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Effects of ceiling inclination on lateral flame spread over vertical Poly(methyl methacrylate) surface
Case Studies in Thermal Engineering 15 (2019) 100519
Contents lists available at ScienceDirect
Case Studies in Thermal Engineering journal homepage: http://www.elsevier.com/locate/csite
Effects of ceiling inclination on lateral flame spread over vertical Poly(methyl methacrylate) surface Fei Peng, Dimeng Lai, Yuan Zheng, Lizhong Yang * State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui, 230026, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Flame spread Ceiling inclination Pyrolysis length poly(methyl methacrylate)
A series of experiments was designed to investigate the effects of ceiling inclination on lateral flame spread over vertical poly(methyl methacrylate) (PMMA) surface. PMMA slabs with width ranged from 3 cm to 9 cm were tested at the ceiling inclination from 30� to 90� . Burning rate, flame spread rate, and flame appearance were investigated experimentally. The results suggest that in the cases of narrow PMMA slabs, the flame spread rate presents a “U” variation with the increasing ceiling inclination. But flame spread rate of wider slabs decreases with ceiling incli nation. Burning rate follows a power-law change with the sample width, which is m_ =W∝W 0:136 0:421sinðαÞ . And the exponential relationship between pyrolysis length, sample width and ceiling inclination can be given as xp ∝W 0:455 0:16sinðαÞ .
1. Introduction Understanding the dynamics of fire inception and growth on organic solid materials is highly important for engineering fire safety in the built environment. Among organic solid materials, various kinds of polymers are used more and more extensively as decorative and construction materials in chemical plants, laboratories, hospitals and so on, due to their low weight, highly customizable prop erties, low cost, and energy efficiency [1-2]. At the same time, high heating value, heavy smoke, and severe toxicity of polymers will cause serious hazards for life and properties once fire occurs in buildings, it is understood that polymers can present a greater fire safety hazard than traditional building materials [3]. In building fires, a combustible solid surface is always subjected to high heat flux from the fire as well as from hot surfaces sur rounding it. Flame spread mechanism under different variable conditions such as warehouses, libraries, chemical plants and building exterior walls can be highly complex and difficult to understand. The maximum spread rate in any of these situations determines the worst-case scenario that should be accounted for, in the design of fire detection and fire suppression systems [4]. Flame spread over the surface of a material has long been recognized in the fire safety field as a highly important process because it is a key determinant of the initial rate of fire growth [5]. Over the recent years, there has been a significant development in the understanding of flame spread over solid materials, a large number of investigations have been conducted in the field of vertical flame spread [6-735]. Many researchers focus on the influence of internal factors of solid materials, such thickness, width, thermal conductivity and melting. Fernandez-Pello, Bhattachariee, Ayani et al. [8–10] indicated that the effect of thickness, following the corresponding flame behavior, can be classified into thermally-thin, thermally-thick, unstable, and extinction regimes. Previous studies pertaining to the * Corresponding author. E-mail address: [email protected] (L. Yang). https://doi.org/10.1016/j.csite.2019.100519 Received 9 August 2019; Received in revised form 20 August 2019; Accepted 24 August 2019 Available online 26 August 2019 2214-157X/© 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Case Studies in Thermal Engineering 15 (2019) 100519
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Fig. 1. Experimental apparatus.
effect of sample width on flame spread are reported in Refs. [11–14]. Pizzo et al. [13] studied width effects on the early stage of upward flame spread use 0.025 m–0.2 m wide sample. For the wider slabs, the flame height, the heat release rate per unit width, and the rate of spread are not influenced by the sample width. Experimental data suggest that the flame remains laminar during the entire spread process. For the narrower slabs a transition from a laminar to a turbulent flame is observed and the value of heat release rate decreases with the slab width. For a sample width of 0.05 m, the flame height is shorter due to the fact that lateral air entrainment increases the mixing above the pyrolysis front. On the contrary heat release rate is not affected. In Tsai’s [14] research, it is reported that wider flames have higher heat release rate per unit width, larger flame height, higher flame temperature and more heat feedback to the surface for turbulent diffusion flames. Crescitelli et al. [15] found that flame spread rate first increase with thermal conductivity and then a continuous decrease appears. The influence of thermal conductivity is mild but not negligible. There are also many researches about the influence of building structures on flame spread. An [20] and Gollner [21] studied the effects of inclination angle of fuel surface on upward flame spread. It was shown that maximum spread rate doesn’t correspond to maximum fuel mass loss rate. Lattimera and Ohlemiller [22-23] studied the flame spread in a combustible corner. Nakamur and Sandra’s researches pay their attentions on the flame spread in enclosures [24-25]. Tsai [26] studied the sidewalls’ effect on flame spread, found that the existence of sidewalls lengthened flame heights and generally reduced heat feedback along the central lines of the flames, resulting in higher flame spread rates for narrower flames and lower flame spread rates for wider flames. Although there are many attentions paid on the structures’ effect on flame spread, but few researchers studied the very common phenomenon of flame spread under ceiling in building fires. Zhou [27] investigated the effects of forced air flow velocity and grid-generated turbulence on the flow-assisted flame spread over a flat solid combustible surface in a ceiling configuration. And found that in ceiling spread, buoyancy has two main competing effects. One is an enhancement of the heat transfer from the flame to the solid surface because the flame stands closer to the surface, the other is an incomplete combustion caused by larger heat losses to the wall and boundary layer stratification. Weng [28] developed a one-dimensional model to predict the ceiling flame spread, but the heat release rate was underestimated. Therefore, the effect of ceiling on flame spread over vertical placed fuel surfaces is lack of understanding, filling up some of the above mentioned knowledge gaps in literature forms the primary motivation to this study. In this paper, a series of experiments was designed to investigate the effects of ceiling on flame spread; burning rate, flame spread rate and flame shape have been carefully measured. The correlations between flame spread rate, burning rate, pyrolysis length and ceiling height, orientation, sample width are given. 2. Experimental set-up Poly(methyl methacrylate) (PMMA) which is widely used in our surroundings is chosen as the sample to conduct the experiments. The PMMA sample were cut into 5 mm thick, 300 mm long with widths of 30, 50, 70 and 90 mm. The samples were held against the back wall, which consists of a 10 mm thick ceramic fiber board (coefficient of thermal conductivity: 0.08 W/(m⋅K)) to keep low thermal conductivity and a 3 mm thick aluminum plate to keep structural strength. The width and height of back wall is 80 mm, 50 mm respectively. The ceiling is also consist of a 10 mm thick ceramic fiber board and a 3 mm thick aluminum plate, the width and height of which is 80 mm and 40 mm. As shown in Fig. 1, an electronic balance is put at the bottom of experimental apparatus to record the realtime mass of PMMA samples during the experiment, the measurement accuracy of the electronic balance is up to 0.01g. A CCD camera is set 1.5 m right in front of the middle point of the sample to record the video data. For each experiment, the sample is ignited at the right side using a 2 kW electrical stainless steel rod. The optimum rod–sample 2
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distance is found to be 10 mm. It is large enough to produce uniform ignition along the slab width, but small enough to make any preheating associated to the igniter only a local effect close to the leading edge of the sample. Ignition times are found to be nearly the same for all experiments, about 45s, which facilitates reproducibility. Time zero is taken as the onset of flaming. The samples were put under the ceiling and on the back wall, the distance (H) between the sample midline and the ceiling is 100 mm. As shown in Fig. 1, there are four different ceiling orientations are applied in the experiments, namely α ¼ -30� , 0� , 30� and 90� . Each test of the same experimental condition was repeated three times to ensure the accuracy. 3. Results and discussion 3.1. Theory analysis of non-ceiling situation 3.1.1. Burning rate During the combustion process, the flame spread is affected by the heat feedback of flame itself. The heat feedback consists of convective and radiant heat flux, thus (1)
q}f ¼ q}c þ q}r where, convective heat flux q}c ¼ hðTf
Tp Þ, radiant heat flux q}r ¼ σεðT 4f
T4P Þ.
Combined with the expression of the flame heat feedback, the burning rate could be written as h � �i � m∝ _ h Tf Tp þ σε T 4f T 4P Spyrolysis
(2)
For flame spread in opposed flow, the spread rate of thermally thin materials is [31], Vf ¼
q}f δph
(3)
T∞ Þ2
ρs cs dðTs
For lateral flame spread, Nuselt number can be expressed as [33], � �14 hW 4 GrW ¼ gðPrÞ kg 3 4 =
NuW ¼
(4)
The Grashof number GrW can be expressed as, GrW ¼
T∞ ÞW 3
gβðTS
(5)
ν
2
Combine formulas (4) (5), the convective heat transfer coefficient h depend on sample width as pffiffi � �1=4 2 2 gβðTS T∞ Þ h¼ kg gðPrÞW 1=4 3 ν2
(6)
According to Ref. [33], the estimation of the heat feedback suggests that for the flame spread over the narrower slabs, the convective heat transfer is much greater than the radiant heat transfer. So if the radiant heat flux on the unburned parts is not counted. formula (3) can be expressed as � � Vf ∝ h Tf Tp ∝W 1=4 ∝m_ W (7) 3.1.2. Pyrolysis length In this study, the flame spread rate is achieved from the video images. In lateral combustion, the Rayleigh number can be expressed as [32]. RaW ¼
gβðTP
T∞ ÞW 3
(8)
να
So the Rayleigh number RaW of sample widths 3 cm, 5 cm, 7 cm, 9 cm, 11 cm and 13 cm are 9:9091 � 104 , 4:5875 � 105 , 1:2588� 106 , 2:6755 � 106 , 4:8848 � 106 and 8:0631 � 106 . This indicate during the combustion, the flame is laminar. For laminar flame [34], m}ðwÞ _ � wPrGrw 1=4 ¼ Cm;L B μ∞ Combine formulas (7) and (9), Z W 1 4 _ m}ðWÞ _ ¼ m}ðwÞdw _ ¼ m}ðWÞ∝W W 0 3
(9)
(10)
1=4
Assuming the burning region to be triangular [33], i.e. 3
Case Studies in Thermal Engineering 15 (2019) 100519
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Fig. 2. Pictures of flames for 7 cm samples of different ceiling inclination.
� Spyrolysis � xp W 2
(11)
The total mass loss can be expressed as, (12)
m_ ¼ m} _ � Spyrolysis ¼ ρdWVf
_ is the average burning rate per unit area over the whole pyrolysis region. Combine formulas (10)–(12), the pyrolysis length where m} can be expressed as (13)
xp ∝W 1=4 3.2. Effect of ceiling inclination
3.2.1. Observed fire behavior The flame shapes of 7 cm wide PMMA samples are shown in Fig. 2. As ceiling inclination α decreases from 90� to -30� , the flame 4
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Fig. 3. The real-time mass loss of PMMA slabs at different ceiling inclination.
Fig. 4. The logarithm coordinate between m_ =W and sample width for different ceiling orientations.
5
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Fig. 5. The relationship between sin α and n, m.
Fig. 6. Flame spread rate for different ceiling inclination.
height in vertical direction decreases, while the flame widths in lateral direction increases. The change of flame shape leads to the differences of radiative and convective heat feedback from flame to sample surface. The differences of heat feedback will affect the burning rate, flame spread rate and pyrolysis length. 3.2.2. Burning rate The mass loss of PMMA slab under varied ceiling inclination was plotted in Fig. 3, The early stage of the flame spread was affected by the ignition and would last for about 500s–600s. In the ignition affected zone, the spread rate continuously increased with the pyrolysis length. When reaching the steady state zone, the test exhibited a stable flame appearance and a constant spread velocity. The steady state was selected to study the effect of ceiling inclination on flame spread. It is obvious that the burning rate in the steady state for α ¼ -30� is much larger than other ceiling inclinations in Fig. 3. The theoretical relationship between burning rate and sample width for situation α ¼ 90� is given in 3.1. The logarithm coordinate was adopted to verify our deduction in Fig. 4. The linear rule between m_ =W and W fits well for α ¼ 90� with the slope of -0.27, which is very close to the theoretical results -0.25. As α decrease from 90� to -30� , the ceiling effect increase. The relations between m_ and W can be given as: (14)
m_ = W∝W n
Here n increases from -0.27 to -0.092, 0.098 and 0.368 for α ¼ 90 , 30 , 0 and -30 respectively. The linear rule between n and sin (α) is given in Fig. 5. Thus, we can conclude that � m_ W∝W 0:136 0:421sinðαÞ (15) �
6
�
�
�
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F. Peng et al.
Fig. 7. The logarithm coordinate between xp and sample width for different ceiling orientations.
3.2.3. Flame spread rate Flame spread rate in a lateral spread condition was defined as the ratio of a specific distance the flame front moved to the time during the spreading process. A linear correlation was obtained, and the slope of the fitted line was defined as the flame spread rate of the flame during the stable burning stage. As shown in Fig. 6, the flame has the largest spread rate when α ¼ -30� , and then shows a decrease when α increases. Flame spread rate of 9 cm slabs decrease with α throughout the entire range. But a “U” shape of flame spread rate profile is found for narrow PMMA slabs (3 cm, 5 cm and 7 cm), after a decreasement the flame spread rate will reaches a minimum and that turns to increase. For 3 cm and 5 cm slabs, the flame spread rate reach the minimum when α ¼ 0� , while the minimum appears at 30� for 7 cm slabs. Tsai et al. [26] point out flames lower than 200 mm were laminar and convection controlled. In our study, all samples were less the 200 mm wide, thus for flames without ceiling (α ¼ 90� ), convection plays a dominate role. However, the air-entrainment is weakened for flames with ceiling (α < 90� ) because of smoke accumulation, thus convection heat feedback from flame is reduced. At the same time, the radiation heat feedback from flame under ceiling is enhanced. The reverse trend of convection and radiation heat feedback leads to the “U” shape profile of flame spread rate. 3.2.4. Pyrolysis length Pyrolysis length is an important parameter in describing the behavior of flame spread which is defined as the length of the burning zone. For lateral flame spread over vertical PMMA board in this study, pyrolysis length is actually the flame width on the fuel surface which is obtained from the video information (Fig. 2). The experimental results of relationship between pyrolysis length and sample width are given in Fig. 7. Natural logarithm of pyrolysis length lnðxp Þ is linearly related to lnðwÞ. So pyrolysis length has an exponential relationship with sample width for different ceiling orientation, that is (16)
xp ∝W m
Pizzo [29] propose the pyrolysis length for turbulent case in upward flame spread should be xp:trubulent ∝W , and in Xiao’s [33] experimental results suggested for inclined(30� –75� ) PMMA surface, xp ∝W0:48 sin1=4 θ. However, the ceiling effects were not considered in their study. In our study, m ¼ 0.28 in non-ceiling (α ¼ 90� ) cases, the value is very close to the theoretical formula (13). As α changes from 90� to -30� , m increases from 0.28 to 0.40, 0.45 and 0.53, so the width effect on pyrolysis length is strengthened. The linear rule between m and sin(α) is given in Fig. 5. 0:35
xp ∝W 0:455
(17)
0:16sinðαÞ
4. Conclusions In this work, the effect of ceiling inclination on lateral flame spread over poly(methyl methacrylate) has been experimentally investigated. The experimental and theoretical results would give a better understanding ceiling inclination effect on lateral flame spread, the main conclusions are as below: The flame has the largest spread rate when α ¼ -30� .The flame spread rate presents a “U” variation with the increasing ceiling inclination for sample width less than 7 cm. For 9 cm width sample, the flame spread rate decrease with α throughout the entire range of α. 7
Case Studies in Thermal Engineering 15 (2019) 100519
F. Peng et al.
The relationship between burning rate, sample width and ceiling inclination is discussed in detail, the experimental results sug gested m_ =W∝W0:136 0:421sinðαÞ . The pyrolysis length follows a power-law increase with the sample width, the exponential relationship between pyrolysis length, sample width and ceiling inclination can be given as xp ∝W0:455 0:16sinðαÞ . Conflicts of interest The authors declared that they have no conflicts of interest to this work. Acknowledgments This research was supported by National Key R & D Program of China under Grant No. 2016YFC0800603, the Key Research Program of the Chinese Academy of Sciences, China under Grant NO. QYZDB-SSW-JSC029 and the Fundamental Research Funds for the Central Universities, China under Grant No. WK2320000040. The authors deeply appreciate the supports. References [1] R.C. Thompson, C.J. Moore, F.S. Vom Saal, S.H. Swan, Plastics, the environment, and human health: current consensus and future trends, Philos. Trans. R. Soc. 364 (2009) 2153–2166, https://doi.org/10.1098/rstb.2009.0053. [2] Junhui Gong, Lizhong Yang, et al., Effects of low atmospheric pressure on combustion characteristics of polyethylene and polymethyl methacrylate, J. Fire Sci. 30 (3) (2012) 224–239, https://doi.org/10.1177/0734904111431863. [3] S. Kerber, Analysis of changing residential fire dynamics and its implications on firefighter operational timeframes, Fire Technol. 48 (2012) 865–891, https:// doi.org/10.1007/s10694-011-0249-2. [4] Govindaraju Avinash, Kumar Amit, Vasudevan Raghavan, Experimental analysis of diffusion flame spread along thin parallel solid fuel surfaces in a natural convective environment, Combust. Flame 165 (2016) 321–333. http://doi.org/10.1016/j.combustflame.2015.12.015. [5] A. Ito, T. Kashiwagi, Characterization of flame spread over PMMA using holographic interferometry sample orientation effects, Combust. Flame 71 (1988) 189–204. https://doi.org/10.1016/0010-2180(88)90007-7. [6] M.A. Delichatsios, M.M. Delichatsios, Upward flame spread and critical conditions for PE/PVC cables in a tray configuration, in: T. Kashiwagi (Ed.), Fire Safety Science: Proceedings of the Fourth International Symposium, International Association for Fire Safety Science. July 13–17, 1994, Ottawa, Canada, Intl. Assoc. For Fire Safety Science, Boston, MA, 1994, pp. 433–444, https://doi.org/10.3801/IAFSS.FSS.4-433. [7] C.C. Ndubizu, R. Ananth, P.A. Tatem, Transient burning rate of a noncharring plate under a forced flow boundary layer flame, Combust. Flame 141 (2005) 131–148. https://doi.org/10.1016/j.combustflame.2004.12.013. [8] A.C. Fernandez-Pello, F.A. Williams, Laminar flame spread over PMMA surfaces, in: Proceedings of the 15th symposium on combustion, 1975, pp. 217–231. https://doi.org/10.1016/S0082-0784(75)80299-2. [9] S. Bhattachariee, M.D. King, S. Takahashi, T. Nagumo, K. Wakai, Downward flame spread over poly(methly) methacrylate, Proc. Combust. Inst. 28 (2000) 2891–2897. https://doi.org/10.1016/S0082-0784(00)80713-4. [10] M.B. Ayani, J.A. Esfahani, R. Mehrabian, Downward flame spread over PMMA sheets in quiescent air: experimental and theoretical studies, Fire Saf. J. 41 (2006) 164–169. https://doi.org/10.1016/j.firesaf.2005.12.003. [11] W.E. Mell, T. Kashiwagi, Effects of finite sample width on transition and flame spread in microgravity, Proc. Combust. Inst. 28 (2000) 2785–2792. https://doi. org/10.1016/S0082-0784(00)80700-6. [12] A.S. Rangwal, S.G. Buckley, J.L. Torero, Upward flame spread on a vertically oriented fuel surface: the effect of finite width, Proc. Combust. Inst. 31 (2007) 2607–2615, in: https://doi.org/10.1016/j.proci.2006.07.235. [13] Y. Pizzo, J.L. Consalvi, P. Querre, M. Coutin, B. Porterie, Width effects on the early stage of upward flame spread over PMMA slabs: experimental observations, Fire Saf. J. 44 (2009) 407–414. https://doi.org/10.1016/j.firesaf.2008.09.003. [14] Kuang-Chung Tsai, Width effect on upward flame spread, Fire Saf. J. 44 (2009) 962–967. https://doi.org/10.1016/j.firesaf.2009.06.003. [15] Silvestro Crescitelli, Pota Franco, Giulio Santo, Vi Ncenzo Tu Fano, Influence of solid phase thermal properties on flame spread over polymers, Combust. Sci. Technol. 27 (1981) 15–78. http://doi.org/10.1080/00102208108946974. [20] Weiguang An, Xinjie Huang, Qingsong Wang, et al., Effects of sample width and inclined angle on flame spread across expanded polystyrene surface in plateau and plain environments, J. Thermoplast. Compos. Mater. 28 (1) (2015) 111–127, https://doi.org/10.1177/0892705713486132. [21] M.J. Gollner, X. Huang, J. Cobian, A.S. Rangwala, F.A. Williams, Experimental study of upward flame spread of an inclined fuel surface, Proc. Combust. Inst. 34 (2013) 2531–2538, in: https://doi.org/10.1016/j.proci.2012.06.063. [22] Brian Y. Lattimera, Sean P. Hunta, Mark Wrighta, Usman Sorathiab, Modeling fire growth in a combustible corner, Fire Saf. J. 38 (2003) 771–796. https://doi. org/10.1016/S0379-7112(03)00067-5. [23] T. Ohlemiller, T. Cleary, J. Shields, Effect of ignition conditions on upward flame spread on a composite material in a corner configuration, Fire Saf. J. 31 (1998) 331–344. https://doi.org/10.1016/S0379-7112(98)00019-8. [24] Sandra L. Olson, Suleyman A. Gokoglu, David L. Urban, et al., Upward flame spread in large enclosures: flame growth and pressure rise, Proc. Combust. Inst. 35 (2015) 2623–2630, in: https://doi.org/10.1016/j.proci.2014.05.069. [25] Yuji Nakamura, Takashi Kashiwagi, et al., Enclosure effects on flame spread over solid fuels in microgravity, Combust. Flame 130 (2002) 307–321. [26] Kuang-Chung Tsai, Influence of sidewalls on width effects of upward flame spread, Fire Saf. J. 46 (2011) 294–304. https://doi.org/10.1016/j.firesaf.2011.03. 006. [27] L. Zhou, A.C. Fernandez-Pello, Turbulent, concurrent, ceiling flame spread: the effect of buoyancy, Combust. Flame 92 (1993) 45–59. https://doi.org/10.1016/ 0010-2180(93)90197-B. [28] W.G. Weng, Y. Hasemi, A numerical model for flame spread along combustible flat solid with charring material with experimental validation of ceiling flame spread and upward flame spread, Fire Mater. 32 (2008) 87–102, https://doi.org/10.1002/fam.952. [29] Y. Pizzo, J.L. Consalvi, P. Querre, et al., Experimental observations on the steady-state burning rate of a vertically oriented PMMA slab, Combust. Flame 152 (2008) 451–460, https://doi.org/10.1016/j.combustflame.2007.06.020. [31] J.G. Quintiere, J. Wiley, Fundamentals of Fire Phenomena, John Wiley, England, 2006. [32] A. Atreya, Convection heat transfer, in: P.J. DiNenno, D. Drysdale (Eds.), SFPE Handbook of Fire Protection Engineering, third ed., the Society of Fire Protection Engineers, Bethesda, Maryland, USA, 2002, pp. 65–68. [33] Xiao Chen, Jiahao Liu, et al., Experimental and theoretical analysis on lateral flame spread over inclined PMMA surface, Int. J. Heat Mass Transf. 91 (2015) 68–76. https://doi.org/10.1016/j.ijheatmasstransfer.2015.07.072. [34] J.G. Quintiere, The effects of angular orientation on flame spread over thin materials, Fire Saf. J. 36 (3) (2001) 291–312. [35] Y. Zhou, et al., Experimental investigation on downward flame spread over rigid polyurethane and extruded polystyrene foams, Experimental Thermal and Fluid Science 92 (2018) 346–352.
8
Contents lists available at ScienceDirect
Case Studies in Thermal Engineering journal homepage: http://www.elsevier.com/locate/csite
Effects of ceiling inclination on lateral flame spread over vertical Poly(methyl methacrylate) surface Fei Peng, Dimeng Lai, Yuan Zheng, Lizhong Yang * State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui, 230026, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Flame spread Ceiling inclination Pyrolysis length poly(methyl methacrylate)
A series of experiments was designed to investigate the effects of ceiling inclination on lateral flame spread over vertical poly(methyl methacrylate) (PMMA) surface. PMMA slabs with width ranged from 3 cm to 9 cm were tested at the ceiling inclination from 30� to 90� . Burning rate, flame spread rate, and flame appearance were investigated experimentally. The results suggest that in the cases of narrow PMMA slabs, the flame spread rate presents a “U” variation with the increasing ceiling inclination. But flame spread rate of wider slabs decreases with ceiling incli nation. Burning rate follows a power-law change with the sample width, which is m_ =W∝W 0:136 0:421sinðαÞ . And the exponential relationship between pyrolysis length, sample width and ceiling inclination can be given as xp ∝W 0:455 0:16sinðαÞ .
1. Introduction Understanding the dynamics of fire inception and growth on organic solid materials is highly important for engineering fire safety in the built environment. Among organic solid materials, various kinds of polymers are used more and more extensively as decorative and construction materials in chemical plants, laboratories, hospitals and so on, due to their low weight, highly customizable prop erties, low cost, and energy efficiency [1-2]. At the same time, high heating value, heavy smoke, and severe toxicity of polymers will cause serious hazards for life and properties once fire occurs in buildings, it is understood that polymers can present a greater fire safety hazard than traditional building materials [3]. In building fires, a combustible solid surface is always subjected to high heat flux from the fire as well as from hot surfaces sur rounding it. Flame spread mechanism under different variable conditions such as warehouses, libraries, chemical plants and building exterior walls can be highly complex and difficult to understand. The maximum spread rate in any of these situations determines the worst-case scenario that should be accounted for, in the design of fire detection and fire suppression systems [4]. Flame spread over the surface of a material has long been recognized in the fire safety field as a highly important process because it is a key determinant of the initial rate of fire growth [5]. Over the recent years, there has been a significant development in the understanding of flame spread over solid materials, a large number of investigations have been conducted in the field of vertical flame spread [6-735]. Many researchers focus on the influence of internal factors of solid materials, such thickness, width, thermal conductivity and melting. Fernandez-Pello, Bhattachariee, Ayani et al. [8–10] indicated that the effect of thickness, following the corresponding flame behavior, can be classified into thermally-thin, thermally-thick, unstable, and extinction regimes. Previous studies pertaining to the * Corresponding author. E-mail address: [email protected] (L. Yang). https://doi.org/10.1016/j.csite.2019.100519 Received 9 August 2019; Received in revised form 20 August 2019; Accepted 24 August 2019 Available online 26 August 2019 2214-157X/© 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Case Studies in Thermal Engineering 15 (2019) 100519
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Fig. 1. Experimental apparatus.
effect of sample width on flame spread are reported in Refs. [11–14]. Pizzo et al. [13] studied width effects on the early stage of upward flame spread use 0.025 m–0.2 m wide sample. For the wider slabs, the flame height, the heat release rate per unit width, and the rate of spread are not influenced by the sample width. Experimental data suggest that the flame remains laminar during the entire spread process. For the narrower slabs a transition from a laminar to a turbulent flame is observed and the value of heat release rate decreases with the slab width. For a sample width of 0.05 m, the flame height is shorter due to the fact that lateral air entrainment increases the mixing above the pyrolysis front. On the contrary heat release rate is not affected. In Tsai’s [14] research, it is reported that wider flames have higher heat release rate per unit width, larger flame height, higher flame temperature and more heat feedback to the surface for turbulent diffusion flames. Crescitelli et al. [15] found that flame spread rate first increase with thermal conductivity and then a continuous decrease appears. The influence of thermal conductivity is mild but not negligible. There are also many researches about the influence of building structures on flame spread. An [20] and Gollner [21] studied the effects of inclination angle of fuel surface on upward flame spread. It was shown that maximum spread rate doesn’t correspond to maximum fuel mass loss rate. Lattimera and Ohlemiller [22-23] studied the flame spread in a combustible corner. Nakamur and Sandra’s researches pay their attentions on the flame spread in enclosures [24-25]. Tsai [26] studied the sidewalls’ effect on flame spread, found that the existence of sidewalls lengthened flame heights and generally reduced heat feedback along the central lines of the flames, resulting in higher flame spread rates for narrower flames and lower flame spread rates for wider flames. Although there are many attentions paid on the structures’ effect on flame spread, but few researchers studied the very common phenomenon of flame spread under ceiling in building fires. Zhou [27] investigated the effects of forced air flow velocity and grid-generated turbulence on the flow-assisted flame spread over a flat solid combustible surface in a ceiling configuration. And found that in ceiling spread, buoyancy has two main competing effects. One is an enhancement of the heat transfer from the flame to the solid surface because the flame stands closer to the surface, the other is an incomplete combustion caused by larger heat losses to the wall and boundary layer stratification. Weng [28] developed a one-dimensional model to predict the ceiling flame spread, but the heat release rate was underestimated. Therefore, the effect of ceiling on flame spread over vertical placed fuel surfaces is lack of understanding, filling up some of the above mentioned knowledge gaps in literature forms the primary motivation to this study. In this paper, a series of experiments was designed to investigate the effects of ceiling on flame spread; burning rate, flame spread rate and flame shape have been carefully measured. The correlations between flame spread rate, burning rate, pyrolysis length and ceiling height, orientation, sample width are given. 2. Experimental set-up Poly(methyl methacrylate) (PMMA) which is widely used in our surroundings is chosen as the sample to conduct the experiments. The PMMA sample were cut into 5 mm thick, 300 mm long with widths of 30, 50, 70 and 90 mm. The samples were held against the back wall, which consists of a 10 mm thick ceramic fiber board (coefficient of thermal conductivity: 0.08 W/(m⋅K)) to keep low thermal conductivity and a 3 mm thick aluminum plate to keep structural strength. The width and height of back wall is 80 mm, 50 mm respectively. The ceiling is also consist of a 10 mm thick ceramic fiber board and a 3 mm thick aluminum plate, the width and height of which is 80 mm and 40 mm. As shown in Fig. 1, an electronic balance is put at the bottom of experimental apparatus to record the realtime mass of PMMA samples during the experiment, the measurement accuracy of the electronic balance is up to 0.01g. A CCD camera is set 1.5 m right in front of the middle point of the sample to record the video data. For each experiment, the sample is ignited at the right side using a 2 kW electrical stainless steel rod. The optimum rod–sample 2
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distance is found to be 10 mm. It is large enough to produce uniform ignition along the slab width, but small enough to make any preheating associated to the igniter only a local effect close to the leading edge of the sample. Ignition times are found to be nearly the same for all experiments, about 45s, which facilitates reproducibility. Time zero is taken as the onset of flaming. The samples were put under the ceiling and on the back wall, the distance (H) between the sample midline and the ceiling is 100 mm. As shown in Fig. 1, there are four different ceiling orientations are applied in the experiments, namely α ¼ -30� , 0� , 30� and 90� . Each test of the same experimental condition was repeated three times to ensure the accuracy. 3. Results and discussion 3.1. Theory analysis of non-ceiling situation 3.1.1. Burning rate During the combustion process, the flame spread is affected by the heat feedback of flame itself. The heat feedback consists of convective and radiant heat flux, thus (1)
q}f ¼ q}c þ q}r where, convective heat flux q}c ¼ hðTf
Tp Þ, radiant heat flux q}r ¼ σεðT 4f
T4P Þ.
Combined with the expression of the flame heat feedback, the burning rate could be written as h � �i � m∝ _ h Tf Tp þ σε T 4f T 4P Spyrolysis
(2)
For flame spread in opposed flow, the spread rate of thermally thin materials is [31], Vf ¼
q}f δph
(3)
T∞ Þ2
ρs cs dðTs
For lateral flame spread, Nuselt number can be expressed as [33], � �14 hW 4 GrW ¼ gðPrÞ kg 3 4 =
NuW ¼
(4)
The Grashof number GrW can be expressed as, GrW ¼
T∞ ÞW 3
gβðTS
(5)
ν
2
Combine formulas (4) (5), the convective heat transfer coefficient h depend on sample width as pffiffi � �1=4 2 2 gβðTS T∞ Þ h¼ kg gðPrÞW 1=4 3 ν2
(6)
According to Ref. [33], the estimation of the heat feedback suggests that for the flame spread over the narrower slabs, the convective heat transfer is much greater than the radiant heat transfer. So if the radiant heat flux on the unburned parts is not counted. formula (3) can be expressed as � � Vf ∝ h Tf Tp ∝W 1=4 ∝m_ W (7) 3.1.2. Pyrolysis length In this study, the flame spread rate is achieved from the video images. In lateral combustion, the Rayleigh number can be expressed as [32]. RaW ¼
gβðTP
T∞ ÞW 3
(8)
να
So the Rayleigh number RaW of sample widths 3 cm, 5 cm, 7 cm, 9 cm, 11 cm and 13 cm are 9:9091 � 104 , 4:5875 � 105 , 1:2588� 106 , 2:6755 � 106 , 4:8848 � 106 and 8:0631 � 106 . This indicate during the combustion, the flame is laminar. For laminar flame [34], m}ðwÞ _ � wPrGrw 1=4 ¼ Cm;L B μ∞ Combine formulas (7) and (9), Z W 1 4 _ m}ðWÞ _ ¼ m}ðwÞdw _ ¼ m}ðWÞ∝W W 0 3
(9)
(10)
1=4
Assuming the burning region to be triangular [33], i.e. 3
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Fig. 2. Pictures of flames for 7 cm samples of different ceiling inclination.
� Spyrolysis � xp W 2
(11)
The total mass loss can be expressed as, (12)
m_ ¼ m} _ � Spyrolysis ¼ ρdWVf
_ is the average burning rate per unit area over the whole pyrolysis region. Combine formulas (10)–(12), the pyrolysis length where m} can be expressed as (13)
xp ∝W 1=4 3.2. Effect of ceiling inclination
3.2.1. Observed fire behavior The flame shapes of 7 cm wide PMMA samples are shown in Fig. 2. As ceiling inclination α decreases from 90� to -30� , the flame 4
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Fig. 3. The real-time mass loss of PMMA slabs at different ceiling inclination.
Fig. 4. The logarithm coordinate between m_ =W and sample width for different ceiling orientations.
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Fig. 5. The relationship between sin α and n, m.
Fig. 6. Flame spread rate for different ceiling inclination.
height in vertical direction decreases, while the flame widths in lateral direction increases. The change of flame shape leads to the differences of radiative and convective heat feedback from flame to sample surface. The differences of heat feedback will affect the burning rate, flame spread rate and pyrolysis length. 3.2.2. Burning rate The mass loss of PMMA slab under varied ceiling inclination was plotted in Fig. 3, The early stage of the flame spread was affected by the ignition and would last for about 500s–600s. In the ignition affected zone, the spread rate continuously increased with the pyrolysis length. When reaching the steady state zone, the test exhibited a stable flame appearance and a constant spread velocity. The steady state was selected to study the effect of ceiling inclination on flame spread. It is obvious that the burning rate in the steady state for α ¼ -30� is much larger than other ceiling inclinations in Fig. 3. The theoretical relationship between burning rate and sample width for situation α ¼ 90� is given in 3.1. The logarithm coordinate was adopted to verify our deduction in Fig. 4. The linear rule between m_ =W and W fits well for α ¼ 90� with the slope of -0.27, which is very close to the theoretical results -0.25. As α decrease from 90� to -30� , the ceiling effect increase. The relations between m_ and W can be given as: (14)
m_ = W∝W n
Here n increases from -0.27 to -0.092, 0.098 and 0.368 for α ¼ 90 , 30 , 0 and -30 respectively. The linear rule between n and sin (α) is given in Fig. 5. Thus, we can conclude that � m_ W∝W 0:136 0:421sinðαÞ (15) �
6
�
�
�
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Fig. 7. The logarithm coordinate between xp and sample width for different ceiling orientations.
3.2.3. Flame spread rate Flame spread rate in a lateral spread condition was defined as the ratio of a specific distance the flame front moved to the time during the spreading process. A linear correlation was obtained, and the slope of the fitted line was defined as the flame spread rate of the flame during the stable burning stage. As shown in Fig. 6, the flame has the largest spread rate when α ¼ -30� , and then shows a decrease when α increases. Flame spread rate of 9 cm slabs decrease with α throughout the entire range. But a “U” shape of flame spread rate profile is found for narrow PMMA slabs (3 cm, 5 cm and 7 cm), after a decreasement the flame spread rate will reaches a minimum and that turns to increase. For 3 cm and 5 cm slabs, the flame spread rate reach the minimum when α ¼ 0� , while the minimum appears at 30� for 7 cm slabs. Tsai et al. [26] point out flames lower than 200 mm were laminar and convection controlled. In our study, all samples were less the 200 mm wide, thus for flames without ceiling (α ¼ 90� ), convection plays a dominate role. However, the air-entrainment is weakened for flames with ceiling (α < 90� ) because of smoke accumulation, thus convection heat feedback from flame is reduced. At the same time, the radiation heat feedback from flame under ceiling is enhanced. The reverse trend of convection and radiation heat feedback leads to the “U” shape profile of flame spread rate. 3.2.4. Pyrolysis length Pyrolysis length is an important parameter in describing the behavior of flame spread which is defined as the length of the burning zone. For lateral flame spread over vertical PMMA board in this study, pyrolysis length is actually the flame width on the fuel surface which is obtained from the video information (Fig. 2). The experimental results of relationship between pyrolysis length and sample width are given in Fig. 7. Natural logarithm of pyrolysis length lnðxp Þ is linearly related to lnðwÞ. So pyrolysis length has an exponential relationship with sample width for different ceiling orientation, that is (16)
xp ∝W m
Pizzo [29] propose the pyrolysis length for turbulent case in upward flame spread should be xp:trubulent ∝W , and in Xiao’s [33] experimental results suggested for inclined(30� –75� ) PMMA surface, xp ∝W0:48 sin1=4 θ. However, the ceiling effects were not considered in their study. In our study, m ¼ 0.28 in non-ceiling (α ¼ 90� ) cases, the value is very close to the theoretical formula (13). As α changes from 90� to -30� , m increases from 0.28 to 0.40, 0.45 and 0.53, so the width effect on pyrolysis length is strengthened. The linear rule between m and sin(α) is given in Fig. 5. 0:35
xp ∝W 0:455
(17)
0:16sinðαÞ
4. Conclusions In this work, the effect of ceiling inclination on lateral flame spread over poly(methyl methacrylate) has been experimentally investigated. The experimental and theoretical results would give a better understanding ceiling inclination effect on lateral flame spread, the main conclusions are as below: The flame has the largest spread rate when α ¼ -30� .The flame spread rate presents a “U” variation with the increasing ceiling inclination for sample width less than 7 cm. For 9 cm width sample, the flame spread rate decrease with α throughout the entire range of α. 7
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The relationship between burning rate, sample width and ceiling inclination is discussed in detail, the experimental results sug gested m_ =W∝W0:136 0:421sinðαÞ . The pyrolysis length follows a power-law increase with the sample width, the exponential relationship between pyrolysis length, sample width and ceiling inclination can be given as xp ∝W0:455 0:16sinðαÞ . Conflicts of interest The authors declared that they have no conflicts of interest to this work. Acknowledgments This research was supported by National Key R & D Program of China under Grant No. 2016YFC0800603, the Key Research Program of the Chinese Academy of Sciences, China under Grant NO. QYZDB-SSW-JSC029 and the Fundamental Research Funds for the Central Universities, China under Grant No. WK2320000040. The authors deeply appreciate the supports. References [1] R.C. Thompson, C.J. Moore, F.S. Vom Saal, S.H. Swan, Plastics, the environment, and human health: current consensus and future trends, Philos. Trans. R. 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