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Transition condition and control mechanism of subatmospheric flame spread rate over horizontal thin paper sample
Combustion and Flame 188 (2018) 90–93
Contents lists available at ScienceDirect
Combustion and Flame journal homepage: www.elsevier.com/locate/combustflame
Brief Communications
Transition condition and control mechanism of subatmospheric flame spread rate over horizontal thin paper sample Jun Fang a, Xuan-ze He a, Kai-yuan Li b,c,∗, Jing-wu Wang a, Yong-ming Zhang a a
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, PR China Univ. Lille, UMR 8207, UMET, Unité Matériaux et Transformations, F 59 000 Lille, France c Department of Civil Engineering, School of Engineering, Aalto University, 02150 Espoo, Finland b
a r t i c l e
i n f o
Article history: Received 7 April 2017 Revised 18 June 2017 Accepted 8 September 2017
a b s t r a c t The horizontal flame spread over paper samples was investigated using a subatmospheric cabin with varied O2 concentration. The 25 kPa is found to be a clear turning point for the flame illumination and structure, radiative heat flux and flame spread rate (FSR), which leads to the transition boundary between the extinction limits and power law regions. In the extinction limits (non-linear) region below 25 kPa, the oxygen partial pressure is low with a small Da number. Consequently, the flame spread is gas phase kinetics controlled, resulting in low burning rate, low radiative heat loss and weak buoyancy, and thus the FSR is more sensitive to the oxygen concentration while less sensitive to the ambient pressure. In the power law (linear) region above 25 kPa, in contrast, the oxygen partial pressure is high and the Da number is large, and the flame spread is heat transfer controlled, which weakens the dependence of FSR on oxygen concentration and enhances the dependence on air pressure. © 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Subatmospheric flame spread is crucial for understanding of the fire behaviors with low buoyancy in microgravity. Olson et al. [1] studied the opposed flow flame spread over thin cellulose material near the extinction limits in microgravity and obtained the flammability map for near extinction limits in flame spread. Jie et al. [2] investigated the effects of subatmospheric pressure and sample width on the characteristics of horizontal flame spread over wood sheets. Frey and T’ien [3] studied the horizontal flame spread in various conditions (oxygen concentration and pressure) in a quiescent subatmospheric environment. They claimed that the power law relation could only correlate the data away the extinction limits. The correlation employing the infinite reaction rate is expressed as [4]:
V f ∝ ( pYOm2 )φ
condition in the previous research [3], therefore, a global model is demanded for the subatmospheric FSR. To come up with a global model, the transition boundary of near extinction limits and power law regions should first be identified. However, no available work focused on this boundary by far as well as the control mechanism of flame spread in different regions. In this paper, the horizontal flame spread over a paper sample was investigated experimentally using a subatmospheric cabin with an adjustable O2 concentration. The transition boundary, flame behaviors, flame temperature and radiative heat flux under varied O2 concentration and pressure were obtained. The literature data are also compared and involved in the analysis. The effects of pressure and O2 concentration on FSR were analyzed in depth with a global correlation developed.
(1)
where Vf is the FSR, p the ambient pressure, YO2 the O2 concentration. The exponent index, m, is found as respective 3.1 and 1 for PMMA and paper while φ approaches unity for both materials [3,4]. Nevertheless, Eq. (1) ignored the near extinction limits
∗ Corresponding author: Department of Civil Engineering, School of Engineering, Aalto University, 02150 Espoo, Finland. E-mail addresses: kaiyuan.li@aalto.fi, [email protected] (K.-y. Li).
2. Experimental setup A cylindrical subatmospheric cabin with a diameter of 50 cm and a length of 40 cm was used, in which the inner pressure can be varied from 0.3 to 100 kPa (±0.01 kPa). Pure O2 is mixed with air to adjust the O2 concentration from 21% to 80% in mole fraction. The experimental setup is shown in Fig. 1. The paper samples were 12 cm long, 2 cm wide and 0.012 cm thick and fixed using two parallel stainless steel plates. A coil heater was used to provide a
https://doi.org/10.1016/j.combustflame.2017.09.010 0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
J. Fang et al. / Combustion and Flame 188 (2018) 90–93
91
Table 2 Varied pressures via increasing oxygen concentration.
Fig. 1. Top view of the experimental setup. Table 1 Varied pressures at 43% O2 . (LOC: Limiting oxygen concentration). No.
Pressure (kPa)
O2 (%)
1 2 3 4 5 6 7 8
10 15 20 25 30 35 40 45
43 (LOC) 43 43 43 43 43 43 43
6 A current to ignite the paper sample, which would be stopped immediately once the flame spread began. To avoid the heat loss caused by intrusive measurements for flame spread near the extinction limits, only one R-type thermocouple with a diameter of 0.1 mm (±0.1 K) was installed to obtain the local flame temperature. The thermocouple was positioned 2 cm to the paper rear side and 2 mm above the paper sample. The thermocouple can quench the flames with low heat release rates, hence, the temperature data were very treasurable. Moreover, a radiometer parallel to the paper sample at the same horizontal level was placed 5 cm away the sample center-point, which was used as a reference to reflect the local flame incident radiative heat flux. The flame spread process was recorded using two Canon cameras (ISO 2500, shutter speed 1/30, F5.6, 1920 × 1080@30 fps) from the top and side views. The experimental conditions are listed in Tables 1 and 2. 3. Experimental results and discussion
No.
Pressure (kPa)
O2 (%)
1 2 3 4 5 6 7
10 20 25 30 50 70 90
43 (LOC), 45, 47, 49, 51 29 (LOC), 31, 33, 35, 37 27 (LOC), 29, 31, 33, 35 25 (LOC), 27, 29, 31, 33 21, 23, 25, 27, 29 21, 23, 25, 27, 29 21, 23, 25, 27, 29
icantly, whereas above 25 kPa, owing to the increasing buoyancy, the flame height increases noticeably and establishes a longitudinal asymmetry structure. Moreover, when the ambient pressure exceeds 25 kPa, with increasing pressure and oxygen concentration, the flame turns more yellow and luminous. Figure 3(a) shows the radiative heat flux 5 cm away from the sample against oxygen concentration and pressure while Fig. 3(b) shows the radiative heat flux and flame temperature at 43% O2 against pressure. It can be seen that 25 kPa is clearly a transition point for the increase rate of radiative heat flux. Furthermore, both the oxygen concentration and pressure have positive effects upon the increase of radiative heat flux, while at the same oxygen concentration the flame temperature has a significant decrease with increasing pressure. It is because that with increasing oxygen concentration and pressure the oxygen partial pressure increases, the combustion becomes stronger with a higher heat release rate, so the radiative heat feedback significantly increases. Moreover, at the same oxygen concentration, with the increasing pressure, the production of soot particles increases, as the soot yield Ys is inversely proportional to the soot formation time and hence in diffusion flames it follows the second order of ambient pressure [5]. Meanwhile, the gaseous combustion products of H2 O and CO2 increase linearly with pressure. Thus the radiation heat loss increases and the flame temperature decreases. Figure 4(a) shows Vf d/W against oxygen concentration and ambient pressure using the experimental data in this work and the work of Frey and T’ien [3], where the extinction, upper and lower limits are given. It is seen that in the extinction limit regions below 25 kPa, the FSR increases non-linearly with the pressure, while in the classical power law region above 25 kPa the FSR increases linearly with the pressure. Figure 4(b) presents the fitting of (V f d/W )/YO1.4 and (V f d/W )/YO2 against ambient pressure. 2
Therefore, the global correlation of FSR involving the two regions is expressed as Eq. (2):
V f ∝ YO12.4 p0.66 V f ∝ YO2 p
( p < 25 kPa ) ( p > 25 kPa )
(2)
In the literature, the FSR has been justified to linearly correlate to the flame heat feedback, which can be calculated using Eq. (3) [6]:
Vf =
q˙f b δ f
(3)
ρ c p d (Tig − Ts )
Here, q˙f b is the net heat flux to the sample surface, q˙f b = ˙ , where q˙ is the flame incident heat flux, which is proq˙f − qloss f portional to the overall reaction rate m˙ = ρg A0Y nY m exp(−E/RT ) F
Figure 2 shows the flame spread images against oxygen concentration and ambient pressure above the flammability limits. It is noted that below 25 kPa the flame is lightless blue and elliptical with a longitudinal symmetry structure. Specially, only when pressure above 25 kPa, the yellow flame will be shown. As the pressure increases, below 25 kPa, the flame size increases signif-
F
O2
˙ where the exponent m is approximately 1.5 [7]. The heat loss qloss mainly includes the radiation losses from the flame and the sample surface. δ f is the distance between flame front and ignition point (preheating length), d the sample thickness, ρ the sample density, cp the sample specific heat, Tig the ignition temperature, Ts the surface temperature.
92
J. Fang et al. / Combustion and Flame 188 (2018) 90–93
Fig. 2. Flame spread images via varied oxygen concentration and ambient pressure.
Fig. 3. Flame incident radiative heat flux and temperature (a) flame incident radiative heat flux 5 cm away from the sample via oxygen concentration and pressure and, (b) incident radiative heat flux and flame temperature against pressure at 43% O2 .
Fig. 4. Flame spread rate against pressure (a) Vf d/W via pressure and O2 concentration and, (b) (V f d/W )/YO12.4 and (V f d/W )/YO2 against pressure. Note, W is the sample width, d is sample thickness, and the subscript f is the flame. d = 0.012 cm, W = 2 cm for this study; d = 0.019 cm, W = 1 cm for the study of Frey and T’ien [3].
J. Fang et al. / Combustion and Flame 188 (2018) 90–93
The Damköhler number (Da) relates to the flow timescale and the chemical reaction timescale. For weak flame spread in quiescent and low ambient pressure conditions, the induced convection is comparatively weak and the induced airflow opposes the flame spread, so the flow time is approximately the same magnitude as the molecular diffusion time, thus, the Da number can be expressed as the ratio of molecular diffusion timescale to chemical reaction timescale. In the extinction limits (non-linear) region, the molecular diffusion coefficient is inversely changing to the ambient pressure, while the oxygen partial pressure is low. Therefore, due to the small diffusion timescale and the large reaction timescale, the Da number is small and the flame spread is gas phase kinetics controlled [6]. Hence, the flame is relatively small with a low burning rate and combustion heat release, q˙f is low and the flame is blue with less radiation loss. As a result, the flame has a higher temperature. For condensed solids, the flame spread is a continuous ignition process, which involves the onset of nearstoichiometric burning and is characterized by a mass flux and a heat release rate that are 2–3 times higher than those at incipient ignition [8]. So although the flame temperature is high, the low mass flux and heat release rate cannot sustain a high FSR. Additionally, the buoyancy is weak so the flame has a small size with ˙ . The distance between the a symmetrical structure and a low qloss gas–solid phases was short and thus q˙ is determined by the gas fb
phase kinetics and the FSR is more sensitive to the oxygen concentration as ∝ q˙ f ∝ YO1.4 . Meanwhile, as the gas phase chemical reac2 tion employs a dynamic equilibrium of the oxygen partial pressure pYO , the FSR has a weak dependence on the ambient pressure as 2
∝p0.66 . In the power law (linear) region, in contrast to the non-linear region, the Da number is relatively large, the flame spread is heat transfer controlled [6]. As the oxygen partial pressure is generally larger, the burning rate increases significantly compared to those in the extinction limits (non-linear) region, and the flame has a larger size with a higher incident heat flux of q˙f , so that the FSR is
93
significantly higher. However, due to the increase of ambient pressure, the buoyancy becomes stronger, as a result, the flame height increases significantly with an asymmetric structure. The distance between the gas–solid phases increases. Additionally, the flame is ˙ and a low flame temmore luminous with more radiative loss qloss perature. Thus, q ˙ is mainly determined by the flow field heat fb
transfer, which reduces the dependence of FSR on the oxygen concentration as ∝ YO and correspondingly enhances the dependence 2 of FSR on the ambient pressure as ∝p. Acknowledgements This work was sponsored by the National Natural Science Foundation of China (no. 51636008, 51576186, 51323010), Key Research Program of the Chinese Academy of Sciences (no. QYZDBSSW-JSC029), National Key R&D Program (2016YFC0801504) and Fundamental Research Funds for the Central Universities (WK2320 0 0 0 034, WK2320 0 0 0 036). K. Li has received funding from the European Research Council (ERC) under the European Union’s H2020 – the Framework programme for Research and Innovation (2014-2020) / ERC Grant Advances Agreement no. 670747 – ERC 2014 AdG/FireBar-Concept. References [1] S.L. Olson, P.V. Ferkul, J.S. T’ien, Near-limit flame spread over a thin solid fuel in microgravity, Symp. (Int.) Combust. 22 (1989) 1213–1222. [2] Y. Zhang, J. Ji, J. Li, J. Sun, Q. Wang, X. Huang, Effects of altitude and sample width on the characteristics of horizontal flame spread over wood sheets, Fire Saf. J. 51 (2012) 120–125. [3] A.E. Frey, J.S. T’ien, Near-limit flame spread over paper samples, Combust. Flame 26 (1976) 257–267. [4] R.F. McAlevy, R.S. Magee, The mechanism of flame spreading over the surface of igniting condensed-phase materials, Symp. (Int.) Combust. 12 (1969) 215–227. [5] J.L. de Ris, P.K. Wu, G. Heskestad, Radiation fire modeling, Proc. Combust. Inst. 28 (20 0 0) 2751–2759. [6] J.G. Quintiere, Fundamentals of fire phenomena, Wiley, 2006. [7] C.K. Westbrook, F.L. Dryer, Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames, Combust. Sci. Technol. 27 (1981) 31–43. [8] R.E. Lyon, J.G. Quintiere, Criteria for piloted ignition of combustible solids, Combust. Flame 151 (2007) 551–559.
Contents lists available at ScienceDirect
Combustion and Flame journal homepage: www.elsevier.com/locate/combustflame
Brief Communications
Transition condition and control mechanism of subatmospheric flame spread rate over horizontal thin paper sample Jun Fang a, Xuan-ze He a, Kai-yuan Li b,c,∗, Jing-wu Wang a, Yong-ming Zhang a a
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, PR China Univ. Lille, UMR 8207, UMET, Unité Matériaux et Transformations, F 59 000 Lille, France c Department of Civil Engineering, School of Engineering, Aalto University, 02150 Espoo, Finland b
a r t i c l e
i n f o
Article history: Received 7 April 2017 Revised 18 June 2017 Accepted 8 September 2017
a b s t r a c t The horizontal flame spread over paper samples was investigated using a subatmospheric cabin with varied O2 concentration. The 25 kPa is found to be a clear turning point for the flame illumination and structure, radiative heat flux and flame spread rate (FSR), which leads to the transition boundary between the extinction limits and power law regions. In the extinction limits (non-linear) region below 25 kPa, the oxygen partial pressure is low with a small Da number. Consequently, the flame spread is gas phase kinetics controlled, resulting in low burning rate, low radiative heat loss and weak buoyancy, and thus the FSR is more sensitive to the oxygen concentration while less sensitive to the ambient pressure. In the power law (linear) region above 25 kPa, in contrast, the oxygen partial pressure is high and the Da number is large, and the flame spread is heat transfer controlled, which weakens the dependence of FSR on oxygen concentration and enhances the dependence on air pressure. © 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Subatmospheric flame spread is crucial for understanding of the fire behaviors with low buoyancy in microgravity. Olson et al. [1] studied the opposed flow flame spread over thin cellulose material near the extinction limits in microgravity and obtained the flammability map for near extinction limits in flame spread. Jie et al. [2] investigated the effects of subatmospheric pressure and sample width on the characteristics of horizontal flame spread over wood sheets. Frey and T’ien [3] studied the horizontal flame spread in various conditions (oxygen concentration and pressure) in a quiescent subatmospheric environment. They claimed that the power law relation could only correlate the data away the extinction limits. The correlation employing the infinite reaction rate is expressed as [4]:
V f ∝ ( pYOm2 )φ
condition in the previous research [3], therefore, a global model is demanded for the subatmospheric FSR. To come up with a global model, the transition boundary of near extinction limits and power law regions should first be identified. However, no available work focused on this boundary by far as well as the control mechanism of flame spread in different regions. In this paper, the horizontal flame spread over a paper sample was investigated experimentally using a subatmospheric cabin with an adjustable O2 concentration. The transition boundary, flame behaviors, flame temperature and radiative heat flux under varied O2 concentration and pressure were obtained. The literature data are also compared and involved in the analysis. The effects of pressure and O2 concentration on FSR were analyzed in depth with a global correlation developed.
(1)
where Vf is the FSR, p the ambient pressure, YO2 the O2 concentration. The exponent index, m, is found as respective 3.1 and 1 for PMMA and paper while φ approaches unity for both materials [3,4]. Nevertheless, Eq. (1) ignored the near extinction limits
∗ Corresponding author: Department of Civil Engineering, School of Engineering, Aalto University, 02150 Espoo, Finland. E-mail addresses: kaiyuan.li@aalto.fi, [email protected] (K.-y. Li).
2. Experimental setup A cylindrical subatmospheric cabin with a diameter of 50 cm and a length of 40 cm was used, in which the inner pressure can be varied from 0.3 to 100 kPa (±0.01 kPa). Pure O2 is mixed with air to adjust the O2 concentration from 21% to 80% in mole fraction. The experimental setup is shown in Fig. 1. The paper samples were 12 cm long, 2 cm wide and 0.012 cm thick and fixed using two parallel stainless steel plates. A coil heater was used to provide a
https://doi.org/10.1016/j.combustflame.2017.09.010 0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
J. Fang et al. / Combustion and Flame 188 (2018) 90–93
91
Table 2 Varied pressures via increasing oxygen concentration.
Fig. 1. Top view of the experimental setup. Table 1 Varied pressures at 43% O2 . (LOC: Limiting oxygen concentration). No.
Pressure (kPa)
O2 (%)
1 2 3 4 5 6 7 8
10 15 20 25 30 35 40 45
43 (LOC) 43 43 43 43 43 43 43
6 A current to ignite the paper sample, which would be stopped immediately once the flame spread began. To avoid the heat loss caused by intrusive measurements for flame spread near the extinction limits, only one R-type thermocouple with a diameter of 0.1 mm (±0.1 K) was installed to obtain the local flame temperature. The thermocouple was positioned 2 cm to the paper rear side and 2 mm above the paper sample. The thermocouple can quench the flames with low heat release rates, hence, the temperature data were very treasurable. Moreover, a radiometer parallel to the paper sample at the same horizontal level was placed 5 cm away the sample center-point, which was used as a reference to reflect the local flame incident radiative heat flux. The flame spread process was recorded using two Canon cameras (ISO 2500, shutter speed 1/30, F5.6, 1920 × 1080@30 fps) from the top and side views. The experimental conditions are listed in Tables 1 and 2. 3. Experimental results and discussion
No.
Pressure (kPa)
O2 (%)
1 2 3 4 5 6 7
10 20 25 30 50 70 90
43 (LOC), 45, 47, 49, 51 29 (LOC), 31, 33, 35, 37 27 (LOC), 29, 31, 33, 35 25 (LOC), 27, 29, 31, 33 21, 23, 25, 27, 29 21, 23, 25, 27, 29 21, 23, 25, 27, 29
icantly, whereas above 25 kPa, owing to the increasing buoyancy, the flame height increases noticeably and establishes a longitudinal asymmetry structure. Moreover, when the ambient pressure exceeds 25 kPa, with increasing pressure and oxygen concentration, the flame turns more yellow and luminous. Figure 3(a) shows the radiative heat flux 5 cm away from the sample against oxygen concentration and pressure while Fig. 3(b) shows the radiative heat flux and flame temperature at 43% O2 against pressure. It can be seen that 25 kPa is clearly a transition point for the increase rate of radiative heat flux. Furthermore, both the oxygen concentration and pressure have positive effects upon the increase of radiative heat flux, while at the same oxygen concentration the flame temperature has a significant decrease with increasing pressure. It is because that with increasing oxygen concentration and pressure the oxygen partial pressure increases, the combustion becomes stronger with a higher heat release rate, so the radiative heat feedback significantly increases. Moreover, at the same oxygen concentration, with the increasing pressure, the production of soot particles increases, as the soot yield Ys is inversely proportional to the soot formation time and hence in diffusion flames it follows the second order of ambient pressure [5]. Meanwhile, the gaseous combustion products of H2 O and CO2 increase linearly with pressure. Thus the radiation heat loss increases and the flame temperature decreases. Figure 4(a) shows Vf d/W against oxygen concentration and ambient pressure using the experimental data in this work and the work of Frey and T’ien [3], where the extinction, upper and lower limits are given. It is seen that in the extinction limit regions below 25 kPa, the FSR increases non-linearly with the pressure, while in the classical power law region above 25 kPa the FSR increases linearly with the pressure. Figure 4(b) presents the fitting of (V f d/W )/YO1.4 and (V f d/W )/YO2 against ambient pressure. 2
Therefore, the global correlation of FSR involving the two regions is expressed as Eq. (2):
V f ∝ YO12.4 p0.66 V f ∝ YO2 p
( p < 25 kPa ) ( p > 25 kPa )
(2)
In the literature, the FSR has been justified to linearly correlate to the flame heat feedback, which can be calculated using Eq. (3) [6]:
Vf =
q˙f b δ f
(3)
ρ c p d (Tig − Ts )
Here, q˙f b is the net heat flux to the sample surface, q˙f b = ˙ , where q˙ is the flame incident heat flux, which is proq˙f − qloss f portional to the overall reaction rate m˙ = ρg A0Y nY m exp(−E/RT ) F
Figure 2 shows the flame spread images against oxygen concentration and ambient pressure above the flammability limits. It is noted that below 25 kPa the flame is lightless blue and elliptical with a longitudinal symmetry structure. Specially, only when pressure above 25 kPa, the yellow flame will be shown. As the pressure increases, below 25 kPa, the flame size increases signif-
F
O2
˙ where the exponent m is approximately 1.5 [7]. The heat loss qloss mainly includes the radiation losses from the flame and the sample surface. δ f is the distance between flame front and ignition point (preheating length), d the sample thickness, ρ the sample density, cp the sample specific heat, Tig the ignition temperature, Ts the surface temperature.
92
J. Fang et al. / Combustion and Flame 188 (2018) 90–93
Fig. 2. Flame spread images via varied oxygen concentration and ambient pressure.
Fig. 3. Flame incident radiative heat flux and temperature (a) flame incident radiative heat flux 5 cm away from the sample via oxygen concentration and pressure and, (b) incident radiative heat flux and flame temperature against pressure at 43% O2 .
Fig. 4. Flame spread rate against pressure (a) Vf d/W via pressure and O2 concentration and, (b) (V f d/W )/YO12.4 and (V f d/W )/YO2 against pressure. Note, W is the sample width, d is sample thickness, and the subscript f is the flame. d = 0.012 cm, W = 2 cm for this study; d = 0.019 cm, W = 1 cm for the study of Frey and T’ien [3].
J. Fang et al. / Combustion and Flame 188 (2018) 90–93
The Damköhler number (Da) relates to the flow timescale and the chemical reaction timescale. For weak flame spread in quiescent and low ambient pressure conditions, the induced convection is comparatively weak and the induced airflow opposes the flame spread, so the flow time is approximately the same magnitude as the molecular diffusion time, thus, the Da number can be expressed as the ratio of molecular diffusion timescale to chemical reaction timescale. In the extinction limits (non-linear) region, the molecular diffusion coefficient is inversely changing to the ambient pressure, while the oxygen partial pressure is low. Therefore, due to the small diffusion timescale and the large reaction timescale, the Da number is small and the flame spread is gas phase kinetics controlled [6]. Hence, the flame is relatively small with a low burning rate and combustion heat release, q˙f is low and the flame is blue with less radiation loss. As a result, the flame has a higher temperature. For condensed solids, the flame spread is a continuous ignition process, which involves the onset of nearstoichiometric burning and is characterized by a mass flux and a heat release rate that are 2–3 times higher than those at incipient ignition [8]. So although the flame temperature is high, the low mass flux and heat release rate cannot sustain a high FSR. Additionally, the buoyancy is weak so the flame has a small size with ˙ . The distance between the a symmetrical structure and a low qloss gas–solid phases was short and thus q˙ is determined by the gas fb
phase kinetics and the FSR is more sensitive to the oxygen concentration as ∝ q˙ f ∝ YO1.4 . Meanwhile, as the gas phase chemical reac2 tion employs a dynamic equilibrium of the oxygen partial pressure pYO , the FSR has a weak dependence on the ambient pressure as 2
∝p0.66 . In the power law (linear) region, in contrast to the non-linear region, the Da number is relatively large, the flame spread is heat transfer controlled [6]. As the oxygen partial pressure is generally larger, the burning rate increases significantly compared to those in the extinction limits (non-linear) region, and the flame has a larger size with a higher incident heat flux of q˙f , so that the FSR is
93
significantly higher. However, due to the increase of ambient pressure, the buoyancy becomes stronger, as a result, the flame height increases significantly with an asymmetric structure. The distance between the gas–solid phases increases. Additionally, the flame is ˙ and a low flame temmore luminous with more radiative loss qloss perature. Thus, q ˙ is mainly determined by the flow field heat fb
transfer, which reduces the dependence of FSR on the oxygen concentration as ∝ YO and correspondingly enhances the dependence 2 of FSR on the ambient pressure as ∝p. Acknowledgements This work was sponsored by the National Natural Science Foundation of China (no. 51636008, 51576186, 51323010), Key Research Program of the Chinese Academy of Sciences (no. QYZDBSSW-JSC029), National Key R&D Program (2016YFC0801504) and Fundamental Research Funds for the Central Universities (WK2320 0 0 0 034, WK2320 0 0 0 036). K. Li has received funding from the European Research Council (ERC) under the European Union’s H2020 – the Framework programme for Research and Innovation (2014-2020) / ERC Grant Advances Agreement no. 670747 – ERC 2014 AdG/FireBar-Concept. References [1] S.L. Olson, P.V. Ferkul, J.S. T’ien, Near-limit flame spread over a thin solid fuel in microgravity, Symp. (Int.) Combust. 22 (1989) 1213–1222. [2] Y. Zhang, J. Ji, J. Li, J. Sun, Q. Wang, X. Huang, Effects of altitude and sample width on the characteristics of horizontal flame spread over wood sheets, Fire Saf. J. 51 (2012) 120–125. [3] A.E. Frey, J.S. T’ien, Near-limit flame spread over paper samples, Combust. Flame 26 (1976) 257–267. [4] R.F. McAlevy, R.S. Magee, The mechanism of flame spreading over the surface of igniting condensed-phase materials, Symp. (Int.) Combust. 12 (1969) 215–227. [5] J.L. de Ris, P.K. Wu, G. Heskestad, Radiation fire modeling, Proc. Combust. Inst. 28 (20 0 0) 2751–2759. [6] J.G. Quintiere, Fundamentals of fire phenomena, Wiley, 2006. [7] C.K. Westbrook, F.L. Dryer, Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames, Combust. Sci. Technol. 27 (1981) 31–43. [8] R.E. Lyon, J.G. Quintiere, Criteria for piloted ignition of combustible solids, Combust. Flame 151 (2007) 551–559.