- Email: [email protected]
Defining the effects of ambient conditions in large-scale fire tests
Experimental Thermal and Fluid Science 34 (2010) 404–411
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Defining the effects of ambient conditions in large-scale fire tests Francesco Tamanini * FM Global, 1151 Boston-Providence Turnpike, Norwood, MA 02062, USA
a r t i c l e
i n f o
Article history: Received 1 October 2009 Received in revised form 27 October 2009 Accepted 27 October 2009
Keywords: Large-scale fire testing Ambient condition effects Fire growth Fire suppression
a b s t r a c t The paper documents the results of an analysis of the effects of ambient conditions, temperature and relative humidity, on the development of large-scale fires during their initial growth. While the study has focused on the behavior of hygroscopic cartoned commodities, because their burning behavior is greatly affected by propensity to absorb ambient moisture, non-hygroscopic materials and their reduced sensitivity to ambient humidity could also be considered. The analysis introduces the heat release rate at the time of first sprinkler activation as a meaningful measure to represent the impact of ambient conditions on the development of a free-burning fire. The next step of estimating the behavior under extinguishment conditions is not possible at this time, though general considerations on expected trends are offered on the basis of the results obtained from another research program. The practical output of the work is in the form of the identification of the desirable range of operating conditions for ambient temperature and relative humidity in large-scale fire testing. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction FM Global has performed large-scale fire testing at its facilities in West Glocester, Rhode Island for several years and has been aware of the importance that ambient conditions have on the outcome of the tests. Recent enhancements of the capabilities of the Fire Technology Laboratory at the FM Global Research Campus have included the addition of features, which provide an unprecedented opportunity to control the environment in the test volume and, therefore, the reproducibility of the test results. This development has prompted the re-examination of the effects on fire behavior of ambient conditions, mainly temperature and relative humidity, which is the object of this paper. Environmental variables have an impact on the commodity itself, particularly in the case of hygroscopic materials, as well as on the characteristics of the combustion air to which the commodity is exposed. Most large-scale fire tests are designed to determine the effectiveness of protection, which is usually water based, with delivery provided by a sprinkler system. Since the protection is designed to activate when the fire has reached a certain size, the period during which the burning commodity is subjected to the extinguishment action is always preceded by a stage characterized by fire growth in a free-burning mode. Due to limitations in the current state of knowledge, the latter phase can be handled by available analytical tools, while the former cannot. This paper presents an analysis of the effects of ambient temperature and relative humidity, which focuses on the initial in* Tel.: +1 781 255 4930; fax: +1 781 255 4024. E-mail address: [email protected] 0894-1777/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2009.10.032
crease in fire intensity up to the point where the protection activates (typically the first sprinkler). The heat release rate at the time of first sprinkler activation is used as a measure of the progress of the combustion process and as a figure of merit to quantify the departure of the fire from what would be expected under standard conditions. 2. Environmental variables and their effects 2.1. Ambient pressure The standard value of atmospheric pressure at sea level is by definition one atmosphere, which is equal to 101,325 Pa. Departures of ambient pressure from this standard datum are due to two causes: the average value of pressure decreases at increasing elevations, and weather conditions add a certain amount of fluctuations about the mean. Although wider changes may be observed during severe atmospheric events, the range of pressure excursions attributable to normal weather patterns is about ±1500 Pa. Since the focus of this work is on the repeatability of operations at one facility, the only factor that possibly needs to be analyzed is the one associated with the daily fluctuations. These, however, are of the order of ±1.5% of absolute pressure and are, therefore, expected to have a negligible impact on the results of fire tests. 2.2. Wind conditions External wind may have an impact on the conditions inside a building since the two environments are not completely decoupled. The FM Global Large Burn Laboratory (LBL) operates at a
405
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
Nomenclature aRH aT bDT cMC cp cO2 cT EMC g M MC psat pv p1 Q_ be
Q_ c
relative humidity coefficient in empirical correlation (kW/%) temperature coefficient in empirical correlation (kW/K) plume radius to the point where the temperature rise has dropped to 0.5 DT0 (m) moisture content correction to fire growth rate (–) specific heat of gases (J/kg K) ambient oxygen correction to fire growth rate (–) temperature correction to fire growth rate (–) equilibrium moisture content (%) acceleration of gravity (m/s2) molecular weight of air (kg/kg mol) moisture content (%) steam saturation pressure (Pa) steam vapor pressure (Pa) ambient absolute pressure (Pa) fire convective heat release rate at the beginning of extinguishment (kW) convective heat release rate of fire (kW)
small vacuum (typically 25 Pa) with respect to the outside, by providing extraction of combustion products at a constant mass flow rate and carefully controlling the uniformity of flow of ventilation air entering the test space. Under a quiescent external atmosphere, uniform inlet flow is ensured. However, a steady wind preferentially impacting on one of the outside wall surfaces could give rise to local conditions that would alter the inlet flow pattern from what is intended. Experience to date, based on monitoring of the pressure differentials across the three sides of the test volume envelope exposed to the external environment, has shown that non-uniformities in inlet air distribution can be considered negligible. 2.3. Oxygen concentration The oxygen concentration in ambient air is constant (essentially independent of total pressure) and approximately equal to 20.95% by volume, with the balance being made up of inert gases, mostly nitrogen. A factor that can affect the ambient oxygen concentration is the ambient humidity. Estimates for the magnitude of this effect will be made in Section 2.5 below dealing with ‘‘Relative Humidity”. Under the circumstances of large-scale fire tests, the oxygen level to which the combustion process is exposed can be lower than the ambient value due to recirculation of combustion products. This effect, however, is one of the outcomes of the experiment itself and should not be considered a controlled test parameter. 2.4. Ambient temperature Some capability to control the temperature of the environment in a large-scale facility prior to a test is generally available. During a test, however, external weather will affect the facility volume, with its temperature tracking that of the outside once the air ventilation flow is activated.1 In most cases, the actual conditions in the test volume will be somewhat dependent on transient effects, which may be significant under certain circumstances. In practice, it is important to determine the effect of seasonal variations in temperature and humidity on the outcome of a fire test. There are two aspects to be considered: 1 In the case of the FM Global Large Burn Laboratory, the air ventilation system provides one total volume change about every 10 min.
Q_ w r R RH RTI t tig Tg Tspk T0 T1 ug u0 XO2 z z0
a a0
nominal cooling power of extinguishing agent (kW) distance from the center of the ceiling layer (m) universal gas constant (J/kg mol K) relative humidity (%) response time index of sprinkler link ((m s)1/2) time (s) ignition time (s) gas temperature at sprinkler link (K) sprinkler link temperature (K) temperature on plume centerline (K) ambient temperature (K) gas velocity at sprinkler link (m/s) vertical velocity on plume centerline (m/s) oxygen volume fraction (%) elevation above the fire source (m) elevation of the virtual origin above the fire source (m) exponential fire growth factor (s1) exponential fire growth factor at standard conditions (s1)
1. Impact of temperature changes on the burning characteristics of the fuel commodity (rate of fire growth). This is mostly determined by the temperature in the volume prior to the test; and 2. Impact on the temperature/velocity field produced by the fire. This is determined by the conditions during the test.
2.4.1. Impact on fire growth The effect of fuel temperature on the rate of fire growth has been addressed by work done recently at FM Global. Based on that analysis, for the case of corrugated board, one can anticipate an increase of about 15% in fire growth rate as the ambient temperature increases from 4 to 32 °C. This estimate, which assumes that all other parameters remain unchanged, has been found to be weakly dependent on the moisture content of the corrugated board. The effect would be somewhat different in cases where the corrugated board constitutes only a fraction of the total fuel package, as in the case of cartoned plastics. 2.4.2. Impact on flow characteristics The second factor related to ambient temperature is the effect on the thermal and dynamic field produced by the fire. Appropriate quantification of the effect can be obtained by considering the flow in the fire plume. Heskestad [1] has proposed correlations for the plume radius (bDT), centerline temperature rise (T0 T1) and vertical velocity (u0). With the constant values recommended in Ref. [2] for rack storage fires, the correlations read as follows:
bDT ¼ 0:12
T0 T1
1=2
ðz z0 Þ;
ð1Þ
!1=3
T0 T1 R2 ¼ 11:0 Q_ c2=3 ðz z0 Þ5=3 ; T1 gc2p p21 M 2 1=3 gR 1=3 : u0 ¼ 4:25 Q_ 1=3 c ðz z0 Þ cp p1 M
ð2Þ ð3Þ
Additional relationships are available for the variation of gas temperature and velocity in the layer produced by the impingement of the fire plume on a horizontal ceiling. The parameters that appear in the above three equations are: bDT, plume radius to the point where the temperature rise has dropped to 0.5DT0; cp, specific heat of gases; g, acceleration of gravity; M, molecular weight of air; p1, ambient absolute pressure; Q_ c , convective heat release
406
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
rate; R, universal gas constant; T0, temperature on plume centerline; T1, ambient temperature; u0, vertical velocity on plume centerline; z, elevation above the fire source; and z0, elevation of the virtual origin above the fire source. Eq. (2) shows that, for a given convective heat release rate, Q_ c , and a fixed distance, z, above the top of the fuel array, the ratio T0/T1 is not a function of T1. Consequently, the plume width, bDT, and centerline velocity, u0, are also independent of T1. However, in terms of sprinkler activation, a device which responds to absolute temperature, it is apparent that changes in ambient temperature will lead to different activation times, even if the fire growth were to remain unaffected by the change. This issue will be revisited in quantitative terms by the analysis presented here.
gle-wall and double tri-wall corrugated board samples behave as thermally thin. However, at the flux levels that are more typical of large fires (say 100 kW/m2 and up), the tri-wall and, to a lesser extent, the single-wall corrugated would behave as thermally thick. Accordingly, another estimate applicable to this regime was provided by a prediction of temperature and moisture effects on piloted ignition time made at FM Global [7]. In that analysis, the ignition time was postulated to be proportional to the square of the enthalpy rise in the solid from initial conditions to pyrolysis temperature. For a value of initial temperature of 25 °C, the enthalpy change estimates of Ref. [7] lead to a dependence of the ignition time on moisture content for thermally thick materials, which can be approximated as:
2.5. Relative humidity
tig / 1 þ 10 MC ð%Þ=100 þ 66 ðMC ð%Þ=100Þ2 :
As in the case of temperature, the relative humidity (RH) has two effects on fire test conditions. First, the addition of water vapor to the combustion air changes its composition and, more notably, the oxygen concentration. The second effect applies to situations where the fuel is hygroscopic, as the air humidity influences the moisture content of the fuel. The importance of this condition is clear, given the fact that soggy material is known to burn less easily than material that is dry.
Regardless of the thermal regime, the fire growth rate of a material is inversely proportional to the ignition time. Therefore, Eq. (4) can be used to estimate how fire growth depends on moisture content. For a variation of MC from 4% to 8%, this equation would predict a decrease of fire growth rate of 32%. This estimate will be revisited in the next section, following consideration of large-scale data.
2.5.1. Effect on composition of atmosphere The effect of air humidity on the oxygen concentration can be significant. On a cold day (4.4 °C) with an RH of 50%, the partial pressure of steam is 4.19 mbar. On a hot (32.2 °C) and humid (RH = 100%) day, it would be 48.3 mbar. This means that, in the ‘‘cold” environment, the composition of the atmosphere is barely affected, with the oxygen concentration dropping from the dry value of 20.95 vol.% to 20.86 vol.%. In the ‘‘hot” (and ‘‘steamy”) environment, the oxygen concentration in the moist air is 20.00 vol.%. The drop of 1 vol.% in oxygen concentration is a significant factor that can be expected to influence the combustion process and, hence, the development of the fire. Data are available to provide a rough estimate of this effect. In experiments with a 0.3-m diameter PMMA pool fire [3], a decrease in oxygen concentration from 21 to 20 vol.% was accompanied by a drop in pyrolysis rate from 12.9 to 12.3 g/m2/s (a 4.6% decrease) and in radiated fraction from 36% to 33% (an 8.3% decrease). The general order of magnitude of the effect (about a 5–8% impact) on these steady-state quantities, which reflect the magnitude of the flame heat flux, is consistent with small-scale data for corrugated board obtained in the ASTM E2058 Fire Propagation Apparatus [4] (cf. Fig. 3–4.59, pp. 3–156). Since the flame spread rate is proportional to the square of the flame heat flux, the effect of the variations considered above on fire growth should be expected to be in the approximate range 10–15%. 2.5.2. Effect on solid fuel combustion Absorption of moisture in surrounding air by the solid fuel has been found to be an important factor in the fire behavior of cellulosic materials. Recent analyses and industry data [5] have confirmed that the equilibrium moisture content (EMC) of corrugated board is essentially a function of ambient relative humidity and that the influence of temperature on moisture content is secondary. In quantitative terms, the cartons used as packaging material for testing at FM Global have been found to reach EMC values of about 6.3% and 12.5% at RH levels of 50% and 90%, respectively. Recently, the effect of moisture content (MC) on the piloted ignition time of corrugated containerboard samples has been carefully quantified in the Fire Propagation Apparatus [6]. That study concluded that, for incident heat fluxes up to 60 kW/m2, both sin-
ð4Þ
3. Experimental results 3.1. Estimating fire growth in large-scale tests Most large-scale fire tests are performed under conditions that make it difficult to obtain a direct measurement of the heat release rate. Even when calorimetric data are collected, as in the case of tests carried out under the FM Global test ceilings, they are obtained too far from the fire source to allow for acceptable resolution of the time variation of the heat release rate. Due to these practical obstacles, indirect methods have to be devised. For the purposes of the evaluations presented in this paper, fire growth rates have been inferred from ceiling temperature data using two approaches. Both take advantage of the known functional relationship between temperature rise in fire plumes and convective heat release rate. Eq. (2) yields such a relationship for the temperature rise, T0 T1, on the plume centerline. The simplified form of this equation, obtained by neglecting the dependence of the virtual source location, z0, on heat release rate, Q_ c ,2 would imply that Q_ c is proportional to the 3/2 power of T0 T1. Even though this relationship is not entirely accurate, it is used here to estimate the rate of fire growth from the temperature rise near the ceiling on the axis of the fire. The second approach relies, again, on ceiling temperature data. Instead of using a single point measurement, this time an average temperature rise is calculated from twenty-five (25) thermocouples on a central grid of 6.1 6.1 m with 1.5-m spacing. As in the case of the centerline temperature rise, the dependence on Q_ c is not simple. In addition to the shift in virtual source discussed above, the radial profile of the maximum ceiling layer temperature, Tm, is also a function of Q_ c through the width of the fire plume, bDT, which is used as a scaling length, as shown in the following formula for Tm T1 [2]:
" T m T 1 ¼ ðT 0 T 1 Þ exp 0:66
r 1:5 bDT
1=2 # :
ð5Þ
2 Data from Ref. [2] indicate that the height of the virtual source above the top of 2=5 the fuel can be expressed as z0 ¼ c1 þ c2 Q_ c , where c1 and c2 are constants, which depend on the characteristics of the fuel array.
407
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
Fire Growth as a Function of Commodity Moisture Content Estimates Based on T41and on Average Rise over 20x20 ft Area Std. Plastic 9 30
0.5 -1
Fire Growth Rate [s ]
Std. Plastic 19 30 Std. Plastic 39 45
0.4
1 + 10 * MC[%]/100 + 66 * (MC[%]/100)^2
0.3 0.2 0.1 Open Symbols Refer to Tests with Center Ignition
0 0
2
4
6
8
10
12
14
Commodity Moisture Content (dry basis) [%] Fig. 1. Estimates of rates of fire growth for tests involving Standard Plastic commodity. (Numbers in the legend refer, respectively, to fuel array and ceiling height in ft.)
When all these dependencies are fully factored in, the relationship between the average ceiling temperature rise and Q_ c cannot be generalized, since it is a function of the specific conditions being considered (fuel array height, ceiling clearance, etc.). Nevertheless, the simple (and somewhat incorrect) 3/2 power dependence is used, with the understanding that this assumption introduces some error, as yet unquantified, in the absolute value of the fire growth rate. Since a few numerical examples have shown that the power exponent is between 1 and 3/2, the above assumption tends to overestimate the fire growth rate as a function of Q_ c . 3.2. Fire growth rate data Fire growth rates were calculated for several large-scale tests using the two methods described in the previous section, assuming an exponentially growing fire. Accordingly, a growth factor, a, defined by3:
Q_ c ¼ Q_ c;0 expðatÞ;
ð6Þ
was calculated as the average of the values given by the two methods, while the difference between them was used as a measure of the uncertainty of the determination. The data cover three different cartoned commodity types (Standard Plastic, Class 2 and Class 3)4 and various array height-ceiling height combinations. The test conditions are further characterized through the moisture content of the commodity, the initial temperature in the test volume and the location of the ignition source (center or offset at rack upright). The fire growth data are shown graphically in Figs. 1 and 2 for the Standard Plastic (SPC) and the Class 2/3 commodity, respectively. As discussed in the preceding section, because of the approximations made by the methods used to calculate the growth rate, direct use of the values in the figures should be made with caution. Nevertheless, a spot check comparison with fire growth data in three-tier high (4.3 m) fuel arrays tested under a 20-MW calorimeter [8] is quite favorable. For example, direct measurement of the time variation of the heat release rate, with corrugated 3 Due to the assumption of exponential growth, time zero in this case is not the time of ignition. It is the time at which the heat release rate is equal to Q_ c;0 . In practice, the choice of the value for Q_ c;0 has little effect on the results, provided that the value is sufficiently small. This condition can be determined by experimentation. 4 The different commodity denominations refer to the contents of the corrugated board box packaging: polystyrene cups for Standard Plastic; a steel liner for Class 2; and paper cups for Class 3.
containerboard moisture contents in the range 5–7% (dry basis), yielded growth rates of 0.25–0.28 s1 for SPC and 0.15–0.24 s1 for Class 2. These numbers compare well with the estimates shown in Figs. 1 and 2. In the case of the SPC shown in Fig. 1, taking 6% as the mid point, the effect of MC over the range from 4% to 8% for the tests with center ignition appears to be of the order of ±15%. This can be compared with the variation implied by the correlation in Eq. (4), which is shown by the line in Fig. 1 (anchored for MC = 6% at the fire growth rate value representing the approximate average of the bulk of the data). Over the 4–8% MC range, the correlation yields a variation of ±20%. Notwithstanding the fact that the polystyrene cups in the SPC also contribute at some point to the fire growth, it would appear that the selected expression for the thermally thick case (Eq. (4)) is a reasonable predictor of the moisture content effect. A similar result is suggested by the Classes 2 and 3 data in Fig. 2, with clearer evidence of a distinct trend possibly due to the more limited information available. In summary, different measures of the effect of moisture content of the corrugated containerboard on the rate of fire growth do seem to provide a degree of consistency in that they all support an estimate of the effect of ±15% variation when MC = 6 ± 2%. This result will be considered later in making recommendations for acceptable ranges of environmental variables. 4. Impact of ambient conditions on first sprinkler activation 4.1. General approach The discussion in the preceding sections has focused on estimates of the individual impacts of variations in different parameters on characteristics of the fire, mainly its growth rate. It would seem that the occurrence of first sprinkler activation should offer a reasonable benchmark for the evaluation of the variability associated with changes in environmental parameters that affect fire development. More specifically, the heat release rate at the time of first sprinkler activation should be considered a relevant variable, since it has been established that control and/or suppression of the fire becomes more difficult, the higher the burning rate at the beginning of extinguishment [8]. First sprinkler response is calculable with reasonable accuracy, even though ceiling layer correlations are not available for all possible conditions of interest. Nevertheless, available knowledge in
408
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
Fire Growth as a Function of Commodity Moisture Content Estimates Based on T41 and on Average Rise over 20x20 ft Area Class 2 19 30
0.5
-1
Fire Growth Rate [s ]
Class 2 34 40/41 Class 3 39 45
0.4
1 + 10 * MC[%]/100 + 66 * (MC[%]/100)^2
0.3 0.2 0.1 0 0
2
4
6
8
10
12
14
Commodity Moisture Content (dry basis) [%] Fig. 2. Estimates of rates of fire growth for tests involving Class 2 and Class 3 commodities. (Numbers in the legend refer, respectively, to fuel array and ceiling height in ft.)
this area should be sufficient for an analysis that is aimed at establishing departures from a baseline case. Finally, owing to the important role assigned to the effect of relative humidity (RH) on the moisture content (MC) of the commodity, the analysis is most applicable to the case of hygroscopic cartoned fuels. The outline of the approach is as follows. A baseline case is established by defining the rate of fire growth for the commodity of interest at standard conditions. Empirical formulas are then used to describe the effect of environmental parameters on the rate of fire growth. A sprinkler location (ceiling clearance above fuel array and distance from fire axis) and type (temperature rating and RTI5) are selected. Finally, the sprinkler link temperature response is calculated and the heat release rate at the time of sprinkler actuation, Q_ be , is compared with that of the baseline case. The final outcome of the exercise is the establishment of a parameter domain within which the variation of Q_ be is less than a certain percentage of baseline value.
The rate of fire growth is defined through the value of the growth coefficient, which has been introduced in Eq. (6). The following ambient values are used as standard conditions: p1,0 = 1 atm (std) (1.01325 105 Pa) T1,0 = 18.3 °C (65 F) RH0 = 35%
Two commodities are considered in the analysis, each characterized by a rate of fire growth at standard conditions as follows: Standard Plastic Class 2
4.3.2. Ambient temperature As already discussed, the ambient temperature is expected to present two effects. The first is a direct impact on the rate of fire growth, which will be estimated based on the considerations of the effect in thermally thick corrugated board. At MC = 5%, the fire growth rate is estimated to increase by 0.56%/°C of ambient temperature change. This factor is somewhat dependent on the moisture content, but not sufficiently to justify more accurate accounting. Accordingly, the temperature effect on fire growth rate is calculated by applying the following correction to the exponential fire growth coefficient:
cT ¼ 1 þ 0:0056ðT 1 T 1;0 Þ ð CÞ:
4.2. Baseline conditions
Absolute pressure Temperature Relative humidity
finding that the burning rate of radiatively-controlled fires is approximately proportional to ambient pressure [9,10]. Based on these results, the changes associated with ambient pressure fluctuations (estimated at ±1.5%) are considered to be of lesser importance and, therefore, negligible.
aSPC,0 = 0.25 s1 aC2,0 = 0.15 s1
The second effect is fully described by the fire plume correlations, which have already been introduced in a previous section. They are used directly in the calculations, since no further simplification is needed. 4.3.3. Ambient humidity Similar to temperature, ambient humidity has an impact on the characteristics of the atmosphere as well as on the moisture content of the commodity and, hence, the fire growth rate. The first effect is taken into account by introducing the partial pressure of steam in the following expression to calculate the resulting oxygen concentration:
X O2 ðvol:%Þ ¼ 4.3. Parameter effects 4.3.1. Ambient pressure The impact of ambient pressure changes is neglected here. Should it be taken into account in future analyses, its effect would be properly described by the role played by this quantity in the plume equations (cf. Eqs. (1)–(3)). Other effects (e.g., on heat flux and, therefore, on pyrolysis rate) have been evaluated, with the 5 RTI, the Response Time Index, is a quantity representing the inertia characteristics of the thermal sensing element of the sprinkler.
ð7Þ
20:95 ; 1 þ pv ðPaÞ=101; 235
ð8Þ
where, pv is the steam vapor pressure (=psat RH/100). At the standard conditions of 18.3 °C and RH = 35%, psat = 2108 Pa and, therefore, it is pv = 738 Pa. Finally, the oxygen concentration at standard conditions is calculated from Eq. (8) as XO2,0 = 20.80 vol.%. The preceding discussion has indicated an average effect of the O2 concentration of about 13% drop in fire growth rate for every percent drop in XO2. Accordingly, this correction is expressed as:
cO2 ¼ 1 þ 0:13ðX O2 X O2;0 Þ ðvol:%Þ:
ð9Þ
409
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
The other effect of ambient humidity is through its impact on the equilibrium moisture content (EMC) of the corrugated containerboard. This can be approximated using the following empirical fit to data in Ref. [6]:
EMC ð%Þ ¼
4 ð1 þ RH ð%Þ=10Þ: 3
ð10Þ
It can be noted that, for RH = 35%, the above expression yields EMC = 6%. This latter value is, therefore, the equilibrium moisture content corresponding to standard conditions. Since changes in RH lead to changes in MC, an equation is needed to capture the effect of MC on the fire growth rate, a. These effects are reflected in the expressions for ignition time, tig, given as Eq. (6), since it is a / 1/tig. Therefore, the correction factor for MC effects is:
cMC ¼
1:838 1 þ 10 MC ð%Þ=100 þ 66 ðMC ð%Þ=100Þ2
ð11Þ
;
5.2. Response prediction results An example of the predictions produced by the calculation procedure is discussed next. Consider the baseline case (T1 = 18.3 °C and RH = 35%) of 4 tiers of Standard Plastic commodity (SPC) burning under a ceiling with a clearance of H = 3.35 m. The sprinkler, with a temperature rating Tlink = 74 °C and a response time index RTI = 27.6 (m s)½, is installed 2.15 m off axis and 0.152 m down from the ceiling. Since the ambient conditions are at standard values, there are no corrections (cT = cO2 = cMC = 1) to the fire growth rate, which is therefore equal to 0.25 s1. For these conditions, the model predicts first sprinkler activation when the heat release rate is Q_ be ¼ 2308 kW. The second case is that of a dry (RH = 20%), cold (T1 = 7.2 °C) day. The correction factors for the fire growth rate and the HRR at the time of sprinkler activation in this case are:
cT ¼ 0:94;
cO2 ¼ 1:01;
Q_ be ¼ 2893 kW:
cMC ¼ 1:22;
ð14Þ
which yields cMC = 1 when MC = 6%, as it should be at the standard condition. The corrections from Eqs. (7), (9), and (11) are applied to calculate the fire growth rate as:
The value of Q_ be has increased by 25%. The third case is that of a wet (RH = 50%), warm (T1 = 29.4 °C) day. The correction factors and the HRR at sprinkler activation now are:
a ¼ cT cO2 cMC a0 ;
cT ¼ 1:06;
ð12Þ
where a0 is the reference value of the exponential fire growth coefficient.
5. Sprinkler response predictions 5.1. Calculation procedure Predictions of the sprinkler link response are made using the known expression for the rate of temperature rise of the fusible link: 1=2 dT spk ug ¼ ðT g T spk Þ; dt RTI
ð13Þ
where Tspk is the sprinkler link temperature (initially taken to be equal to the ambient temperature, T1), ug is the local gas velocity, Tg is the temperature of the gases near the link, and RTI is the response time index of the sprinkler, measured in (m s)1/2.
cO2 ¼ 0:97;
Q_ be ¼ 1763 kW;
cMC ¼ 0:83;
ð15Þ
representing a 24% drop in Q_ be relative to the baseline. Other cases could be considered, for example by predicting the response of a high-temperature (141 °C), slow-response (166 (m s)½) sprinkler. The three scenarios detailed above provide an indication of the magnitude of the effects, which is substantial. Rather than introducing additional numeric examples, the limitations that should be considered in defining acceptable parameters for large-scale tests are considered in the following section. 5.3. Target operating envelope Based on the premise that the variation of the HRR at the time of sprinkler activation (i.e., the response variable) should be limited (by control of the other variables), one can attempt to define the range of conditions that achieve that goal within a certain prescribed tolerance. As an example, one can consider additional cases representing departures from the baseline conditions outlined in the previous section. The results of the parametric exploration of the range of ambient temperature from 0 to 29.4 °C and relative
Acceptable Operating Ranges of Ambient Temperature and Humidity
Temperatures [°F]
100
Min Ta [°F] Max Ta [°F] Std. Condition
80
60
40
20 20
30
40
50
60
70
80
Relative Humidity [%] Fig. 3. Temperature/relative humidity domain corresponding to a ±15% variation in HRR at sprinkler activation. Case of sprinkler with: temperature rating 74 °C, RTI 27.6 (m s)½, 3.35-m ceiling clearance, 2.15 m off axis. Fire growth rate of a0 = 0.25 s1.
410
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
humidity from 20% to 80% yield extreme values of 1287 and 3263 kW calculated for Q_ be at T1 = 29.4 °C, RH = 80% and T1 = 0 °C, RH = 20%, respectively. The relationship between HRR at sprinkler activation, ambient temperature and relative humidity can be approximated by a linear function, leading to the following more usable form:
Q_ be ¼ Q_ be;0 þ aT ðT 1 T 1;0 Þ þ aRH ðRH RH0 Þ;
ð16Þ
where the subscript ‘‘0” refers to the standard conditions of the baseline case and the two coefficients aT and aRH are determined by fitting the model results. Having the results of the prediction expressed through the fit in Eq. (16) provides a quick way to define the domain of ambient conditions that corresponds to a certain variation of the HRR at sprinkler activation relative to its baseline value. As an example, one could prescribe a limit of ±15% for that variability, i.e. Q_ be ¼ 2308 346 kW. Graphically this can be represented as the domain between two lines in a plot of T1 vs. RH. For the case of the fast-response sprinkler considered here, this translates into the graph shown in Fig. 3. This figure defines the range of acceptable RH at a given T1, and vice versa. For example, if T1 = 18.3 °C (65 F), then the allowable range for RH is about 18–52%. Similarly, at RH = 35%, the allowable range for T1 is from about 8 to 28 °C (47 to 83°F). Use of the results of this analysis would be greatly simplified if it was not for the fact that the range of acceptable conditions, based on the limit on HRR variation, is dependent on the selected sprinkler conditions. This point could be illustrated by repeating the calculations for a different case involving a sprinkler with a higher temperature rating and a slower response. That example would show acceptable boundaries for the same ±15% HRR variation, which are somewhat different from those shown by the example in Fig. 3. This result underscores the fact that the response of the fire to ambient conditions is a function of the details of the fuel array and of the protection. Therefore, each situation has to be evaluated individually. A rectangular area is shown in Fig. 3. It covers a temperature range from 10 to 26.7 °C (50 to 80 F) and relative humidity from 20% to 50%. In the absence of more case-specific analyses, this may be considered a reasonable domain for acceptable operating conditions. It is included in the figure as a frame of reference to evaluate error bounds defined by the analysis. However, it should be noted that, for the case of Fig. 3, the upper right and lower left corners of the domain correspond to departures from the HRR at standard conditions of 27% and +27%, respectively. 6. Implications for protection requirements The preceding analysis has focused on the HRR at the time of sprinkler activation as a figure of merit, which is appropriate to characterize the effects of environmental conditions on the outcome of large-scale fire tests. While a useful indicator, this parameter does not quantify directly the impact on protection performance. Some guidance, however, is provided by recent results obtained as part of a separate project [8]. In that work, the response of a rack-storage array to extinguishment action by water was analyzed and a correlation was developed to express the protection requirement, represented by Q_ w ,6 as a function of the HRR at the beginning of extinguishment, Q_ be : c
1 Q_ w / Q_ be b :
ð17Þ
6 This is the potential cooling power of the suppression water (kW), calculated as water mass flow times the heat of vaporization of water – 2450 kJ/kg.
The data in Ref. [8] yield information on the value of the exponent 1 c/b for the various commodities tested. For the case of Class 2 and Standard Plastic, it is 1 c/b = 0.46 and 0.73, respectively. The fact that this exponent is less than 1 means that a percent variation in Q_ be is reflected as a smaller variation in the protection requirement, as expressed by Q_ w . As a result, the ±15% variation considered earlier for Q_ be becomes about ±7% and ±11% for the water requirements of the Class 2 and Standard Plastic commodities. It should be noted that the quantity Q_ w refers to the water flux applied to the top of the fuel array, which has been labeled in Ref. [8] as the Critical Delivered Flux (CDF). The effect on the water flux at the sprinkler elevation (the Sprinkler Discharged Flux (SDF)) should be somewhat greater. Furthermore, all test results from this study were obtained by delivering water over the entire top surface of the fuel. In actual suppression tests, the water flux is not spatially uniform because of the delay between subsequent sprinkler activations. This fact leads to some uncertainty in the application of the data from Ref. [8] to the suppression of large-scale fires. 7. Summary and conclusions The analysis presented in this paper has considered the potential sources of variability in large-scale fire tests carried out with hygroscopic cartoned commodities. It has quantified the effects of temperature and relative humidity on the size of the fire at the time of first sprinkler activation, a quantity selected as the significant parameter to represent the evolution of the test. In the analysis, the relative humidity (RH) has been used to reflect the moisture content (MC) of the cellulosic commodity, with an RH variation from 20% to 50% corresponding to MC varying from 4% to 8% (dry basis). Pre-test conditioning of the commodity, and limitations in its exposure to changes towards different RH values in the surrounding air prior to test ignition, would broaden the acceptable range for the values of the two variables, ambient temperature and RH, at the time of ignition. In summary, the issue of quantifying the effects of environmental conditions on the outcome of large-scale fire tests has been addressed by using a simple analysis to predict the impact of ambient temperature and relative humidity changes on a parameter which represents the conditions of the fire at the beginning of the extinguishment process. At best, this approach provides a partial view of a very complex physical phenomenon. Unfortunately, current limitations in fire modeling prevent a consideration of the problem through analytical means, which extends into the extinguishment phase of the fire. Until such a time where significant progress can me made with modeling, the type of analysis presented in this paper, in combination with thoughtful interpretations of fire test results, will have to suffice.
References [1] G. Heskestad, Engineering relations for fire plumes, Fire Safety Journal 7 (1984) 25–32. [2] H.-C. Kung, H.-Z. You, R.D. Spaulding, Ceiling flows of growing rack storage fires, in: Twenty-first Symposium (International) on Combustion, The Combustion Institute, 1986, pp.121–128. [3] G. Santo, F. Tamanini, Influence of oxygen depletion on the radiative properties of PMMA flames, in: Eighteenth Symposium (International) on Combustion, The Combustion Institute, 1981, pp. 619–631. [4] A. Tewarson, Generation of heat and chemical compounds in fires, in: SFPE Handbook of Fire Protection Engineering, third ed., 2002 (Chapter 4). [5] J. Marcondes, Corrugated fibreboard in modified atmospheres: moisture sorption/desorption and shock cushioning, Packaging Technology and Science 9 (1996) 87–98. [6] M.M. Khan, J.L. deRis, S.D. Ogden, Effect of moisture on ignition time of corrugated paper cardboard samples, Paper presented at the 9th International
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411 Symposium of Fire Safety Science, 21–26 September 2008, University of Karlsruhe, Germany. [7] J.L. deRis, private communication, 2005. [8] Y. Xin, F. Tamanini, Assessment of commodity classification for sprinkler protection using representative fuels, in: Fire Safety Science – Proceedings of the Ninth International Symposium, 2008, pp. 527–538.
411
[9] R.L. Alpert, Pressure modeling of fires controlled by radiation, in: Sixteenth Symposium (International) on Combustion, 1977, pp. 1489– 1500. [10] J.L. deRis, P.K. Wu, G. Heskestad, Radiation fire modeling, in: Twenty-eighth Symposium (International) on Combustion, 2000, pp. 2751–2759.
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Defining the effects of ambient conditions in large-scale fire tests Francesco Tamanini * FM Global, 1151 Boston-Providence Turnpike, Norwood, MA 02062, USA
a r t i c l e
i n f o
Article history: Received 1 October 2009 Received in revised form 27 October 2009 Accepted 27 October 2009
Keywords: Large-scale fire testing Ambient condition effects Fire growth Fire suppression
a b s t r a c t The paper documents the results of an analysis of the effects of ambient conditions, temperature and relative humidity, on the development of large-scale fires during their initial growth. While the study has focused on the behavior of hygroscopic cartoned commodities, because their burning behavior is greatly affected by propensity to absorb ambient moisture, non-hygroscopic materials and their reduced sensitivity to ambient humidity could also be considered. The analysis introduces the heat release rate at the time of first sprinkler activation as a meaningful measure to represent the impact of ambient conditions on the development of a free-burning fire. The next step of estimating the behavior under extinguishment conditions is not possible at this time, though general considerations on expected trends are offered on the basis of the results obtained from another research program. The practical output of the work is in the form of the identification of the desirable range of operating conditions for ambient temperature and relative humidity in large-scale fire testing. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction FM Global has performed large-scale fire testing at its facilities in West Glocester, Rhode Island for several years and has been aware of the importance that ambient conditions have on the outcome of the tests. Recent enhancements of the capabilities of the Fire Technology Laboratory at the FM Global Research Campus have included the addition of features, which provide an unprecedented opportunity to control the environment in the test volume and, therefore, the reproducibility of the test results. This development has prompted the re-examination of the effects on fire behavior of ambient conditions, mainly temperature and relative humidity, which is the object of this paper. Environmental variables have an impact on the commodity itself, particularly in the case of hygroscopic materials, as well as on the characteristics of the combustion air to which the commodity is exposed. Most large-scale fire tests are designed to determine the effectiveness of protection, which is usually water based, with delivery provided by a sprinkler system. Since the protection is designed to activate when the fire has reached a certain size, the period during which the burning commodity is subjected to the extinguishment action is always preceded by a stage characterized by fire growth in a free-burning mode. Due to limitations in the current state of knowledge, the latter phase can be handled by available analytical tools, while the former cannot. This paper presents an analysis of the effects of ambient temperature and relative humidity, which focuses on the initial in* Tel.: +1 781 255 4930; fax: +1 781 255 4024. E-mail address: [email protected] 0894-1777/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2009.10.032
crease in fire intensity up to the point where the protection activates (typically the first sprinkler). The heat release rate at the time of first sprinkler activation is used as a measure of the progress of the combustion process and as a figure of merit to quantify the departure of the fire from what would be expected under standard conditions. 2. Environmental variables and their effects 2.1. Ambient pressure The standard value of atmospheric pressure at sea level is by definition one atmosphere, which is equal to 101,325 Pa. Departures of ambient pressure from this standard datum are due to two causes: the average value of pressure decreases at increasing elevations, and weather conditions add a certain amount of fluctuations about the mean. Although wider changes may be observed during severe atmospheric events, the range of pressure excursions attributable to normal weather patterns is about ±1500 Pa. Since the focus of this work is on the repeatability of operations at one facility, the only factor that possibly needs to be analyzed is the one associated with the daily fluctuations. These, however, are of the order of ±1.5% of absolute pressure and are, therefore, expected to have a negligible impact on the results of fire tests. 2.2. Wind conditions External wind may have an impact on the conditions inside a building since the two environments are not completely decoupled. The FM Global Large Burn Laboratory (LBL) operates at a
405
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
Nomenclature aRH aT bDT cMC cp cO2 cT EMC g M MC psat pv p1 Q_ be
Q_ c
relative humidity coefficient in empirical correlation (kW/%) temperature coefficient in empirical correlation (kW/K) plume radius to the point where the temperature rise has dropped to 0.5 DT0 (m) moisture content correction to fire growth rate (–) specific heat of gases (J/kg K) ambient oxygen correction to fire growth rate (–) temperature correction to fire growth rate (–) equilibrium moisture content (%) acceleration of gravity (m/s2) molecular weight of air (kg/kg mol) moisture content (%) steam saturation pressure (Pa) steam vapor pressure (Pa) ambient absolute pressure (Pa) fire convective heat release rate at the beginning of extinguishment (kW) convective heat release rate of fire (kW)
small vacuum (typically 25 Pa) with respect to the outside, by providing extraction of combustion products at a constant mass flow rate and carefully controlling the uniformity of flow of ventilation air entering the test space. Under a quiescent external atmosphere, uniform inlet flow is ensured. However, a steady wind preferentially impacting on one of the outside wall surfaces could give rise to local conditions that would alter the inlet flow pattern from what is intended. Experience to date, based on monitoring of the pressure differentials across the three sides of the test volume envelope exposed to the external environment, has shown that non-uniformities in inlet air distribution can be considered negligible. 2.3. Oxygen concentration The oxygen concentration in ambient air is constant (essentially independent of total pressure) and approximately equal to 20.95% by volume, with the balance being made up of inert gases, mostly nitrogen. A factor that can affect the ambient oxygen concentration is the ambient humidity. Estimates for the magnitude of this effect will be made in Section 2.5 below dealing with ‘‘Relative Humidity”. Under the circumstances of large-scale fire tests, the oxygen level to which the combustion process is exposed can be lower than the ambient value due to recirculation of combustion products. This effect, however, is one of the outcomes of the experiment itself and should not be considered a controlled test parameter. 2.4. Ambient temperature Some capability to control the temperature of the environment in a large-scale facility prior to a test is generally available. During a test, however, external weather will affect the facility volume, with its temperature tracking that of the outside once the air ventilation flow is activated.1 In most cases, the actual conditions in the test volume will be somewhat dependent on transient effects, which may be significant under certain circumstances. In practice, it is important to determine the effect of seasonal variations in temperature and humidity on the outcome of a fire test. There are two aspects to be considered: 1 In the case of the FM Global Large Burn Laboratory, the air ventilation system provides one total volume change about every 10 min.
Q_ w r R RH RTI t tig Tg Tspk T0 T1 ug u0 XO2 z z0
a a0
nominal cooling power of extinguishing agent (kW) distance from the center of the ceiling layer (m) universal gas constant (J/kg mol K) relative humidity (%) response time index of sprinkler link ((m s)1/2) time (s) ignition time (s) gas temperature at sprinkler link (K) sprinkler link temperature (K) temperature on plume centerline (K) ambient temperature (K) gas velocity at sprinkler link (m/s) vertical velocity on plume centerline (m/s) oxygen volume fraction (%) elevation above the fire source (m) elevation of the virtual origin above the fire source (m) exponential fire growth factor (s1) exponential fire growth factor at standard conditions (s1)
1. Impact of temperature changes on the burning characteristics of the fuel commodity (rate of fire growth). This is mostly determined by the temperature in the volume prior to the test; and 2. Impact on the temperature/velocity field produced by the fire. This is determined by the conditions during the test.
2.4.1. Impact on fire growth The effect of fuel temperature on the rate of fire growth has been addressed by work done recently at FM Global. Based on that analysis, for the case of corrugated board, one can anticipate an increase of about 15% in fire growth rate as the ambient temperature increases from 4 to 32 °C. This estimate, which assumes that all other parameters remain unchanged, has been found to be weakly dependent on the moisture content of the corrugated board. The effect would be somewhat different in cases where the corrugated board constitutes only a fraction of the total fuel package, as in the case of cartoned plastics. 2.4.2. Impact on flow characteristics The second factor related to ambient temperature is the effect on the thermal and dynamic field produced by the fire. Appropriate quantification of the effect can be obtained by considering the flow in the fire plume. Heskestad [1] has proposed correlations for the plume radius (bDT), centerline temperature rise (T0 T1) and vertical velocity (u0). With the constant values recommended in Ref. [2] for rack storage fires, the correlations read as follows:
bDT ¼ 0:12
T0 T1
1=2
ðz z0 Þ;
ð1Þ
!1=3
T0 T1 R2 ¼ 11:0 Q_ c2=3 ðz z0 Þ5=3 ; T1 gc2p p21 M 2 1=3 gR 1=3 : u0 ¼ 4:25 Q_ 1=3 c ðz z0 Þ cp p1 M
ð2Þ ð3Þ
Additional relationships are available for the variation of gas temperature and velocity in the layer produced by the impingement of the fire plume on a horizontal ceiling. The parameters that appear in the above three equations are: bDT, plume radius to the point where the temperature rise has dropped to 0.5DT0; cp, specific heat of gases; g, acceleration of gravity; M, molecular weight of air; p1, ambient absolute pressure; Q_ c , convective heat release
406
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
rate; R, universal gas constant; T0, temperature on plume centerline; T1, ambient temperature; u0, vertical velocity on plume centerline; z, elevation above the fire source; and z0, elevation of the virtual origin above the fire source. Eq. (2) shows that, for a given convective heat release rate, Q_ c , and a fixed distance, z, above the top of the fuel array, the ratio T0/T1 is not a function of T1. Consequently, the plume width, bDT, and centerline velocity, u0, are also independent of T1. However, in terms of sprinkler activation, a device which responds to absolute temperature, it is apparent that changes in ambient temperature will lead to different activation times, even if the fire growth were to remain unaffected by the change. This issue will be revisited in quantitative terms by the analysis presented here.
gle-wall and double tri-wall corrugated board samples behave as thermally thin. However, at the flux levels that are more typical of large fires (say 100 kW/m2 and up), the tri-wall and, to a lesser extent, the single-wall corrugated would behave as thermally thick. Accordingly, another estimate applicable to this regime was provided by a prediction of temperature and moisture effects on piloted ignition time made at FM Global [7]. In that analysis, the ignition time was postulated to be proportional to the square of the enthalpy rise in the solid from initial conditions to pyrolysis temperature. For a value of initial temperature of 25 °C, the enthalpy change estimates of Ref. [7] lead to a dependence of the ignition time on moisture content for thermally thick materials, which can be approximated as:
2.5. Relative humidity
tig / 1 þ 10 MC ð%Þ=100 þ 66 ðMC ð%Þ=100Þ2 :
As in the case of temperature, the relative humidity (RH) has two effects on fire test conditions. First, the addition of water vapor to the combustion air changes its composition and, more notably, the oxygen concentration. The second effect applies to situations where the fuel is hygroscopic, as the air humidity influences the moisture content of the fuel. The importance of this condition is clear, given the fact that soggy material is known to burn less easily than material that is dry.
Regardless of the thermal regime, the fire growth rate of a material is inversely proportional to the ignition time. Therefore, Eq. (4) can be used to estimate how fire growth depends on moisture content. For a variation of MC from 4% to 8%, this equation would predict a decrease of fire growth rate of 32%. This estimate will be revisited in the next section, following consideration of large-scale data.
2.5.1. Effect on composition of atmosphere The effect of air humidity on the oxygen concentration can be significant. On a cold day (4.4 °C) with an RH of 50%, the partial pressure of steam is 4.19 mbar. On a hot (32.2 °C) and humid (RH = 100%) day, it would be 48.3 mbar. This means that, in the ‘‘cold” environment, the composition of the atmosphere is barely affected, with the oxygen concentration dropping from the dry value of 20.95 vol.% to 20.86 vol.%. In the ‘‘hot” (and ‘‘steamy”) environment, the oxygen concentration in the moist air is 20.00 vol.%. The drop of 1 vol.% in oxygen concentration is a significant factor that can be expected to influence the combustion process and, hence, the development of the fire. Data are available to provide a rough estimate of this effect. In experiments with a 0.3-m diameter PMMA pool fire [3], a decrease in oxygen concentration from 21 to 20 vol.% was accompanied by a drop in pyrolysis rate from 12.9 to 12.3 g/m2/s (a 4.6% decrease) and in radiated fraction from 36% to 33% (an 8.3% decrease). The general order of magnitude of the effect (about a 5–8% impact) on these steady-state quantities, which reflect the magnitude of the flame heat flux, is consistent with small-scale data for corrugated board obtained in the ASTM E2058 Fire Propagation Apparatus [4] (cf. Fig. 3–4.59, pp. 3–156). Since the flame spread rate is proportional to the square of the flame heat flux, the effect of the variations considered above on fire growth should be expected to be in the approximate range 10–15%. 2.5.2. Effect on solid fuel combustion Absorption of moisture in surrounding air by the solid fuel has been found to be an important factor in the fire behavior of cellulosic materials. Recent analyses and industry data [5] have confirmed that the equilibrium moisture content (EMC) of corrugated board is essentially a function of ambient relative humidity and that the influence of temperature on moisture content is secondary. In quantitative terms, the cartons used as packaging material for testing at FM Global have been found to reach EMC values of about 6.3% and 12.5% at RH levels of 50% and 90%, respectively. Recently, the effect of moisture content (MC) on the piloted ignition time of corrugated containerboard samples has been carefully quantified in the Fire Propagation Apparatus [6]. That study concluded that, for incident heat fluxes up to 60 kW/m2, both sin-
ð4Þ
3. Experimental results 3.1. Estimating fire growth in large-scale tests Most large-scale fire tests are performed under conditions that make it difficult to obtain a direct measurement of the heat release rate. Even when calorimetric data are collected, as in the case of tests carried out under the FM Global test ceilings, they are obtained too far from the fire source to allow for acceptable resolution of the time variation of the heat release rate. Due to these practical obstacles, indirect methods have to be devised. For the purposes of the evaluations presented in this paper, fire growth rates have been inferred from ceiling temperature data using two approaches. Both take advantage of the known functional relationship between temperature rise in fire plumes and convective heat release rate. Eq. (2) yields such a relationship for the temperature rise, T0 T1, on the plume centerline. The simplified form of this equation, obtained by neglecting the dependence of the virtual source location, z0, on heat release rate, Q_ c ,2 would imply that Q_ c is proportional to the 3/2 power of T0 T1. Even though this relationship is not entirely accurate, it is used here to estimate the rate of fire growth from the temperature rise near the ceiling on the axis of the fire. The second approach relies, again, on ceiling temperature data. Instead of using a single point measurement, this time an average temperature rise is calculated from twenty-five (25) thermocouples on a central grid of 6.1 6.1 m with 1.5-m spacing. As in the case of the centerline temperature rise, the dependence on Q_ c is not simple. In addition to the shift in virtual source discussed above, the radial profile of the maximum ceiling layer temperature, Tm, is also a function of Q_ c through the width of the fire plume, bDT, which is used as a scaling length, as shown in the following formula for Tm T1 [2]:
" T m T 1 ¼ ðT 0 T 1 Þ exp 0:66
r 1:5 bDT
1=2 # :
ð5Þ
2 Data from Ref. [2] indicate that the height of the virtual source above the top of 2=5 the fuel can be expressed as z0 ¼ c1 þ c2 Q_ c , where c1 and c2 are constants, which depend on the characteristics of the fuel array.
407
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
Fire Growth as a Function of Commodity Moisture Content Estimates Based on T41and on Average Rise over 20x20 ft Area Std. Plastic 9 30
0.5 -1
Fire Growth Rate [s ]
Std. Plastic 19 30 Std. Plastic 39 45
0.4
1 + 10 * MC[%]/100 + 66 * (MC[%]/100)^2
0.3 0.2 0.1 Open Symbols Refer to Tests with Center Ignition
0 0
2
4
6
8
10
12
14
Commodity Moisture Content (dry basis) [%] Fig. 1. Estimates of rates of fire growth for tests involving Standard Plastic commodity. (Numbers in the legend refer, respectively, to fuel array and ceiling height in ft.)
When all these dependencies are fully factored in, the relationship between the average ceiling temperature rise and Q_ c cannot be generalized, since it is a function of the specific conditions being considered (fuel array height, ceiling clearance, etc.). Nevertheless, the simple (and somewhat incorrect) 3/2 power dependence is used, with the understanding that this assumption introduces some error, as yet unquantified, in the absolute value of the fire growth rate. Since a few numerical examples have shown that the power exponent is between 1 and 3/2, the above assumption tends to overestimate the fire growth rate as a function of Q_ c . 3.2. Fire growth rate data Fire growth rates were calculated for several large-scale tests using the two methods described in the previous section, assuming an exponentially growing fire. Accordingly, a growth factor, a, defined by3:
Q_ c ¼ Q_ c;0 expðatÞ;
ð6Þ
was calculated as the average of the values given by the two methods, while the difference between them was used as a measure of the uncertainty of the determination. The data cover three different cartoned commodity types (Standard Plastic, Class 2 and Class 3)4 and various array height-ceiling height combinations. The test conditions are further characterized through the moisture content of the commodity, the initial temperature in the test volume and the location of the ignition source (center or offset at rack upright). The fire growth data are shown graphically in Figs. 1 and 2 for the Standard Plastic (SPC) and the Class 2/3 commodity, respectively. As discussed in the preceding section, because of the approximations made by the methods used to calculate the growth rate, direct use of the values in the figures should be made with caution. Nevertheless, a spot check comparison with fire growth data in three-tier high (4.3 m) fuel arrays tested under a 20-MW calorimeter [8] is quite favorable. For example, direct measurement of the time variation of the heat release rate, with corrugated 3 Due to the assumption of exponential growth, time zero in this case is not the time of ignition. It is the time at which the heat release rate is equal to Q_ c;0 . In practice, the choice of the value for Q_ c;0 has little effect on the results, provided that the value is sufficiently small. This condition can be determined by experimentation. 4 The different commodity denominations refer to the contents of the corrugated board box packaging: polystyrene cups for Standard Plastic; a steel liner for Class 2; and paper cups for Class 3.
containerboard moisture contents in the range 5–7% (dry basis), yielded growth rates of 0.25–0.28 s1 for SPC and 0.15–0.24 s1 for Class 2. These numbers compare well with the estimates shown in Figs. 1 and 2. In the case of the SPC shown in Fig. 1, taking 6% as the mid point, the effect of MC over the range from 4% to 8% for the tests with center ignition appears to be of the order of ±15%. This can be compared with the variation implied by the correlation in Eq. (4), which is shown by the line in Fig. 1 (anchored for MC = 6% at the fire growth rate value representing the approximate average of the bulk of the data). Over the 4–8% MC range, the correlation yields a variation of ±20%. Notwithstanding the fact that the polystyrene cups in the SPC also contribute at some point to the fire growth, it would appear that the selected expression for the thermally thick case (Eq. (4)) is a reasonable predictor of the moisture content effect. A similar result is suggested by the Classes 2 and 3 data in Fig. 2, with clearer evidence of a distinct trend possibly due to the more limited information available. In summary, different measures of the effect of moisture content of the corrugated containerboard on the rate of fire growth do seem to provide a degree of consistency in that they all support an estimate of the effect of ±15% variation when MC = 6 ± 2%. This result will be considered later in making recommendations for acceptable ranges of environmental variables. 4. Impact of ambient conditions on first sprinkler activation 4.1. General approach The discussion in the preceding sections has focused on estimates of the individual impacts of variations in different parameters on characteristics of the fire, mainly its growth rate. It would seem that the occurrence of first sprinkler activation should offer a reasonable benchmark for the evaluation of the variability associated with changes in environmental parameters that affect fire development. More specifically, the heat release rate at the time of first sprinkler activation should be considered a relevant variable, since it has been established that control and/or suppression of the fire becomes more difficult, the higher the burning rate at the beginning of extinguishment [8]. First sprinkler response is calculable with reasonable accuracy, even though ceiling layer correlations are not available for all possible conditions of interest. Nevertheless, available knowledge in
408
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
Fire Growth as a Function of Commodity Moisture Content Estimates Based on T41 and on Average Rise over 20x20 ft Area Class 2 19 30
0.5
-1
Fire Growth Rate [s ]
Class 2 34 40/41 Class 3 39 45
0.4
1 + 10 * MC[%]/100 + 66 * (MC[%]/100)^2
0.3 0.2 0.1 0 0
2
4
6
8
10
12
14
Commodity Moisture Content (dry basis) [%] Fig. 2. Estimates of rates of fire growth for tests involving Class 2 and Class 3 commodities. (Numbers in the legend refer, respectively, to fuel array and ceiling height in ft.)
this area should be sufficient for an analysis that is aimed at establishing departures from a baseline case. Finally, owing to the important role assigned to the effect of relative humidity (RH) on the moisture content (MC) of the commodity, the analysis is most applicable to the case of hygroscopic cartoned fuels. The outline of the approach is as follows. A baseline case is established by defining the rate of fire growth for the commodity of interest at standard conditions. Empirical formulas are then used to describe the effect of environmental parameters on the rate of fire growth. A sprinkler location (ceiling clearance above fuel array and distance from fire axis) and type (temperature rating and RTI5) are selected. Finally, the sprinkler link temperature response is calculated and the heat release rate at the time of sprinkler actuation, Q_ be , is compared with that of the baseline case. The final outcome of the exercise is the establishment of a parameter domain within which the variation of Q_ be is less than a certain percentage of baseline value.
The rate of fire growth is defined through the value of the growth coefficient, which has been introduced in Eq. (6). The following ambient values are used as standard conditions: p1,0 = 1 atm (std) (1.01325 105 Pa) T1,0 = 18.3 °C (65 F) RH0 = 35%
Two commodities are considered in the analysis, each characterized by a rate of fire growth at standard conditions as follows: Standard Plastic Class 2
4.3.2. Ambient temperature As already discussed, the ambient temperature is expected to present two effects. The first is a direct impact on the rate of fire growth, which will be estimated based on the considerations of the effect in thermally thick corrugated board. At MC = 5%, the fire growth rate is estimated to increase by 0.56%/°C of ambient temperature change. This factor is somewhat dependent on the moisture content, but not sufficiently to justify more accurate accounting. Accordingly, the temperature effect on fire growth rate is calculated by applying the following correction to the exponential fire growth coefficient:
cT ¼ 1 þ 0:0056ðT 1 T 1;0 Þ ð CÞ:
4.2. Baseline conditions
Absolute pressure Temperature Relative humidity
finding that the burning rate of radiatively-controlled fires is approximately proportional to ambient pressure [9,10]. Based on these results, the changes associated with ambient pressure fluctuations (estimated at ±1.5%) are considered to be of lesser importance and, therefore, negligible.
aSPC,0 = 0.25 s1 aC2,0 = 0.15 s1
The second effect is fully described by the fire plume correlations, which have already been introduced in a previous section. They are used directly in the calculations, since no further simplification is needed. 4.3.3. Ambient humidity Similar to temperature, ambient humidity has an impact on the characteristics of the atmosphere as well as on the moisture content of the commodity and, hence, the fire growth rate. The first effect is taken into account by introducing the partial pressure of steam in the following expression to calculate the resulting oxygen concentration:
X O2 ðvol:%Þ ¼ 4.3. Parameter effects 4.3.1. Ambient pressure The impact of ambient pressure changes is neglected here. Should it be taken into account in future analyses, its effect would be properly described by the role played by this quantity in the plume equations (cf. Eqs. (1)–(3)). Other effects (e.g., on heat flux and, therefore, on pyrolysis rate) have been evaluated, with the 5 RTI, the Response Time Index, is a quantity representing the inertia characteristics of the thermal sensing element of the sprinkler.
ð7Þ
20:95 ; 1 þ pv ðPaÞ=101; 235
ð8Þ
where, pv is the steam vapor pressure (=psat RH/100). At the standard conditions of 18.3 °C and RH = 35%, psat = 2108 Pa and, therefore, it is pv = 738 Pa. Finally, the oxygen concentration at standard conditions is calculated from Eq. (8) as XO2,0 = 20.80 vol.%. The preceding discussion has indicated an average effect of the O2 concentration of about 13% drop in fire growth rate for every percent drop in XO2. Accordingly, this correction is expressed as:
cO2 ¼ 1 þ 0:13ðX O2 X O2;0 Þ ðvol:%Þ:
ð9Þ
409
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
The other effect of ambient humidity is through its impact on the equilibrium moisture content (EMC) of the corrugated containerboard. This can be approximated using the following empirical fit to data in Ref. [6]:
EMC ð%Þ ¼
4 ð1 þ RH ð%Þ=10Þ: 3
ð10Þ
It can be noted that, for RH = 35%, the above expression yields EMC = 6%. This latter value is, therefore, the equilibrium moisture content corresponding to standard conditions. Since changes in RH lead to changes in MC, an equation is needed to capture the effect of MC on the fire growth rate, a. These effects are reflected in the expressions for ignition time, tig, given as Eq. (6), since it is a / 1/tig. Therefore, the correction factor for MC effects is:
cMC ¼
1:838 1 þ 10 MC ð%Þ=100 þ 66 ðMC ð%Þ=100Þ2
ð11Þ
;
5.2. Response prediction results An example of the predictions produced by the calculation procedure is discussed next. Consider the baseline case (T1 = 18.3 °C and RH = 35%) of 4 tiers of Standard Plastic commodity (SPC) burning under a ceiling with a clearance of H = 3.35 m. The sprinkler, with a temperature rating Tlink = 74 °C and a response time index RTI = 27.6 (m s)½, is installed 2.15 m off axis and 0.152 m down from the ceiling. Since the ambient conditions are at standard values, there are no corrections (cT = cO2 = cMC = 1) to the fire growth rate, which is therefore equal to 0.25 s1. For these conditions, the model predicts first sprinkler activation when the heat release rate is Q_ be ¼ 2308 kW. The second case is that of a dry (RH = 20%), cold (T1 = 7.2 °C) day. The correction factors for the fire growth rate and the HRR at the time of sprinkler activation in this case are:
cT ¼ 0:94;
cO2 ¼ 1:01;
Q_ be ¼ 2893 kW:
cMC ¼ 1:22;
ð14Þ
which yields cMC = 1 when MC = 6%, as it should be at the standard condition. The corrections from Eqs. (7), (9), and (11) are applied to calculate the fire growth rate as:
The value of Q_ be has increased by 25%. The third case is that of a wet (RH = 50%), warm (T1 = 29.4 °C) day. The correction factors and the HRR at sprinkler activation now are:
a ¼ cT cO2 cMC a0 ;
cT ¼ 1:06;
ð12Þ
where a0 is the reference value of the exponential fire growth coefficient.
5. Sprinkler response predictions 5.1. Calculation procedure Predictions of the sprinkler link response are made using the known expression for the rate of temperature rise of the fusible link: 1=2 dT spk ug ¼ ðT g T spk Þ; dt RTI
ð13Þ
where Tspk is the sprinkler link temperature (initially taken to be equal to the ambient temperature, T1), ug is the local gas velocity, Tg is the temperature of the gases near the link, and RTI is the response time index of the sprinkler, measured in (m s)1/2.
cO2 ¼ 0:97;
Q_ be ¼ 1763 kW;
cMC ¼ 0:83;
ð15Þ
representing a 24% drop in Q_ be relative to the baseline. Other cases could be considered, for example by predicting the response of a high-temperature (141 °C), slow-response (166 (m s)½) sprinkler. The three scenarios detailed above provide an indication of the magnitude of the effects, which is substantial. Rather than introducing additional numeric examples, the limitations that should be considered in defining acceptable parameters for large-scale tests are considered in the following section. 5.3. Target operating envelope Based on the premise that the variation of the HRR at the time of sprinkler activation (i.e., the response variable) should be limited (by control of the other variables), one can attempt to define the range of conditions that achieve that goal within a certain prescribed tolerance. As an example, one can consider additional cases representing departures from the baseline conditions outlined in the previous section. The results of the parametric exploration of the range of ambient temperature from 0 to 29.4 °C and relative
Acceptable Operating Ranges of Ambient Temperature and Humidity
Temperatures [°F]
100
Min Ta [°F] Max Ta [°F] Std. Condition
80
60
40
20 20
30
40
50
60
70
80
Relative Humidity [%] Fig. 3. Temperature/relative humidity domain corresponding to a ±15% variation in HRR at sprinkler activation. Case of sprinkler with: temperature rating 74 °C, RTI 27.6 (m s)½, 3.35-m ceiling clearance, 2.15 m off axis. Fire growth rate of a0 = 0.25 s1.
410
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411
humidity from 20% to 80% yield extreme values of 1287 and 3263 kW calculated for Q_ be at T1 = 29.4 °C, RH = 80% and T1 = 0 °C, RH = 20%, respectively. The relationship between HRR at sprinkler activation, ambient temperature and relative humidity can be approximated by a linear function, leading to the following more usable form:
Q_ be ¼ Q_ be;0 þ aT ðT 1 T 1;0 Þ þ aRH ðRH RH0 Þ;
ð16Þ
where the subscript ‘‘0” refers to the standard conditions of the baseline case and the two coefficients aT and aRH are determined by fitting the model results. Having the results of the prediction expressed through the fit in Eq. (16) provides a quick way to define the domain of ambient conditions that corresponds to a certain variation of the HRR at sprinkler activation relative to its baseline value. As an example, one could prescribe a limit of ±15% for that variability, i.e. Q_ be ¼ 2308 346 kW. Graphically this can be represented as the domain between two lines in a plot of T1 vs. RH. For the case of the fast-response sprinkler considered here, this translates into the graph shown in Fig. 3. This figure defines the range of acceptable RH at a given T1, and vice versa. For example, if T1 = 18.3 °C (65 F), then the allowable range for RH is about 18–52%. Similarly, at RH = 35%, the allowable range for T1 is from about 8 to 28 °C (47 to 83°F). Use of the results of this analysis would be greatly simplified if it was not for the fact that the range of acceptable conditions, based on the limit on HRR variation, is dependent on the selected sprinkler conditions. This point could be illustrated by repeating the calculations for a different case involving a sprinkler with a higher temperature rating and a slower response. That example would show acceptable boundaries for the same ±15% HRR variation, which are somewhat different from those shown by the example in Fig. 3. This result underscores the fact that the response of the fire to ambient conditions is a function of the details of the fuel array and of the protection. Therefore, each situation has to be evaluated individually. A rectangular area is shown in Fig. 3. It covers a temperature range from 10 to 26.7 °C (50 to 80 F) and relative humidity from 20% to 50%. In the absence of more case-specific analyses, this may be considered a reasonable domain for acceptable operating conditions. It is included in the figure as a frame of reference to evaluate error bounds defined by the analysis. However, it should be noted that, for the case of Fig. 3, the upper right and lower left corners of the domain correspond to departures from the HRR at standard conditions of 27% and +27%, respectively. 6. Implications for protection requirements The preceding analysis has focused on the HRR at the time of sprinkler activation as a figure of merit, which is appropriate to characterize the effects of environmental conditions on the outcome of large-scale fire tests. While a useful indicator, this parameter does not quantify directly the impact on protection performance. Some guidance, however, is provided by recent results obtained as part of a separate project [8]. In that work, the response of a rack-storage array to extinguishment action by water was analyzed and a correlation was developed to express the protection requirement, represented by Q_ w ,6 as a function of the HRR at the beginning of extinguishment, Q_ be : c
1 Q_ w / Q_ be b :
ð17Þ
6 This is the potential cooling power of the suppression water (kW), calculated as water mass flow times the heat of vaporization of water – 2450 kJ/kg.
The data in Ref. [8] yield information on the value of the exponent 1 c/b for the various commodities tested. For the case of Class 2 and Standard Plastic, it is 1 c/b = 0.46 and 0.73, respectively. The fact that this exponent is less than 1 means that a percent variation in Q_ be is reflected as a smaller variation in the protection requirement, as expressed by Q_ w . As a result, the ±15% variation considered earlier for Q_ be becomes about ±7% and ±11% for the water requirements of the Class 2 and Standard Plastic commodities. It should be noted that the quantity Q_ w refers to the water flux applied to the top of the fuel array, which has been labeled in Ref. [8] as the Critical Delivered Flux (CDF). The effect on the water flux at the sprinkler elevation (the Sprinkler Discharged Flux (SDF)) should be somewhat greater. Furthermore, all test results from this study were obtained by delivering water over the entire top surface of the fuel. In actual suppression tests, the water flux is not spatially uniform because of the delay between subsequent sprinkler activations. This fact leads to some uncertainty in the application of the data from Ref. [8] to the suppression of large-scale fires. 7. Summary and conclusions The analysis presented in this paper has considered the potential sources of variability in large-scale fire tests carried out with hygroscopic cartoned commodities. It has quantified the effects of temperature and relative humidity on the size of the fire at the time of first sprinkler activation, a quantity selected as the significant parameter to represent the evolution of the test. In the analysis, the relative humidity (RH) has been used to reflect the moisture content (MC) of the cellulosic commodity, with an RH variation from 20% to 50% corresponding to MC varying from 4% to 8% (dry basis). Pre-test conditioning of the commodity, and limitations in its exposure to changes towards different RH values in the surrounding air prior to test ignition, would broaden the acceptable range for the values of the two variables, ambient temperature and RH, at the time of ignition. In summary, the issue of quantifying the effects of environmental conditions on the outcome of large-scale fire tests has been addressed by using a simple analysis to predict the impact of ambient temperature and relative humidity changes on a parameter which represents the conditions of the fire at the beginning of the extinguishment process. At best, this approach provides a partial view of a very complex physical phenomenon. Unfortunately, current limitations in fire modeling prevent a consideration of the problem through analytical means, which extends into the extinguishment phase of the fire. Until such a time where significant progress can me made with modeling, the type of analysis presented in this paper, in combination with thoughtful interpretations of fire test results, will have to suffice.
References [1] G. Heskestad, Engineering relations for fire plumes, Fire Safety Journal 7 (1984) 25–32. [2] H.-C. Kung, H.-Z. You, R.D. Spaulding, Ceiling flows of growing rack storage fires, in: Twenty-first Symposium (International) on Combustion, The Combustion Institute, 1986, pp.121–128. [3] G. Santo, F. Tamanini, Influence of oxygen depletion on the radiative properties of PMMA flames, in: Eighteenth Symposium (International) on Combustion, The Combustion Institute, 1981, pp. 619–631. [4] A. Tewarson, Generation of heat and chemical compounds in fires, in: SFPE Handbook of Fire Protection Engineering, third ed., 2002 (Chapter 4). [5] J. Marcondes, Corrugated fibreboard in modified atmospheres: moisture sorption/desorption and shock cushioning, Packaging Technology and Science 9 (1996) 87–98. [6] M.M. Khan, J.L. deRis, S.D. Ogden, Effect of moisture on ignition time of corrugated paper cardboard samples, Paper presented at the 9th International
F. Tamanini / Experimental Thermal and Fluid Science 34 (2010) 404–411 Symposium of Fire Safety Science, 21–26 September 2008, University of Karlsruhe, Germany. [7] J.L. deRis, private communication, 2005. [8] Y. Xin, F. Tamanini, Assessment of commodity classification for sprinkler protection using representative fuels, in: Fire Safety Science – Proceedings of the Ninth International Symposium, 2008, pp. 527–538.
411
[9] R.L. Alpert, Pressure modeling of fires controlled by radiation, in: Sixteenth Symposium (International) on Combustion, 1977, pp. 1489– 1500. [10] J.L. deRis, P.K. Wu, G. Heskestad, Radiation fire modeling, in: Twenty-eighth Symposium (International) on Combustion, 2000, pp. 2751–2759.