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Temperature development in steel members exposed to localized fire in large enclosure
Safety Science 62 (2014) 319–325
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Temperature development in steel members exposed to localized fire in large enclosure Zhang Guo-wei a,b, Zhu Guo-qing a,⇑, Huang Li-li c a
School of Safety Engineering, China University of Mining and Technology, Xuzhou 221008, China Jiangsu Key Laboratory for Environmental Impact and Structural Safety in Civil Engineering, Xuzhou 221008, China c Institute of Industry Technology, Guangzhou and Chinese Academy of Sciences, Guangzhou 510000, China b
a r t i c l e
i n f o
Article history: Received 28 September 2012 Received in revised form 14 September 2013 Accepted 16 September 2013 Available online 8 October 2013 Keywords: Structural fire protection design Structural safety Fire experiment Localized fire
a b s t r a c t Accurately predicting the time–temperature relationship in steel members exposed to localized fire in large enclosures is a key issue in the design of structural fire protection. Although numerous methods for predicting the development of steel temperatures in compartment fires have been proposed, heat transfer between steel and flame in large spaces is disregarded in these classical methods. On the basis of the lumped heat capacity method, a modified model for tracing the temperature profile in steel members exposed to fire in large enclosures is proposed. In this model, a localized fire source is treated as a single-point fire source in evaluating flame net heat flux to steel. The increase in smoke temperature is used as a basis to develop a new approach to accurately predict the development of steel temperatures in large enclosures under fire conditions. To validate the model and approach, experiments are conducted which show that the predicted temperatures are satisfactorily consistent with the experimental data. The conclusions and experimental data serve as reference for fire simulation, hazard assessment, and fire protection design. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction
q00 ¼ F s ac ðT g T s Þ
The collapse of steel structures in standard fires has been extensively investigated by disaster prevention and mitigation engineers, who believe that temperature development in steel members is the key issue for consideration in the design of fire protection measures for steel structures. Accordingly, numerous methods for predicting steel temperature development have been proposed (Ghojel and Wong, 2005; Dwaikat and Kodur, 2012; Kay et al., 1996; Gardner and Ng, 2006; Wald et al., 2006; Barnard, 1976; Shi et al., 2011; Latham et al., 1987). In the developed methods, the heat that a steel element receives is classified into thermal radiation and heat convection between the steel member and the hot smoke. These relationships are depicted in Eqs. (1) and (2). Nevertheless, the heat transfer between the steel member and the flame is disregarded in these methods. In actual large enclosure fires, especially when the flame surrounds the steel members, steel members would receive considerable thermal radiation from flames at the same time. Thus current methods for calculating heat transfer between steel and localized fire in large spaces is incomprehensive.
where r0 is the Stefan–Boltzmann constant, 5.67 108 W/m2 K4, Fs is the steel external surface area per meter (m2/m), e is the effective emissivity of steel, Tg is the smoke temperature (K), Ts is the steel temperature (K), and ac is the convective heat transfer coefficient. Previous investigations focused on steel temperature development in normal enclosure fires. The smoke temperature (shown in Eqs. (1) and (2)) in normal-enclosure fires is mainly based on standard fire curves such as the ISO 834 curve, ASTM-E119 curve, external fire curve and hydrocarbon curve. However, current research shows that the smoke temperature development in actual large-space fires highly differs from these standard fire curves. In large-enclosure fires, smoke temperature develops in a more complex manner; it is directly affected by heat release rate, enclosure profile, and fire size. Aside from the problems stated above, experiments on steel temperature development in large spaces are seldom carried out. The actual development of smoke and steel temperatures under localized fires in large spaces remains to be examined via full-scaled experiments. Motivated by the discussions above, this paper experimentally investigates the development of smoke and steel temperatures under localized fires in large spaces. On the basis of observations, a new approach to accurately predict smoke temperature development in large-enclosure fires is put forward. This approach is
q0 ¼ r0 eF s ðT 4g T 4s Þ
⇑ Corresponding author. Tel./fax: +86 0516 83590598. E-mail address: [email protected] (Z. Guo-qing). 0925-7535/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssci.2013.09.006
ð1Þ
ð2Þ
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expected to be more accurate than the use of standard fire curves. A modified model for tracing the temperature profile in steel members exposed to large-enclosure fires is also proposed. In the modified model, a localized fire source is treated as a single-point fire source in evaluating the flame net heat flux to steel elements. The experiments validate the accuracy of the proposed approach. The predicted temperatures are found to be consistent with the experimental data. 2. Smoke temperature rise in large-enclosure fires Given that large enclosures are of huge dimensions (height and width), localized fires in large spaces mainly consist of a stabilized flame, a discontinuous flame, plume and ceiling jet, as shown in Fig. 1. The temperature distributions in different regions vary greatly. In these regions, the plume and ceiling jet are two primary factors which directly affect steel temperature development. 2.1. Plume temperature The plume centerline is located in the center of the fire plume above the flame and its mean increase in centerline temperature, DT0, at and above the mean flame height is provided by Eq. (3) from Heskestad (1984)
DT 0 ¼ 9:1
Ta gc2p q2a
!1=3 5=3 Q 2=3 c ðz zv Þ
ð3Þ
where cp is the specific heat of air at constant pressure (kJ/(kg K)), Ta denotes the ambient temperature (K), g represents the acceleration due to gravity (m s2), qa is the ambient air density (kg m3), z is the height above the base of fire source (m), and Zv refers to the height of virtual origin (m) (Fig. 1). Qc is the convective fraction of the heat release rate of the fire source, as calculated by Eq. (4) in kilowatts (kW).
Q c ¼ ð1 vÞQ
ð4Þ
where Q is the fire heat release rate (kW), and v is the radiant energy release factor. Yang et al. (1994) and Koseki and Yumoto (1988) determined the value of v on the basis of a series of experiments conducted by Yang et al. (1994) and Koseki and Yumoto (1988):
v ¼ 0:35e0:05D :
ð5Þ
On the basis of Heskestad (2002), the DT0 under atmospheric conduction (g = 9.81 m s2; cp = 1.00 kJ/(kg K); qa = 1.2 kg m3; Ta = 293 K) can be simplified to
Ceiling jet
Plume centerline
Z
P
R
Object
5=3 DT 0 ¼ 25:0Q 2=3 c ðz zv Þ
ð6Þ
where Zv is the elevation of the virtual origin above the fire source. As described in Fig. 1, the virtual origin is a point source from which the fire plume above a flame appears to originate. Virtual origin height Zv is estimated by Eq. (7) with reference to Heskestad (1972); this approach is recommended in ISO 16734.
8 !1=5 < Zv cp T a ¼ 1:02 þ 15:6 : g q2a ðDH=sÞ3 D 0:158½ðcp qa Þ4=5 T a3=5 g 2=5
1=2
a2=5
1=2 T 0L
DT 3=5 0L
)
Q 2=5 D ð7Þ
where D is the fire source diameter (m), DH is the net heat of combustion(kJ/kg), a is the convective fraction of the heat release rate, and T0L is the mean temperature on the plume centerline at mean flame height (K). The Zv, in terms of Q and D under normal atmospheric conditions [g = 9.81 m s2; cp = 1.00 kJ/(kg K); qa = 1.2 kg m3; Ta = 293 K] could be reproduced as
Z v ¼ 1:02D þ 0:083Q 2=5 :
ð8Þ
2.2. Ceiling jet temperature After smoke plumes impinge on a ceiling, the ceiling surface causes these plumes to turn and move horizontally under the ceiling to other building areas that are distantly located from the fire. Consequently, a ceiling jet forms under the ceiling. Unlike the mean centerline temperature rise, DT0, the increase in ceiling jet temperature, DTjet, is determined by Alpert (1975): 2=3
DT jet ¼ 16:9 QH5=3 DT jet ¼
ðr=H 6 0:18Þ
2=3 5:38 ðr=HÞQ2=3 H5=3
ðr=H P 0:18Þ
ð9Þ
where H is the height of the ceiling (m); and r is the horizontal distance from the plume axis (m). 3. Modified model of steel temperature development in localized fire 3.1. Energy balance equation Fig. 2 shows that a localized fire in a large enclosure transfers smoke radiation, smoke convection, and flame radiation to the steel member. We assume that steel members are black bodies and that no temperature gradients occur along or across these components. This assumption is created for the convenience of studying the heat transfer between the steel element and the localized fire. Considering such an assumption, a correction coefficient to accurately predict the net heat that steel members absorb is proposed. Following the guidelines in EN 1993-1-2:2005 (2005), a correction factor for the shadow effect is used to correct the net energy that is transferred between the fire and steel. The net energy is reproduced as
Q s ¼ ðQ gr þ Q fr þ Q sc Þ es
ð10Þ
L Zv Virtual origin Fig. 1. Localized fire in large enclosure.
where Qs is the net heat flux (kW), Qgr is the smoke radiation heat flux (kW), Qfr is the flame radiation heat flux (kW), Qsc is the smoke convention heat flux (kW), and es is a correction factor for shadow effects.
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qi ¼
Steel
n X F ik ðsgik Ebk þ eik g Ebg Þ Ebi :
Although Eq. (16) is complex, the radiant heat exchange between a black enclosure at temperature Ts and an isothermal gas at temperature Tg can be simplified as follows (Ghojel, 1998):
Thermal radiation of steel
q ¼ r0 ðeg T 4g ag T 4s Þ Heat convection of smoke
ð16Þ
k¼1
ð17Þ
Given the assumptions that steel members are treated as black bodies and the theory of heat transfer between gases and black bodies, the smoke radiation heat flux to steel can be evaluated as
Thermal radiation of smoke Hot smoke
Q gr ¼ r0 F s ðeg T 4g ag T 4s Þ
ð18Þ
where eg is the effective emissivity of smoke, ag is the absorptivity of smoke, Tg is the smoke temperature (K), Ts is the steel temperature (K), and r0 is the Stefan–Boltzmann constant, 5.67 108 W/ m2 K4. The thermal coefficients in Eq. (17) are based largely on the thermal properties of gases (Wong and Ghojel, 2003). Several studies have shown that ag can be equal to eg in large-enclosure fires (Ozisik, 1985). Edwards and Matavosian (1984) found the relation between eg and Tg through numerous experiments. This relation is expressed as follows:
Thermal radiation of flame
eg ¼ 0:458 1:29 104 ðT g 273Þ:
Fig. 2. Energy balance of steel components in fire.
ð19Þ
EN 1993-1-2:2005 states that for I-sections under nominal fire actions, the correction factor for the shadow effects may be determined from
3.2.2. Convention heat flux The smoke convention heat flux to steel can be evaluated by the following equation.
es ¼ 0:9½F s =V s b =½F s =V s
Q sc ¼ F s ac ðT g T s Þ
ð11Þ 3
where Vs is the volume per meter (m /m), Fs represents the steel external surface area per meter (m2/m) and [Fs/Vs]b is the box value of the section factor. In all other cases, the value of es should be taken as
es ¼ ½F s =V s b =½F s =V s :
ð12Þ
Steel is a good conductor with a Biot number less than 0.1; thus we can use the lumped heat capacity method to model the temperature development in steel members exposed to fire. The energy balance equation is built as:
Q s ¼ V s qs C s
dT s dt
ð13Þ
where qs is the density of steel (kg m3), Ts is the steel temperature (K), and Cs is the specific heat of steel (J/(kg K)). The ECCS and BSI (EN 1993-1-2, 2005) have provided the accurate calculation of Cs when steel temperature is lower than 600 °C, as in the following equation (EN 1993-1-2, 2005)
C s ¼ 425 þ 7:73 101 T s 1:69 103 T 2s þ 2:22 106 T 3s : ð14Þ
ð20Þ
where ac is the convective heat transfer coefficient, which varies between 20 W/(m2 K) and 35 W/(m2 K), and the coefficient ac is assigned a value of 25 W/(m2 K) for typical fire exposures, as indicated in EN 1993-1-2:2005 (2005). 3.3. Flame net heat flux to steel As stated in the SFPE (Society of Fire Protection Engineers) handbook, localized fire in large spaces can be treated as a single-point source located at the center of flames. Modeling a point source to predict the thermal radiation field of flames is a typical approach. The point source releases heat to the global surroundings and the incident radiation heat flux on one target can be evaluated by Beyler (2002)
q¼
vQ ; 4pR2
ð21Þ
where R is the distance from a point source p to the target as shown in Fig. 1. The point source p is at the center of the fire surface and mid-height of the flame. Flame height is calculated using
H ¼ 1:02D þ 0:235Q 2=5 3.2. Smoke net heat flux to steel Smoke net heat flux to steel contains two components: radiation heat flux and convention heat flux, as in Equation 15.
Q gs ¼ Q gr þ Q sc :
ð15Þ
3.2.1. Radiation heat flux A gas combustion theory for radiation exchange between a gray gaseous body and a black body is used to express the radiant heat across the ith surface between n black surfaces in one enclosure with isothermal non-gray gas at temperature Tg:
ð22Þ
Not all the external surfaces of steel can receive radiation from flames. Thus, a shape factor c is proposed to correct the effective surface area. By analyzing flame radiation in fire, it is observed that half of the steel surface area can receive flame radiation. Thus, c is assigned a value of 0.5. Meanwhile, part of the incident radiation heat flux is absorbed by the smoke layer. Therefore, the radiation flux that steel members receive from flames should be corrected as (1 ag)q. The effective flame radiation flux that the steel members receive from the smoke layer in fire could be evaluated by
Q fr ¼ Fs c
vQ 4pR2
ð1 ag Þ:
ð23Þ
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10000
Thermocouples
Mass of fuel/g
Steel 0.8m
Computer
First experiment Second experiment Third experiment
8000 6000 4000 2000
Centerline 0 0
100
200
300
400
500
600
700
Time/s Data collector
Pool fire Fig. 5. Mass loss rate of diesel.
Weighing sensor
Table 1 HRR of pool fire.
Fig. 3. Experimental instruments.
3.4. Model of steel temperature development in localized fire On the basis of the discussion above and the combination of Eqs. (10)–(23), the steel temperature development in localized fire can be evaluated by using
es FsDt DT ¼ ½r0 ðeg T 4g ag T 4s Þ þ ac ðT g T s Þ þ vcQ ð1 ag Þ=4pR2 : V s qs C s ð24Þ
4. Verification experiment 4.1. Experiment design Three verification experiments were conducted in a large enclosure with the dimensions 9 m 20 m 14 m (height length width). The items used in the experiment were a steel member, pool fire, thermocouples, weighing sensor, data collector, computers and a camera (Fig. 3). The steel section was an I beam with a length of 1.60 m, a depth of 0.15 m, a section perimeter of 0.61 m, and a weight per meter of 50 kg. The steel member was placed 8.5 m above the fire source in the first and second experiments, and 7.5 m above the fire source in the third experiment. The pool fire (diesel) was placed on a weighing sensor and the camera was used to capture images of the flames and smoke layer. Two thermocouples were separately located on both sides (0.8 m away from the centerline) of the steel member; the thermocouples were intended to collect data on the steel temperature development. Another two thermocouples were located off the surface (0.8 m away from the centerline) of the steel also for the collection of data on smoke temperature
Experiment groups
First experiment
Second experiment
Third experiment
Mass loss rate/(g/s) HRR of pool fire(kW)
11.4 387.7
12.5 427
11.02 375
development. The thermocouples have a measurement range of 0– 200 °C, with a 0.4% allowable error. 4.2. Heat release rate of pool fire During the experiment, the pool fire exhibited stable combustion, as indicated by the 2.0 m flame and 0.7 m fire source diameter; the smoke layer decreased rapidly to 1.0 m above the floor at approximately 300 s after the ignition of diesel (Fig. 4). Fig. 5 shows that the diesel mass linearly decreased and that the mass loss rate of the fuel was constant. Thus, the heat release rate (HRR) of the pool fire could be evaluated using Eq. (25). The results are shown in Table 1.
Q ¼ gmDH;
ð25Þ
where m is the mass loss rate of diesel (kg/s), DH is the heat value of diesel (kJ/kg), and g is the efficiency factor. YI Liang et al. (2006) recommended 0.8 as the value of g. 5. Experiment results and analysis 5.1. Smoke temperature The smoke temperature time profiles in the fire experiments highly differ from the standard fire curves. The maximum temperatures in these experiments do not exceed 100 °C, which is lower than the ISO 834 curve, ASTM-E119 curve, external fire curve, and
Fig. 4. Pool fire and smoke.
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Z. Guo-wei et al. / Safety Science 62 (2014) 319–325
hydrocarbon curve (Figs. 6–8). The smoke temperature measured by the thermocouples gradually increased during the fire growth stage and then became relatively steady burning. In the fire experiment, the thermocouples in the ceiling were 0.8 m away from the plume centerline. Thus Alpert’s equation could be adopted to predict smoke temperature development. The theoretical results are in good agreement with the experimental data obtained at the steady burning stage. In conclusion, the theory discussed in Section 2 could satisfactorily predict increases in smoke temperature in large-enclosure fires (Figs. 6–8).
60
O
Temperature/ C
55 50 45 40 Experimental data (1# measurement point) Experimental data (2# measurement point) Theoretical result (1# measurement point) Theoretical result (1# measurement point)
35 30 25 0
100
200
300
400
500
600
700
5.2. Steel temperature
800
Time/s Using the model of steel temperature development in a localized fire (see Section 3) as basis, the HRR of fire and theoretical smoke temperature is incorporated into Eq. (24) to evaluate the steel temperature development in each experiment. The comparison of the experimental steel temperatures and theoretical results show that the latter are consistent with the experimental data, with 0.6 °C as the maximum absolute error (Figs. 9–11, Table 2).
Fig. 6. Experiment data and theoretical results of the first experiment.
65
O
Temperature/ C
60 55
6. Conclusions
50 45
This study investigated the development of smoke and steel temperatures under localized fires in large spaces. A new approach and a modified model for accurately predicting smoke and steel temperature development in large-enclosure fires were put forward. The conclusions and experimental data can serve as reference for fire simulation, hazard assessment, and fire protection design. The conclusions drawn are summarized as follows.
Experimental data (1# measurement point) Experimental data (2# measurement point) Theoretical result (1# measurement point) Theoretical result (2# measurement point)
40 35 30 25 0
100
200
300
400
500
600
700
800
Time/s Fig. 7. Experimental data and theoretical results of the second experiment.
(1) The actual temperature–time profiles exhibited by real fires in large spaces differ highly from standard fire curves. Smoke temperatures in localized fires in large spaces increased at the fire growth stage and then stabilized at the steady burning stage. The proposed theory of the increase in smoke temperature can satisfactorily predict increases in smoke temperature at the steady burning stage. (2) The heat transfer between steel and flame was disregarded by previous studies on steel temperature development. On the basis of the lumped heat capacity method, we construct a modified model of steel temperature development in localized fires. In the new model, the localized fire source in large spaces is treated as a single-point fire source in evaluating flame net heat flux to steel. (3) Combining the theory on smoke temperature increase with the modified model of steel temperature development enables the accurate prediction of smoke and steel temperature development in large-enclosure fires even when the smoke temperature curves are initially unknown. The exper-
70
O
Temperature/ C
65 60 55 50 45 Experimental data (1# measurement point) Experimental data (2# measurement point) Theoretical result (1# measurement point) Theoretical result (2# measurement point)
40 35 30 25 0
100
200
300
400
500
600
700
800
Time/s Fig. 8. Experimental data and theoretical results of the third experiment.
40
40
38 O
Temperature/ C
O
Temperature/ C
38 36 34 32 30 28
Experimental data (1# measurement point) Theoretical result (1# measurement point)
26 0
100
200
300
400
Time/s
500
600
700
36 34 32 30 28
Experimental data (2# measurement point) Theoretical result (2# measurement point)
26 800
0
100
200
300
400
Time/s
Fig. 9. Experimental steel temperatures and theoretical results of the first experiment.
500
600
700
800
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Z. Guo-wei et al. / Safety Science 62 (2014) 319–325
50
50 Experimental data (1# measurement point) Theoretical result (1# measurement point)
Experimental data (2# measurement point) Theoretical result (2# measurement point)
Temperature/ C
45 O
O
Temperature/ C
45 40 35 30
40 35 30 25
25 0
100
200
300
400
500
600
700
800
0
100
200
300
Time/s
400
500
600
700
800
Time/s
Fig. 10. Experimental steel temperatures and theoretical results of the second experiment.
50
50 Experimental data (1# measurement point) Theoretical result (1# measurement point)
Experimental data (2# measurement point) Theoretical result (2# measurement point)
O
Temperature/ C
45
O
Temperature/ C
45 40 35 30
40 35 30 25
25 0
100
200
300
400
500
600
700
800
0
100
Time/s
200
300
400
500
600
700
800
Time/s
Fig. 11. Experimental steel temperatures and theoretical results of the third experiment.
Table 2 Theoretical steel temperature calculated using the modified model and experimental data. Experiment groups
Experimental steel temperature (°C)
Theoretical steel temperature (°C)
Absolute error (°C)
First experiment
37.9 37.7 40.5 40.4 41.3 40.1
37.3 37.4 40.6 40.1 40.7 40.1
0.6 0.3 0.1 0.3 0.4 0.0
Second experiment Third experiment
iments validated the accuracy of the proposed approach. The predicted temperatures were consistent with the experimental data. Given the limitations in experimental conditions and several unavoidable combustibles in the experiment hall, the HRR of the pool fire was controlled. Meanwhile, the verification experiments were conducted in a 9.0 m high large enclosure. The temperatures of the ceiling jet and steel were considerably lower than that of the plumes. As a result, the steel temperature in these fire experiments did not exceed 45 °C. Thus, the applicability of the new approach to higher intensity fires still remains to be verified in future work. More verification experiments, especially high-intensity fire tests, will be conducted to investigate how the accuracy of the proposed approach could be extended to these conditions as well. Acknowledgments This study was supported by the open foundation of Jiangsu Key Laboratory for Environmental Impact and Structural Safety in Civil Engineering (JSKL2011YB11).
References Alpert, R.L., 1975. Turbulent ceiling-jet induced by large-scale fires. Combustion Science and Technology 11, 197–213. Barnard, B., 1976. Heating calculations of structural steel members. J Struct Div ASCE 102, 49–58. Beyler, C.L., 2002. Fire hazard calculations for large, open hydrocarbon fires. In: DiNenno, P.J. (Ed.), SFPE Handbook of Fire Protection Engineering. National Fire Protection Association, Quincy, MA. pp. 3-268-3-310. CEN, 2005. EN 1993-1-2. Eurocade 3: design of steel structures—Part 1–2: general rules-structural fire design. Dwaikat, M.M.S., Kodur, V.K.R., 2012. A simplified approach for predicting temperature profile in steel members with locally damaged fire protection. Fire Technology 48, 493–512. Edwards, D.K., Matavosian, R., 1984. Scaling rules for total absorptivity and emissivity of gases. Heat Transfer 106, 684–689. Gardner, L., Ng, K.T., 2006. Temperature development in structural stainless steel sections exposed to fire. Fire Safety Journal 41, 185–203. Ghojel, J.I., 1998. A new approach to modeling heat transfer in compartment fire. Fire Safety Journal 31, 227–237. Ghojel, J.I., Wong, M.B., 2005. Heat transfer model for unprotected steel members in a standard compartment fire with participating medium. Journal of Constructional Steel Research 61, 825–833. Heskestad, G., 1972. Virtual origins of fire plumes. Fire Safety Journal 5, 109–114. Heskestad, G., 1984. Fire plume behavior in temperature stratified ambients. Combustion Science and Technology 106, 207–228. Heskestad, G., 2002. Fire plume, flame height and air entrainment. In: DiNenno, P. J. (Ed.), SFPE Handbook of Fire Protection Engineering, National Fire Protection Association, Quincy, MA. pp. 3-82-3-161. Kay, T.R., Kirby, B.R., Preston, R.R., 1996. Calculation of heating rate of an unprotected steel member in a standard fire resistance test. Fire Safety Journal 26 (4), 327–350. Koseki, H., Yumoto, T., 1988. Air entrainment and thermal radiation from heptane pool fires. Fire Technology 24, 33–47. Latham, D.J., Kirby, B.R., Thomson, G., 1987. The temperatures attained by unprotected steelwork in experimental natural fires. Fire Safety Journal 12, 139–152. Yi, Liang, Huo, Ran, Zhang, Jing-yan, 2006. Characteristics of heat release rate of diesel oil poor fire. J Combust Sci Technol 12, 164–168. Ozisik, M.N., 1985. Heat Transfer—A Basic Approach. McGraw-Hill Book Company, New York.
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Contents lists available at ScienceDirect
Safety Science journal homepage: www.elsevier.com/locate/ssci
Temperature development in steel members exposed to localized fire in large enclosure Zhang Guo-wei a,b, Zhu Guo-qing a,⇑, Huang Li-li c a
School of Safety Engineering, China University of Mining and Technology, Xuzhou 221008, China Jiangsu Key Laboratory for Environmental Impact and Structural Safety in Civil Engineering, Xuzhou 221008, China c Institute of Industry Technology, Guangzhou and Chinese Academy of Sciences, Guangzhou 510000, China b
a r t i c l e
i n f o
Article history: Received 28 September 2012 Received in revised form 14 September 2013 Accepted 16 September 2013 Available online 8 October 2013 Keywords: Structural fire protection design Structural safety Fire experiment Localized fire
a b s t r a c t Accurately predicting the time–temperature relationship in steel members exposed to localized fire in large enclosures is a key issue in the design of structural fire protection. Although numerous methods for predicting the development of steel temperatures in compartment fires have been proposed, heat transfer between steel and flame in large spaces is disregarded in these classical methods. On the basis of the lumped heat capacity method, a modified model for tracing the temperature profile in steel members exposed to fire in large enclosures is proposed. In this model, a localized fire source is treated as a single-point fire source in evaluating flame net heat flux to steel. The increase in smoke temperature is used as a basis to develop a new approach to accurately predict the development of steel temperatures in large enclosures under fire conditions. To validate the model and approach, experiments are conducted which show that the predicted temperatures are satisfactorily consistent with the experimental data. The conclusions and experimental data serve as reference for fire simulation, hazard assessment, and fire protection design. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction
q00 ¼ F s ac ðT g T s Þ
The collapse of steel structures in standard fires has been extensively investigated by disaster prevention and mitigation engineers, who believe that temperature development in steel members is the key issue for consideration in the design of fire protection measures for steel structures. Accordingly, numerous methods for predicting steel temperature development have been proposed (Ghojel and Wong, 2005; Dwaikat and Kodur, 2012; Kay et al., 1996; Gardner and Ng, 2006; Wald et al., 2006; Barnard, 1976; Shi et al., 2011; Latham et al., 1987). In the developed methods, the heat that a steel element receives is classified into thermal radiation and heat convection between the steel member and the hot smoke. These relationships are depicted in Eqs. (1) and (2). Nevertheless, the heat transfer between the steel member and the flame is disregarded in these methods. In actual large enclosure fires, especially when the flame surrounds the steel members, steel members would receive considerable thermal radiation from flames at the same time. Thus current methods for calculating heat transfer between steel and localized fire in large spaces is incomprehensive.
where r0 is the Stefan–Boltzmann constant, 5.67 108 W/m2 K4, Fs is the steel external surface area per meter (m2/m), e is the effective emissivity of steel, Tg is the smoke temperature (K), Ts is the steel temperature (K), and ac is the convective heat transfer coefficient. Previous investigations focused on steel temperature development in normal enclosure fires. The smoke temperature (shown in Eqs. (1) and (2)) in normal-enclosure fires is mainly based on standard fire curves such as the ISO 834 curve, ASTM-E119 curve, external fire curve and hydrocarbon curve. However, current research shows that the smoke temperature development in actual large-space fires highly differs from these standard fire curves. In large-enclosure fires, smoke temperature develops in a more complex manner; it is directly affected by heat release rate, enclosure profile, and fire size. Aside from the problems stated above, experiments on steel temperature development in large spaces are seldom carried out. The actual development of smoke and steel temperatures under localized fires in large spaces remains to be examined via full-scaled experiments. Motivated by the discussions above, this paper experimentally investigates the development of smoke and steel temperatures under localized fires in large spaces. On the basis of observations, a new approach to accurately predict smoke temperature development in large-enclosure fires is put forward. This approach is
q0 ¼ r0 eF s ðT 4g T 4s Þ
⇑ Corresponding author. Tel./fax: +86 0516 83590598. E-mail address: [email protected] (Z. Guo-qing). 0925-7535/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssci.2013.09.006
ð1Þ
ð2Þ
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expected to be more accurate than the use of standard fire curves. A modified model for tracing the temperature profile in steel members exposed to large-enclosure fires is also proposed. In the modified model, a localized fire source is treated as a single-point fire source in evaluating the flame net heat flux to steel elements. The experiments validate the accuracy of the proposed approach. The predicted temperatures are found to be consistent with the experimental data. 2. Smoke temperature rise in large-enclosure fires Given that large enclosures are of huge dimensions (height and width), localized fires in large spaces mainly consist of a stabilized flame, a discontinuous flame, plume and ceiling jet, as shown in Fig. 1. The temperature distributions in different regions vary greatly. In these regions, the plume and ceiling jet are two primary factors which directly affect steel temperature development. 2.1. Plume temperature The plume centerline is located in the center of the fire plume above the flame and its mean increase in centerline temperature, DT0, at and above the mean flame height is provided by Eq. (3) from Heskestad (1984)
DT 0 ¼ 9:1
Ta gc2p q2a
!1=3 5=3 Q 2=3 c ðz zv Þ
ð3Þ
where cp is the specific heat of air at constant pressure (kJ/(kg K)), Ta denotes the ambient temperature (K), g represents the acceleration due to gravity (m s2), qa is the ambient air density (kg m3), z is the height above the base of fire source (m), and Zv refers to the height of virtual origin (m) (Fig. 1). Qc is the convective fraction of the heat release rate of the fire source, as calculated by Eq. (4) in kilowatts (kW).
Q c ¼ ð1 vÞQ
ð4Þ
where Q is the fire heat release rate (kW), and v is the radiant energy release factor. Yang et al. (1994) and Koseki and Yumoto (1988) determined the value of v on the basis of a series of experiments conducted by Yang et al. (1994) and Koseki and Yumoto (1988):
v ¼ 0:35e0:05D :
ð5Þ
On the basis of Heskestad (2002), the DT0 under atmospheric conduction (g = 9.81 m s2; cp = 1.00 kJ/(kg K); qa = 1.2 kg m3; Ta = 293 K) can be simplified to
Ceiling jet
Plume centerline
Z
P
R
Object
5=3 DT 0 ¼ 25:0Q 2=3 c ðz zv Þ
ð6Þ
where Zv is the elevation of the virtual origin above the fire source. As described in Fig. 1, the virtual origin is a point source from which the fire plume above a flame appears to originate. Virtual origin height Zv is estimated by Eq. (7) with reference to Heskestad (1972); this approach is recommended in ISO 16734.
8 !1=5 < Zv cp T a ¼ 1:02 þ 15:6 : g q2a ðDH=sÞ3 D 0:158½ðcp qa Þ4=5 T a3=5 g 2=5
1=2
a2=5
1=2 T 0L
DT 3=5 0L
)
Q 2=5 D ð7Þ
where D is the fire source diameter (m), DH is the net heat of combustion(kJ/kg), a is the convective fraction of the heat release rate, and T0L is the mean temperature on the plume centerline at mean flame height (K). The Zv, in terms of Q and D under normal atmospheric conditions [g = 9.81 m s2; cp = 1.00 kJ/(kg K); qa = 1.2 kg m3; Ta = 293 K] could be reproduced as
Z v ¼ 1:02D þ 0:083Q 2=5 :
ð8Þ
2.2. Ceiling jet temperature After smoke plumes impinge on a ceiling, the ceiling surface causes these plumes to turn and move horizontally under the ceiling to other building areas that are distantly located from the fire. Consequently, a ceiling jet forms under the ceiling. Unlike the mean centerline temperature rise, DT0, the increase in ceiling jet temperature, DTjet, is determined by Alpert (1975): 2=3
DT jet ¼ 16:9 QH5=3 DT jet ¼
ðr=H 6 0:18Þ
2=3 5:38 ðr=HÞQ2=3 H5=3
ðr=H P 0:18Þ
ð9Þ
where H is the height of the ceiling (m); and r is the horizontal distance from the plume axis (m). 3. Modified model of steel temperature development in localized fire 3.1. Energy balance equation Fig. 2 shows that a localized fire in a large enclosure transfers smoke radiation, smoke convection, and flame radiation to the steel member. We assume that steel members are black bodies and that no temperature gradients occur along or across these components. This assumption is created for the convenience of studying the heat transfer between the steel element and the localized fire. Considering such an assumption, a correction coefficient to accurately predict the net heat that steel members absorb is proposed. Following the guidelines in EN 1993-1-2:2005 (2005), a correction factor for the shadow effect is used to correct the net energy that is transferred between the fire and steel. The net energy is reproduced as
Q s ¼ ðQ gr þ Q fr þ Q sc Þ es
ð10Þ
L Zv Virtual origin Fig. 1. Localized fire in large enclosure.
where Qs is the net heat flux (kW), Qgr is the smoke radiation heat flux (kW), Qfr is the flame radiation heat flux (kW), Qsc is the smoke convention heat flux (kW), and es is a correction factor for shadow effects.
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qi ¼
Steel
n X F ik ðsgik Ebk þ eik g Ebg Þ Ebi :
Although Eq. (16) is complex, the radiant heat exchange between a black enclosure at temperature Ts and an isothermal gas at temperature Tg can be simplified as follows (Ghojel, 1998):
Thermal radiation of steel
q ¼ r0 ðeg T 4g ag T 4s Þ Heat convection of smoke
ð16Þ
k¼1
ð17Þ
Given the assumptions that steel members are treated as black bodies and the theory of heat transfer between gases and black bodies, the smoke radiation heat flux to steel can be evaluated as
Thermal radiation of smoke Hot smoke
Q gr ¼ r0 F s ðeg T 4g ag T 4s Þ
ð18Þ
where eg is the effective emissivity of smoke, ag is the absorptivity of smoke, Tg is the smoke temperature (K), Ts is the steel temperature (K), and r0 is the Stefan–Boltzmann constant, 5.67 108 W/ m2 K4. The thermal coefficients in Eq. (17) are based largely on the thermal properties of gases (Wong and Ghojel, 2003). Several studies have shown that ag can be equal to eg in large-enclosure fires (Ozisik, 1985). Edwards and Matavosian (1984) found the relation between eg and Tg through numerous experiments. This relation is expressed as follows:
Thermal radiation of flame
eg ¼ 0:458 1:29 104 ðT g 273Þ:
Fig. 2. Energy balance of steel components in fire.
ð19Þ
EN 1993-1-2:2005 states that for I-sections under nominal fire actions, the correction factor for the shadow effects may be determined from
3.2.2. Convention heat flux The smoke convention heat flux to steel can be evaluated by the following equation.
es ¼ 0:9½F s =V s b =½F s =V s
Q sc ¼ F s ac ðT g T s Þ
ð11Þ 3
where Vs is the volume per meter (m /m), Fs represents the steel external surface area per meter (m2/m) and [Fs/Vs]b is the box value of the section factor. In all other cases, the value of es should be taken as
es ¼ ½F s =V s b =½F s =V s :
ð12Þ
Steel is a good conductor with a Biot number less than 0.1; thus we can use the lumped heat capacity method to model the temperature development in steel members exposed to fire. The energy balance equation is built as:
Q s ¼ V s qs C s
dT s dt
ð13Þ
where qs is the density of steel (kg m3), Ts is the steel temperature (K), and Cs is the specific heat of steel (J/(kg K)). The ECCS and BSI (EN 1993-1-2, 2005) have provided the accurate calculation of Cs when steel temperature is lower than 600 °C, as in the following equation (EN 1993-1-2, 2005)
C s ¼ 425 þ 7:73 101 T s 1:69 103 T 2s þ 2:22 106 T 3s : ð14Þ
ð20Þ
where ac is the convective heat transfer coefficient, which varies between 20 W/(m2 K) and 35 W/(m2 K), and the coefficient ac is assigned a value of 25 W/(m2 K) for typical fire exposures, as indicated in EN 1993-1-2:2005 (2005). 3.3. Flame net heat flux to steel As stated in the SFPE (Society of Fire Protection Engineers) handbook, localized fire in large spaces can be treated as a single-point source located at the center of flames. Modeling a point source to predict the thermal radiation field of flames is a typical approach. The point source releases heat to the global surroundings and the incident radiation heat flux on one target can be evaluated by Beyler (2002)
q¼
vQ ; 4pR2
ð21Þ
where R is the distance from a point source p to the target as shown in Fig. 1. The point source p is at the center of the fire surface and mid-height of the flame. Flame height is calculated using
H ¼ 1:02D þ 0:235Q 2=5 3.2. Smoke net heat flux to steel Smoke net heat flux to steel contains two components: radiation heat flux and convention heat flux, as in Equation 15.
Q gs ¼ Q gr þ Q sc :
ð15Þ
3.2.1. Radiation heat flux A gas combustion theory for radiation exchange between a gray gaseous body and a black body is used to express the radiant heat across the ith surface between n black surfaces in one enclosure with isothermal non-gray gas at temperature Tg:
ð22Þ
Not all the external surfaces of steel can receive radiation from flames. Thus, a shape factor c is proposed to correct the effective surface area. By analyzing flame radiation in fire, it is observed that half of the steel surface area can receive flame radiation. Thus, c is assigned a value of 0.5. Meanwhile, part of the incident radiation heat flux is absorbed by the smoke layer. Therefore, the radiation flux that steel members receive from flames should be corrected as (1 ag)q. The effective flame radiation flux that the steel members receive from the smoke layer in fire could be evaluated by
Q fr ¼ Fs c
vQ 4pR2
ð1 ag Þ:
ð23Þ
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10000
Thermocouples
Mass of fuel/g
Steel 0.8m
Computer
First experiment Second experiment Third experiment
8000 6000 4000 2000
Centerline 0 0
100
200
300
400
500
600
700
Time/s Data collector
Pool fire Fig. 5. Mass loss rate of diesel.
Weighing sensor
Table 1 HRR of pool fire.
Fig. 3. Experimental instruments.
3.4. Model of steel temperature development in localized fire On the basis of the discussion above and the combination of Eqs. (10)–(23), the steel temperature development in localized fire can be evaluated by using
es FsDt DT ¼ ½r0 ðeg T 4g ag T 4s Þ þ ac ðT g T s Þ þ vcQ ð1 ag Þ=4pR2 : V s qs C s ð24Þ
4. Verification experiment 4.1. Experiment design Three verification experiments were conducted in a large enclosure with the dimensions 9 m 20 m 14 m (height length width). The items used in the experiment were a steel member, pool fire, thermocouples, weighing sensor, data collector, computers and a camera (Fig. 3). The steel section was an I beam with a length of 1.60 m, a depth of 0.15 m, a section perimeter of 0.61 m, and a weight per meter of 50 kg. The steel member was placed 8.5 m above the fire source in the first and second experiments, and 7.5 m above the fire source in the third experiment. The pool fire (diesel) was placed on a weighing sensor and the camera was used to capture images of the flames and smoke layer. Two thermocouples were separately located on both sides (0.8 m away from the centerline) of the steel member; the thermocouples were intended to collect data on the steel temperature development. Another two thermocouples were located off the surface (0.8 m away from the centerline) of the steel also for the collection of data on smoke temperature
Experiment groups
First experiment
Second experiment
Third experiment
Mass loss rate/(g/s) HRR of pool fire(kW)
11.4 387.7
12.5 427
11.02 375
development. The thermocouples have a measurement range of 0– 200 °C, with a 0.4% allowable error. 4.2. Heat release rate of pool fire During the experiment, the pool fire exhibited stable combustion, as indicated by the 2.0 m flame and 0.7 m fire source diameter; the smoke layer decreased rapidly to 1.0 m above the floor at approximately 300 s after the ignition of diesel (Fig. 4). Fig. 5 shows that the diesel mass linearly decreased and that the mass loss rate of the fuel was constant. Thus, the heat release rate (HRR) of the pool fire could be evaluated using Eq. (25). The results are shown in Table 1.
Q ¼ gmDH;
ð25Þ
where m is the mass loss rate of diesel (kg/s), DH is the heat value of diesel (kJ/kg), and g is the efficiency factor. YI Liang et al. (2006) recommended 0.8 as the value of g. 5. Experiment results and analysis 5.1. Smoke temperature The smoke temperature time profiles in the fire experiments highly differ from the standard fire curves. The maximum temperatures in these experiments do not exceed 100 °C, which is lower than the ISO 834 curve, ASTM-E119 curve, external fire curve, and
Fig. 4. Pool fire and smoke.
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hydrocarbon curve (Figs. 6–8). The smoke temperature measured by the thermocouples gradually increased during the fire growth stage and then became relatively steady burning. In the fire experiment, the thermocouples in the ceiling were 0.8 m away from the plume centerline. Thus Alpert’s equation could be adopted to predict smoke temperature development. The theoretical results are in good agreement with the experimental data obtained at the steady burning stage. In conclusion, the theory discussed in Section 2 could satisfactorily predict increases in smoke temperature in large-enclosure fires (Figs. 6–8).
60
O
Temperature/ C
55 50 45 40 Experimental data (1# measurement point) Experimental data (2# measurement point) Theoretical result (1# measurement point) Theoretical result (1# measurement point)
35 30 25 0
100
200
300
400
500
600
700
5.2. Steel temperature
800
Time/s Using the model of steel temperature development in a localized fire (see Section 3) as basis, the HRR of fire and theoretical smoke temperature is incorporated into Eq. (24) to evaluate the steel temperature development in each experiment. The comparison of the experimental steel temperatures and theoretical results show that the latter are consistent with the experimental data, with 0.6 °C as the maximum absolute error (Figs. 9–11, Table 2).
Fig. 6. Experiment data and theoretical results of the first experiment.
65
O
Temperature/ C
60 55
6. Conclusions
50 45
This study investigated the development of smoke and steel temperatures under localized fires in large spaces. A new approach and a modified model for accurately predicting smoke and steel temperature development in large-enclosure fires were put forward. The conclusions and experimental data can serve as reference for fire simulation, hazard assessment, and fire protection design. The conclusions drawn are summarized as follows.
Experimental data (1# measurement point) Experimental data (2# measurement point) Theoretical result (1# measurement point) Theoretical result (2# measurement point)
40 35 30 25 0
100
200
300
400
500
600
700
800
Time/s Fig. 7. Experimental data and theoretical results of the second experiment.
(1) The actual temperature–time profiles exhibited by real fires in large spaces differ highly from standard fire curves. Smoke temperatures in localized fires in large spaces increased at the fire growth stage and then stabilized at the steady burning stage. The proposed theory of the increase in smoke temperature can satisfactorily predict increases in smoke temperature at the steady burning stage. (2) The heat transfer between steel and flame was disregarded by previous studies on steel temperature development. On the basis of the lumped heat capacity method, we construct a modified model of steel temperature development in localized fires. In the new model, the localized fire source in large spaces is treated as a single-point fire source in evaluating flame net heat flux to steel. (3) Combining the theory on smoke temperature increase with the modified model of steel temperature development enables the accurate prediction of smoke and steel temperature development in large-enclosure fires even when the smoke temperature curves are initially unknown. The exper-
70
O
Temperature/ C
65 60 55 50 45 Experimental data (1# measurement point) Experimental data (2# measurement point) Theoretical result (1# measurement point) Theoretical result (2# measurement point)
40 35 30 25 0
100
200
300
400
500
600
700
800
Time/s Fig. 8. Experimental data and theoretical results of the third experiment.
40
40
38 O
Temperature/ C
O
Temperature/ C
38 36 34 32 30 28
Experimental data (1# measurement point) Theoretical result (1# measurement point)
26 0
100
200
300
400
Time/s
500
600
700
36 34 32 30 28
Experimental data (2# measurement point) Theoretical result (2# measurement point)
26 800
0
100
200
300
400
Time/s
Fig. 9. Experimental steel temperatures and theoretical results of the first experiment.
500
600
700
800
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50
50 Experimental data (1# measurement point) Theoretical result (1# measurement point)
Experimental data (2# measurement point) Theoretical result (2# measurement point)
Temperature/ C
45 O
O
Temperature/ C
45 40 35 30
40 35 30 25
25 0
100
200
300
400
500
600
700
800
0
100
200
300
Time/s
400
500
600
700
800
Time/s
Fig. 10. Experimental steel temperatures and theoretical results of the second experiment.
50
50 Experimental data (1# measurement point) Theoretical result (1# measurement point)
Experimental data (2# measurement point) Theoretical result (2# measurement point)
O
Temperature/ C
45
O
Temperature/ C
45 40 35 30
40 35 30 25
25 0
100
200
300
400
500
600
700
800
0
100
Time/s
200
300
400
500
600
700
800
Time/s
Fig. 11. Experimental steel temperatures and theoretical results of the third experiment.
Table 2 Theoretical steel temperature calculated using the modified model and experimental data. Experiment groups
Experimental steel temperature (°C)
Theoretical steel temperature (°C)
Absolute error (°C)
First experiment
37.9 37.7 40.5 40.4 41.3 40.1
37.3 37.4 40.6 40.1 40.7 40.1
0.6 0.3 0.1 0.3 0.4 0.0
Second experiment Third experiment
iments validated the accuracy of the proposed approach. The predicted temperatures were consistent with the experimental data. Given the limitations in experimental conditions and several unavoidable combustibles in the experiment hall, the HRR of the pool fire was controlled. Meanwhile, the verification experiments were conducted in a 9.0 m high large enclosure. The temperatures of the ceiling jet and steel were considerably lower than that of the plumes. As a result, the steel temperature in these fire experiments did not exceed 45 °C. Thus, the applicability of the new approach to higher intensity fires still remains to be verified in future work. More verification experiments, especially high-intensity fire tests, will be conducted to investigate how the accuracy of the proposed approach could be extended to these conditions as well. Acknowledgments This study was supported by the open foundation of Jiangsu Key Laboratory for Environmental Impact and Structural Safety in Civil Engineering (JSKL2011YB11).
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