An investigation of horizontal opening effect on pool fire behavior in a confined compartment: A study based on global equivalence ratio

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1 Original Article An investigation of horizontal opening effect on pool fire behavior in a confined compartment: A study based on global equivalence ratio Journal of Fire Sciences 2016, Vol. 34(1) Ó The Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalspermissions.nav DOI: / jfs.sagepub.com Xiao Chen 1,2, Shouxiang Lu 1 and Kim Meow Liew 2 Date received: 18 June 2015; accepted: 15 October 2015 Abstract This article involves an experimental study of horizontal opening effect on pool fire behavior in a confined compartment. Five pan diameters and six horizontal opening sizes were adopted and measurements included extinction time, mass loss, oxygen concentration, temperature in the compartment and horizontal opening and pressure difference at the top and bottom of compartment. The global equivalence ratio was theoretically simplified under the horizontal opening condition. The global equivalence ratio coupling the horizontal opening and fuel areas was proposed to deal with these measuring parameters obtained. The results show that extinction time presents different variation trends for the burning out and self-extinction modes. Then, the critical global equivalence ratio value can be used to divide the self-extinction and burning out regions based on the mass loss rate and oxygen concentration values. Moreover, the opening size affects the smoke layer interfaces in the compartment, and the maximum and average temperature rises in the vent present first increase and then decrease distribution with an increase in global equivalence ratio. Pressure difference in the compartment decays exponentially as horizontal ventilation increases. Keywords Global equivalence ratio, pool fire behavior, confined compartment, self-extinction, burning out 1 State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, People s Republic of China 2 Department of Architectural and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong Corresponding author: Shouxiang Lu, State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei , People s Republic of China. sxlu@ustc.edu.cn

2 14 Journal of Fire Sciences 34(1) Introduction Ventilation openings play a key role as a means of mass and energy transfer for compartment fires; hence, their effects, especially those of vertical openings, on compartment p fire behavior have been widely studied. 1 4 As for the vertical opening, the term A ffiffiffiffi H is commonly known as the ventilation pffiffiffiffi factor for evaluating flashover fire. 5 Utiskul et al. 4 presented p ffiffiffi a ventilation parameter A 0 H r g =Af with a quasi-steady theory to divide the following three distinct regimes of burning behavior: (1) extinction because of filling, (2) extinction occurring as blow-off, and (3) extinction until burn out. For horizontal openings, salt-water modeling has been widely adopted as a clear and simple way to study fire behavior in compartments with horizontal partitions. 6 8 The ratio of vent thickness and equivalent diameter of vent (L/D) is generally considered a factor for dealing with density-driven flow parameters in tanks. 6,7 In recent years, many researchers have conducted experiments on compartment fires to study the horizontal opening effect on fire behavior Jansson et al. 9 were the first to conduct wood fire experiments in a 6 m 3 6m 3 6 m ceiling-vented compartment. In the study, the mass loss rate (MLR) of wood cribs, temperature in the upper compartment, and oxygen and carbon dioxide concentration in the lower compartment were measured to show that increasing the opening size could increase heat release rate and smoke temperature. Takeda 10 investigated ship fire behavior using a reduced-scale enclosure with a ventilation opening in the center of the ceiling and found two major effects of the opening on the model ship fire. Tu 11 discovered that pool fire behaviors such as choking, extinction, steady burning, and ghosting vary with vent size; this finding has been expanded in the studies of Wakatsuki, 12 Li, 13 and Chen. 14 Chen et al. 15 and He et al. 16 analyzed the effect of vent size on the pool fire parameters of ceiling-vented compartments. Yu and Joshi 17 considered the effects of four different types of vent configurations on the thermal performance of discrete components in partially opened horizontal enclosures. Zhang et al. 18,19 conducted a preliminary study on the impact of vent location on ceilingvented compartment fire with computational fluid dynamics (CFD) technology. As stated previously, many studies have explored important fire parameters, such as burning rate, 9,12 compartment temperature, 9,10,12 and burning behavior, as well as opening parameters such as size, 15,16 form (rectangle or circle), 17 and location. 18,19 It is not enough to analyze the compartment fire behavior with the horizontal opening size and fire size separately; besides, the fire behavior could not be characterized in the over- to under-ventilated fire conditions with the two factors either. However, the research considering the coupling effect of fire size and horizontal opening on the compartment fire parameters has not been discussed comprehensively. Therefore, focus should be directed toward the analysis of coupling parameters on the fire parameters. This article reports the results of small-scale experiments performed by State Key Laboratory of Fire Science (SKLFS). The major goal was to investigate the horizontal opening effect on heptane pool fire behavior in a confined compartment. First, the experimental facilities and sets of small-scale tests are described in detail, and several parameters are obtained, such as MLR, temperature in the compartment and the horizontal opening, oxygen concentration, and pressure difference in the compartment. Then, a global equivalence ratio (GER) coupling horizontal opening and fuel areas was proposed to deal with horizontal opening effect on the fire behavior. Moreover, the effects of GER on MLR, temperature in the vent, oxygen concentration, and pressure variation were also studied.

3 Chen et al. 15 Theory In ventilation-controlled fires, the effects of the mass flow rate of air and fuel MLR are characterized by the GER, 20 which is normalized so that transition from over- to underventilated fire conditions occurs at near-unity values. The GER is given as 20 f = r o _m 00 f A f Y o2, air _m air ð1þ where f is the GER; r o is the stoichiometric oxygen-to-fuel mass ratio (g/g), for heptane, it equals 3.52; A f is the fuel area (m 2 ); Y o2, air is the mass fraction of oxygen in air (0.23); _m air is the mass flow rate of air and _m 00 f is the fuel MLR (kg/m 2 s). Epstein 6 derived an empirical equation for predicting the air mass flow rate for orifice vents based on salt-water experiments; this equation is expressed as follows _m air = 0:068r A 5=4 pffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 g 2(1 u) ð2þ (1 + u) 1=2 where u = T T g ð3þ and r, A 0, g, T, and T g are the ambient air density, opening area, acceleration of gravity, ambient air temperature, and gas temperature in the compartment, respectively. The compartment MLR could be estimated in terms of free burning rate with the effect of oxygen concentration and temperature 19,21 _m 00 f = _m 00 f, (1 e t=t s ) Y o2 Y o2, air + Fs(T 4 g T 4 ) L where _m 00 f, is the free burning rate, refer to Chen et al.,22 the free burning rate per area changes insignificantly with pan size. Hence, we selected the free burning rate _m 00 f, for heptane of kg/m 2 s in this study. t s is the steady burning time; Y o2 is the oxygen mass fraction in the compartment; Y o2, air is the ambient mass fraction of oxygen; F is the radiation view factor, which is assumed to be 1; s is the Stefan Boltzmann constant, s = 5: kw=m 2 K; T g and T are the upper compartment gas temperature and ambient temperature, respectively; L is the latent heat of vaporization of the fuel, and it could be 320 kj/kg for heptanes. 23 Set the case 14-cm pool fire under the 10-cm horizontal opening as an example; the fuel MLR calculated in Equation (4) is illustrated in Figure 1, and the oxygen term and radiation term are also shown in the figure. As we can see from Figure 1, the MLR in the radiant term is much smaller than that of oxygen term; hence, the radiant term could be ignored with considering the MLR in the steady burning stage. Therefore, equation (4) could be simplified as _m 00 f _m 00 Y o2 f, ð5þ Y o2, air ð4þ

4 16 Journal of Fire Sciences 34(1) Figure 1. Fuel mass loss rate calculated with the effect of oxygen and radiant. Substituting equations (2) and (5) into equation (1) Y o2 r o _m 00 f, A f f = qffiffiffiffiffiffiffiffiffiffi 0:068Yo 2 2, air r A 5=4 0 g 1=2 2(1 u) 1 + u ð6þ Factor b can be defined as follows b = r o _m 00 f, 0:068Y 2 o 2, air r g 1=2 ð7þ Thus, the GER was adopted in dealing with the fire parameters. In this case, r would be 1.2 kg/m 3, and g would be 9.8 m/s 2. Hence, b is a constant of 3.9 (m 1/2 ) only for heptanes in this study. Hence, the GER can be expressed as f = by o2 A f qffiffiffiffiffiffiffiffiffiffi A 5=4 0 2(1 u) 1 + u ð8þ Experiment The experiments were conducted in a confined compartment with a horizontal opening as shown in Figure 2. The inner dimensions of the compartment are 1.0 m m m. The compartment is enclosed with toughened glass (a glass supporting temperature up to 950 C) fixed by stainless steel on each side. The thickness of the steel and the glass is 5 mm. The compartment is fully enclosed except for a horizontal central partition in the ceiling. In order to investigate the horizontal opening effect on pool fire behavior, five circle pans with diameters of 7, 10, 14, 20, and 25 cm and six opening sizes (5, 10, 20, 30, 40, and 50 cm)

5 Chen et al. 17 Figure 2. Schematic of experimental setup. were used. The circle pan was placed in the center of the floor and n-heptane was selected as fuel. The depth of fuel was kept 1.3 cm before ignition in each experiment. The horizontal opening was located in the center of the ceiling level, and only one opening was used in each experimental test. A Shimadzu load cell with a maximum capacity of 6.2 kg and a resolution of 0.1 g was used to obtain the mass loss. In the experiment, the mass loss was recorded at an interval of 1 s. Three thermocouple trees were positioned in the compartment; each thermocouple was K-type with diameter of 1 mm. Two of these trees were used to measure the gas temperature in the compartment, and the rest thermocouple tree was to obtain the gas temperature variation in the horizontal opening. Gas analyzer was used to measure oxygen concentration at the base of fire and calibrated before every experiment. Two differential pressure sensors with a maximum capacity of 500 Pa and a resolution of 0.01 Pa were installed 5 cm apart from the floor and ceiling, respectively, to measure the pressure difference between the top and bottom of the compartment. A video camera was used to record the process of the fire to obtain the extinction time more accurately, and the camera was also adopted to determine the extinction mode. Each test was repeated at least twice. Results and discussion Extinction time In general, flame extinction is divided into two modes based on the lack of fuel or oxygen at extinction: fuel burn out mode (lack of fuel) and self-extinction mode (lack of oxygen). The experimental results for the extinction time and extinction mode are listed in Table 1. Flame

6 18 Journal of Fire Sciences 34(1) Table 1. Summary of experimental results. Test no. Vent size (cm) Pool size (cm) Fire duration (s) Extinction mode Self-extinction Fuel burn out Fuel burn out Fuel burn out Fuel burn out Fuel burn out Fuel burn out Self-extinction Self-extinction Self-extinction Fuel burn out Fuel burn out Fuel burn out Fuel burn out Self-extinction Self-extinction Self-extinction Fuel burn out Fuel burn out Fuel burn out Fuel burn out Self-extinction Self-extinction Self-extinction Self-extinction Self-extinction Self-extinction Self-extinction Self-extinction extinction is widely known to be affected by flame heat loss and energy release rate, 24 and the mechanism of flame extinction is so complicated that it will not be discussed in this article. As a significant parameter for inspecting pool fire behavior in compartments, 25 flame extinction time has been analyzed by several researchers under the self-extinction mode. 26,27 Beyler 28,29 proposed a self-extinction time model for closed rooms with an assumption of steady burning and limiting oxygen index. Meanwhile, for ceiling-vented compartments, He et al. 16 made a preliminary attempt to deal with the effect of vent size on the self-extinction of pool fires and found an exponential relationship between self-extinction time ratio and dimensionless ceiling vent size on the basis of species concentration. In this work, the extinction times for the burning out and self-extinction modes are discussed separately. The variations in the extinction times under the burning out mode with the GER are illustrated in Figure 3. With the increasing GER, the extinction times of the pool fires with three diameters presented an increasing trend. Figure 4 presents the dimensionless extinction time ratio, which reduced with the increasing GER for the cases wherein the flame extinction was under the self-extinction mode. The dimensionless extinction time

7 Chen et al. 19 Figure 3. Extinction time versus global equivalence ratio in the burning out cases. Figure 4. Self-extinction time ratio versus global equivalence ratio. ratio t E, vent =t E, closed is defined as an extinction time ratio of a ceiling-vented compartment and a closed compartment. The experimental results on extinction time in the closed compartment are listed in Table 1. As shown in Figure 3, t E, vent =t E, closed grew exponentially as f increased. The correlation is hypothetically fitted as follows t E, vent = a exp f + c ð9þ t E, closed b

8 20 Journal of Fire Sciences 34(1) Figure 5. Mass loss rate per area versus global equivalence ratio. where a, b, and c are constants. The time ratio is sufficiently fitted with a correlation coefficient of 0.98 as follows t E, vent = 17:4 exp f + 1:1 ð10þ t E, closed 1:8 The fitting results and those of He et al. 16 under the self-extinction mode all present the exponential relationship. MLR and oxygen concentration The MLR and oxygen concentration have been studied, along with the horizontal opening effect. 30,31 In this part, we attempt to determine the proposed GER for dealing with MLR and oxygen concentration under the confined compartment with the horizontal opening condition. Figure 5 demonstrates that the average values of MLR varied with the GER. The average MLR values were calculated over the stable burning period or the whole burning period. A decreasing trend can be found in the MLR for the burning out mode with GER increasing (Figure 5). Whereas for the MLR in the self-extinction mode, it keeps stable with an increase in the GER. The experimental data in the work of Wakatsuki 12 also conform to this distribution. When the GER f was larger than 1, the pool fire extinction was observed because of the lack of sufficient oxygen (self-extinction region). Meanwhile, when f was smaller than 1, the pool fire was extinguished because of fuel burn out (burning out region). The critical GER value of 1 to divide the burning out and self-extinction regions was in consistence with the previous study. 20,32 In this figure, the point at a diameter of 7 cm for the 5- and 10-cm horizontal openings (the red dotted line circle) does not follow the trend. It may be that the predicted mass flow rate value in Epstein s equation was smaller than that of the real value. It would take much

9 Chen et al. 21 Figure 6. Variation in oxygen concentration with global equivalence ratio. burning time for the smaller pool fire under the smaller horizontal opening that the thermal storage of the compartment is much less, and the convective heat loss is much bigger. Nevertheless, this trend indicates that the GER could be used to distinguish fire extinction behavior in the ceiling-vented compartment. The oxygen concentrations (volume concentrations) at extinction time are plotted against the GER (Figure 6). These experimental results show good agreement with the Boltzmann fitting, with the correlation coefficient being The division of the self-extinction and burning out regions is consistent with that of MLR of the critical GER. In the self-extinction region, oxygen concentration varied from 13.9% to 16.3%, which is well within the range reported by Wakatsuki. 12 Meanwhile, oxygen concentration ranged from 17.5% to 20.6% in the burning out region. Gas temperature profile The smoke movement and temperature distributions have unique characteristics for the ceiling-vented compartment. The smoke front, indicated by the point where the gas temperature begins to rise, reaches the compartment bottom after ignition and ever since, the temperatures seem to increase linearly with the height. 13,14,33 The typical vertical gas temperature profiles for the compartment fire with a horizontal opening are presented in Figure 7. In the figure, the gas temperature presents piecewise linearity with the compartment height under different horizontal opening sizes. The black line denotes the smoke layer interface, which is defined with the vertical temperature distribution, and could be roughly estimated with the mean vertical variations in gas temperature. Figure 7(a) shows that the smoke layer was divided into two layers and the smoke layer interface was kept at a height of 85 cm. The temperature gradient in the lower layer increased over the burning time. Hence, the 0.2-m horizontal opening above the pool fire was not large enough to make the air and smoke mix uniformly in the lower smoke layer over the burning time. Meanwhile, for the large opening (Figure 7 (b)), the smoke layer interface changed over

10 22 Journal of Fire Sciences 34(1) Figure 7. Vertical temperature distribution for 10-cm pool fire in the compartment: (a) opening size of 20 cm and (b) opening size of 40 cm. the whole burning stage. At the early stage (0 50 s), the smoke layer split into two layers, similar to the case of the 0.2-m horizontal opening. At the middle stage ( s) and later stage ( s), the smoke layers split into three layers. The smoke layer interfaces were observed at the heights of 85 and 35 cm at the middle stage and at the heights of 55 and 35 cm at the later stage. Therefore, opening size affects the temperature distribution in a compartment for the same pool fire size. The average rate of gas temperature rise in a compartment with fire at different locations (center, wall, and corner) has been discussed. 34 The average rate of gas temperature rise for center fires is larger than that for wall and corner fires. Meanwhile, the average rates of gas temperature rise for fires at the center of a compartment are relatively dispersed compared with other conditions. In the previous study, the average rate of gas temperature rise was defined as the following equation dt g = (T g, peak T 0 ) ð11þ dt aver t peak where T g, peak is the peak temperature rise in the compartment, T 0 is the ambient temperature, and t peak is the duration from ignition to peak temperature rise. A good exponential fitting was found in the average rate of gas temperature rise and pool size (Figure 8). The influence of pool size on the average rate of gas temperature rise could be expressed as the following power equation: (dt g =dt) aver = 2: D 3:64 f, and R 2 = Zhang 34 found that the relationship between the average rate of gas temperature rise and pool size is (dt g =dt) aver ; D 3:16 f. In this study, the influence of the horizontal opening on the average rate of gas temperature rise was also considered. Figure 9 presents the average rate of the gas temperature rise affected by the horizontal opening for the three pool fires. The (dt g =dt) aver varies with horizontal opening (L). The correlations are expressed in the following equations. For the three pool fires, (dt g =dt) aver demonstrated a quadratic relationship with the increasing horizontal

11 Chen et al. 23 Figure 8. Average rate of gas temperature rise affected by pool size. Figure 9. Average rate of gas temperature rise affected by horizontal opening size. opening. The 20- and 30-cm openings for the three pool fires presented small average rates of gas temperature rise: D = 14 cm,(dt g =dt) aver ; L 2, R 2 = 0:94; D = 10 cm,(dt g =dt) aver ; L 2, R 2 = 0:91; (12) D = 7 cm,(dt g =dt) aver ; L 2, R 2 = 0:90.

12 24 Journal of Fire Sciences 34(1) Figure 10. Variation in temperature rise in the horizontal opening with global equivalence ratio for different pool fires. As shown in Figure 10, the maximum and average values of the rise in hot smoke temperature in the horizontal opening (T v T amb ) varied with the GER f for the 7-, 10-, and 14-cm pool fires. The maximum values of the temperature rise were the peak values during the smoke flow period, and the average values of the temperature rise were calculated over the whole flow period. Figure 10 shows an apparent trend, that is, the maximum and average values of the temperature rise show an increase trend and then decrease with the increasing GER. Figure 10 also shows that pool fire size affects variation trends and temperature peaks. For the large pool fire (D = 14 cm), the maximum and average temperature peaks were equal to 133 C and 80 C, which exceeded those under the other pool fires. Pressure difference in the compartment In general, pressure in an enclosure is considered uniform. 35 In this study, the pressure difference in the compartment with a vertical opening served as the main driving force that affected the vent flow in the opening. Meanwhile, the pressure difference in the horizontal opening was mainly affected by thermal expansion and the buoyancy of the hot gas. Although a small leakage may not cause a very high pressure rise, the effect of leakage will affect the heat transfer and distribution inside a compartment. In addition, a large leakage will affect the fire-induced flow patterns through horizontal partitions. However, little research attention has been directed to pressure variations induced by pool fires in ceilingvented compartments. For the main study, we focus on the pressure difference in the top layer of the compartment and utilize such pressure difference as the foundation of the mathematical modeling of the compartment with a horizontal opening. The pressure histories in the bottom and top levels of the compartment are illustrated in Figure 11. The variation tendency of pressure in the top and bottom levels of the compartment is similar to that in the closed compartment. After pool fire ignition, the pressure reached its maximum value within a short period. Then, the pressure decreased and

13 Chen et al. 25 Figure 11. Pressure variation in the bottom and top levels of the compartment. P top, Pressure in the top level of the compartment; P bot, Pressure in the bottom level of the compartment. oscillated steadily in a certain range. When the fire was extinguished, the pressure reached its minimum value. Notably, the maximum and minimum pressure values changed insignificantly in the case of a large leakage. This phenomenon is verified in the following sections on the basis of the over-pressure and low-pressure peaks. According to the four figures in Figure 11, the pressure values in the steady burning stage remained stable initially and then changed in the extinction time. The over-pressure and low-pressure peaks in the top level of the compartment under small leakages are listed in Table 2. Five pool fires were used for comparison. The pool size (i.e. 25 cm) was expected to significantly affect the pressure peaks. With the increasing pool size, the absolute values of the over-pressure and low-pressure peaks increased, and the lowpressure peak increased toward the negative direction. The changing range of the overpressure or low-pressure peaks for the 20-cm horizontal opening was smaller than that for the 5-cm horizontal opening. Given the heat expansion force developed by the pool fire, the pressure distribution in the compartment was not uniform, and a pressure gradient was observed along the compartment height. In this test, two pressure probes were utilized to test the pressure difference in the top and bottom levels of the compartment. The pressure gradient obtained would then

14 26 Journal of Fire Sciences 34(1) Table 2. Over-pressure and low-pressure peaks (in the top level) under different horizontal opening sizes. Pool size (cm) Horizontal opening (cm) Pressure peak (Pa) Pressure peak (Pa) Pressure peak (Pa) Over Low Over Low Over Low Figure 12. Pressure difference between the top and bottom levels of the compartment under different pool fires. be used to analyze the pressure distribution of the compartment. The pressure differences between the top and bottom levels in the compartment for different pool fires are illustrated in Figure 12. Under the same leakage, the pressure difference in the compartment increased with the increasing pool size. For the same pool fire, the pressure difference in the compartment decreased with the increasing horizontal opening. Meanwhile, the pressure difference among the three horizontal opening sizes was larger for the large pool fire (i.e. 25 cm) than for the small pool fire (7 cm). Figure 13 illustrates the variation in the average pressure difference in the confined compartment with a horizontal opening with the GER f. The average pressure differences were calculated over the stable burning period. As can be seen in Figure 13, the pressure difference in the compartment for the burning out mode and self-extinction mode shows an increasing

15 Chen et al. 27 Figure 13. Variation in the pressure difference in the compartment with the global equivalence ratio. trend with the GER rising, and the pressure difference in the compartment correlates well with the GER in the exponential form for the different pool fires. Conclusion An experimental study of pool fire behavior in a confined compartment was conducted with consideration of the horizontal opening effect. Extinction time, mass loss, oxygen concentration, temperature in the compartment, and horizontal opening and pressure difference at the top and bottom levels of the compartment were measured. A dimensionless GER coupling the horizontal opening and fuel areas was proposed with the theoretically simplified method for the horizontal opening condition. The extinction time under the burning out mode presented an increasing trend with the increasing GER, whereas the extinction time for the selfextinction mode showed a decreasing trend. The critical GER to divide the self-extinction and burning out regions was consistent with that in the compartment fire with vertical opening condition. The opening size obviously affected the smoke layer interfaces in the compartment, and the maximum and average temperature rise in the vent presented a similar Poisson distribution with the increasing GER. The pressure difference in the compartment increased exponentially as the GER increased. We have conducted this research in the scaled compartment in advance, and we will conduct a large-scale study in the later. However, we still seek to do some exploration; the GER, which is a dimensionless parameter, was adopted to analyze the compartment fire behavior from over- to under-ventilated fire conditions. We try our best to explore based on the existing condition. Of course, the scalability needs further discussion. Many parameters could affect the fire behavior in the confined compartment, such as the physical parameters of the wall material and the fuel type. In the future, more work should be conducted to investigate the horizontal opening effect with considering these factors.

16 28 Journal of Fire Sciences 34(1) Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Research Fund for the Doctoral Program of Higher Education of China (Project no ), the National Natural Science Foundation of China (Project no ), and the Research Grants Council of the Hong Kong Special Administrative Region, China (Project no , CityU ). References 1. Bullen ML and Thomas PH. Compartment fires with noncellulosic fuels. Symp Combust 1979; 17(1): Steckler KD, Baum HR and Quintiere JG. Fire induced flows through room openings flow coefficients. Symp Combust 1985; 20(1): Quintiere JG. Fire behavior in building compartments. P Combust Inst 2002; 29: Utiskul Y, Quintiere JG, Rangwala AS, et al. 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17 Chen et al Williams MP. Application of thermodynamic and detailed chemical kinetic modeling to understanding combustion product generation in enclosure fires. Fire Safety J 1994; 23: Yuan M, Lu S, Zhou Y, et al. A simplified mathematical model for predicting the vertical temperature profiles in enclosure fires without vertical opening. Fire Technol 2014; 50(4): Zhang JQ. Fire dynamics in ship enclosures considering the effects of ceiling vent and fire locations. PhD Thesis, University of Science and Technology of China, Hefei, China, Quintiere JG. Compartment fire modeling. In: DiNenno PJ, Drysdale D, Beyler CL, et al. (eds) The SFPE handbook of fire protection engineering. 3rd ed.quincy, MA: National Fire Protection Association, 2002, pp Appendix 1 Notation A f fuel area (m 2 ) A 0 opening area (m 2 ) D f fuel pan diameter (m) F radiation view factor ( ) g acceleration of gravity (g/m 2 s) L latent heat of vaporization of fuel (kj/kg) _m air mass flow rate of air (g/s) _m 00 f fuel mass loss rate (kg/m 2 s) _m 00 f, free burning rate (kg/m 2 s) r o stoichiometric oxygen-to-fuel mass ratio (g/g) t peak duration from ignition to peak temperature rise (s) t s steady burning time (s) T g gas temperature in the compartment (K) T g, peak peak temperature rise in the compartment (K) T ambient air temperature (K) Y o2 oxygen mass fraction in the compartment ( ) Y o2, air mass fraction of oxygen in air ( ) Greek symbols u temperature ratio ( ) r ambient air density (kg/m 3 ) s Stefan Boltzmann constant f global equivalence ratio ( ) Author biographies Xiao Chen received her PhD degree in State Key Laboratory of Fire Science in University of Science and Technology of China in Currently she is a postdoctoral researcher in SKLFS. Her research interest includes compartment fire behavior, liquid fuel combustion, and CFD simulation. Shouxiang Lu received his PhD degree from Nanjing University of Science and Technology in He joined State Key Laboratory of Fire Science in University of Science and Technology of China as a professor in Currently his research interest includes ship fire safety engineering,fire risk assessment methodology, and dynamic of vapor cloud fire and exploration. Kim Moew Liew is the head of Department of Architecture and Civil Engineering and chair professor of Civil Engineering in City University of Hong Kong. His research interest includes civil engineering, structural dynamics, and carbon nanotubes, etc.