, Combust. Flame 22 (1974) 353–363. [6] O.P. Korobeinichev, A.G. Tereshchenko, A.A. Paletsky, et al., in: 7th International Conference on Forest Fire Research, Coimbra, 2014. [7] J.W. Dold, R.O. Weber, M. Gill, R. McRae, N. Cooper, in: 5th Asia-Pacific Conference on Combustion, Adelaide, 2005. [8] J.W. Dold, in: 6th International Conference on Forest Fire Research, Coimbra, 2010. [9] J.W. Dold, A. Zinoviev, Combust. Theory Modell. 13 (2009) 763–793. [10] G. Cox, R. Chitty, S. Kumar, Fire Safety J. 15 (1989) 103–106. [11] D.D. Drysdale, A.J.R. Macmillan, D. Shilitto, Fire Safety J. 18 (1992) 75–82. [12] P.J. Woodburn, D.D. Drysdale, Fire Safety J. 31 (1998) 143–164. [13] G.T. Atkinson, D.D. Drysdale, Y. Wu, Fire Safety J. 25 (1995) 141–158. [14] D.A. Smith, Fire Safety J. 18 (1992) 231–244. [15] N.A. Liu, J.M. Wu, H.X. Chen, et al., Proc. Combust. Inst. 35 (2015) 2691–2698. [16] J.L. Dupuy, J. Maréchal, Int. J. Wildland Fire 20 (2011) 289–307. [17] D.X. Viegas, Int. J. Wildland Fire 15 (2006) 169–177.
This work was sponsored by the National Natural Science Foundation of China
Please cite this article as: X. Xie et al., Upslope fire spread over a pine needle fuel bed in a trench associated with eruptive fire, Proceedings of the Combustion Institute (2016), http://dx.doi.org/10.1016/j.proci.2016.07.091