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Fire Technology, 49, 269–291, 2013 2012 Springer Science+Business Media, LLC. Manufactured in The United States DOI: 10.1007/s10694-012-0261-1
Heat Fluxes and Flame Lengths from Fires Under Ceilings Brian Y. Lattimer*, Department of Mechanical Engineering, Virginia Tech, 203 Randolph Hall (MC0238), Blacksburg, VA 24060, USA Brian Y. Lattimer, Christopher Mealy and Jesse Beitel, Hughes Associates, Inc, 3610 Commerce Drive, Suite 817, Baltimore, MD 21227, USA Received: 16 December 2008/Accepted: 2 April 2012
Abstract. This study compiles the research that has been conducted on thermal conditions produced by fires under ceilings as well as additional new data for fires beneath ceilings in a corridor configuration. This includes fires in corridor/tunnel, unbounded ceiling, and corner configurations. For each configuration, the thermal conditions produced for both initiating fires impinging on the ceiling and burning ceiling fires are discussed. Thermal characterization includes flame length and heat flux at the ceiling, and correlations are proposed to predict these quantities for each configuration. Comparison of available data in the different configurations indicates that the highest heat flux conditions are produced with initiating fires impinging on a corridor ceiling. Keywords: Heat flux, Gas temperature, Flame length, Ceiling, Corridor, Tunnels, Corner, Unbounded List of symbols A C Cp D g H Lf Lf,cont Lf,tip LH n Q Q0 Q0 p r T T¥ x z0 q¥
Surface area of initiating fire (m2) Coefficient on decay correlation (–) Specific heat capacity of air at initial ambient conditions (1.0 kJ/(kg K)) Diameter of initiating fire or diameter of ceiling fire burner (m) Gravitational acceleration (9.81 m/s2) Distance between the base of the fire and the ceiling (m) Average total flame length or flame extension (m) Continuous flame length (m) Total flame length to the flame tip (m) Flame extension along ceiling from the stagnation point to the flame tip (m) Power on dimensionless distance in decay heat flux correlation (–) Heat release rate of the fire (kW) Heat release rate per unit width of the corridor (kW/m) Heat release rate of the burning ceiling per perimeter of the burning area at the average radius of the burning (kW/m) Radial distance along ceiling from burn front or radial distance from corner along ceiling (m) Gas temperature in (C) Temperature at initial ambient conditions (293 K) Distance along the corridor away from the point of impingement (m) Virtual source origin correction from equations below (m) Density of air at initial ambient conditions (1.2 kg/m3)
* Correspondence should be addressed to: Brian Y. Lattimer, E-mail:
[email protected]
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1. Introduction Heat transfer to the ceiling of a room is important in a variety of fire protection problems including detection, sprinkler activation, material ignition and flame spread, and ceiling/roof structural response. Data and analysis in this paper includes heat transfer in applications for material ignition and flame spread as well as ceiling/roof structural response without the effects of sprinklers. In these applications, fires can become large with flames impinging and flowing along the ceiling. Several experimental studies have been performed to quantify the heat transfer from fires impinging and flowing along flat ceilings. Walls supporting the ceiling can affect the gas flow, which in turn may affect the heat transfer to the ceiling. As a result, heat flux measurements have been performed with the fire in different configurations. The three basic configurations that have been studied include fire beneath a corridor ceiling, fire in a room corner, and fire beneath an unbounded ceiling. Fires in these studies have either been initiating fires impinging and flowing along the ceiling or fires at the ceiling to represent a burning surface. The focus of this study was to collect the existing data on heat flux and flame lengths from fires in the three configurations provided above. Data was collected for initiating fires impinging on the ceiling and for fires representing burning ceiling surfaces. With this data, correlations were developed for predicting the heat flux and flame lengths for fires in the different configurations. These correlations along with other data available from larger scale tests were then used to determine the relative severity of heat transfer to the ceiling for the different configurations.
2. Ceilings in a Corridor 2.1. Initiating Fire Impinging on Corridor Ceiling Hinkley et al. [1, 2] conducted a study to measure the heat fluxes from fires impinging on a corridor ceiling for use in evaluating flame spread along ceiling materials. Hinkley et al. [1, 2] determined heat fluxes to the ceiling using both slug calorimeters and differential temperature measurements across an insulating board. Heat fluxes to ceilings in other configurations (i.e., unbounded, corner) were measured using either Gardon or Schmidt-Boelter water-cooled heat flux gauges. To have a direct comparison with heat fluxes measured in these configurations, a series of tests were conducted in a corridor apparatus similar to that used by Hinkley et al. [1, 2] except heat fluxes to the non-combustible ceiling were measured using Schmidt-Boelter heat flux gauges. 2.1.1. Corridor Apparatus. The corridor apparatus used in this study is shown in Figure 1. The apparatus consisted of a steel frame corridor and a gas sand burner. The corridor was 2.44 m long, 1.22 m wide, and 2.1 m high with one end of the corridor blocked. The bottom portion of the corridor was open to allow air to freely flow into the corridor along its length. The corridor was constructed of a steel frame with 12.7 mm thick plywood walls and ceiling covered with 15 mm
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thick Type X gypsum wallboard on the interior of the corridor. Tests were conducted with the interior surface of the corridor apparatus lined with 25 mm thick, 96 kg/m3 Unifrax Durablanket non-combustible ceramic blanket. A rectangular gas sand burner was located at the blocked end of the corridor. Propane gas was used as the fuel. The burner had dimensions of 1.15 m wide and 0.46 m deep and was elevated above the laboratory floor using concrete block. In the test series, the distance the burner was located below the ceiling was changed to evaluate the impact of this variable on the thermal environment produced at the ceiling. 2.1.2. Measurements. Thermal characterization included the measurement of flame lengths, total heat flux to the ceiling, and gas temperatures just below the ceiling. As shown in Figure 2, heat flux and gas temperature were measured at four locations along the length of the corridor. Total heat flux was measured using water-cooled Schmidt-Boelter type heat flux gauges. Gas temperatures were measured using Type K, bare bead thermocouples positioned 25 mm (1 in.) below the ceiling. Flame lengths were determined visually using markings made at 0.15 m (6 in.) intervals along the length of the corridor. The visual flame lengths were recorded during the tests and confirmed through review of video. Continuous flame lengths was defined as the length where flaming was always present dur-
Gas Outflow
L hall
0.6 m 1.2 m
1.2 m 2.1 m Side Wall
0.46m
Gas Burner Concrete Block Laboratory Floor
Figure 1.
Side view of the corridor apparatus.
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0.025m
0.6 m
Heat Flux Gauge
0.3m
Thermocouple
H
1.2 m
2.1 m 0.46m
Gas Burner Concrete Block
Figure 2. testing.
Instrumentation included in the thermal characterization
ing the test. Flame tip length was the furthest length at which flaming was observed. 2.1.3. Test Matrix. A test matrix was developed using the corridor data from Hinkley et al. [2] and heat flux data from Hasemi et al. [3]. Flame lengths were estimated using data reported by Hinkley et al. [2] for fire produced using the same sand burner and corridor. Based on the heat flux data from Hasemi et al. [3], heat fluxes for fires impinging on an unbounded ceiling begin to plateau to a maximum heat flux of 90 kW/m2 when (x + H)/Lf,tip < 0.50, where x is the distance along the corridor, H is the distance the burner is below the ceiling width, and Lf,tip is the total flame length determined by adding flame height below the ceiling with flame extension along the ceiling. Based on these data, fire heat release rates were developed for two different burner elevations to provide heat flux data over a range of (x + H)/Lf,tip to determine whether heat fluxes to the ceiling plateau and determine the rate of decay of heat flux along the flame length and beyond.
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The test matrix for the thermal characterization of the corridor apparatus is provided in Table 1. The two test variables are the distance the burner is below the ceiling and the heat release rate. Tests were conducted with the burner located 0.60 m and 1.1 m below the ceiling and using heat release rates ranging from 100 kW to 400 kW. 2.1.4. Test Procedure. The exposure fires outlined in Table 1 were allowed to burn until measured heat fluxes had reached steady-state values (about 3 to 5 min). After this steady-state was reached approximately 2 min of data were collected. The corridor was permitted to cool for approximately 20 min in between thermal characterization tests.
2.2. Initiating Fires Impinging on Corridor Ceiling—Results The results of the testing are provided in this section. In addition, correlations for predicting flame length, heat flux and gas temperatures were developed to allow the prediction of these quantities. 2.2.1. Flame Length. Flame lengths measured during the tests were reported as total flame lengths, which includes the part of the height of the flame below the ceiling and the flame extension along the ceiling. Table 2 contains both the continTable 1
Test Matrix for Thermal Characterization Test no.
Burner distance below ceiling (m)
Heat release rate (kW)
1.1 1.1 1.1 1.1 0.6 0.6 0.6 0.6
150 200 300 400 100 200 300 400
1 2 3 4 5 6 7 8
Table 2
Flame Length Data Q (kW) 147 195 296 404 99 195 296 405
Width (m)
H (m)
Q0 (kW/m)
Lf,tip (m)
Lf,cont (m)
1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
1.1 1.1 1.1 1.1 0.6 0.6 0.6 0.6
122.3 162.6 246.6 336.6 82.3 162.8 246.8 337.3
0.92 1.56 2.32 3.54 1.06 1.97 3.04 3.35
0.46 0.92 1.56 2.32 0.38 1.06 2.13 2.74
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uous flame length, Lf,cont, and flame tip lengths, Lf,tip, for tests conducted in this study. The heat release rate per unit width of corridor, Q0 , ranged from 80 kW/m to 340 kW/m. Figure 3 contains a plot of the flame length data from this study along with data from Hinkley et al. [2] in a similar corridor apparatus. The flame length data from these tests agree well with flame lengths report by Hinkley et al. [2] but is on the lower end of the flame lengths reported. The differences in the flame lengths reported by Hinkley et al. [2] and those measured in this study are not known. The line in Figure 3 was determine in this study through regression analysis of the data from Hinkley et al. [2], data from the current study, and data from large scale tunnel tests [4]. This study proposes the following correlation, shown as a line in the plot, to correlate the data, Lf ;tip ¼ 0:075Q02=3
ð1Þ
A plot of all of the corridor data and the tunnel data along with the correlation in Eq. 1 is provided in Figure 4. The data is a reasonable fit for all the data, but does underpredict the higher heat release rate data by Hinkley et al. [2] as shown in Figure 3. 2.2.2. Heat Fluxes to Ceiling. Heat fluxes to the ceiling were measured as a function of exposure time. A sample plot of the heat fluxes with time along the length of the corridor is provided in Figure 5. Average heat fluxes during the steady state part of the tests are provided in Table 3. A plot of the average heat fluxes is provided in Figure 6 as a function of dimensionless distance along the flame length. Also shown in the plot is data from Hinkley et al. [2]. The data from this study match well with data from the tests by
Flame Length, L f,tip (m)
10 Hinkley et al. (1968) H=1.1m H=0.6m 2/3 L f =0.075 Q'
8
6
4
2
0 0
100
200
300
400
500
600
Heat Release Rate per unit Width, Q' (kW/m)
Figure 3. Flame length data from these tests compared with data from Hinkley et al. [2].
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120 Tunnel Data Corridor Data L f =0.075 Q' 2/3
Flame Length, L f,tip (m)
100 80 60 40 20 0 0
10000
20000
30000
40000
50000
Heat Release Rate per Unit Width, Q' (kW/m)
Figure 4. Flame length correlation compared with corridor and tunnel data [4].
180
Averaging Period
160
x=2.1m x=1.5m x=0.9m x=0.3m
Heat Flux (kW/m 2 )
140 120 100 80 60 40 20 0 0
50
100
150
200
250
300
350
Time (sec)
Figure 5.
Heat fluxes to the ceiling with Q = 400 kW and H = 0.6 m.
Hinkley et al. [2]. Using regression analysis on the average data in Figure 6, correlations for the heat flux along the ceiling were developed q00 ¼ 160
ðx þ H Þ=Lf ;tip < 0:25
1:3 q00 ¼ 26:39 ðx þ H Þ Lf ;tip
ðx þ H Þ=Lf ;tip 0:25
ð2Þ
ð3Þ
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Table 3
Average Heat Flux and Gas Temperature Data From Testing x (m) 0.29 0.89 1.51 2.12 0.29 0.89 1.51 2.12 0.29 0.89 1.51 2.12 0.29 0.89 1.51 2.12 0.29 0.89 1.51 2.12 0.29 0.89 1.51 2.12 0.29 0.89 1.51 2.12 0.29 0.89 1.51 2.12
H (m)
Lf,tip (m)
(x + H)/Lf,tip (–)
q00 avg (kW/m2)
T avg (C)
1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60
0.92 0.92 0.92 0.92 1.56 1.56 1.56 1.56 2.32 2.32 2.32 2.32 3.54 3.54 3.54 3.54 1.06 1.06 1.06 1.06 1.97 1.97 1.97 1.97 3.04 3.04 3.04 3.04 3.35 3.35 3.35 3.35
1.53 2.18 2.86 3.53 0.89 1.28 1.67 2.06 0.60 0.86 1.13 1.39 0.39 0.56 0.74 0.91 0.84 1.41 2.00 2.57 0.45 0.75 1.07 1.38 0.29 0.49 0.69 0.90 0.27 0.45 0.63 0.81
26.4 17.2 8.9 7.0 38.0 24.3 12.5 9.7 74.0 43.9 23.5 17.4 108.6 62.9 32.6 22.7 31.3 15.3 7.7 6.7 75.3 36.2 18.5 13.3 124.3 66.3 31.0 16.7 152.5 82.1 47.3 27.4
400 354 312 270 507 444 389 332 736 633 545 458 887 770 641 529 494 426 355 290 800 658 532 432 1026 849 659 527 1144 973 788 630
The value of 160 kW/m2 in the constant heat flux region was the average of the higher points in this portion of the flame. This correlation is shown as the line in Figure 6. 2.2.3. Gas Temperatures Along Ceiling. Gas temperatures at the ceiling were measured as a function of exposure time. A sample plot of the gas temperatures with time along the length of the corridor is provided in Figure 7. Average gas temperatures during the steady state part of the tests are provided in Table 3. A plot of the average gas temperatures is provided in Figure 8 as a function of dimensionless distance along the flame length. Through regression analysis of the data, correlations for the gas temperature along the ceiling were developed:
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2
Heat Flux, q" (kW/m )
1000
100
10
Hinkley et al. (1968) q"=160 (x+H)/L f,tip =0.25 q"=26.39*[(x+H)/L f,tip ] H=1.1m H=0.6m
1 0.01
0.1
1
10
(x+H)/L f,tip
Figure 6. length.
Heat fluxes with dimensionless distance along the flame
1400
Averaging Period
x=2.1m x=1.5m x=0.9m x=0.3m
Temperature (°C)
1200 1000 800 600 400 200 0 0
50
100
150
200
250
300
350
Time (s)
Figure 7. Gas temperatures at the ceiling with Q = 400 kW and H = 0.6 m.
T ¼ 1; 150
ðx þ H Þ=Lf ;tip < 0:25
0:55 T ¼ 536:5 ðx þ H Þ Lf ;tip
ðx þ H Þ=Lf ;tip 0:25
ð4Þ
ð5Þ
The magnitude of the constant temperature region of 1150C was taken as the highest temperature measured in the testing. The lines in Figure 8 represent these correlations.
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(x+H)/L f,tip =0.25
1000
100 0.1
1
10
(x+H)/L f,tip
Figure 8. Gas temperatures as a function of dimensionless distance along the flame length.
2.3. Burning Corridor Ceiling Hasemi et al. [5] conducted experiments with a burner located at the ceiling of the closed end of a corridor to quantify heat fluxes from burning ceilings in a corridor. To quantify the flame lengths and heat fluxes from these fires, a series of experiments were performed in a noncombustible corridor. Measured flame lengths are provided in Figure 9. Hasemi et al. [5] determined that the flame extension along the ceiling scales with the heat release rate per width of corridor. As a result, the following correlation was developed through regression analysis to predict flame lengths in this configuration Lf ¼ 0:0198Q00:9
ð6Þ
where, Lf is the average flame extension from the base of the burning [m]. This correlation is also shown in Figure 9. The heat flux levels measured by Hasemi et al. [5] in this configuration are provided in Figure 10. These heat fluxes were measured using water cooled heat flux gauges mounted at different locations along the length of the corridor. A correlation was developed in this study to describe heat fluxes in this configuration. The line in the plot is a correlation to the data which is provided below q00 ¼ 25
x=Lf 0:10
ð7Þ
q00 ¼ 25 ð10=6Þ x Lf 0:1 ð25 10Þ 0:10 > x=Lf > 0:70
ð8Þ
1:25 q00 ¼ 6:4 x Lf
ð9Þ
x=Lf 0:70
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Flame Extension, L f (m)
2.5 Data L f =0.0198Q' 0.9
2.0
1.5
1.0
0.5
0.0 0
50
100
150
200
Heat Release Rate per unit Width, Q' (kW/m)
Figure 9. Flame extension correlation for a burning ceiling only compared with data of Hasemi et al. [5]. 100 0.10
