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1 Fire Safety Journal 44 (29) Contents lists available at ScienceDirect Fire Safety Journal journal homepage: Eperimental study of fire growth in a reduced-scale compartment under different approaching eternal wind conditions Hong Huang a,, Ryozo Ooka a, Naian Liu b, Linhe Zhang b, Zhihua Deng b, Shinsuke Kato a a Institute of Industrial Science, The University of Tokyo, Komaba, Meguro-ku, Tokyo , Japan b State Key Laboratory of Fire Science, University of Science and Technology of China, Jinzhai 96, Hefei 2326, Anhui, China article info Article history: Received 18 February 28 Received in revised form 1 July 28 Accepted 21 July 28 Available online 9 September 28 Keywords: Reduced-scale compartment fire Eternal wind condition Fire tunnel eperiment Eternal flame abstract In order to clarify the fire growth process in compartments under eternal wind conditions, detailed fire tunnel eperiments were conducted in a reduced-scale compartment. The approaching eternal wind velocity was set to., 1.5 and 3. m/s, and the location of the fire source was changed between the downwind corner, upwind corner and center of the compartment. The eperiments considered the effect of wind on a through-ventilation situation. The temperatures of the air and the wall surfaces in the compartment and the temperatures of the flames ejected from the opening were measured. The fuel mass loss rate and the heat flu from the opening were also recorded. Different fire growth characteristics are shown under different wind and fire source conditions. The temperature rises faster and burnout time is reduced under windy conditions. It is found that eternal wind has two opposing effects. One is to promote combustion within the compartment and thus raise the temperature, the other is to blow away and dilute the combustible gases in the compartment and decrease the temperature, or hasten its etinction. When the approaching wind velocity is high, the eternal plume is greatly inclined to the downwind side, and the flame becomes larger, thus increasing the risk of the fire spreading to neighboring buildings. The dimensionless temperature of the eternal flame was a little lower than the results indicated by Yokoi s eperiments without wind. & 28 Elsevier Ltd. All rights reserved. 1. Introduction A fire initiated in a compartment will spread to the neighboring compartment and adjacent buildings by igniting the other combustible materials and the eposed combustible surfaces. Compartment fires can generally be divided into the following stages: ignition and early growth, pre-flashover period, flashover, fully developed or post-flashover period, and decay period. Numerous studies have been undertaken to investigate the fire s characteristics during these stages [1 3]. The pyrolysis gases generated from the combustible materials will not all burn in the compartment. Under ventilation-dominant conditions, usually in the fully developed stage, the quantity of air necessary for all pyrolysis gases to burn is not supplied, such that part of the pyrolysis gases are projected from the window as eternal flames. This provides a mechanism for fire to spread to the upper floors and adjacent buildings [4 6]. Fire damage is thought to spread notably under windy conditions. Many studies have been conducted on eternal flames in the absence of wind. Yokoi [4] investigated the trajectory and temperature distribution of the Corresponding author. Tel.: ; fa: address: hhong@iis.u-tokyo.ac.jp (H. Huang). eternal flame from a window in several full-scale eperimental fires. The proposed method for estimating eternal flames using the dimensionless temperature is still commonly used now. Bullen and Thomas [7] studied the effect of the fuel area on the eternal flame temperature profiles. Omiya and Hori [8] investigated the properties of eternal flames, taking into consideration the combustion of ecess fuel gas ejected from the fire compartment by conducting a small-scale fire test. Yamaguchi and Tanaka [9] found that the dimensionless temperature is independent of size and fire temperature, but is determined by geometrical conditions. However, the effect of eternal wind has hardly been considered in these studies, including compartment fire growth in a room and eternal flames. In the case of urban fires, wind entering through broken openings will increase the pressure in the burning room. Thus, high-temperature gas may be violently ejected, increasing the risk of the fire spreading. There is some research regarding eternal flame characteristics in windy conditions [1]; however, a detailed fire growth process from the initial fire to the fully developed fire in a compartment, in the presence of eternal wind, has not been eamined. In this study, a reducedscale compartment fire eperiment with consideration for eternal wind has been conducted in a fire wind tunnel. The fire growth process from the initial fire to the fully developed fire in the compartment and the eternal flames from the opening were /$ - see front matter & 28 Elsevier Ltd. All rights reserved. doi:1.116/j.firesaf

2 312 H. Huang et al. / Fire Safety Journal 44 (29) Nomenclature B width of the opening (m) C wind pressure coefficient C p specific heat (kj/kg/k) H height of the opening (m) H l height of the bottom of the opening (m) H u height of the top of the opening (m) m in flow rate entering the opening (m 3 /s) m out outflow rate from the opening (m 3 /s) p w wind pressure on the wall surface (Pa) Dp pressure difference between inside and outside (Pa) Q enthalpy of the ejected gas (kw) r pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi equivalent radius of the opening ( BH=2p,m) DT temperature difference between the inside and outside of the compartment (K) DT temperature rise at arbitrary position along the plume ais (K) T N temperature of the ambient environment (K) V N approaching wind velocity (m/s) Z n neutral plane height (m) a opening flow coefficient r density (kg/m 3 ) r in density of the air in the compartment (kg/m 3 ) r N density of the ambient air (kg/m 3 ) Y dimensionless temperature measured, and the effect of the eternal wind was analyzed in detail. 2. Eperiments 2.1. Fire tunnel and reduced-scale compartment model The fire tunnel used has dimensions of 1.8 m (width) 1.8 m (height) 14 m (length). Fig. 1 shows the fire wind tunnel and reduced-scale compartment model. The wind approaches from the right side in the figure. The compartment model size is mm 3. Because the width of the possible test zone of the fire tunnel is 6 mm, a 6 m m cubic compartment model was chosen for this eperiment. This is also approimately 1 5 scale of a typical Japanese compartment room. The sidewalls of the model are made of wooden cedar boards (25 mm), fire-resistant boards (32 mm) and stainless steel sheets (2 mm) from the inside to outside. The ceiling and floor are made of the same fireresistant boards and stainless steel sheets. Windows of 2 2 mm 2 are opened at the center of the upwind and downwind sides of the model. Two hundred and fifty milliliters of n-heptane was used as the fuel, which was placed in a stainless container (1 1 mm 2 ) and ignited Measurement As shown in Fig. 1, the approaching wind was measured at three points vertically on the upwind side at heights of 3, 6 and 9 mm above the floor. The uniformity of the wind speed was confirmed in the vertical direction. A wind velocity measurement point was also positioned on the upwind side of the compartment model to monitor the wind velocity before entering the window. Hot-wire anemometers (Kanoma, KA12) were used to measure the wind velocity. Fig. 2 shows a schematic Fire Wind Tunnel diagram of the eperimental measurement configuration around the compartment model. The temperatures were measured in the compartment, on the wall and outside the opening. K-type thermocouples (j ¼ 1 mm) were used for temperature measurements. The air temperatures in the compartment were measured at nine points in the horizontal direction along the four aes in the vertical direction; thus, a total of 36 points were measured. The wall temperatures were measured uniformly on each wall at nine points (for those walls with openings, eight points were measured). The thermocouples were attached to the surfaces of the wooden wall by fine wires to ensure enough contact between the thermocouple sensor and the wall surface. The thermocouples measuring the eternal flame temperature were fied on a steel lattice. A total of 48 points were placed at 2 mm intervals. A heat flu meter (FMMI, HYJ-1) was positioned at one point outside the model to measure the heat flu from the window. This is a no water-cooled Gardon-type total heat flu transducer without a window. The mass loss rate of the fuel was measured by an electronic balance (Sartorius, LA641S, made in Germany) set underneath the fuel container. The range is 64. kg, with an accuracy of.1 g Eperimental cases The eperimental cases are shown in Table 1. Three approaching wind velocity conditions,., 1.5 and 3. m/s, were set. The fire source was either in an upwind corner, a downwind corner or the center of the compartment. In order to facilitate verification of the flame characteristics, the eperiments were also conducted under the same conditions, ecept that the sidewall was made of fireresistant glass for easy recording by a video camera. 3. Results and discussion 3.1. Flame characteristics and temporal temperature variation in the compartment 6mm Model 2mm 3mm 3mm Wind velocity measuring points 32mm 3mm WIND 6mm 3 mm 3mm Fig. 1. Fire wind tunnel and reduced-scale compartment model. z The fire progression ehibits different characteristics in different cases. In general, it is found that after several minutes of fire growth the wall surfaces began to burn, the upper layer ignited, and there was a sudden transition from being a localized fire to a conflagration in the compartment in every case. Based on visual inspections, and the variations of temperature and fuel mass rate, it is thought that flashover occurred in this eperiment. Flames etended out of the openings both with and without wind; the flames were ejected not only from the downwind opening but also from the upwind opening during the fully developed fire

3 H. Huang et al. / Fire Safety Journal 44 (29) mm 2mm 2mm 2mm 2mm Thermocouple for air temp. Thermocouple for wall temp Fire Source A A y Measurement ID (From top to bottom) 1mm 2mm 2mm 1mm 15mm 2mm 2mm 15mm 15mm z Heat flu transducer Fire Fig. 2. Measurement configuration. Table 1 Eperimental cases Cases Approaching wind velocity (m/s) Fire source location Case 1. Corner Case Upwind corner Case Downwind corner Case 4 3. Upwind corner Case 5 3. Downwind corner Case 6. Center Case Center Case 8 3. Center period. The wood was burned in the fire, but it was charred and not totally consumed. The pictures of the flames of the early fire in the case of wind velocities of 1.5 and 3. m/s are shown in Fig. 3. When the fire source is in the center, the flame inclined to the downwind direction due to the effect of the approaching wind through the opening. When the fire source is in the upwind corner the flame inclined upwind a little towards the wall surface, whereas when the fire source is in the downwind corner the flame significantly inclined to the upwind direction. This flow characteristic can be eplained in Fig. 4, which is the assumed wind flow pattern at the horizontal section of the compartment model. If there is a main flow through the opening, vortices can be formed in the corners, which leads to the inclination of the flame towards the upwind. Furthermore, when the fire source is in the downwind corner, the flame inclined to the upwind direction more in the case of 3. m/s than that in the case of 1.5 m/s, implying that a greater vorte is formed in the downwind corner in the case of 3. m/s. Fig. 5 shows the mass loss rate of n-heptane for all cases compared with the case where the fuel is burned in free air, outside the compartment. In the free-air cases, in the presence of wind, the rate increases. Air movement tends to enhance the rate of entrainment of air into the fire plume. This is likely to promote combustion within the flame [1], and may lead to the higher burning rate. It is found that the mass loss rate in the compartment is larger than that in the case of free air. In compartment fires, Kawagoe and Sekine [11] found that the

4 314 H. Huang et al. / Fire Safety Journal 44 (29) dm/dt (g/s) U =., Corner Center U =., Center U =., Free air Corner Downwind corner Upwind corner Center.4.2 Free Downwind corner Upwind corner Center Fig. 3. Flame characteristics in early fire. (a) U ¼ 1.5 m/s and (b) U ¼ 3. m/s. dm/dt (g/s) Downwind corner U = 1.5, Upwind corner U = 1.5, Downwind corner U = 1.5, Center U = 1.5, Free air Center Upwind corner Free Horizontal section Fig. 4. Image of the flow in the model. burning rate strongly depends on the size and shape of the ventilation opening. Thomas et al. [12] emphasized that if the opening is enlarged the burning rate becomes independent of the opening size and is determined instead by the surface area. In this study, the mass loss rate in the case of 3. m/s is a little higher than the case of 1.5 m/s and no wind in Fig. 5. This demonstrates the possibility of eternal wind affecting fuel combustion, which should be further investigated. Hasemi [13] and Ohmiya [14] found that there is a good correlation between the incident heat flu to fuels and the burning rate of the fuels. Radiation from hot compartment surfaces and compartment gases may lead to the increase in the incident heat flu, thus resulting in the increased combustion rate. As eamples of the temperature measurement in the reducedscale compartment, Fig. 6 shows the temporal variations of the air temperature at the measurement points 7, 31, 15 and 23 (also refer to Fig. 2), which are at the height of the center of the opening. Points 7 and 31 are at the upwind and downwind side of the fire source, respectively; points 15 and 23 are at the sides of the fire source, respectively. Fig. 7 shows the temporal variations of the wall temperature at the measurement points 38, 55, 49 and 66 (also refer to Fig. 2), which are also at the height of the center of the opening. Points 38 and 55 are at the upwind and downwind side of the fire source, respectively; points 49 and 66 are at the sides of the fire source, respectively. It is found that compartment dm/dt (g/s) Downwind corner Free Center Upwind corner U = 3., Upwind corner U = 3., Downwind corner U = 3., Center U = 3., Free air Fig. 5. Mass loss rate of the fuel. (a) U ¼. m/s, (b) U ¼ 1.5 m/s and (c) U ¼ 3. m/s. fire growth showed different behavior between cases, with windy and still conditions. The temperature rises, the cedar board comprising the wall surface is gradually warmed by the fire source until it reaches its ignition point, and the fire burned out within 8 s in all cases in windy conditions. On the other hand, in the absence of wind, the cedar board on the wall burns for over 8 s. The temperature rises faster and the burnout time is reduced under windy conditions. When the fire source is in the upwind or downwind corner, the temperature rises and decreases faster in the case of wind velocity of 3. m/s than in the case of 1.5 m/s. This implies that a faster-approaching wind seems to enhance the entrainment of oygen to promote the combustion of the fuel, which hastens the temperature rise. On the other hand, it may be assumed that combustible gases are blown out of the compartment by the wind, and the wall surfaces are also cooled by the wind. This may lead to the decrease in temperature. Therefore, stronger wind leads to a faster temperature decrease. When the fire source is in the center, the temperature rises faster

5 H. Huang et al. / Fire Safety Journal 44 (29) U =., Corner U = 1.5, Downwind Corner U = 3., Downwind Corner U = 1.5, Center U = 1.5, Upwind corner U = 3., Upwind corner U =., Center U = 3., Center , 23 7 WIND 23 y Fire z Air Temperature ( C) p Air Temperature ( C) p Air Temperature ( C) p Air Temperature ( C) p Fig. 6. Temporal variations of the air temperature in the model. in the case of a wind velocity of 1.5 m/s than in the case of 3. m/s. This is because the fire plume is strongly suppressed in the case of 3. m/s wind directly from the opening. However, the temperature decreases faster in the case of 3. m/s in the same way as the upwind and downwind corner cases because of the larger cooling effect of the wind as mentioned above. In terms of the wall surface temperature, it has almost the same tendency as the air temperature. At the downwind position (point 55), the fastest temperature rise is in Case 1 (no wind, fire source: downwind corner). This coincides with the fact that the flame is inclined towards the upwind in the presence of eternal wind, as mentioned above. Fig. 8 shows the highest vertical temperature distribution at measurement points in section A A in different fire source locations (see Fig. 2). The temperature at the ceiling is highest in the case where the fire source is at the center in still conditions. On the other hand, higher temperatures appear in the middle in the vertical direction in windy conditions. This implies that the hot gas is blown out of the compartment before it rises to the ceiling. It is found that in the case of an approaching wind velocity of 3. m/s the highest temperature is shown near the outlet and the lowest temperature is shown near the inlet, at the height of the center of the opening compared with other cases. This is also indicative of the combustion-promoting effect and the cooling effect of the wind. From the above analysis, it can be concluded that eternal wind has two opposing effects. One is to promote combustion within the compartment and thus raise the temperature, the other is to blow away and dilute the combustible gases in the compartment and decrease the temperature, or hasten its etinction. Which effect predominates depends on the approaching wind velocity, the position of the fuel, and the geometry of the opening and compartment.

6 316 H. Huang et al. / Fire Safety Journal 44 (29) U =., Corner U = 1.5, Downwind Corner U = 3., Downwind Corner U = 1.5, Center 49 U = 1.5, Upwind corner U = 3., Upwind corner U =., Center U = 3., Center WIND y 66 Wall Temperature ( C) p Wall Temperature ( C) p Wall Temperature ( C) p Wall Temperature ( C) p Fig. 7. Temporal variations of the wall temperature in the model Eternal flame temperature Dimensionless flame temperature Yokoi s [4] research is well known concerning the temperature measurement of eternal flames from windows in the absence of wind. He found that the dimensionless temperature along the ais of the eternal flame can be epressed by the below equation: Y ¼ DT r 5=3 =ðt 1 Q 2 =c 2 pr 2 gþ 1=3 (1) Q ¼ c p m out DT (2) where DT is the temperature rise at an arbitrary position along the pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi plume ais (K), r is the equivalent radius of the opening ( BH=2p, m), B and H are the width and height of the opening, respectively, Q is the enthalpy of the ejected gas (kw), DT is the temperature difference between the inside and outside of the compartment (K), C p is the specific heat (kj/kg/k), r is the density (kg/m 3 ), and m out is the outflow rate from the opening (m 3 /s). The calculations of the outflow rate (m out )andinflowrate(m in ) are as follows. When the density of the ambient air is larger than the density of the indoor air, that is, when r N 4r in,theoutflowrateand the inflow rate which pass by each opening can be calculated: ( pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m out ¼ 2 3 ab 2gr in ðr 1 r in ÞfðH u Z n Þ 3=2 ðh l Z n Þ 3=2 g Z n ph l m in ¼ 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi < m out ¼ 2 3 ab 2gr in ðr 1 r in ÞðH u Z n Þ 3=2 H l oz n oh u m in ¼ 2 3 ab p : ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gr 1 ðr 1 r in ÞðZ n H l Þ 3=2 ( m out ¼ H u pz n m in ¼ 2 3 ab p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gr 1 ðr 1 r in ÞfðZ n H l Þ 3=2 ðz n H u Þ 3=2 g (3)

7 H. Huang et al. / Fire Safety Journal 44 (29) U =.m/s 1.5m/s 3. m/s U =., Corner U =., Center Heat flu (W/cm 2 ) Fire source: Center U = 1.5, Upwind corner U = 1.5, Downwind corner U = 1.5, Center Heat flu (W/cm 2 ) Fire source: Downwind corner Heat flu (W/cm 2 ) U = 3.,Upwind corner U = 3.,Downwind corner U = 3.,Center Fire source: Upwind corner Fig. 8. Vertical distribution of air temperature in the model Fig. 9. Total heat flu in the eternal flame. (a) U ¼. m/s, (b) U ¼ 1.5 m/s and (c) U ¼ 3. m/s. by the neutral plane height, Z n, using Eq. (3) (see Appendi A), where H u and H l are the height of the top and bottom of the opening (m), respectively, and a is the opening flow coefficient (set to be.7 here [6]). Furthermore, the neutral plane height can be calculated from (see Appendi A) Z n ¼ Dp þ p w ðr 1 r in Þg ; p w ¼ C 1 2 r 1 V 2 1 (4) where p w is the wind pressure on the wall surface, C is the wind pressure coefficient (generally.75 and.3 are used for the upwind and downwind, respectively [1]), and V N is the approaching wind velocity. By substituting Eq. (4) in Eq. (3) and coupling the mass continuity equation of the outflow and the inflow rate through the opening, the pressure difference Dp between the inside and outside can be calculated. Then,

8 318 H. Huang et al. / Fire Safety Journal 44 (29) Fig. 11. Determining the flame etension. Fig. 1. Temperature rises in the eternal flame (1C). the outflow and inflow rate that pass by the opening can be calculated using Dp. Finally, by substituting Eq. (2) in Eq. (1), the dimensionless temperature can be obtained Temperature distribution and comparison with Yokoi s results Fig. 9 shows the total heat flu measured in the eternal flame (refer to Fig. 2). The heat flu increases as the approaching wind increases. According to the measurement of the heat flu outside the compartment, after the heat flu reached its maimum it maintained an almost constant value for a certain period (about 2 s). This period is thought to be the steady-state fully developed fire period. The average temperature rises of the eternal flames during this period are shown in Fig. 1. It is found that when the approaching wind velocity increases the inclination of the eternal flame increases and the flame becomes wider. Concerning the temperature rise, it is found to be higher in the case where the wind velocity is 3. m/s than 1.5 m/s. It is also higher when the fire source is placed in the downwind corner rather than in the upwind corner. The flame temperatures seem low, relative to typical flame temperatures. As has been mentioned, the wind has an effect to blow away and dilute the combustible gases and decrease the temperature. This effect is likely to lead to a slightly lower flame temperature. The flame etension can be determined through visual inspection, video and digital camera recordings, or temperature distribution. In this study, we used both digital photos and temperature distribution in the fully developed period. As an eample, Fig. 11 shows the digital photos and temperature distribution for cases 3 and 4. The flame front is found to be mostly in the range C, so the flame area is defined as the area over 24 1C in this study. This accords with the results of Sugawa et al. [15] and Oka et al. [16].

9 H. Huang et al. / Fire Safety Journal 44 (29) z/r 1 1 U =.,Corner U = 1.5, Upwnwind corner U = 1.5, Downwind corner U = 3., Upwnwind corner U = 3., Downwind corner U =.,Center U = 1.5,Center U = 3.,Center Yokoi's equation wind has two opposing effects. One is to promote combustion within the compartment and thus raise the temperature, the other is to blow away and dilute the combustible gases in the compartment and decrease the temperature, thus hastening its etinction. Which effect predominates depends on the approaching wind velocity, the position of the fuel, and the geometry of the opening and compartment. When the approaching wind velocity is high, the ejected plume is greatly inclined to the downwind side, and the flame becomes wider. The dimensionless temperature of the ejected flame was a little lower than the results from Yokoi s eperiments without wind. Yokoi [4] and Yamaguchi [9] investigated the window jet flame without eternal wind using reduced- and large-scale models, and found that the dimensionless temperature is independent of the model size and that the results can be used to predict full-scale window jet plumes. In this study, as the first stage in investigating the effects of eternal wind, a reduced-scale eperiment was performed, and the scaling effects will be confirmed in future large-scale eperiments. A CFD simulation coupled with the material pyrolysis model will also be developed to analyze this fire-spreading process in the near future. 1 Acknowledgements Θ This work was supported by Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (No ) and the China National Key Project of Scientific and Technical Supporting Programs (No. 26BAD4B5). The authors would also like to thank Yuanfu Diao, Changshan Ding, Jian Ye, Qiong Liu and Zhengang Zhai (University of Science and Technology of China) for their hard work in the eperiments. Fig. 12. Dimensionless temperature on the ais of the eternal flame. The flame central ais is determined from the temperature distribution during the fully developed fire period as follows: The start point involves the maimum temperature points at the opening, and then a curve is produced by connecting the points of maimum temperature in the same level or net higher measurement level. The length along this flame central ais was used in the following comparison. The dimensionless temperature of the eternal flame on the flame ais compared with Yokoi s [4] study is shown in Fig. 12 (z: length on the flame ais). This agrees with the results of Yokoi s study in the case of windless conditions. The dimensionless temperature of the ejected flame in the presence of wind was a little lower than the results from Yokoi s eperiments without wind. The eternal flame is suppressed by the wind, which may lead to this difference. Appendi A: Derivation of. Eqs. (3) and (4) Fig. 13 shows the pressure difference between the outside and inside of the compartment. If the pressure at the standard height in one space is set as p(), then the pressure at a height z above the standard height will be pðzþ ¼pðÞ g Z z rðzþ dz If the density is constant along the height, then pðzþ ¼pðÞ rgz Δp(z) ρ gz ρ in gz 4. Conclusions In this study, fire tunnel eperiments in a scaled down compartment were conducted in the presence of eternal wind in order to clarify the fire growth process in and between compartments under windy conditions. The approaching wind velocity was set to., 1.5 and 3. m/s, and the location of the fire source was changed between the upwind corner, downwind corner and the center. The temperatures in the compartment and of the flame ejected from the opening were measured. The heat flu from the opening and the wall temperature in the compartment were also recorded. The temperature rose and the fire burnt out faster under windy conditions. It was found that the eternal z Neutral plane Zn p in() p () + p w Fig. 13. Pressure difference between the outside and inside of the compartment considering the eternal wind.

10 32 H. Huang et al. / Fire Safety Journal 44 (29) Net, consider two connected spaces, which are inside and outside the model here. If the densities are r in, r N, and the pressures at the standard height are p in, p N, then the pressures at a height z are in in in p in ðzþ ¼p in ðþ r in gz and p 1 ðzþ ¼p 1 ðþ r 1 gz m out Then, the pressure difference between the compartment and the outside is DpðzÞ ¼p in ðzþ p 1 ðzþ ¼p in ðþ p 1 ðþ ðr in r 1 Þgz On the neutral plane, the pressure difference is zero; thus, the neutral plane height Z n will be obtained as Z n ¼ p inðþ p 1 ðþ ðr in r 1 Þg ¼ Dp ðr in r 1 Þg When there is an eternal wind, the wind pressure p w should be added to p N, thus Z n ¼ p 1ðÞþp w p in ðþ ¼ Dp þ p w ðr 1 r in Þg ðr 1 r in Þg In general, the wind pressure on the wall surface is defined as p w ¼ C 1 2 r 1 V 2 1 where C is the wind pressure coefficient (generally.75 and.3 are used for the upwind and downwind, respectively [1]), and V N is the approaching wind velocity. Thus, Eq. (4) is obtained. Eq. (3) is derived as follows: Fig. 14 shows the airflow passing through the opening. If the standard height is set at the neutral plane and r in or N, then the pressure difference at a height z is DpðzÞ ¼ ðr in r 1 Þgz Substituting this into Bernoulli s equation, then the flow velocity will be vðzþ ¼ð2DpðzÞ=r in Þ 1=2 ¼ð2gjr in r 1 j=r in Þ 1=2 z 1=2 The mass flow rate will be obtained using Z m ¼ ab rvðzþ dz where a and B are the opening flow coefficient (set as.7 here [6]) and the width of the opening, respectively. Fig. 15 shows the three cases of neutral height. The mass flow rates for each case are derived as follows: (1) Z n ph l Z n H l m out ¼ ab m out Z Hu Zn r in vðzþ dz qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ab 2gr in ðr 1 r in Þ Z Hl Zn Z Hu Zn r in vðzþ dz z 1=2 dz Z Hl Zn z 1=2 dz ¼ 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 ab 2gr in ðr 1 r in ÞfðH u Z n Þ 3=2 ðh l Z n Þ 3=2 g m in ¼ (2) H l oz n oh u Z Hu Zn m out ¼ ab r in vðzþ dz qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z Hu Zn ¼ ab 2gr in ðr 1 r in Þ z 1=2 dz ¼ 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 ab 2gr in ðr 1 r in ÞðH u Z n Þ 3=2 Z Zn H l m in H l < Z n < H u m in ¼ ab r 1 vðzþ dz qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z Zn H l ¼ ab 2gr 1 ðr 1 r in Þ z 1=2 dz ¼ 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 ab 2gr 1 ðr 1 r in ÞðZ n H l Þ 3=2 m in H u Z n Fig. 15. Pressure and velocity distributions for the airflow passing through the opening. (3) H u pz n z Δp(z) v(z) ρ in m out H u -Z n m out ¼ m in ¼ ab Z Zn H l r 1 vðzþ dz qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ab 2gr 1 ðr 1 r in Þ Z Zn Hn Z Zn H l r 1 vðzþ dz z 1=2 dz Z Zn Hn z 1=2 dz ¼ 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 ab 2gr 1 ðr 1 r in ÞfðZ n H l Þ 3=2 ðz n H u Þ 3=2 g Neutral plane References z n m in ρ Fig. 14. Airflow passing through the opening. Z n -H l [1] D. Drysdale, An Introduction to Fire Dynamics, second ed., Wiley, New York, [2] D.J. Rasbash, Major fire disasters involving flashover, Fire Saf. J. 17 (1991) [3] W.D. Walton, P.H. Thomas, Estimating temperatures in compartment fires, in: SFPE Handbook of Fire Protection Engineering, second ed., Society of Fire Protection Engineers, Boston, 1995, pp [4] S. Yokoi, Study on the prevention of fire-spread caused by hot upward current, Report of the Building Research Institute No. 34, 196.

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