A CALCULATION METHOD OF FULLY DEVELOPED FIRE TEMPERATURE FOR MULTI-ROOM FIRE SPREAD SCENARIOS

Transcription

1 A CALCULATION METHOD OF FULLY DEVELOPED FIRE TEMPERATURE FOR MULTI-ROOM FIRE SPREAD SCENARIOS K. Harada Department of Arhiteture and Arhitetural Engineering, Kyoto University Building C2-46, Kyoto University Katsura Campus, Nishigyo, Kyoto , Japan ABSTRACT A model was proposed to alulate the severity of fully developed fires in a multi room spreading senario. The model is intended for use in fire resistane design. The model onsists of a heat balane of rooms, networ ventilation for mass flow rates through openings and heat ondution in enlosure walls. The model was ompared with a full-sale experiment. Even though the verifiation is not perfet, the model ould alulate the orridor temperature properly. Using the model, the effet of burning in adaent rooms is examined for a simple two-room building and a realisti building with orridor and offie rooms. KEYWORDS: Fully developed fires, Multi-room spread, Room heat onservation ventilation networ INTRODUCTION In the pratial fire resistane design based on performane, the severity and duration of a fully -developed fire is often alulated based on post flashover ompartment fire models. For example, Japanese Building Standards Law adopts a alulation method 1 originally proposed by MCaffrey et al. The fundamental theory for predition of fully-developed fire temperature was proposed by Seine and Kawagoe in the 166 s 2. Based on experimental data, MCaffrey et al. proposed a simple losed form formula for fuel-ontrolled fires 3. Matsuyama et al. extended the formula to ventilationontrolled fires as well 4. The model is prinipally foused on single ompartment fires only. However, in real buildings, rooms are interonneted by door openings and lightweight walls that are not neessarily fire rated. Thus the appliability of single fire ompartment model is limited. If fire spreads between multiple ompartments, then the fire severity might be different from that alulated under the assumption of single fire ompartment. To examine the effet of multi room fire spread, a omputer model was developed in this paper. CALCULATION METHOD OF FULLY DEVELOPED FIRE IN MULTIROOM BUILDINGS As shown in Fig. 1, a building with multiple rooms is onsidered. Fire starts in one of the rooms. As fire grows to fully developed stage, spread to adaent rooms may tae plae at some ey event suh as flashover and/or breaing of doors and so on. To alulate the fire spread senario, heat and oxygen onservation of rooms, mass flow rate of gas between rooms and heat ondution through room enlosures are solved simultaneously. 1) Room Heat Conservation Even in multi-room senario, heat balane of a room ould be desribed by a onventional way if we fous on one of the rooms, Q, i Qa, i + Ql, i + Qr, i + Qw, i = [1] 1 Copyright International Assoiation for Fire Safety Siene

2 fire initiation spread to adaent room flashover in room of origin flashover of seond room and further spread to other rooms FIGURE 1. Shemati of fire spread senario between rooms As proposed by Seine and Kawagoe, where Q is the heat release rate, Q a is the rate of heat aumulation by room gas, Q l is the rate of heat loss by ventilation, Q r is the rate of heat loss by radiation, Q w is the rate of heat absorption by room enlosure materials [W]. Subsript i denotes the room number. In single ompartment models, the heat balane equation is approximated by losed form formula with the aid of empirial relationships using opening fator and thermal inertia. However, in ase of multiroom senarios, this type of simplifiation is not possible, but eah term has to be alulated expliitly. Rate of heat loss by radiation is expressed by using mass flow rate through openings between room i and adaent rooms. Q = Σ( m T m T ) [2] l, i p i i i where m i is the mass flow arte of gas from room i to room, m i is the mass flow arte of gas from room to room i, p is the speifi heat of gas [J/g. K], T i is the temperature [K] of room i, and T is the temperature of adaent room. The summation denotes the sum of all the openings faing to room i. Assuming that fire gas is approximated by bla body gas, the rate of heat loss by radiation is: Q 4 4 = Σ A σ ( T T ) [3] r, i i i where A i is opening area [m 2 ] between rooms i and, and s is the Stefan-Boltzman onstant (= 5.67 x 1-11 W/m 2. K 4 ). The rate of heat absorption by wall surfaes is alulated by: Q w, i w, i, i, ( i w, i, = Σ A h T T ) [4] where A w is wall area [m 2 ], h is overall heat transfer oeffiient [W/m 2. K] between fire gas and wall surfae, and T w is wall surfae temperature. The summation over denotes the sum over all the 2

3 elements of onstrution of room i. Summarizing above relationships, temperature in room i an be alulated by: T i Q i + ( p Σ i + Σ i r, i ) + Σ w, i, i, w, i, = [5] p m Σ m i A h + Σ A h i r, i T + Σ A A h h w, i, i, T where h r,i is radiative heat transfer oeffiient between rooms i and. 2 2 h = σ ( T + T )( T + T ). [6] r, i i i After nowing heat release rate Q i, mass flow rates m i and m i, wall surfae temperature T w,i,, room temperature an be alulated by equation [5]. room i Q i,t i,y O2,i room Q,T,Y O2, m i m i heat released by ombustion Q absorption by wall surfae Q w ventilation loss Q l radiation loss Q r FIGURE 2. Heat onservation of fire room (room heat balane) 2) Heat Release Rate Heat release rate would be determined by the rate of deomposition of volatile materials and rate of inoming air to fire room. As is well nown, heat release rate is proportional to fuel surfae area if suffiient air is supplied (so-alled fuel surfae ontrol). Under poor ventilation, heat release rate is limited by the rate of oxygen inflow (so-alled ventilation ontrol). Considering these two limiting states, heat release rate is given by using burning type index. In ase of single fire ompartment, heat release rate is alulated by 5 : where χ is burning type index [m 1/2 ].7 (.8 < χ.1) Q = 16,A fuel [7].12χ exp( 11χ ) +.3 (.1 < χ) χ = A H / [8] A fuel 3

4 determined by the ratio of ventilation fator A H [m 5/2 ] and fuel surfae area A fuel [m 2 ]. In multi-room senarios, desription by ventilation fator is not valid but replaed with mass flow rate of oxygen inoming to fire room. In ase of single opening where formula [7] has been developed, mass flow of air inoming to fire room is expressed by: m air =. 52A H [9] Multiplying with oxygen onentration Y O 2 [g/g], mass flow of air inoming to fire room is:, m O =. 52 A H Y [1] 2 O 2, Therefore, burning type index an be re-written by: A H mo /.52Y 2 O2, χ = =. [11] A fuel A fuel In ase of multiple openings, summation over all the opening should be introdued as: Σ m iyo, /.52Y O, 2 2 χ = [12] A fuel where Y O2, is the oxygen onentration in adaent rooms. 3) Mass Flow Rates between Rooms Mass flow rates were alulated by single-layered, ventilation networ smoe transport model developed by Matsushita et al. 6 4) Wall Surfae Temperature Wall surfae temperature was alulated by finite differene method for one-dimensional heat ondution. COMPARISON WITH EXPERIMENTAL DATA Experimental Condition To examine the auray of developed alulation method, a full-sale experiment was simulated 7. As shown in Fig. 3, four rooms were involved with the experiment. Fire was put in room-3 where 4 tons of wood stas were ignited. Part of the exterior windows was fitted with steel plates to redue opening area in order to reate ventilation ontrol ondition. The other part of window is fitted with ordinary float glass, whih was broen down 1 minutes after ignition. Room-2 (orridor) is onneted to the fire room. The door to fire room was left open during experiments. At the end of the orridor, a water loset is loated, where a small ventilation opening is equipped on an exterior wall. Room-4 was speially reated for the purpose of observation during the experiment, separated from fire room by a onrete blo wall and steel shutter. Other walls and floors were made of onrete blos. Ceiling is made of suspended lightweight board. 4

5 The size of opening is listed in Table 1. opening-4 (shutter, losed) room-4 (observation room) opening-5 (initially losed, broen down at 1minutes) fire origin opening-3 (left open) room-3 (fire room) room-1 room-2 (orridor) opening-2 (left open) opening- 1 (left open) FIGURE 3. Arrangement of full-sale fire experiment TABLE 1. Geometry of opening Height Opening Width Remars Conneting rooms Sill Soffit no. [m] [m] [m] - 1 WC outside orridor WC fire room orridor observation room fire room Only leaage area was onsidered. 5 fire room outside Initially losed, broen at 1 minutes Calulation Results The alulated results are shown in Fig. 4. Fire room temperature is inreased for the first several minutes. Then the inrease is stopped, and the temperature dereases beause of the burning is quenhed. After 1 minutes when the window glass is broen, burning is intensified and inreases temperature. This tendeny is ommon in both experiment and alulation results. Quantitatively, the alulated results are fairly lose to experimental data. In ase of fire room, the alulated temperature is a bit higher than the average of experimental values exluding the measurement lose to fire soure denoted by open irle. In ase of other rooms, the temperature history is reprodued fairly well. 5

6 temperature [ o C] temperature [ o C] 火災温度 temperature [ o C] fire room orridor al. meas.(ave.) max. min. al. meas.(ave.) max. ave. min. ave. al. meas.(ave.) observation room max. ave. min time [min] FIGURE 4. Comparison with experimental data SIMULATION OF MULTIROOM SPREADING FIRE TEMPERATURE Calulation Examples for Simple Geometry Building In order to examine the effet of multi-room fire spread senario, parametri study was arried out for a building with simple geometry. The building geometry is shown in Fig. 5. Offie use is onsidered to have 56MJ/m 2 of fuel load density per floor area. Two rooms are the same size, 1 m (width) x 1 m (depth) x 4 m (height). Eah room has one opening onneting outside. Another opening onnets the two rooms. Fire starts in room 1. Heat release rate is given by: 2 Q = αt [W], [13] 6 5/3 α = (.26 1 ) =.1 [W/s 2 ] [14] q l during the initial stage of fire. If the heat release rate alulated by formula [13] exeeds the value for fully developed fire, formula [7] is adopted. As to the fire spread onditions, unertain fators are to be onsidered for sophistiated analysis. However, in this alulation, fire spread would tae plae when the temperature in room 2 is inreased by 14 o C above initial temperature. After fire spread, same method was applied to room 2 to alulate heat release rate. 6

7 partition wall 1m 1m Opening3 2m 4m Opening1 Room1 Room2 Walls, slabs = RC 1mm 1m Opening2 floor area 1m 2 (1m 1m) fuel load density 56MJ/m 2 FIGURE 5. Two-rooms onfiguration Calulation results are shown in Fig. 6. As shown in upper graph, only room 1 is burning up to 4 minutes. Maximum heat release rate is ahieved during this period beause burning in room 1 is supported by the air entering from opening 1 as well as from opening 2 via opening 3. After fire spread to room 2, heat release rate in room 1 is dereased beause the air from opening 2 annot be onsumed in room 1. The heat release rate in eah room agrees exatly with ventilation limit Q = 1,5A H = 1,5 (5 2) 2 = 21,2W [15] beause the building geometry is symmetri along partition wall. The temperature history is shown in lower part of Fig. 6. The temperature in both rooms is quite similar. The distint differene is the time gap for fire spread. However, the maximum temperature in room 2 is slightly higher than that of room 1. This is beause of the preheating effet. During the first four minutes, heat from room 1 flows into room 2. Then the wall surfaes are heated in prior to fire spread to room 2. In another senario, size of opening was hanged. Opening 2 was losed, while the size of opening 1 was doubled. The results are shown in Fig. 7. As shown in upper graph, maximum heat release rate is less than the ventilation limit (42.4 MW). Thus the fire is fuel ontrolled. On the other hand, heat release rate in room 2 is very small up to 65 minutes. After the ombustion in room 1 is finished, suffiient air is supplied to room 2 through openings 1 and 3. As shown in the lower graph, fire temperature in room 1 is mild. Maximum temperature is about 6 o C. On the other hand, temperature in room 2 is quite severe. During the first half, temperature is about 4 o C. In this period, room enlosure is pre-heated. Thus the temperature rise during the last half is signifiant. As is demonstrated, burning in one room may affet the severity of fire in other rooms. 7

8 heat release rate [MW] temperature [ o C] , room 1 ventilation limit (21.2MW 2) room 2 room 1 room 2 room 1 room 2 fire temperature wall surfae time [min] opening 1 (W5.xH2.) room 1 opening 3 (W5.xH2.) room 2 opening 2 (W5.xH2.) FIGURE 6. Calulation results of two-rooms onfiguration (opening 1-3: Width 5. m Height 2. m) temperature [ o C] heat release rate [MW] , room 1: fuel-ontrol room 2: (fuel-ontrol) (vent.-ontrol) room 1 room 2 fire temperature room 2: wall surfae 2 room 1: wall surfae time [min] opening 1 (W1.xH2.) room 1 opening 3 (W5.xH2.) room 2 opening 2 (losed) FIGURE 7. Calulation results of two-rooms onfiguration (opening 1,3: Width 1. m Height 2. m, opening 2: losed) Calulation Examples for Realisti Geometry Building 1) Building Speifiations To simulate the fire severity in realisti building, alulation was arried out for the building shown in Fig. 8. Configuration of rooms is shown in Table 2. Fire load density is 56 MJ/m 2 for offies, 16 MJ/m 2 for meeting rooms, and 8 MJ/m 2 for orridor. Interior linings are semi-nonombustible grade 8

9 materials. Geometry of openings is shown in Table 3. It is assumed that all the doors exept for stairases and elevators were opened. All the partition walls eep their initial shape throughout fire. mtg-2 5 mtg-1 4 WC WC Uty. orridor offie offie-2 FIGURE 8. Plan of building TABLE 2. Room onfiguration room name floor area [m 2 ] area of opening to outdoor air [m 2 ] Fire load [MJ] Corridor ,44 offie ,744 offie ,16 meeting room ,26 meeting room ,91 TABLE 3. Geometry of inter-room opening Position opening area [m 2 ] (offie-1) (orridor) 6.4 (offie-2) (orridor) 6.4 (meeting room -1) (orridor) 1.6 (meeting room -2) (orridor) 1.6 2) Fire spread senario In realisti buildings, there are many different fire senarios. However, in this paper, five fires starting at one of the rooms are onsidered. Triangle symbols in Fig. 8 denote the position of fire initiation for fires 1 to 5. Similar to previous alulations, all the fires spread to adaent rooms, if the temperature in adaent rooms is inreased by 14 o C above initial temperature. For omparison, fires terminated in eah room of origin are also alulated. 3) Calulation results Calulated temperature histories for all the fires are shown in Fig. 9. In ase of fire starting at orridor, burning in orridor is finished at 3 minutes. However, at this stage, fire has already spread to offie-1 and offie 2. These two rooms are in the stage of fully developed fire. Thus the orridor temperature is ept at about 4 o C. At 12 minutes, burning in offies is almost finished. Then the 9

10 orridor temperature deays along with offie temperature. Similar tendenies are shown for fires starting in another room. Corridor temperatures are ept high until the burning in offies is finished. (post-heating effet) As is exemplified, fire severity of a room is affeted by the burning of adaent rooms. When the single ompartment fire models for fire resistane design are applied, burning of adaent rooms shall have to be onsidered properly. temp.[ o C] 1,2 6 o1 m1 m2 o2 Fire starts in orridor. 1,2 temp.[ o C] 6 o1 m1 o2 Fire starts in offie-1. 1,2 m2 Fire starts in offie-1. temp.[ o C] 6 o2 m1 o1 1,2 m2 Fire starts in meeting room-1. temp.[ o C] 6 m1 o2 m2 o1 1,2 Fire starts in meeting room-2. temp.[ o C] 6 m2 m1 o2 o time [min.] FIGURE 9. Calulation results of spreading fires in realisti building ( = orridor, o1 = offie-1, o2 = offie-2, m1 = meeting room-1, m2 = meeting room-2) 1

11 In summary of alulation results, maximum temperature and equivalent fire duration were extrated and summarized in Fig. 1. The effet of initial fire room is not so signifiant in this series of alulation. The differene is less than 1% both in maximum temperatures and equivalent fire duration. In the same graph, alulated results of fires terminated only in the room of origin are shown by bla bars. In the maximum temperatures, the error is not so signifiant. On the other hand, onsiderable differenes are found in equivalent fire duration. Espeially in ase of orridor, equivalent fire duration is underestimated to half of spreading fires. This is beause of the effet of burning in adaent rooms as was already pointed out. 12 equivalent fire duration [min.] maximum temperature [ o C] 廊下事務室 1 事務室 2 会議室 1 会議室 2 廊下 orridor fire origin 事務室 offie-1 1 事務室 offie-2 2 会議室 meeting 1 room-1 会議室 meeting 2 room-2 single room 各室毎の火災 orridor offie-1 offie-2 meeting meeting 廊下事務室 1 事務室 2 room-1 会議室 1 会議室 room-2 2 FIGURE 1. Variation of maximum temperature and equivalent fire duration depending on the room of fire origin CONCLUSIONS AND FUTURE DEVELOPMENT In this paper, a model was proposed to alulate the severity of fully developed fires in multi room spreading senario. The model onsists of heat balane of rooms, networ ventilation for mass flow rates through openings and heat ondution in enlosure walls. The model was ompared with a full sale experiment arried out so far. Even though the verifiation is not perfet, the model ould alulate the orridor temperature properly. By using the model, multiple fire-spreading senarios were analyzed. By the alulation of simple two-room building it was found that, 11

12 1) If the openings to outside are evenly distributed, the fire behavior is not affeted by the burning of adaent rooms. 2) On the ontrary, if the opening is unevenly distributed, fire severity of a room is affeted by the burning in adaent rooms. Fire severity was alulated for multiple fire senarios. As a result, the following feature was analyzed; 3) The effet of seletion of fire origin is relatively small. 4) The effets of burning in adaent rooms are not negligible. As a future development the author would lie to mention that; 5) For the use in pratial fire resistane design, use of single ompartment fire model is not adequate. 6) A simple and rational method to aount for the effet of burning in adaent rooms is desired. REFERENCES 1. Ministry of Land, Infrastruture and Transportation, Notifiation 1433, Seine, T. and Kawagoe, K., Estimation of Fire Temperature Rise Curves in Conrete Buildings, Transation of Arhitetural Institute of Japan, No. 85, pp , 1963, No. 86, pp. 4-45,1963, No. 14, pp. 63-7, MCaffrey, B.J., Quintiere, J.G. and Harleroad, M.F., Estimating Room Temperatures and the Lielihood of Flashover Using Fire Test Data Correlations, Fire Tehnology, 17:2, , Matsuyama, K., Fuita, T., Kaneo, H., Ohmiya, Y., Tanaa, T. and Waamatsu, T., A Simple Preditive Method for Room Fire Behavior, Journal of Strutural and Constrution Engineering, 469, , Arhitetural Institute of Japan, Ohmiya, Y., Sato, M. Tanaa, T. and Waamatsu, T., Inident Heat Flux to Fuel and Burning Rate in Ventilation Controlled Fires, Journal of Strutural and Constrution Engineering, 472, , Arhitetural Institute of Japan, Matsushita T., SMKFLW-Single Layer Smoe Transport Model, Building Center of Japan, Toyo Fire Department, Toyo Kaio Building Fire Experiment Report,