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Estimation of chemical heat release rate in rack storage fires based on flame volume
Fire Safety Journal 63 (2014) 29–36
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Estimation of chemical heat release rate in rack storage fires based on flame volume Yibing Xin n FM Global, Engineering and Research, 1151 Boston-Providence Turnpike, Norwood, MA 02062, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 3 October 2012 Received in revised form 1 October 2013 Accepted 16 November 2013 Available online 10 December 2013
Quantification of heat release rate is crucial to many fire research works. Under certain conditions, such as very large fires and fire tests with sprinklers, measurements of fire heat release rate can be a challenging problem. This study attempted to develop a methodology of estimating chemical heat release rate using flame volume. This method is based on the theory that heat release rate per unit flame volume is relatively invariant, as long as the combustion is controlled by diffusion in buoyant fires under well-ventilated conditions. Test data were examined from a variety of fire experimental conditions to evaluate the proposed method. The results demonstrate that the flame-volume based method can provide reasonable estimation of heat release rate compared to oxygen-consumption based method. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Heat release rate Flame volume Buoyant diffusion flame Sprinkler protection
1. Introduction Heat release rate (HRR) is an important global quantity in characterizing fire hazards. In fire experiments and tests, ranging from laboratory-scale to full-scale, heat release rates have been measured based on either fuel and oxygen consumption or combustion product generation. When the fuel consumption based method is used, the fuel mass loss is often measured using load cells and the heat release rate is calculated by the use of heat of combustion as well as the combustion efficiency. When the oxygen consumption or combustion product generation based method is used, the O2 concentration and CO and CO2 concentrations are usually measured in the exhaust flow using gas analyzers together with mass flow rates determined by temperature and velocity probes. The methods based on O2 consumption or CO and CO2 generation form the basis of most fire calorimeters [1] and large-scale fire products collectors (FPC) [2]. The aforementioned experimental methods encounter serious challenges when applied to sprinklered fire tests, especially for multi-component fuels. When the fuel consumption based method is used for a single-component fuel, the total fuel mass needs to be measured accurately. This can be achieved reasonably well during the free burn stage of the fire, but becomes unreliable when sprinklers discharge water to the solid fuel. When the fuel consumption based method is used for multi-component fuels, not only the total fuel mass, but also the fraction of each component being consumed need to be measured accurately, since the heat of combustion of each component may vary significantly, e.g., cellulosic vs. plastic materials. n
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This can be a very challenging task to undertake. When the O2 or CO and CO2 based method is used, these gaseous species in the burning zone need to be entrained to the exhaust flow while avoiding any potential disturbance along the entrainment path. This can usually be achieved by the buoyancy generated by the fire itself, and by positioning the entrance to the exhaust flow relatively close to the fire. However, when the sprinklered fire test is conducted under a movable ceiling, which is frequently used in modern large fire test facilities, the entrance to the exhaust has to be placed at some distance above the ceiling, resulting in oxygen and combustion products mixing in the plenum space between the ceiling and the exhaust flow entrance (Fig. 1). This can cause serious smearing and delay for the measurements of gas concentrations including both oxygen and combustion products. Hence only the integrated chemical energy, not the time-resolved heat release rate, can be measured with reasonable accuracy. This situation can become even worse when the combustion products are dragged down to the floor (Fig. 1), instead of rising upward, because of the spray cooling and entrainment effects. These challenges make the measurement of fire HRR in sprinklered fire tests an unsolved problem, which severely limits the quantification of fire test results. In addition to fires with sprinkler protection, very large experimental setup and very large fire size can also cause difficulties for HRR measurements using calorimeters. In order to address this problem, a new method is needed to measure the fire heat release rate, especially for fires with sprinkler protection.
2. Heat release rate per unit flame volume The method proposed in this work allows for the determination of fire heat release rate by quantifying flame volume and by
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and thus can be treated as a constant. Introducing Eq. (1) into Eq. (2), we have
ρO2 ;1 V O2 ;1 ΔhO2 T 1 Q_ ¼ : V flame τk ðV fuel;1 þ V air;1 ÞT flame
ð3Þ
Note that, for most hydrocarbon-based fuels, the adiabatic flame temperature is approximately constant (2200–2300 K, see Ref. [15]) and the air to fuel molecular ratio is very high [1]. Thus Eq. (3) can be simplified to
ρO ;1 ðV O2 ;1 =V air;1 ÞΔhO2 T 1 Q_ ¼ 2 : τk T flame V flame Fig. 1. Flow patterns of combustion products in sprinkler fire tests.
making use of a constant converting the flame volume to chemical heat release rate. This constant is the heat release rate per unit flame volume, q_ ‴ Q_ =V flame , that will be discussed in this section. The methodology of how to determine flame volume will be discussed in the next section. Experimental data on flame volumes related to fire phenomena have been reported for many decades by Rashbash et al., [3] O’Dogherty et al., [4] Markstein [5] and Orloff et al. [6] It was suggested by de Ris et al. [7] that buoyancy-driven fires were controlling by Kolmogorov scale; consequently the HRR can be quantified by the use of a constant of 1100 kW/m3 and estimated flame volumes. This value was subsequently used by de Ris and Orloff [8] and Khan et al. [9] Rashbash [10] also proposed an empirical correlation, i.e., V flame ¼ 1:21Q 1:18 , for fire size of 0.2– 2.8 MW, which was used by Stratton [11] to investigate flame height and pulsation frequency. For laboratory-scale fires (o1 kW), Linters and Rafferty [12] suggested that HRRs could be well correlated to flame area for a number of gaseous hydrocarbon and polymers fuels. Beyond fire related data, Bradley [13] reviewed energy release intensities in various combustion processes such as hydrocarbon atmospheric laminar flame, aero gas turbine primary zone and gasoline engine. It appears that the aforementioned studies are either pertinent to momentum driven flames, or limited to the fire size (o2.8 MW) and simple fire geometry (cylindrical open fires). Given the importance of rack storage of commodities in industrial fires, the present work attempts to provide a theoretical basis of the flame volume based approach and evaluate the applicability of such an approach in large fire ( 45 MW) tests in rack storage configuration especially under suppression conditions. Fires release chemical energy through buoyant diffusion flames. Under normal ambient air pressure (1 atm), the flame volume V flame is related to the adiabatic flame temperature (T flame ) and the ambient temperature T 1 through the ideal gas law ðV fuel;1 þ V air;1 Þ=V flame ¼ T 1 =T flame
ð1Þ
where V fuel;1 and V air;1 are ambient fuel and stoichiometric air volume, respectively, before the combustion takes place. In the present work, the boundary of flame volume is determined based on visual observation of flame images. If one assumes that the combustion occurs in a time scale τk , then the chemical heat release rate per unit volume can be determined from oxygen consumption as Q_ =V flame ¼ ρO2 ;1 V O2 ;1 ΔhO2 =ðτk V flame Þ
ð2Þ
where ρO2 ;1 is ambient oxygen density, V O2 ;1 is stoichiometric oxygen volume required for complete combustion and ΔhO2 is the heat release per unit of oxygen mass consumed. Based on Ref. [14], the quantity ΔhO2 is insensitive to most hydrocarbon fuels
ð4Þ
where the fuel volume was neglected from Eq. (3). On the right hand side of Eq. (4), it appears that each quantity except τk is approximately constant for normal ambient conditions, e.g., 1 atm and 20 1C, if one assumes the oxygen/air ratio is an invariant. It should be pointed out that for under-ventilated fires, the ratio of ðV O2 ;1 =V air;1 Þ can be affected by the ventilation condition, and thus may vary significantly among different fire scenarios. As a result, Eq. (4) only applies to well-ventilated fire conditions such as industrial warehouse. For buoyant diffusion flames, the combustion process is controlled by the molecular mixing time scale τk . This time scale could be the result of either Kolmogorov turbulent cascading [7] or Rayleigh–Taylor instability controlled mixing [16,17]. If the time scale is controlled by viscous and buoyant forces due to Rayleigh– Taylor instability, then dimensional analysis shows that this scale can be estimated as
τk ðν=g 2 Þ1=3 :
ð5Þ
In this equation, the gravitational acceleration g is a constant, while the viscosity ν is a function of characteristic temperature. Since the adiabatic flame temperature is approximately constant for most hydrocarbon based fuels, the time scale τk becomes a constant. Consequently, the heat release rate per unit flame volume is a constant under the aforementioned assumptions, i.e., q_ ‴
ρO ;1 ðV O2 ;1 =V air;1 ÞΔhO2 T 1 Q_ 2 constant: V flame ðν=g 2 Þ1=3 T flame
ð6Þ
On the other hand, if the time scale τk is controlled by viscous force and eddy dissipation rate ðεÞ, as in Kolmogorov cascading, the scaling of τk can be estimated as
τk ðν=εÞ1=2 ðνlflame =u3flame Þ1=2 :
ð7Þ
Note that, for buoyant fires, the characteristic flame velocity uflame scales with flame height lflame , while the flame height lflame scales with the heat release rate Q_ , i.e., pffiffiffiffiffiffiffiffiffiffiffiffiffi 2=5 uflame glflame ; lflame Q_ ð8Þ By combining Eqs. (7) and (8), the time scale τk can be shown to be a weak function of fire size
τk Q_
1=10
ð9Þ
Taking Eqs. (6) and (9) together, the chemical heat release rate per unit flame volume should be relatively invariant for a wide range of fire sizes and fuels. The theory of constant q_ ‴ is supported by experimental observations [6,18], and the data listed in Ref. [10], and has been applied in a number of fire modeling studies [7–9]. In the present work, the constant q_ ‴ is taken to be
Y. Xin / Fire Safety Journal 63 (2014) 29–36
1100 kW/m3 as suggested by Refs. [8,9], and used in all experimental results discussed later. Given that the heat release rate per unit flame volume is a constant, it becomes possible to quantify the heat release rate if the flame volume can be determined.
3. Determination of flame volume Determination of the flame volume is critical for estimating heat release rate, and has to be performed by considering the specific geometry of the fire and the fuel of interest. The simplest fire and fuel geometry where flame volume can be determined is probably that of a pool fire. For a pool fire with a circular fuel base, flame photos can often be taken directly or generated from videos for the entire flame length. Under the assumption that the flame is axisymmetric, the flame volume can be estimated as Z lflame V flame ¼ ðπ D2flame =4Þdz ð10Þ 0
for the entire fire can be determined, and so can the fire diameter at each elevation above the fire base. However, it is also clear that the determination of flame height and diameter is sensitive to the use of either brightness or the RGB values of the digital flame photo, resulting in uncertainties of the estimated flame volume. At this time, an automatic recognition method has not been developed; the flaming region was determined visually based on brightness in snapshots taken from high-definition test videos. The assumption of axisymmetric flame shape can also create uncertainties, and the square base of the fire needs to be converted to equivalent circular base to obtain the flame volume. Fig. 3 shows the comparison of HRR of the 1.52-m square pool fire determined using the oxygen consumption based method and the flame-volume based method. Note that there are only a limited number of data points using the flame-volume based method since this method has not been automated. The comparison suggests that the flame-volume based method can provide a reasonable approximation of the O2 consumption based measurements. It should be pointed out that, since heat release rate is a global quantity, the actual uncertainty associated with the chemical heat release rate values may often be less than that associated with local estimations, e.g., the flame diameter at a particular elevation above the fire base. The uncertainties are also expected to be reduced as the heat release rate variation decreases with time. In general, the heat release rate estimation of steadystate fires can be expected to have less uncertainty than for other temporally-evolving fires. It should also be noted that pool fires often puff at specific frequencies under room temperature and normal pressure. Since most calorimeter measurements do not resolve the puffing frequencies, they often appear much smoother than HRRs determined based on the visible flame volume. For an open (unconfined) fire, the flame volume can be determined in general as Z V flame ¼
lflame
12000
O2 Consumption
10000
Flame volume
8000 6000 4000 2000 0
Fig. 2. Determination of flame length (lflame) and flame diameter (Dflame) based on instantaneous flame photos. The heptane pool fire has a square base of 1.52 m 1.52 m.
ð11Þ
Axy dz 0
where Axy is the cross-sectional area in x–y plane perpendicular to the flame height (z-direction in Fig. 2). The most challenging problem of applying this equation to flame volume estimation is probably due to the blockage of view to the flames. For example, commodities in rack storage can make it almost impossible to view the entire flame from any angle. This problem can be solved when the flame shapes are symmetric along either an axis or a plane. However, the flamevolume based method can become hardly applicable when the flames are highly non-symmetric, or there is significant shielded burning inside solid fuels. For highly non-symmetric flames, the use of two cameras from two perpendicular directions may be better for
Chemical HRR (kW)
where lflame is flame height, Dflame is flame diameter at an elevation z above the fire base. An example is shown in Fig. 2 for a heptane pool fire (1.52 m 1.52 m, square base) established under a 20MW calorimeter in the large-burn lab of FM Global Research Campus in West Gloucester, RI, USA. The inlet of the calorimeter was a 10.7 m diameter hood at 11.3 m above the lab floor. The exhaust air flow rate in the calorimeter is 113 m/s at ambient temperature. The combustion products were taken into the calorimeter and transported via a 3-m diameter duct vertically and then horizontal to an instrumentation station where temperatures, pressures and gas concentrations were measured. The oxygen consumption based HRR was calculated using the total mass flow rate, the decrease of oxygen mass fraction from the ambient value and a constant heat value of 12.8 kJ/g as suggested by Tewarson [1]. For this particular instant shown in Fig. 2, the flame is burning in the steady state with a visible flame height (lflame ) of 4.1 m. It can be seen that, using this visible flame photo, the flame height
31
0
50
100 Time (s)
150
200
Fig. 3. Chemical HRRs determined by flame-volume based method and O2consumption based measurements for a pool fire with a square base of 1.52 m 1.52 m.
32
Y. Xin / Fire Safety Journal 63 (2014) 29–36
estimating the flame volume than the current study where only one camera is used. In the present work, rack storage fires with cartoned commodities are investigated as the first attempt to evaluate the feasibility of flame-volume based measurement of HRR. Figure 4 illustrates the simple shapes used in determining flame volumes at representative locations in the rack storage. The ignition location was at the center of the rack storage on the floor level. The fuel array is typically double-row rack storage of two-pallet load wide, fourpallet load long and three-tier high (see Fig. 5 for more details). For rack storage fires, one can usually assume that the flames burn
in the flue space, unless there is significant change of fuel geometry such as burnout or collapse. Under this assumption, the flames can be approximate as trapezoids within the rack storage and as a truncated cone above the top fuel surface. The flame volumes in rack storage fires can be grouped into four categories as shown in Fig. 4: V flame;t represents those flame volumes in vertical flue space between commodities; V flame;g stands for flame volumes in the horizontal gaps; V flame;e are flame volumes extended beyond the fuel array; and the V flame;c is the truncated conical flame volume above the fuel array. For rack storage with uniform flue space (δf ¼ constant), the total flame
wcu
hfc
wcl
weu Vflame,c
hfe wel hfg
wgl
Vflame,e
wgu Vflame,g Vflame,t
hft
wtl wtu Fig. 4. Determination of flame volumes for rack storage fires using simple flame shapes. The four typical flame volumes are estimated using Eqs. (12)–(17) (Eq. (12) for Vflame,t, Eqs. (13)–(15) for Vflame,g, Eq. (16) for Vflame,c and Eq. (17) for Vflame,e).
Y. Xin / Fire Safety Journal 63 (2014) 29–36
33
Suppression water pipe
W Heat Flux Gage (4.6m above floor)
0.20
Nozzle
S
≈ 4.6
Triple DoubleWall Box 4.24
Radiometer (6.1m above floor)
1.07
Steel beam
1.07
≈
0.13
Rack Segment
0.15
6.1
1.07
Igniter
Platform Floor
0.13 Instrumented Igniter Boxes
N E
0.15
Water collector
1.07
0.15 0.15 Instrumented Surfaces
Fig. 5. Experimental setup of water application tests of commodities in rack storage (Left - elevation view; Right - plan view).
volume within all flue space of the storage tiers, V flame;t , can be estimated as i ¼ nt
V flame;t ¼ ∑ hf t ½ðwtl þ wtu Þδf δf 2
ð12Þ
i¼1
where nt is the number of tiers of the rach storage, hf t is the vertical flame height at each tier, wtl and wtu are flame widths at the lower and upper end of the trapezoid shown in Fig. 4. Note that, hf t is equal to or less than the height of the commodity in 2 each tier; the volume of the cross section hf t δf was counted twice when calculating two symmetric trapezoids perpendicular to each other, and thus was subtracted once in Eq. (12). For flame volumes between horizontal tier gaps, V flame;g , one has to consider horizontal flame spread. The minimum flame volume occurs when there is no horizontal flame spread, which can be estimated as i ¼ ng
V flame;gmin ¼ ∑ hf g ½ðwgl þ wgu Þδf δf 2
i¼1
ð13Þ
where hf g is the vertical flame height in each horizontal tier gap, and wgl and wgu are flame widths at the lower and upper end of the trapezoid shown in Fig. 4. This minimum value was estimated similar to the flame volume in flue space between commodities (Eq. (12)). However, one has to consider horizontal flame spread in estimating V flame;g , which results in its maximum value. The maximum flame volume between the horizontal gaps occurs when the flame spreads at the same rate as that in the flue, resulting in truncated conical flame volumes i ¼ ng
V flame;gmax ¼ ∑ hf g ½π i¼1
ðw2gl þ w2gu Þ=8
ð14Þ
Without direct measurement of the flame spread rate, one can treat the flame volume as the average of the upper- and lower-end estimation, i.e., V flame;g ¼ ðV flame;gmin þ V flame;gmax Þ=2
ð15Þ
It should be noted that Eq. (15) tends to result in overestimation of V flame;g at early stage of fire growth and underestimation at late stage. As a result, the application of Eq. (15) to calculate multiple flame volumes in horizontal gaps appears to mitigate the overall uncertainty, i.e., overestimation at upper tiers and underestimation at lower tiers tend to cancel each other. Similar estimations can be made for the flame volumes above the fuel
array top, i.e., V flame;c ¼ hf c ½ð2wcl δf δf Þ þ π w2cu =4=2 2
ð16Þ
It can be seen from Eq. (16) that for the conical flame on top of the fuel array, the bottom surface is approximated as a crossshaped area, instead of a circular area. As for the flames burning outside the fuel loads, they may not occur uniformly along all external surfaces and in the flue of adjacent fuel columns. Therefore, it is assumed that the volume of external flames on one side of the fuel array only need to be doubled, instead of being quadrupled, to account for nonsymmetric flame bias. Accordingly, the flame volumes can be estimated as i ¼ ne
V flame;e ¼ ∑ hf e ½ðwel þ weu Þδe =2 2 i¼1
ð17Þ
Based on experimental observation, the thickness of external flames (δe ) is 0.15 m on average. It should be pointed out that the particular choice of doubling instead of quadrupling the external flame volumes from one side of the fuel array deviates from the symmetric assumption entirely due to test observations in the present work, and should not be applied universally to all fire scenarios. The total flame volume for rack storage fire thus becomes V flame ¼ V flame;t þV flame;g þ V flame;c þV flame;e
ð18Þ
From the aforementioned analysis, the uncertainties associated with the flame volume estimation can be the result of several factors: simplified flame shapes, axisymmetric assumption, and non-uniform flames on external surfaces. These factors can be further complicated by the fact that visible flames may be obscured by smoke and steam, when water is applied during a suppression test. In order to evaluate the uncertainty, the flamevolume based method was applied to estimate the chemical heat release rates in four rack storage tests with water application. The results are compared to calorimeter measurements in the next section. It should be pointed out that, there could also be problems with large fuel arrays for the proposed method, compared to the relatively small fuel arrays examine in the present work. 4. Experimental results Four suppression tests using the water application apparatus (see Fig. 5) were selected to evaluate the flame-volume based
Y. Xin / Fire Safety Journal 63 (2014) 29–36
12000
Chemical HRR (kW)
method. Table 1 shows the major experimental conditions of these tests. All tests were conducted under a 20-MW FPC where HRR can be measured directly. The fuel array were all two-pallet-load wide, four-pallet-load long, and three-tier high (2 4 3) rack storage, with ignition location at the center of the bottom tier on the floor level. The first two tests were Tests 5 and 6 conducted in the commodity classification study [19] where wood pallets were used to support the Class 2 and the standard plastic commodities. Each pallet load of the Class 2 commodities consisted of either two layers of triple-wall or three-layers of double-wall corrugated cardboard boxes with nominal dimensions of 1.07 m 1.07 m 1.07 m, filled with a metal liner inside and placed on a hardwood pallet (1.07 m 1.07 m 0.13 m); each pallet load of the standard plastic commodities consisted of eight single-wall corrugated cardboard boxes with 125 polystyrene plastic cups placed in each box in 5 5 5 matrix and separated by cardboard dividers. More details of these commodities can be found in Ref. [20]. The last two tests were also water application tests using Class 2 commodities. They are similar to the first two tests except that the Class 2 commodities were supported by 13-cm steel beams instead of wood pallets. During the first three tests, the fires were suppressed by uniform water fluxes, while in the last test (WAAP01T06), the fire was out of control under a uniform water flux of 4.1 mm/min. It is expected that these tests cover a range of experimental conditions and commodities that can provide a strong assessment of the flame-volume based method for determining the HRR. Figures 6–9 show the comparisons of HRRs based on the flame volume and the O2 consumption methods. The O2 consumption based HRR measurements were selected for the comparison due to the universal heat release associated with oxygen [1,14]. In contrast, the CO2 and CO generation based HRR measurements are more complicated in applying the heat release values at different stages of the burning process, when the fuel, e.g., standard plastic commodity, contains multiple components such as corrugated cardboard and polystyrene plastics. In addition,
O2 Consumption Flame volume
10000 8000 6000 4000 2000 0
0
20
40
60 80 100 120 140 160 Time (s)
Fig. 7. Chemical HRRs determined by the flame-volume based method and O2consumption based measurements for 2 4, 3-tier standard plastic commodity (Test CmmClsT06, water flux 18.3 mm/min).
Chemical HRR (kW)
34
12000
O2 Consumption Flame volume
10000 8000 6000 4000 2000 0
0
50
100 Time (s)
Commodity
Fuel array
2 4, 3-tier CmmClsT06 2 4, 3-tier WAAP01T01 Class 2 2 4, (3 layer, double-wall) 3-tier WAAP01T06 Class 2 2 4, (3 layer, double-wall) 3-tier
Chemical HRR (kW)
CmmClsT05
Class 2 (2 layer, triple-wall) Standard plastic
12000
Water flux (mm/min)
Pallet load support
18.3
Wood pallet
18.3
Wood pallet
12.2
Steel beam
4.1
Steel point
O2 Consumption Flame volume
10000 8000 6000 4000 2000 0
0
20
40
60 80 Time (s)
100
120
Fig. 6. Chemical HRRs determined by the flame-volume based method and O2consumption based measurements for 2 4, 3-tier standard Class commodity (Test CmmClsT05, water flux 18.3 mm/min).
Chemical HRR (kW)
Test label
200
Fig. 8. Chemical HRRs determined by the flame-volume based method and O2consumption based measurements for 2 4, 3-tier idealized Class 2 commodity (Test WAAP01T01, water flux 12.2 mm/min).
12000 Table 1 Test conditions.
150
O2 Consumption Flame volume
10000 8000 6000 4000 2000 0
0
50
100
150 200 Time (s)
250
300
Fig. 9. Chemical HRRs determined by the flame-volume based method and O2consumption based measurements for 2 4, 3-tier idealized Class 2 commodity (Test WAAP01T06, water flux 4.1 mm/min).
the calorimeter measurements in Figs. 6–9 were time-shifted based on visual observation to best match the flame-volume based data. Such an adjustment provides better comparison of the two sets of data, given the uncertainties associated with ignition time in the calorimeter measurements, as well as the relative insignificance of the initial fire development for many practical applications such as sprinkler protection. To obtain the flame volume based HRRs, snapshots were taken from high-definition test videos at relatively short time intervals (10–20 s) during the fast growing stage and relatively longer intervals during the slow decay stage (50 s). The flame volumes were estimated using the method discussed in previous section. Qualitatively the fire growth and suppression trends are captured by the flame-volume based method just as well as the
Y. Xin / Fire Safety Journal 63 (2014) 29–36
Table 2 Comparison of ΔE and HRRmax. Test label
CmmClsT05 CmmClsT06 WAAP01T01 WAAP01T06
ΔE (MJ)
HRRmax (kW)
Flame volume
Error O2 consumption (%)
Flame volume
O2 Error consumption (%)
283 418 529 171
270 432 600 167
5.6 5.5 6.2 7.7
6.2 4.1 7.2 8.3
4.5 3.4 11.8 2.7
8.3 35.0 14.1 6.8
calorimeter measurements based on O2 consumption. In each test case, the flame-volume based method is in good agreement with the O2 consumption based method. Since the O2 consumption based method is generally accepted as a fair representation of all stages of the fire, the comparisons in these figures basically validate the use of the flame-volume based method. It also appears from Figs. 6–9 that the flame-volume based method provides better estimation of the HRR in the growing phase of the fire than that in the suppression phase. To further quantify the accuracy of the flame-volume based method, two variables were computed using the two sets of experimental data, i.e., accumulated chemical energy (ΔE) and averaged peak heat release rate (HRRmax). The accumulated chemical energy, ΔE, is defined as the integrated heat release for a given period of time after ignition, i.e., the area below the curves in Figs. 6–9. For the flamevolume based method, the digitization of the flame photo and the determination of the flame shape are carried out manually at this time. Therefore, only a limited number of flame photos were analyzed, with relatively long time intervals between the symbols showing in Figs. 6–9. An approximate value of ΔE is calculated using the relatively large time intervals as shown in these plots. The value of HRRmax is calculated for the flame-volume based method by averaging the two highest values. For the O2 consumption based method, the value of HRRmax was computed using data for the same period of time as the flame-volume based method. The values of ΔE and HRRmax are reported in Table 2, where the relative errors were computed as the difference between the values obtained using the flame-volume based method and those using the O2 consumption based method divided by the latter. From Table 2, the relative differences between each set of data based on the two different methods can vary from almost identical to each other to as large as 35%. Overall, the uncertainties associated with the accumulated chemical energy ΔE are less than 12%, which is noticeably better than those of the averaged peak HRR. If one only considers the Class 2 commodities, i.e., excluding Test CmmClasT06 of the standard plastics, the uncertainties are all less than 15% for both ΔE and HRRmax. These results suggest that the flame-volume based method can provide both qualitative and quantitative characterization for the fire behavior, considering the rough estimation presented in previous sections. From Table 2, the variations of the flame-volume based results are generally larger for specific variables of interest such as the peak HRR than for integrated variables such as ΔE. However, given the fact that there is no other reliable method to measure the HRR of large fires with sprinkler protection under a movable ceiling, and the simplicity of the flame-volume based method, the uncertainties in comparison to calorimeter data are probably still acceptable for many engineering applications.
5. Conclusions and future work An experimental method for determining the HRR was developed based on estimation of flame volumes. The theoretical basis
35
of this method is that the time scale controlling gas-phase combustion is either independent or very weakly dependent upon the fire size. As a result, a constant HRR per unit volume can be applied to a wide range of buoyant fires. The application of this constant in conjunction with flame volume estimation can help determine the chemical HRR, under certain fire scenarios where flame volumes can be estimated with confidence. The flame-volume based method was evaluated by comparing the results to the O2 consumption based HRR measurements in four fire tests with suppression in rack storage configuration. It is demonstrated that the flame-volume based method can capture fire growth and suppression trends qualitatively. Furthermore, it can also provide quantitative measurements of chemical HRR with an uncertainty of less than 35% for both Class 2 and Standard Plastic fires. When only the Class 2 commodity is considered, the uncertainties are less than 15% for the accumulated energy and the averaged peak HRR. These results suggest that the flame-volume based method can be another tool for HRR measurements, especially when the fire geometries are simple. Such a tool can be combined with other techniques, e.g., accumulated chemical energy measurements by calorimeters, and combustion product concentration measurements by gas analyzers, and flame propagation by thermocouples, to provide a set of global variables to help quantify fire test results, and provide validation data for numerical models. It should also be pointed out that the flame-volume based method is applicable only to fire scenarios where flames are buoyancy-driven and visible flame volumes can be estimated with reasonable confidence, often under well-ventilated conditions. Common fire scenarios preventing reasonable flame volume estimations may include those with significant view blockage and overlapping of flames, major burning inside fuel/solid containers, highly non-symmetric fire development, and substantial deviation from hydrocarbon dominated fuels that can alter the oxygen/air ratio and thus the HRR per unit of flame volume. Similar effects can also occur when air entrainment to the flames is severely restricted such as in under-ventilated fires.
Acknowledgements The author would like to acknowledge Dr. John de Ris and Dr. Francesco Tamanini for their invaluable discussions on the technical approach of this work. References [1] A. Tewarson, Generation of heat and chemical compounds in fires, The SFPE Handbook of Fire Protection EngineeringNational Fire Protection Association, Quincy MA, 2002. (Chapter 3–4). [2] G. Heskestad, A Fire Products Collector for Calorimetry into the MW Range, FM Global Technical Report, J.I. 0C2E1.RA, June 01, 1981. [3] D.J. Rashbash, et al., fuel 35 (1956) 94–106. [4] M.J. O’Dogherty, et al., Fire Research Technical Paper No, HMSO, London, 1967. [5] G. Markstein, Proc. Combust. Inst. 16 (1976) 1407–1419. [6] L. Orloff, J. deRies, Proc. Combust. Inst. 19 (1982) 885–895. [7] J.L. de Ris, P.K. Wu, G. Heskestad, Proc. Combust. Inst. 28 (2000) 2751–2759. [8] J.L. de Ris, L. Orloff, Fire Safety Science—Proceedings of the Eighth Symposium, International Association for Fire Safety Science, 2005, p. 999. [9] M.M. Khan, K.L.T. Jamison, J.L. de Ris, Fire Safety Science—Proceedings of the Tenth Symposium, International Association for Fire Safety Science, 2011, p. 513. [10] D. Rashbash, Evaluation of Fire Safety, John Wiley and Sons (2004) 96. [11] B.J. Stratton, Determining Flame Height and Flame Pulsation Frequency and Estimating Heat Release Rate from 3D Flame Reconstruction, MS Thesis, University of Canterbury, New Zealand, 2005. [12] G.T. Linters, I.P. Rafferty, Fire Saf. J. 43 (2008) 442–450. [13] D. Bradley, Proc. Combust. Inst. 24 (1992) 247–262. [14] C. Huggett, Fire Mater. 12 (1980) 61–65. [15] S.R. Turns, An Introduction to Combustion, McGraw-Hill Inc., 1996. [16] P.E. DesJardin, T.J. O’Hern, S.R. Tieszen, Phys. Fluids 13 (2001) 3097–3100.
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[17] S.R. Tieszen, H. Pitsch, G. Blanquart, S. Abarzhi, Toward the development of a LES-SGS closure model for buoyant plumes, in: Proceedings of the Summer Program, Center for Turbulence Research, Stanford University, 2004, pp. 341–352. [18] G.H. Markstein, J.L. de Ris, Proc. Combust. Inst. 23 (1990) 1685–1692.
[19] Y. Xin, F. Tamanini, Fire Safety Science—Proceedings of the Ninth International Symposium, International Association for Fire Safety Science, 2008, pp. 527. [20] FM Global Approval Standard, “Approval Standard for Automatic Control Mode Sprinklers for Fire Protection,” Class Number 2000, March 2006, FM Approvals LLC.
Contents lists available at ScienceDirect
Fire Safety Journal journal homepage: www.elsevier.com/locate/firesaf
Estimation of chemical heat release rate in rack storage fires based on flame volume Yibing Xin n FM Global, Engineering and Research, 1151 Boston-Providence Turnpike, Norwood, MA 02062, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 3 October 2012 Received in revised form 1 October 2013 Accepted 16 November 2013 Available online 10 December 2013
Quantification of heat release rate is crucial to many fire research works. Under certain conditions, such as very large fires and fire tests with sprinklers, measurements of fire heat release rate can be a challenging problem. This study attempted to develop a methodology of estimating chemical heat release rate using flame volume. This method is based on the theory that heat release rate per unit flame volume is relatively invariant, as long as the combustion is controlled by diffusion in buoyant fires under well-ventilated conditions. Test data were examined from a variety of fire experimental conditions to evaluate the proposed method. The results demonstrate that the flame-volume based method can provide reasonable estimation of heat release rate compared to oxygen-consumption based method. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Heat release rate Flame volume Buoyant diffusion flame Sprinkler protection
1. Introduction Heat release rate (HRR) is an important global quantity in characterizing fire hazards. In fire experiments and tests, ranging from laboratory-scale to full-scale, heat release rates have been measured based on either fuel and oxygen consumption or combustion product generation. When the fuel consumption based method is used, the fuel mass loss is often measured using load cells and the heat release rate is calculated by the use of heat of combustion as well as the combustion efficiency. When the oxygen consumption or combustion product generation based method is used, the O2 concentration and CO and CO2 concentrations are usually measured in the exhaust flow using gas analyzers together with mass flow rates determined by temperature and velocity probes. The methods based on O2 consumption or CO and CO2 generation form the basis of most fire calorimeters [1] and large-scale fire products collectors (FPC) [2]. The aforementioned experimental methods encounter serious challenges when applied to sprinklered fire tests, especially for multi-component fuels. When the fuel consumption based method is used for a single-component fuel, the total fuel mass needs to be measured accurately. This can be achieved reasonably well during the free burn stage of the fire, but becomes unreliable when sprinklers discharge water to the solid fuel. When the fuel consumption based method is used for multi-component fuels, not only the total fuel mass, but also the fraction of each component being consumed need to be measured accurately, since the heat of combustion of each component may vary significantly, e.g., cellulosic vs. plastic materials. n
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0379-7112/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.firesaf.2013.11.004
This can be a very challenging task to undertake. When the O2 or CO and CO2 based method is used, these gaseous species in the burning zone need to be entrained to the exhaust flow while avoiding any potential disturbance along the entrainment path. This can usually be achieved by the buoyancy generated by the fire itself, and by positioning the entrance to the exhaust flow relatively close to the fire. However, when the sprinklered fire test is conducted under a movable ceiling, which is frequently used in modern large fire test facilities, the entrance to the exhaust has to be placed at some distance above the ceiling, resulting in oxygen and combustion products mixing in the plenum space between the ceiling and the exhaust flow entrance (Fig. 1). This can cause serious smearing and delay for the measurements of gas concentrations including both oxygen and combustion products. Hence only the integrated chemical energy, not the time-resolved heat release rate, can be measured with reasonable accuracy. This situation can become even worse when the combustion products are dragged down to the floor (Fig. 1), instead of rising upward, because of the spray cooling and entrainment effects. These challenges make the measurement of fire HRR in sprinklered fire tests an unsolved problem, which severely limits the quantification of fire test results. In addition to fires with sprinkler protection, very large experimental setup and very large fire size can also cause difficulties for HRR measurements using calorimeters. In order to address this problem, a new method is needed to measure the fire heat release rate, especially for fires with sprinkler protection.
2. Heat release rate per unit flame volume The method proposed in this work allows for the determination of fire heat release rate by quantifying flame volume and by
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Y. Xin / Fire Safety Journal 63 (2014) 29–36
and thus can be treated as a constant. Introducing Eq. (1) into Eq. (2), we have
ρO2 ;1 V O2 ;1 ΔhO2 T 1 Q_ ¼ : V flame τk ðV fuel;1 þ V air;1 ÞT flame
ð3Þ
Note that, for most hydrocarbon-based fuels, the adiabatic flame temperature is approximately constant (2200–2300 K, see Ref. [15]) and the air to fuel molecular ratio is very high [1]. Thus Eq. (3) can be simplified to
ρO ;1 ðV O2 ;1 =V air;1 ÞΔhO2 T 1 Q_ ¼ 2 : τk T flame V flame Fig. 1. Flow patterns of combustion products in sprinkler fire tests.
making use of a constant converting the flame volume to chemical heat release rate. This constant is the heat release rate per unit flame volume, q_ ‴ Q_ =V flame , that will be discussed in this section. The methodology of how to determine flame volume will be discussed in the next section. Experimental data on flame volumes related to fire phenomena have been reported for many decades by Rashbash et al., [3] O’Dogherty et al., [4] Markstein [5] and Orloff et al. [6] It was suggested by de Ris et al. [7] that buoyancy-driven fires were controlling by Kolmogorov scale; consequently the HRR can be quantified by the use of a constant of 1100 kW/m3 and estimated flame volumes. This value was subsequently used by de Ris and Orloff [8] and Khan et al. [9] Rashbash [10] also proposed an empirical correlation, i.e., V flame ¼ 1:21Q 1:18 , for fire size of 0.2– 2.8 MW, which was used by Stratton [11] to investigate flame height and pulsation frequency. For laboratory-scale fires (o1 kW), Linters and Rafferty [12] suggested that HRRs could be well correlated to flame area for a number of gaseous hydrocarbon and polymers fuels. Beyond fire related data, Bradley [13] reviewed energy release intensities in various combustion processes such as hydrocarbon atmospheric laminar flame, aero gas turbine primary zone and gasoline engine. It appears that the aforementioned studies are either pertinent to momentum driven flames, or limited to the fire size (o2.8 MW) and simple fire geometry (cylindrical open fires). Given the importance of rack storage of commodities in industrial fires, the present work attempts to provide a theoretical basis of the flame volume based approach and evaluate the applicability of such an approach in large fire ( 45 MW) tests in rack storage configuration especially under suppression conditions. Fires release chemical energy through buoyant diffusion flames. Under normal ambient air pressure (1 atm), the flame volume V flame is related to the adiabatic flame temperature (T flame ) and the ambient temperature T 1 through the ideal gas law ðV fuel;1 þ V air;1 Þ=V flame ¼ T 1 =T flame
ð1Þ
where V fuel;1 and V air;1 are ambient fuel and stoichiometric air volume, respectively, before the combustion takes place. In the present work, the boundary of flame volume is determined based on visual observation of flame images. If one assumes that the combustion occurs in a time scale τk , then the chemical heat release rate per unit volume can be determined from oxygen consumption as Q_ =V flame ¼ ρO2 ;1 V O2 ;1 ΔhO2 =ðτk V flame Þ
ð2Þ
where ρO2 ;1 is ambient oxygen density, V O2 ;1 is stoichiometric oxygen volume required for complete combustion and ΔhO2 is the heat release per unit of oxygen mass consumed. Based on Ref. [14], the quantity ΔhO2 is insensitive to most hydrocarbon fuels
ð4Þ
where the fuel volume was neglected from Eq. (3). On the right hand side of Eq. (4), it appears that each quantity except τk is approximately constant for normal ambient conditions, e.g., 1 atm and 20 1C, if one assumes the oxygen/air ratio is an invariant. It should be pointed out that for under-ventilated fires, the ratio of ðV O2 ;1 =V air;1 Þ can be affected by the ventilation condition, and thus may vary significantly among different fire scenarios. As a result, Eq. (4) only applies to well-ventilated fire conditions such as industrial warehouse. For buoyant diffusion flames, the combustion process is controlled by the molecular mixing time scale τk . This time scale could be the result of either Kolmogorov turbulent cascading [7] or Rayleigh–Taylor instability controlled mixing [16,17]. If the time scale is controlled by viscous and buoyant forces due to Rayleigh– Taylor instability, then dimensional analysis shows that this scale can be estimated as
τk ðν=g 2 Þ1=3 :
ð5Þ
In this equation, the gravitational acceleration g is a constant, while the viscosity ν is a function of characteristic temperature. Since the adiabatic flame temperature is approximately constant for most hydrocarbon based fuels, the time scale τk becomes a constant. Consequently, the heat release rate per unit flame volume is a constant under the aforementioned assumptions, i.e., q_ ‴
ρO ;1 ðV O2 ;1 =V air;1 ÞΔhO2 T 1 Q_ 2 constant: V flame ðν=g 2 Þ1=3 T flame
ð6Þ
On the other hand, if the time scale τk is controlled by viscous force and eddy dissipation rate ðεÞ, as in Kolmogorov cascading, the scaling of τk can be estimated as
τk ðν=εÞ1=2 ðνlflame =u3flame Þ1=2 :
ð7Þ
Note that, for buoyant fires, the characteristic flame velocity uflame scales with flame height lflame , while the flame height lflame scales with the heat release rate Q_ , i.e., pffiffiffiffiffiffiffiffiffiffiffiffiffi 2=5 uflame glflame ; lflame Q_ ð8Þ By combining Eqs. (7) and (8), the time scale τk can be shown to be a weak function of fire size
τk Q_
1=10
ð9Þ
Taking Eqs. (6) and (9) together, the chemical heat release rate per unit flame volume should be relatively invariant for a wide range of fire sizes and fuels. The theory of constant q_ ‴ is supported by experimental observations [6,18], and the data listed in Ref. [10], and has been applied in a number of fire modeling studies [7–9]. In the present work, the constant q_ ‴ is taken to be
Y. Xin / Fire Safety Journal 63 (2014) 29–36
1100 kW/m3 as suggested by Refs. [8,9], and used in all experimental results discussed later. Given that the heat release rate per unit flame volume is a constant, it becomes possible to quantify the heat release rate if the flame volume can be determined.
3. Determination of flame volume Determination of the flame volume is critical for estimating heat release rate, and has to be performed by considering the specific geometry of the fire and the fuel of interest. The simplest fire and fuel geometry where flame volume can be determined is probably that of a pool fire. For a pool fire with a circular fuel base, flame photos can often be taken directly or generated from videos for the entire flame length. Under the assumption that the flame is axisymmetric, the flame volume can be estimated as Z lflame V flame ¼ ðπ D2flame =4Þdz ð10Þ 0
for the entire fire can be determined, and so can the fire diameter at each elevation above the fire base. However, it is also clear that the determination of flame height and diameter is sensitive to the use of either brightness or the RGB values of the digital flame photo, resulting in uncertainties of the estimated flame volume. At this time, an automatic recognition method has not been developed; the flaming region was determined visually based on brightness in snapshots taken from high-definition test videos. The assumption of axisymmetric flame shape can also create uncertainties, and the square base of the fire needs to be converted to equivalent circular base to obtain the flame volume. Fig. 3 shows the comparison of HRR of the 1.52-m square pool fire determined using the oxygen consumption based method and the flame-volume based method. Note that there are only a limited number of data points using the flame-volume based method since this method has not been automated. The comparison suggests that the flame-volume based method can provide a reasonable approximation of the O2 consumption based measurements. It should be pointed out that, since heat release rate is a global quantity, the actual uncertainty associated with the chemical heat release rate values may often be less than that associated with local estimations, e.g., the flame diameter at a particular elevation above the fire base. The uncertainties are also expected to be reduced as the heat release rate variation decreases with time. In general, the heat release rate estimation of steadystate fires can be expected to have less uncertainty than for other temporally-evolving fires. It should also be noted that pool fires often puff at specific frequencies under room temperature and normal pressure. Since most calorimeter measurements do not resolve the puffing frequencies, they often appear much smoother than HRRs determined based on the visible flame volume. For an open (unconfined) fire, the flame volume can be determined in general as Z V flame ¼
lflame
12000
O2 Consumption
10000
Flame volume
8000 6000 4000 2000 0
Fig. 2. Determination of flame length (lflame) and flame diameter (Dflame) based on instantaneous flame photos. The heptane pool fire has a square base of 1.52 m 1.52 m.
ð11Þ
Axy dz 0
where Axy is the cross-sectional area in x–y plane perpendicular to the flame height (z-direction in Fig. 2). The most challenging problem of applying this equation to flame volume estimation is probably due to the blockage of view to the flames. For example, commodities in rack storage can make it almost impossible to view the entire flame from any angle. This problem can be solved when the flame shapes are symmetric along either an axis or a plane. However, the flamevolume based method can become hardly applicable when the flames are highly non-symmetric, or there is significant shielded burning inside solid fuels. For highly non-symmetric flames, the use of two cameras from two perpendicular directions may be better for
Chemical HRR (kW)
where lflame is flame height, Dflame is flame diameter at an elevation z above the fire base. An example is shown in Fig. 2 for a heptane pool fire (1.52 m 1.52 m, square base) established under a 20MW calorimeter in the large-burn lab of FM Global Research Campus in West Gloucester, RI, USA. The inlet of the calorimeter was a 10.7 m diameter hood at 11.3 m above the lab floor. The exhaust air flow rate in the calorimeter is 113 m/s at ambient temperature. The combustion products were taken into the calorimeter and transported via a 3-m diameter duct vertically and then horizontal to an instrumentation station where temperatures, pressures and gas concentrations were measured. The oxygen consumption based HRR was calculated using the total mass flow rate, the decrease of oxygen mass fraction from the ambient value and a constant heat value of 12.8 kJ/g as suggested by Tewarson [1]. For this particular instant shown in Fig. 2, the flame is burning in the steady state with a visible flame height (lflame ) of 4.1 m. It can be seen that, using this visible flame photo, the flame height
31
0
50
100 Time (s)
150
200
Fig. 3. Chemical HRRs determined by flame-volume based method and O2consumption based measurements for a pool fire with a square base of 1.52 m 1.52 m.
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Y. Xin / Fire Safety Journal 63 (2014) 29–36
estimating the flame volume than the current study where only one camera is used. In the present work, rack storage fires with cartoned commodities are investigated as the first attempt to evaluate the feasibility of flame-volume based measurement of HRR. Figure 4 illustrates the simple shapes used in determining flame volumes at representative locations in the rack storage. The ignition location was at the center of the rack storage on the floor level. The fuel array is typically double-row rack storage of two-pallet load wide, fourpallet load long and three-tier high (see Fig. 5 for more details). For rack storage fires, one can usually assume that the flames burn
in the flue space, unless there is significant change of fuel geometry such as burnout or collapse. Under this assumption, the flames can be approximate as trapezoids within the rack storage and as a truncated cone above the top fuel surface. The flame volumes in rack storage fires can be grouped into four categories as shown in Fig. 4: V flame;t represents those flame volumes in vertical flue space between commodities; V flame;g stands for flame volumes in the horizontal gaps; V flame;e are flame volumes extended beyond the fuel array; and the V flame;c is the truncated conical flame volume above the fuel array. For rack storage with uniform flue space (δf ¼ constant), the total flame
wcu
hfc
wcl
weu Vflame,c
hfe wel hfg
wgl
Vflame,e
wgu Vflame,g Vflame,t
hft
wtl wtu Fig. 4. Determination of flame volumes for rack storage fires using simple flame shapes. The four typical flame volumes are estimated using Eqs. (12)–(17) (Eq. (12) for Vflame,t, Eqs. (13)–(15) for Vflame,g, Eq. (16) for Vflame,c and Eq. (17) for Vflame,e).
Y. Xin / Fire Safety Journal 63 (2014) 29–36
33
Suppression water pipe
W Heat Flux Gage (4.6m above floor)
0.20
Nozzle
S
≈ 4.6
Triple DoubleWall Box 4.24
Radiometer (6.1m above floor)
1.07
Steel beam
1.07
≈
0.13
Rack Segment
0.15
6.1
1.07
Igniter
Platform Floor
0.13 Instrumented Igniter Boxes
N E
0.15
Water collector
1.07
0.15 0.15 Instrumented Surfaces
Fig. 5. Experimental setup of water application tests of commodities in rack storage (Left - elevation view; Right - plan view).
volume within all flue space of the storage tiers, V flame;t , can be estimated as i ¼ nt
V flame;t ¼ ∑ hf t ½ðwtl þ wtu Þδf δf 2
ð12Þ
i¼1
where nt is the number of tiers of the rach storage, hf t is the vertical flame height at each tier, wtl and wtu are flame widths at the lower and upper end of the trapezoid shown in Fig. 4. Note that, hf t is equal to or less than the height of the commodity in 2 each tier; the volume of the cross section hf t δf was counted twice when calculating two symmetric trapezoids perpendicular to each other, and thus was subtracted once in Eq. (12). For flame volumes between horizontal tier gaps, V flame;g , one has to consider horizontal flame spread. The minimum flame volume occurs when there is no horizontal flame spread, which can be estimated as i ¼ ng
V flame;gmin ¼ ∑ hf g ½ðwgl þ wgu Þδf δf 2
i¼1
ð13Þ
where hf g is the vertical flame height in each horizontal tier gap, and wgl and wgu are flame widths at the lower and upper end of the trapezoid shown in Fig. 4. This minimum value was estimated similar to the flame volume in flue space between commodities (Eq. (12)). However, one has to consider horizontal flame spread in estimating V flame;g , which results in its maximum value. The maximum flame volume between the horizontal gaps occurs when the flame spreads at the same rate as that in the flue, resulting in truncated conical flame volumes i ¼ ng
V flame;gmax ¼ ∑ hf g ½π i¼1
ðw2gl þ w2gu Þ=8
ð14Þ
Without direct measurement of the flame spread rate, one can treat the flame volume as the average of the upper- and lower-end estimation, i.e., V flame;g ¼ ðV flame;gmin þ V flame;gmax Þ=2
ð15Þ
It should be noted that Eq. (15) tends to result in overestimation of V flame;g at early stage of fire growth and underestimation at late stage. As a result, the application of Eq. (15) to calculate multiple flame volumes in horizontal gaps appears to mitigate the overall uncertainty, i.e., overestimation at upper tiers and underestimation at lower tiers tend to cancel each other. Similar estimations can be made for the flame volumes above the fuel
array top, i.e., V flame;c ¼ hf c ½ð2wcl δf δf Þ þ π w2cu =4=2 2
ð16Þ
It can be seen from Eq. (16) that for the conical flame on top of the fuel array, the bottom surface is approximated as a crossshaped area, instead of a circular area. As for the flames burning outside the fuel loads, they may not occur uniformly along all external surfaces and in the flue of adjacent fuel columns. Therefore, it is assumed that the volume of external flames on one side of the fuel array only need to be doubled, instead of being quadrupled, to account for nonsymmetric flame bias. Accordingly, the flame volumes can be estimated as i ¼ ne
V flame;e ¼ ∑ hf e ½ðwel þ weu Þδe =2 2 i¼1
ð17Þ
Based on experimental observation, the thickness of external flames (δe ) is 0.15 m on average. It should be pointed out that the particular choice of doubling instead of quadrupling the external flame volumes from one side of the fuel array deviates from the symmetric assumption entirely due to test observations in the present work, and should not be applied universally to all fire scenarios. The total flame volume for rack storage fire thus becomes V flame ¼ V flame;t þV flame;g þ V flame;c þV flame;e
ð18Þ
From the aforementioned analysis, the uncertainties associated with the flame volume estimation can be the result of several factors: simplified flame shapes, axisymmetric assumption, and non-uniform flames on external surfaces. These factors can be further complicated by the fact that visible flames may be obscured by smoke and steam, when water is applied during a suppression test. In order to evaluate the uncertainty, the flamevolume based method was applied to estimate the chemical heat release rates in four rack storage tests with water application. The results are compared to calorimeter measurements in the next section. It should be pointed out that, there could also be problems with large fuel arrays for the proposed method, compared to the relatively small fuel arrays examine in the present work. 4. Experimental results Four suppression tests using the water application apparatus (see Fig. 5) were selected to evaluate the flame-volume based
Y. Xin / Fire Safety Journal 63 (2014) 29–36
12000
Chemical HRR (kW)
method. Table 1 shows the major experimental conditions of these tests. All tests were conducted under a 20-MW FPC where HRR can be measured directly. The fuel array were all two-pallet-load wide, four-pallet-load long, and three-tier high (2 4 3) rack storage, with ignition location at the center of the bottom tier on the floor level. The first two tests were Tests 5 and 6 conducted in the commodity classification study [19] where wood pallets were used to support the Class 2 and the standard plastic commodities. Each pallet load of the Class 2 commodities consisted of either two layers of triple-wall or three-layers of double-wall corrugated cardboard boxes with nominal dimensions of 1.07 m 1.07 m 1.07 m, filled with a metal liner inside and placed on a hardwood pallet (1.07 m 1.07 m 0.13 m); each pallet load of the standard plastic commodities consisted of eight single-wall corrugated cardboard boxes with 125 polystyrene plastic cups placed in each box in 5 5 5 matrix and separated by cardboard dividers. More details of these commodities can be found in Ref. [20]. The last two tests were also water application tests using Class 2 commodities. They are similar to the first two tests except that the Class 2 commodities were supported by 13-cm steel beams instead of wood pallets. During the first three tests, the fires were suppressed by uniform water fluxes, while in the last test (WAAP01T06), the fire was out of control under a uniform water flux of 4.1 mm/min. It is expected that these tests cover a range of experimental conditions and commodities that can provide a strong assessment of the flame-volume based method for determining the HRR. Figures 6–9 show the comparisons of HRRs based on the flame volume and the O2 consumption methods. The O2 consumption based HRR measurements were selected for the comparison due to the universal heat release associated with oxygen [1,14]. In contrast, the CO2 and CO generation based HRR measurements are more complicated in applying the heat release values at different stages of the burning process, when the fuel, e.g., standard plastic commodity, contains multiple components such as corrugated cardboard and polystyrene plastics. In addition,
O2 Consumption Flame volume
10000 8000 6000 4000 2000 0
0
20
40
60 80 100 120 140 160 Time (s)
Fig. 7. Chemical HRRs determined by the flame-volume based method and O2consumption based measurements for 2 4, 3-tier standard plastic commodity (Test CmmClsT06, water flux 18.3 mm/min).
Chemical HRR (kW)
34
12000
O2 Consumption Flame volume
10000 8000 6000 4000 2000 0
0
50
100 Time (s)
Commodity
Fuel array
2 4, 3-tier CmmClsT06 2 4, 3-tier WAAP01T01 Class 2 2 4, (3 layer, double-wall) 3-tier WAAP01T06 Class 2 2 4, (3 layer, double-wall) 3-tier
Chemical HRR (kW)
CmmClsT05
Class 2 (2 layer, triple-wall) Standard plastic
12000
Water flux (mm/min)
Pallet load support
18.3
Wood pallet
18.3
Wood pallet
12.2
Steel beam
4.1
Steel point
O2 Consumption Flame volume
10000 8000 6000 4000 2000 0
0
20
40
60 80 Time (s)
100
120
Fig. 6. Chemical HRRs determined by the flame-volume based method and O2consumption based measurements for 2 4, 3-tier standard Class commodity (Test CmmClsT05, water flux 18.3 mm/min).
Chemical HRR (kW)
Test label
200
Fig. 8. Chemical HRRs determined by the flame-volume based method and O2consumption based measurements for 2 4, 3-tier idealized Class 2 commodity (Test WAAP01T01, water flux 12.2 mm/min).
12000 Table 1 Test conditions.
150
O2 Consumption Flame volume
10000 8000 6000 4000 2000 0
0
50
100
150 200 Time (s)
250
300
Fig. 9. Chemical HRRs determined by the flame-volume based method and O2consumption based measurements for 2 4, 3-tier idealized Class 2 commodity (Test WAAP01T06, water flux 4.1 mm/min).
the calorimeter measurements in Figs. 6–9 were time-shifted based on visual observation to best match the flame-volume based data. Such an adjustment provides better comparison of the two sets of data, given the uncertainties associated with ignition time in the calorimeter measurements, as well as the relative insignificance of the initial fire development for many practical applications such as sprinkler protection. To obtain the flame volume based HRRs, snapshots were taken from high-definition test videos at relatively short time intervals (10–20 s) during the fast growing stage and relatively longer intervals during the slow decay stage (50 s). The flame volumes were estimated using the method discussed in previous section. Qualitatively the fire growth and suppression trends are captured by the flame-volume based method just as well as the
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Table 2 Comparison of ΔE and HRRmax. Test label
CmmClsT05 CmmClsT06 WAAP01T01 WAAP01T06
ΔE (MJ)
HRRmax (kW)
Flame volume
Error O2 consumption (%)
Flame volume
O2 Error consumption (%)
283 418 529 171
270 432 600 167
5.6 5.5 6.2 7.7
6.2 4.1 7.2 8.3
4.5 3.4 11.8 2.7
8.3 35.0 14.1 6.8
calorimeter measurements based on O2 consumption. In each test case, the flame-volume based method is in good agreement with the O2 consumption based method. Since the O2 consumption based method is generally accepted as a fair representation of all stages of the fire, the comparisons in these figures basically validate the use of the flame-volume based method. It also appears from Figs. 6–9 that the flame-volume based method provides better estimation of the HRR in the growing phase of the fire than that in the suppression phase. To further quantify the accuracy of the flame-volume based method, two variables were computed using the two sets of experimental data, i.e., accumulated chemical energy (ΔE) and averaged peak heat release rate (HRRmax). The accumulated chemical energy, ΔE, is defined as the integrated heat release for a given period of time after ignition, i.e., the area below the curves in Figs. 6–9. For the flamevolume based method, the digitization of the flame photo and the determination of the flame shape are carried out manually at this time. Therefore, only a limited number of flame photos were analyzed, with relatively long time intervals between the symbols showing in Figs. 6–9. An approximate value of ΔE is calculated using the relatively large time intervals as shown in these plots. The value of HRRmax is calculated for the flame-volume based method by averaging the two highest values. For the O2 consumption based method, the value of HRRmax was computed using data for the same period of time as the flame-volume based method. The values of ΔE and HRRmax are reported in Table 2, where the relative errors were computed as the difference between the values obtained using the flame-volume based method and those using the O2 consumption based method divided by the latter. From Table 2, the relative differences between each set of data based on the two different methods can vary from almost identical to each other to as large as 35%. Overall, the uncertainties associated with the accumulated chemical energy ΔE are less than 12%, which is noticeably better than those of the averaged peak HRR. If one only considers the Class 2 commodities, i.e., excluding Test CmmClasT06 of the standard plastics, the uncertainties are all less than 15% for both ΔE and HRRmax. These results suggest that the flame-volume based method can provide both qualitative and quantitative characterization for the fire behavior, considering the rough estimation presented in previous sections. From Table 2, the variations of the flame-volume based results are generally larger for specific variables of interest such as the peak HRR than for integrated variables such as ΔE. However, given the fact that there is no other reliable method to measure the HRR of large fires with sprinkler protection under a movable ceiling, and the simplicity of the flame-volume based method, the uncertainties in comparison to calorimeter data are probably still acceptable for many engineering applications.
5. Conclusions and future work An experimental method for determining the HRR was developed based on estimation of flame volumes. The theoretical basis
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of this method is that the time scale controlling gas-phase combustion is either independent or very weakly dependent upon the fire size. As a result, a constant HRR per unit volume can be applied to a wide range of buoyant fires. The application of this constant in conjunction with flame volume estimation can help determine the chemical HRR, under certain fire scenarios where flame volumes can be estimated with confidence. The flame-volume based method was evaluated by comparing the results to the O2 consumption based HRR measurements in four fire tests with suppression in rack storage configuration. It is demonstrated that the flame-volume based method can capture fire growth and suppression trends qualitatively. Furthermore, it can also provide quantitative measurements of chemical HRR with an uncertainty of less than 35% for both Class 2 and Standard Plastic fires. When only the Class 2 commodity is considered, the uncertainties are less than 15% for the accumulated energy and the averaged peak HRR. These results suggest that the flame-volume based method can be another tool for HRR measurements, especially when the fire geometries are simple. Such a tool can be combined with other techniques, e.g., accumulated chemical energy measurements by calorimeters, and combustion product concentration measurements by gas analyzers, and flame propagation by thermocouples, to provide a set of global variables to help quantify fire test results, and provide validation data for numerical models. It should also be pointed out that the flame-volume based method is applicable only to fire scenarios where flames are buoyancy-driven and visible flame volumes can be estimated with reasonable confidence, often under well-ventilated conditions. Common fire scenarios preventing reasonable flame volume estimations may include those with significant view blockage and overlapping of flames, major burning inside fuel/solid containers, highly non-symmetric fire development, and substantial deviation from hydrocarbon dominated fuels that can alter the oxygen/air ratio and thus the HRR per unit of flame volume. Similar effects can also occur when air entrainment to the flames is severely restricted such as in under-ventilated fires.
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