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Simplified model for predicting difference between flammability limits of a thin material in normal gravity and microgravity environments
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Proceedings of the Combustion Institute 35 (2015) 2535–2543
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Simplified model for predicting difference between flammability limits of a thin material in normal gravity and microgravity environments Shuhei Takahashi a,⇑, Tomoya Ebisawa a, Subrata Bhattacharjee b, Tadayoshi Ihara a b
a Department of Mechanical Engineering, Gifu University, Japan Department of Mechanical Engineering, San Diego State University, United States
Available online 28 July 2014
Abstract Most flammability tests for a material to be used for manned spacecraft are conducted on the ground, although several studies have reported that the flammability limit in microgravity is different from that in normal gravity. Hence, an important task is to predict the margin between the limiting oxygen concentrations (LOCs) in normal gravity and microgravity. We set up a simplified scale model to describe the opposed-flow flame spread over a thin material and derived expressions for the Damko¨hler number (Da) and the nondimensional radiative loss factor (Rrad) for the flame spread over a thermally thin poly methyl methacrylate (PMMA) sheet. The empirical constants for these nondimensional numbers were evaluated by fitting with the experimental results in a N2 balance. The obtained model was validated under varying gas-phase properties. First, we obtained the experimental blow-off limits via downward spread tests in normal gravity with different balance gases (N2, Ar, and CO2). We compared the predicted blow-off limits, which corresponded to the limiting oxygen index (LOI) condition, with the experimental results for each balance condition and found that the predicted limits agreed well quantitatively with the experimental results. Then, using Da and Rrad, we drew a flammability map for opposed-flow flame spread over a thin PMMA sheet, which predicted the flammable conditions under the LOI. The developed simplified model predicted the minimum LOCs (MLOCs) and the critical opposed-flow velocity for the N2, Ar, and CO2 balance conditions. The model underestimated the MLOCs because it considered the effect of either the radiation or the kinetics, whereas both these effects are actually coupled near the MLOC. Nevertheless, the predicted margin between the MLOC and the LOI illustrated the behavior of the flame spread near extinction. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Flame spread; Extinction; Scale analysis; Microgravity
⇑ Corresponding author. Address: 1-1 Yanagido, Gifu-
shi, Gifu 501 1193, Japan. E-mail address: [email protected] (S. Takahashi).
1. Introduction Recently, human activity in space has increased and the duration of stay in spacecraft
http://dx.doi.org/10.1016/j.proci.2014.07.017 1540-7489/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
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Nomenclature A aabs B1 B2 cBC cg cs Da E Lgx Lgy Lsx Lsy Rrad Tf Tv T1
pre-exponential factor absorption coefficient of gas empirical constant for Da empirical constant for Rrad empirical constant for buoyant flow velocity specific heat of gas specific heat of solid damko¨hler number activation energy gas-phase diffusion length scale in xdirection gas-phase diffusion length scale in ydirection length of preheated solid phase thickness of preheated layer radiation loss factor adiabatic flame temperature vaporization temperature ambient temperature
such as the International Space Station (ISS) is becoming increasingly longer. Then, the reduction of fire risk in a microgravity environment and performing convenient flammability tests for materials used in space have become important research issues. Extensive studies have been conducted on flame spread over a thermally thin material with opposed flow under microgravity conditions [1–10]. One of the most characteristic features of a microgravity environment is the absence of buoyant flow, which is essential in normal gravity. Therefore, most of these previous studies were focused on flame behavior with a mild or slow flow whose velocity was smaller than that of the buoyant flow. Many studies conducted in the Space Shuttle and drop towers reported that flame spread with a slow ambient flow was suppressed by radiative heat loss, which eventually caused radiative extinction under a quiescent condition [4-6]. Thus, flame spread in microgravity may be considered as being on the “safe side.” Olson et al. [6] investigated the flame spread in microgravity under varying ambient flow velocity and reported that the spread rate achieved the maximum peak with an ambient flow velocity of 6 cm/s. Kumar et al. [7] also conducted numerical simulations and demonstrated that the minimum oxygen concentration required for a thin material to burn became lowest when the flow velocity was about 5 cm/s. Similar results have been reported by other researchers, and it is common knowledge that the curve of the limiting oxygen concentration (LOC) versus the opposed-flow velocity is U-shaped [8]. This trend implies that the flammability limit of a thin material is lower
Vg Vf Vf,th Vr Vcr W ag e kg ks g qg qs s
opposed-flow velocity flame spread rate flame spread rate in thermal regime velocity relative to flame, Vr = Vg + Vf critical opposed-flow velocity width of fuel in z-direction thermal diffusivity of gas, evaluated at Tv surface emissivity gas-phase conductivity evaluated at Tv solid-phase conductivity nondimensional spread rate gas density evaluated at Tv solid density fuel half-thickness
in microgravity than in normal gravity. Despite this fact, however, many flammability tests have been conducted in normal gravity, such as NASA STD-6001 or ASTM D2863. The obtained results are extremely vast, but using the collected data to estimate the flammability in microgravity requires careful consideration, because the minimum oxygen concentration in microgravity may be much lower than that in normal gravity. Olson et al. [9] reported that the upward LOI (ULOI) and the maximum oxygen concentration (MOC) varied depending on the gravity level and the kind of material used. Consequently, in order to confirm the fire safety at different gravity levels, including microgravity, additional flammability tests should be conducted under the corresponding gravity conditions or detailed numerical simulations should be performed; however, both these approaches are time consuming and expensive. Hence, the objective of the present study was to develop a simple model that can predict the difference between the flammability limits of thin materials in normal gravity and microgravity environments. To this end, we defined the minimum limiting oxygen concentration (MLOC) as the oxygen concentration at which the flame cannot exist with any opposedflow velocity. We also defined the critical opposed velocity Vcr at which the MLOC is observed. We derived two nondimensional variables, including an experimental constant, and predicted the MLOC and Vcr in microgravity as well as the LOI in normal gravity. In order to validate the developed model, we first investigated the effect of diluent-gas properties on the flammability map; to this end, we conducted flame spread
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experiments over a thin polymethyl methacrylate (PMMA) film under normal and microgravity conditions with various kinds of diluent gases in ambient flow. We then compared the results predicted by the model with the experimental results and discussed the effect of the difference in the properties of diluent gases on the developed model. 1.1. Scale modeling The flame spread rate over a thermally thin material with moderate opposed flow, which is comparable to buoyant flow, has been formulated by de Ris [11], and its validity has been confirmed both experimentally and numerically by numerous researchers [12–15]. Bhattacharjee et al. [16,17] also derived the expression for flame spread over a thin material with an opposed flow by establishing scale modeling on a two-dimensional (2D) flame, as shown in Fig. 1. The length of the preheat zone in the gas phase, Lgx, is proportional to ag/Vr, where ag is the thermal diffusivity of the ambient gas and Vr is the relative opposedflow velocity, which is expressed as Vr = Vg + Vf. Other lengths, i.e., Lgy, Lsx, and Lsy, for a thin material are also expressed as follows:
V f qs cs LsyW ðT v T 1 Þ þ Qrad kg
2537
ðT f T v Þ Lgx W ; Lgy ð3Þ
aabs ÞrðT 4v
T 41 ÞLsx W
where Qrad ¼ eð1 . Upon introducing the nondimensional spread rate g, which is defined as g = Vf/Vf,th, Eq. (1) is reduced to the following nondimensional equation [28]: g þ Rrad ¼ 1; where Rrad
ð1 aabs ÞrðT 4v T 41 Þ qg cg V r ðT f T v Þ
ð4Þ
If the heat conduction through the preheat zone in the gas phase is balanced with the heat supplied to the preheat zone in the solid phase, which is defined as a thermal regime, the following equation holds: ðT f T v Þ V f ;th qs cs Lsy W ðT v T 1 Þ kg Lgx W ð1Þ Lgy
Rrad is a nondimensional radiative loss factor. In this study, we assume that the only factor that causes extinction near the quiescent condition is surface radiation. This is a crude assumption but it can simplify the model, although there are several coupling factors for the extinction phenomenon, such as gas/soot radiation fed back from the flame. Equation (4) implies that if Rrad approaches unity, g approaches zero; thus, radiative extinction occurs. It is found that Rrad becomes larger as the relative opposed-flow Vr becomes smaller. Therefore, if the opposed-flow velocity Vg is small enough such that Rrad 1, the regime changes to the microgravity regime. On the other hand, if the opposed-flow velocity Vg is much higher, blow-off occurs. When Vg is large, the residence time in the gas-phase preheat zone becomes comparable to the chemical reaction time. We define the residence time treg and the chemical reaction time tchem as follows:
Solving Eq. (1) gives the flame spread rate in the thermal regime, Vf,th, as
tres ¼ Lgx =V r ; tchem mF =xF L2g W
Lsx Lgx Lgy ag =V r and Lsy ¼ s:
V f ;th
kg T f T v ; qs cs ss T v T 1
ð2Þ
which is almost identical to the equation derived by de Ris, except for the constant. If the radiative heat loss from the solid preheat zone to the surroundings is considered, the radiative term, Qrad, is added to Eq. (1), as follows:
¼ ½qg Y O A expðE=RT f Þ1 ; where xF is the reaction rate, expressed as xF ¼ ðqg Y F Þðqg Y O ÞA expðE=RT f Þ; and mF is the mass of fuel in the gas-phase preheat zone, expressed as mF ¼ qg Y F L2g W . Then, we obtain the Damko¨hler number Da [18,19] as
Fig. 1. Schematic of two-dimensional flame used for scale analysis.
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Da
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tres ag q Y o A expðE=RT f Þ tchem V 2r g
ð5Þ
If Da is close to unity, the regime is thought to change to the kinetic regime. Using the two nondimensional factors Rrad and Da, we can draw the flammability map for a thin material as described later.
Table 1 Properties of PMMA for scale analysis. PMMA Density, qs (kg/m3) Specific heat, cs (kJ/kg K) Vaporization temperature, Tv (K) Enthalpy of reaction, DHr (kJ/kg) Surface emissivity, e Pre-exponential factor, A (m3/kg s) Activation energy, E (J/mol)
2. Experimental setup In ASTM D2863, the downward spread experiments are conducted to obtain the LOI. Hence, we first measured the downward spread rate and the LOC at which the flame could spread over a thin solid material. The sample used in this experiment was a thermally thin PMMA sheet (Acryplen: Mitsubishi Rayon Co., Ltd.) with a thickness of 0.125 mm. The PMMA sample, which was 8 cm in length and 2 cm in width, was set vertically in a closed chamber of volume 35 L, as shown in Fig. 2. The sample was ignited at the top with an electrically heated Ni-Cr wire. The pressure and temperature in the chamber were kept at 101 kPa and room temperature, respectively. The flame spread behavior was recorded with a visible CCD camera and an IR camera to obtain the spread rate and the length of the preheat zone on the PMMA sheet, respectively. The experiments were conducted by decreasing the initial oxygen concentration, and the oxygen concentration at which the flame could not spread after the ignition was measured. In this study, the measured oxygen concentration was defined as the LOI. The downward spread tests were conducted by changing the diluent of the ambient gas—to N2, CO2, and Ar—in order to confirm whether the developed model could predict the difference in the LOIs among these gases. The properties of the PMMA and diluents are presented in Table 1 and Table 2, respectively.
1190 1.465 670 25900 1.0 1.36 109 1.50 105
As indicated in Table 2, we set the aabs value of CO2 as 0.8 on the basis of our previous work [20], by fitting the experimental results to the model. As mentioned in the previous section, this value includes not only the effect of reabsorption but also the heat fed back by gas radiation from the flame to the preheat zone [21,22]. In order to obtain the LOC in a microgravity environment, we then conducted 20-s parabolic flight experiments by availing the Diamond Air Service (DAS). Figure 2 shows the schematic of the test chamber used for these flight experiments. This test chamber was also 35 L in volume, in which a rolled PMMA sheet was placed, which is similar to the setup in the work of Ferkul et al. [23]. The chamber had a suction fan for creating a flow ranging from 0 to 20 cm/s in the test section. The dimensions of the test section were 14 cm 14 cm 13 cm, and honeycomb plates were installed on both the upstream side and the downstream side of the test section. The PMMA sheet in the test section was 8 cm in length and 2 cm in width. The downstream end of the sample was ignited by the Ni–Cr wire 10 s before the onset of microgravity, and the flame that spread upstream was recorded with a CCD camera and IR camera to capture the flame behavior and the preheat zone on the sample, respectively. Under the conditions in which the initial oxygen concentration was lower than the LOI, we could not
Fig. 2. Schematic of experimental apparatus for parabolic flight experiments.
S. Takahashi et al. / Proceedings of the Combustion Institute 35 (2015) 2535–2543
N2 Ar CO2
Cp [J/mol K]
kg [W/m K]
ag [mm2/s]
aabs
30.47 20.78 48.94
0.0444 0.0312 0.0396
80.1 82.7 44.5
0.0 0.0 0.8
ignite the sample before the onset of microgravity. Hence, under such conditions, we ignited the sample at the onset of microgravity. When the sample was ignited right at the onset of microgravity, the time remained for flame spread was 10 s because the ignition procedure took about 10 s. If the flame survived until the end of the microgravity environment, we judged it as being flammable; else, we judged it as being extinct. Then, we defined the MLOC as the minimum LOC at which the flame survived. The spread rate Vf was defined as the average spread rate in 5 s. The flame near the extinction limit was blue and faint. Therefore, it might become extinct if the microgravity duration was longer, but the obtained extinction limit was considered as conservative. Molecular sieves and zeolites were packed inside the test chamber to absorb the water and carbon dioxide generated during the combustion process. A pressure transducer, a thermocouple, and an oxygen sensor were also installed to monitor the pressure, temperature, and oxygen concentration, respectively. We wound the rolled sheet to feed a new sample area after the completion of combustion. After the complete combustion of the 8-cm-long PMMA sheet, the oxygen concentration in the chamber decreased by 0.8%, but the actual decreased concentration of oxygen depended on the consumed length of the sample in the experiment. After filling an oxygen/nitrogen mixture in the chamber, we repeated the combustion test without adding consumed oxygen, and so, the oxygen concentration in the chamber decreased gradually during the experiment. We conducted four flight experiments for a N2 balance condition, and the initial oxygen concentrations in these four experiments were 20%, 19%, 17%, and 15%. The initial pressure was 101 kPa; it decreased to 97 kPa after a series of parabolic flight experiments. For the CO2 balance condition, we replaced the molecular sieves with glass beads and conducted two flight experiments in which the initial oxygen concentrations were set as 25.5% and 20%, respectively.
measured, as shown in Fig. 3. At higher oxygen concentrations, the spread rates in the N2 balance and Ar balance were almost the same; that in the N2 balance was slightly higher. As shown in Table 2, the flame temperature in the Ar balance is expected to be higher than that in the N2 balance, but the heat conductivity of N2 is larger than that of Ar. Therefore, the effect of Tf depending on cg canceled the effect of kg in Eq. (2). The spread rate in the CO2 balance was lowest owing to a large cg and small ag, which were the advantageous features of CO2 as an extinguishing agent. The oxygen concentration at which extinction occurred was lowest when Ar was used as the balance gas, owing to its small cg. In contrast, the oxygen concentration at which extinction occurred was highest when CO2 was used as the balance gas. Upon conducting more detailed downward spread tests near the extinction limit, we obtained the LOIs for each balance gas, which are presented in Table 3 (LOI: Measured). The obtained results are well-known facts and are consistent with the results of a large number of conducted ground flammability tests [24]. 3.2. Flammability maps by scale modeling In order to draw the flammability map by using the nondimensional factors in Eqs. (4) and (5), we first attempted to determine the empirical constants for Da and Rrad to make them quantitative variables. In downward spread tests, extinction was observed when the oxygen concentration was 17.2%. This extinction is thought to be caused by a kinetic limit; therefore, the Damko¨hler number,
7
Flame spread rate (mm/sec)
Table 2 Properties of balance gases at Tv = 670 K and 1 atm.
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6
N2 Ar CO2
5 4 3 2 1 0 10 12 14 16 18 20 22 24 26 28 30
3. Results and discussion 3.1. Downward spread in normal gravity First, the downward spread rates in normal gravity under varying ambient oxygen concentrations for N2, CO2, and Ar balances were
Oxygen level (%) Fig. 3. Downward flame spread rates in normal gravity under varying oxygen concentrations in N2, Ar, and CO2 balances. The oxygen concentration at which extinction occurs corresponds to the limiting oxygen index (LOI).
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Table 3 Limiting oxygen index (LOI) in downward spread and minimum limiting oxygen concentration (MLOC) in microgravity for each balance gas. Balance gas
N2
Ar
CO2
LOI
17% 17.0% 11% 14.7% 6% 2.3% 6 cm/s 10 cm/s
11% 12.9% 8% N/A 3% N/A 8 cm/s N/A
24% 24.3% 12% 19.2% 12% 5.1% 1.4 cm/s 2 cm/s
MLOC DO2 Vcr
Predicted Measured Predicted Measured Predicted Measured Predicted Measured
expressed in Eq. (5), should be unity under this condition. In our previous scale analysis [25], the buoyant flow velocity VBC was estimated as 1=3 ag gðT v T 1 Þ V BC ¼ cBC ; ð6Þ T1 where {cBC}= 5.32. The constant cBC was determined by assuming that VBC, which corresponded to Vg in the model, was 35 cm/s for the N2 balance condition, which is a typical value observed in practice. By using the properties of PMMA listed in Table 1 and by calculating the adiabatic temperature under the considered condition, Tf, we derived an empirical constant, B1, for Da: ag Da ¼ B1 2 qg Y O A expðE=RT f Þ; ð7Þ Vr where B1 = 0.131. The thermodynamic properties in the gas phase were estimated at Tv by using the Chapman–Enskog theory; Yo is the value of the ambient gas in the chamber. The thermodynamic properties in the reaction zone can be varied by Tf. which is a function of Yo, but ag qg kg =cg has a relatively temperature dependence pffiffiffiffiffismall ffi because kg T f and cg increases with increasing Tf. Hence, for simplicity, we used Eq. (7) to discuss the blow-off limit. Then, we derived the empirical constant for Rrad. From our previous experiments with a drop tower, we had found that when the opposed-flow velocity was 3 cm/s or less, radiative extinction occurred at an oxygen level of 21% for a PMMA sample that was almost identical to that used in the present study, the only difference being its width of 1 cm [20,26]. Therefore, in our model, the radiative loss factor Rrad should be unity under this condition, i.e., Vg = 3 cm/s. We similarly obtained the empirical constant B2 for Rrad: Rrad ¼ B2
eð1 aabs ÞrðT 4m T 41 Þ ; qg cg V r ðT f T m Þ
where B2 = 2.67.
ð8Þ
Using the obtained empirical constants B1 and B2 and the properties listed in Table 2, we calculated the condition of the opposed-flow velocity and the oxygen concentration at which Rrad = 1 or Da = 1 is achieved. The kinetic and radiative limits predicted using the constants in Eqs. (7) and (8), respectively, are shown in Fig. 4. for N2, Ar, and CO2 balances. The properties of the balance gases were estimated at Tv, and the parameters for the Arrhenius equation listed in Table 1 were used. The vertical dotted lines in the figure indicate the buoyant flow velocity, which is estimated using Eq. (6) for each balance gas condition. The constants cBC, B1, and B2 have the same values as those mentioned under Eqs. (6)–(8), respectively, for all balance gas conditions. The intersections of the dotted line and the kinetic limit correspond to the blow-off limits, which are 11% and 24% for the Ar and CO2 balance conditions, respectively. The experimental LOIs listed in Table 3 are superimposed in the plot of Fig. 4. As mentioned earlier, the constants B1 and cBC were evaluated with the N2 balance condition at a 21% oxygen level, but it was found that these constants are also valid for quantitatively estimating the LOIs under different balance conditions. The predicted LOIs are presented in Table 3 (LOI: Predicted). The predicted values agree well with the measured LOIs even for diluents gases other than N2. The developed model for the blow-off limit is a simplified one, but it can accurately predict the effect of a change in thermal properties. The intersection of the kinetic and radiative limits implies the condition of the MLOC for a PMMA sheet under each balance condition. The predicted MLOCs are 11%, 8%, and 12% for N2, Ar, and CO2 balances, respectively, which are listed in Table 3 (MLOC: Predicted). These values are lower than the corresponding LOIs, but the difference between the LOI and MLOC, DO2, is different for the three diluent gases (see Table 3, DO2: Predicted). Under each condition, there exists a region on the flammability map where the flame can survive even below the LOI. From among all the gas balance conditions, the LOI is lowest under the Ar balance condition, and the risk of a fire hazard is most severe for this diluent gas. However, the DO2 value for this gas is only 4%, which is the smallest among all three diluent gases, and the information obtained in these ground tests is relatively reliable. However, the DO2 value for the CO2 balance is 12%; this value is so large that the flammability data obtained in the ground tests are not sufficiently reliable. The difference in the values of DO2 among the diluent gases was attributed to the difference in their properties, but a similar difference could be caused by differences in the properties of the solid material, such as DHr, A, and E.
S. Takahashi et al. / Proceedings of the Combustion Institute 35 (2015) 2535–2543
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Fig. 4. Flammability map of a thin PMMA sheet with the kinetic limit and radiative limit predicted by Eqs. (7) and (8), respectively: (a) in N2 balance, (b) in Ar balance, and (c) in CO2 balance. The kinetic limit corresponds to Da = 1, and the radiative limit corresponds to Rrad = 1. In all flammability maps, identical constants, B1, B2, and CBC were used. The symbol “G.C.” refers to the ground condition, which corresponds to Vg = VBC in Eq. (6) and an oxygen concentration of 21%.
21
3.3. Flammability test below LOI
20
2.09
1.70 1.62
19
Oxygen level (%)
Figure 5 shows the flammability map with the N2 balance as obtained from the parabolic flight experiments. The data obtained in the downward spread tests are superimposed on the flammability map by assuming that the buoyant flow velocity is 35 cm/s. The preheat zone length observed by the IR camera is inversely proportional to the opposed-flow velocity (not shown in the figure); this trend is consistent with the prediction of the scale analysis. We observed the flame spread below the LOI, and the MLOC in the experiments was 14.7%, which was 2.3% lower than the LOI. The measured MLOC was 14.7%, whereas that predicted by the model was 11%. Therefore, the simplified model underestimated the flammability limit. This is because the model takes into account either the radiation effect or the kinetic effect. In reality, near the flammability limit, both these effects suppress the flame spread. Therefore, the actual curve of the flammability limit is U-shaped (shown in Fig. 5. by the dotted line), and not V-shaped as predicted. However, the predicted MLOC can be considered “conservative,” and the sharp bottom of the model illustrates the MLOC as well as the critical opposed-flow velocity Vcr. Figure 6 shows the spread rate calculated by the values mentioned beside the symbols in Fig. 5. by using an interpolation method. The curve of the spread rate versus the opposed flow velocity has a peak near Vg10 cm/s, which is consistent with the observations in our previous work [31] and other previous works [6,7]. In particular, it is found that at the 16% oxygen level, steady spread can be observed only under the microgravity condition or a reduced gravity
1.10
1.00
18
0.49
LOI
17
1.15
0.26
0.81 0.67
16
0.50 0.45
15
0.38
0.79 0.78 0.80 0.63 0.50
1.19
0.83 0.83 0.63
14 13 12
Flammable Extinct
MLOC
11 2
4
6
8 10
20
40
Opposed flow velocity, Vg (cm/sec) Fig. 5. Flame spread rates obtained by parabolic flight experiments under N2 balance condition. The open symbols indicate the results of downward spread tests. The numbers beside the symbols are the spread rates in mm/s.
condition. It is difficult to identify the opposedflow velocity at which the flame is strongest from just the flammability map, but this velocity is obvious from Fig. 6. The peak velocity should correspond to Vcr. The measured Vcr was close to 10 cm/s, which is comparable to the predicted Vcr of 6 cm/s. When the opposed flow velocity was 2 cm/s, we could not observe the flame spread in the N2 balance. The parabolic flight had a G-jitter [27,28] of 102 g (0.51 Hz), and consequently, a mild flow of around 3 cm/s was expected. Therefore, the data obtained with the
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Flame spread rate (mm/s)
2
1.5
28
O2: 18% O2: 17% O2: 16%
26
Oxygen level (%)
2542
1
1.44 1.88 1.42
LOI
24
1.17
1.13
1.06
22
1.17 1.13 0.80
0.97
0.65
0.75 0.46
0.48
20
0.35
0.56 0.48
0.46
0.31
18 16
0.5
Flammable Extinct
14 MLOC
12
0
0.96 0.88
10
20
30
1
40
Opposed flow velocity (cm/s)
opposed flow of 2 cm/s may include some error; however, the drastic weakening of the flame at a low opposed-flow velocity was the characteristic behavior of the flame in the N2 balance, which was quite different from that in the CO2 balance, as explained later. Then, we drew the flammability map in the CO2 balance, as shown in Fig. 7. The measured and predicted LOIs in the CO2 balance were 24.3% and 25%, as shown in Figs. 4 and 6, respectively. It was found that the flammable condition expanded further below the LOI, which was consistent with the results shown in Fig. 4c. The MLOC was 19.2%, which was 5.1% lower than the LOI (see Table 3, DO2: Measured). The actual DO2 value was smaller than the predicted value of 12%, for the same reason as that mentioned earlier in the discussion of Fig. 5. However, the trend of the DO2 value in the CO2 balance being much larger than that in the N2 balance agreed with the prediction. It is interesting that the flame survived in a slow opposed flow of 2 cm/s, but the flame was unable to spread in this same flow in the N2 balance. The fact that the flame survived much below the LOI with very slow opposed flow in the CO2 balance is attributed to the lower Rrad resulting from the reabsorption effect of CO2, as has also been pointed out by the other researchers. [29–31] As shown in Fig. 4c, Vcr in this case was predicted at Vg = 1.4 cm/s, which was much lower than the Vcr value in the N2 balance (6 cm/s). Fig. 8. shows the flame spread rate in the CO2 balance obtained in the same manner as the data plotted in Fig. 6. When the oxygen level was close to the MLOC, the opposed-flow velocity at which the spread rate showed a peak shifted from 10 cm/ s to 2 cm/s. Even under a quiescent condition, the
4
6 8 10
20
40
Fig. 7. Flame spread rates obtained by parabolic flight experiments under CO2 balance condition. The open symbols indicate the results of downward spread tests. The numbers beside the symbols are the spread rates in mm/s.
flame spread could be observed in the CO2 balance. However, as mentioned earlier, the G-jitter could have caused mild flow around the flame. Therefore, the obtained result was rather qualitative, but the observed trend that the flame could survive in a low opposed flow was consistent with the prediction. According to Eq. (6), a buoyant flow of 1.43.0 cm/s corresponds to G-level of 104–103 g. Therefore, this means, for example, that the PMMA in a CO2 balance is more hazardous at a much lower gravity level, as is the case in the ISS. The predicted DO2 and Vcr correspond to
2
Flame spread rate (mm/s)
Fig. 6. Flame spread rates under N2 balance condition as estimated from the data in Fig. 5. by the interpolation method.
2
Opposed flow velocity, Vg (cm/sec)
1.5
O2: 24% O2: 22% O2: 20%
1
0.5
0
10
20
30
Opposed flow velocity (cm/s) Fig. 8. Flame spread rates under CO2 balance condition as estimated from the data in Fig. 7. by the interpolation method.
S. Takahashi et al. / Proceedings of the Combustion Institute 35 (2015) 2535–2543
the behavior of the flame for each the N2 and CO2 balances in a microgravity environment. These trends can be predicted by the simplified model, and the results are helpful in judging the risk involved in applying the data obtained in ground tests to the evaluation of the flammability of a material in space. In this paper, we discussed the effect of diluent-gas properties on the developed model. As future work, we will validate the model with different materials, and accordingly discuss the effects of various solid properties on the model. 4. Conclusions By introducing nondimensional factors, Da and Rrad, we developed a simplified model for the spread of an opposed-flow flame in order to predict the kinetic and radiative limits for the flammability of a thermally thin material. Empirical constants were obtained via downward spread tests in normal gravity and via extinction tests near a quiescent condition in microgravity. The expression of the kinetic limit successfully predicted the blowoff condition irrespective of the balance gas used (N2, Ar, or CO2). Using the kinetic limit and radiative limit, we could successfully estimate the margin between the LOI and the MLOC, which is a measure of the risk involved in applying ground data to the evaluation of fire safety of a material in space. The developed model underestimated the MLOC owing to the lack of a coupling effect between the radiation and the kinetics, but the predicted flammability map under the LOI was found to well describe the behavior of the flame spread with a slow or mild opposed flow. Additionally, the developed model can predict the critical flow velocity at which the flame spread becomes most intensive. The model can also be used to determine the most hazardous gravity level for the material under consideration.
Acknowledgments This study was conducted as part of the SOLID COMBUSTION project and FLARE project supported by JAXA and the working group supported by the Japan Space Forum. We are thankful to the staff of DAS for their excellent technical support.
References [1] H. Shih, J.S. Tien, Proc. Combust. Inst. 28 (2000) 2777–2784. [2] K. Prasad, Y. Nakamura, S.L. Olson, et al., Proc. Combust. Inst. 29 (2002) 2553–2560.
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[3] T. Kashiwagi, K.B. McGrattan, S.L. Olson, et al., Proc. Combust. Inst. 26 (1996) 1345–1352. [4] S.L. Olson, P.V. Ferkul, J.S. T’ien, Proc. Combust. Inst. 22 (1989) 1213–1222. [5] S.L. Olson, F.J. Miller, Proc. Combust. Inst. 32 (2009) 2445–2452. [6] S.L. Olson, T. Kashiwagi, O. Fujita, M. Kikuchi, K. Ito, Combust. Flame 125 (2001) 852–864. [7] A. Kumar, H.Y. Shih, J.S. T’ien, Combust. Flame 132 (2003) 667–677. [8] K.R. Sacksteder, J.S. Tien, Proc. Combust. Inst. 25 (1994) 1685–1692. [9] S.L. Olson and P.V. Ferkul, “Evaluating Materials Flammability in Microgravity and Martian Gravity Compared to NASA’s Normal Gravity Materials Flammability Testing”, 42st International Conference on Environmental Systems (ICES), 15–19 July 2012, San Diego, CA. [10] C. Jiang, J.S. T’ien, H. Shih, Proc. Combust. Inst. 26 (1996) 1353–1360. [11] J.N. de Ris, Proc. Combust. Inst. 12 (1969) 241–255. [12] S. Rybanin, Proc. Combust. Inst. 27 (1998) 2791– 2796. [13] L.K. Honda, P.D. Ronney, Proc. Combust. Inst. 28 (2000) 2793–2801. [14] I.T. Leventon, S.I. Stoliarov, Proc. Combust. Inst. 34 (2013) 2523–2530. [15] Y. Kudo, A. Ito, Proc. Combust. Inst. 29 (2002) 237–243. [16] S. Bhattachrjee, J. West, R.A. Altenkirch, Proc. Combust. Inst. 26 (1996) 1477–1485. [17] S. Bhattacharjee, R. Ayala, K. Wakai, S. Takahashi, Proc. Combust. Inst. 30 (2005) 2279–2286. [18] A.C. Fernandez-Pello, S.R. Ray, I. Glassman, Proc. Combust. Inst. 18 (1981) 579–589. [19] S. Rybanin, Proc. Combust. Inst. 26 (1996) 1487– 1493. [20] S. Takahashi, S. Bhattacharjee, T. Ihara, K. Wakai, J. Japan Soc. Microgravity Appl. 24 (3) (2007) 225– 230. [21] F. Jiang, J.L. de Ris, H. Qi, M.M. Khan, Proc. Combust. Inst. 33 (2011) 2657–2664. [22] A.F. Osorio, C. Fernandez-Pello, D.L. Urban, G.A. Ruff, Proc. Combust. Inst. 34 (2013) 2691– 2697. [23] P.V. Ferkul, J. Kleinhenz, H. Shih, R. Pettegrew, K. Sacksteder, J. T’ien, Microgr, Sci. Technol. XV/2 (2004) 3–12. [24] D.W. Schroll, Flammability and Sensitivity of Materials in Oxygen Enriched Atmospheres, ASTM 3 (1988) 252. [25] S. Bhattacharjee, M.D. King, S. Takahashi, T. Nagumo, K. Wakai, Proc. Combust. Inst. 28 (2000) 2891–2897. [26] S. Takahashi, T. Nagata, M. Hotta, S. Bhattacharjee, T. Ihara, K. Wakai, JSASS Space Technology Japan, 10/ists28, 2012, Ph_9–Ph_13. [27] C. Kumar, A. Kumar, Proc. Combust. Inst. 34 (2013) 2675–2682. [28] S. Rouvreau, P. Cordeiro, J.L. Torero, P. Joulain, Proc. Combust. Inst. 30 (2005) 519–526. [29] Y. Son, G. Zouein, P.D. Ronney, S. Gokoglu, J. ASTM Int. 3 (2006). [30] Y. Son, P.D. Ronney, Proc. Combust. Inst. 29 (2002) 2587–2594. [31] O. Fujita, M. Kikuchi, K. Ito, K. Nishizawa, Proc. Combust. Inst. 28 (2000) 2905–2911.
Proceedings
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Proceedings of the Combustion Institute 35 (2015) 2535–2543
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Simplified model for predicting difference between flammability limits of a thin material in normal gravity and microgravity environments Shuhei Takahashi a,⇑, Tomoya Ebisawa a, Subrata Bhattacharjee b, Tadayoshi Ihara a b
a Department of Mechanical Engineering, Gifu University, Japan Department of Mechanical Engineering, San Diego State University, United States
Available online 28 July 2014
Abstract Most flammability tests for a material to be used for manned spacecraft are conducted on the ground, although several studies have reported that the flammability limit in microgravity is different from that in normal gravity. Hence, an important task is to predict the margin between the limiting oxygen concentrations (LOCs) in normal gravity and microgravity. We set up a simplified scale model to describe the opposed-flow flame spread over a thin material and derived expressions for the Damko¨hler number (Da) and the nondimensional radiative loss factor (Rrad) for the flame spread over a thermally thin poly methyl methacrylate (PMMA) sheet. The empirical constants for these nondimensional numbers were evaluated by fitting with the experimental results in a N2 balance. The obtained model was validated under varying gas-phase properties. First, we obtained the experimental blow-off limits via downward spread tests in normal gravity with different balance gases (N2, Ar, and CO2). We compared the predicted blow-off limits, which corresponded to the limiting oxygen index (LOI) condition, with the experimental results for each balance condition and found that the predicted limits agreed well quantitatively with the experimental results. Then, using Da and Rrad, we drew a flammability map for opposed-flow flame spread over a thin PMMA sheet, which predicted the flammable conditions under the LOI. The developed simplified model predicted the minimum LOCs (MLOCs) and the critical opposed-flow velocity for the N2, Ar, and CO2 balance conditions. The model underestimated the MLOCs because it considered the effect of either the radiation or the kinetics, whereas both these effects are actually coupled near the MLOC. Nevertheless, the predicted margin between the MLOC and the LOI illustrated the behavior of the flame spread near extinction. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Flame spread; Extinction; Scale analysis; Microgravity
⇑ Corresponding author. Address: 1-1 Yanagido, Gifu-
shi, Gifu 501 1193, Japan. E-mail address: [email protected] (S. Takahashi).
1. Introduction Recently, human activity in space has increased and the duration of stay in spacecraft
http://dx.doi.org/10.1016/j.proci.2014.07.017 1540-7489/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
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Nomenclature A aabs B1 B2 cBC cg cs Da E Lgx Lgy Lsx Lsy Rrad Tf Tv T1
pre-exponential factor absorption coefficient of gas empirical constant for Da empirical constant for Rrad empirical constant for buoyant flow velocity specific heat of gas specific heat of solid damko¨hler number activation energy gas-phase diffusion length scale in xdirection gas-phase diffusion length scale in ydirection length of preheated solid phase thickness of preheated layer radiation loss factor adiabatic flame temperature vaporization temperature ambient temperature
such as the International Space Station (ISS) is becoming increasingly longer. Then, the reduction of fire risk in a microgravity environment and performing convenient flammability tests for materials used in space have become important research issues. Extensive studies have been conducted on flame spread over a thermally thin material with opposed flow under microgravity conditions [1–10]. One of the most characteristic features of a microgravity environment is the absence of buoyant flow, which is essential in normal gravity. Therefore, most of these previous studies were focused on flame behavior with a mild or slow flow whose velocity was smaller than that of the buoyant flow. Many studies conducted in the Space Shuttle and drop towers reported that flame spread with a slow ambient flow was suppressed by radiative heat loss, which eventually caused radiative extinction under a quiescent condition [4-6]. Thus, flame spread in microgravity may be considered as being on the “safe side.” Olson et al. [6] investigated the flame spread in microgravity under varying ambient flow velocity and reported that the spread rate achieved the maximum peak with an ambient flow velocity of 6 cm/s. Kumar et al. [7] also conducted numerical simulations and demonstrated that the minimum oxygen concentration required for a thin material to burn became lowest when the flow velocity was about 5 cm/s. Similar results have been reported by other researchers, and it is common knowledge that the curve of the limiting oxygen concentration (LOC) versus the opposed-flow velocity is U-shaped [8]. This trend implies that the flammability limit of a thin material is lower
Vg Vf Vf,th Vr Vcr W ag e kg ks g qg qs s
opposed-flow velocity flame spread rate flame spread rate in thermal regime velocity relative to flame, Vr = Vg + Vf critical opposed-flow velocity width of fuel in z-direction thermal diffusivity of gas, evaluated at Tv surface emissivity gas-phase conductivity evaluated at Tv solid-phase conductivity nondimensional spread rate gas density evaluated at Tv solid density fuel half-thickness
in microgravity than in normal gravity. Despite this fact, however, many flammability tests have been conducted in normal gravity, such as NASA STD-6001 or ASTM D2863. The obtained results are extremely vast, but using the collected data to estimate the flammability in microgravity requires careful consideration, because the minimum oxygen concentration in microgravity may be much lower than that in normal gravity. Olson et al. [9] reported that the upward LOI (ULOI) and the maximum oxygen concentration (MOC) varied depending on the gravity level and the kind of material used. Consequently, in order to confirm the fire safety at different gravity levels, including microgravity, additional flammability tests should be conducted under the corresponding gravity conditions or detailed numerical simulations should be performed; however, both these approaches are time consuming and expensive. Hence, the objective of the present study was to develop a simple model that can predict the difference between the flammability limits of thin materials in normal gravity and microgravity environments. To this end, we defined the minimum limiting oxygen concentration (MLOC) as the oxygen concentration at which the flame cannot exist with any opposedflow velocity. We also defined the critical opposed velocity Vcr at which the MLOC is observed. We derived two nondimensional variables, including an experimental constant, and predicted the MLOC and Vcr in microgravity as well as the LOI in normal gravity. In order to validate the developed model, we first investigated the effect of diluent-gas properties on the flammability map; to this end, we conducted flame spread
S. Takahashi et al. / Proceedings of the Combustion Institute 35 (2015) 2535–2543
experiments over a thin polymethyl methacrylate (PMMA) film under normal and microgravity conditions with various kinds of diluent gases in ambient flow. We then compared the results predicted by the model with the experimental results and discussed the effect of the difference in the properties of diluent gases on the developed model. 1.1. Scale modeling The flame spread rate over a thermally thin material with moderate opposed flow, which is comparable to buoyant flow, has been formulated by de Ris [11], and its validity has been confirmed both experimentally and numerically by numerous researchers [12–15]. Bhattacharjee et al. [16,17] also derived the expression for flame spread over a thin material with an opposed flow by establishing scale modeling on a two-dimensional (2D) flame, as shown in Fig. 1. The length of the preheat zone in the gas phase, Lgx, is proportional to ag/Vr, where ag is the thermal diffusivity of the ambient gas and Vr is the relative opposedflow velocity, which is expressed as Vr = Vg + Vf. Other lengths, i.e., Lgy, Lsx, and Lsy, for a thin material are also expressed as follows:
V f qs cs LsyW ðT v T 1 Þ þ Qrad kg
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ðT f T v Þ Lgx W ; Lgy ð3Þ
aabs ÞrðT 4v
T 41 ÞLsx W
where Qrad ¼ eð1 . Upon introducing the nondimensional spread rate g, which is defined as g = Vf/Vf,th, Eq. (1) is reduced to the following nondimensional equation [28]: g þ Rrad ¼ 1; where Rrad
ð1 aabs ÞrðT 4v T 41 Þ qg cg V r ðT f T v Þ
ð4Þ
If the heat conduction through the preheat zone in the gas phase is balanced with the heat supplied to the preheat zone in the solid phase, which is defined as a thermal regime, the following equation holds: ðT f T v Þ V f ;th qs cs Lsy W ðT v T 1 Þ kg Lgx W ð1Þ Lgy
Rrad is a nondimensional radiative loss factor. In this study, we assume that the only factor that causes extinction near the quiescent condition is surface radiation. This is a crude assumption but it can simplify the model, although there are several coupling factors for the extinction phenomenon, such as gas/soot radiation fed back from the flame. Equation (4) implies that if Rrad approaches unity, g approaches zero; thus, radiative extinction occurs. It is found that Rrad becomes larger as the relative opposed-flow Vr becomes smaller. Therefore, if the opposed-flow velocity Vg is small enough such that Rrad 1, the regime changes to the microgravity regime. On the other hand, if the opposed-flow velocity Vg is much higher, blow-off occurs. When Vg is large, the residence time in the gas-phase preheat zone becomes comparable to the chemical reaction time. We define the residence time treg and the chemical reaction time tchem as follows:
Solving Eq. (1) gives the flame spread rate in the thermal regime, Vf,th, as
tres ¼ Lgx =V r ; tchem mF =xF L2g W
Lsx Lgx Lgy ag =V r and Lsy ¼ s:
V f ;th
kg T f T v ; qs cs ss T v T 1
ð2Þ
which is almost identical to the equation derived by de Ris, except for the constant. If the radiative heat loss from the solid preheat zone to the surroundings is considered, the radiative term, Qrad, is added to Eq. (1), as follows:
¼ ½qg Y O A expðE=RT f Þ1 ; where xF is the reaction rate, expressed as xF ¼ ðqg Y F Þðqg Y O ÞA expðE=RT f Þ; and mF is the mass of fuel in the gas-phase preheat zone, expressed as mF ¼ qg Y F L2g W . Then, we obtain the Damko¨hler number Da [18,19] as
Fig. 1. Schematic of two-dimensional flame used for scale analysis.
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Da
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tres ag q Y o A expðE=RT f Þ tchem V 2r g
ð5Þ
If Da is close to unity, the regime is thought to change to the kinetic regime. Using the two nondimensional factors Rrad and Da, we can draw the flammability map for a thin material as described later.
Table 1 Properties of PMMA for scale analysis. PMMA Density, qs (kg/m3) Specific heat, cs (kJ/kg K) Vaporization temperature, Tv (K) Enthalpy of reaction, DHr (kJ/kg) Surface emissivity, e Pre-exponential factor, A (m3/kg s) Activation energy, E (J/mol)
2. Experimental setup In ASTM D2863, the downward spread experiments are conducted to obtain the LOI. Hence, we first measured the downward spread rate and the LOC at which the flame could spread over a thin solid material. The sample used in this experiment was a thermally thin PMMA sheet (Acryplen: Mitsubishi Rayon Co., Ltd.) with a thickness of 0.125 mm. The PMMA sample, which was 8 cm in length and 2 cm in width, was set vertically in a closed chamber of volume 35 L, as shown in Fig. 2. The sample was ignited at the top with an electrically heated Ni-Cr wire. The pressure and temperature in the chamber were kept at 101 kPa and room temperature, respectively. The flame spread behavior was recorded with a visible CCD camera and an IR camera to obtain the spread rate and the length of the preheat zone on the PMMA sheet, respectively. The experiments were conducted by decreasing the initial oxygen concentration, and the oxygen concentration at which the flame could not spread after the ignition was measured. In this study, the measured oxygen concentration was defined as the LOI. The downward spread tests were conducted by changing the diluent of the ambient gas—to N2, CO2, and Ar—in order to confirm whether the developed model could predict the difference in the LOIs among these gases. The properties of the PMMA and diluents are presented in Table 1 and Table 2, respectively.
1190 1.465 670 25900 1.0 1.36 109 1.50 105
As indicated in Table 2, we set the aabs value of CO2 as 0.8 on the basis of our previous work [20], by fitting the experimental results to the model. As mentioned in the previous section, this value includes not only the effect of reabsorption but also the heat fed back by gas radiation from the flame to the preheat zone [21,22]. In order to obtain the LOC in a microgravity environment, we then conducted 20-s parabolic flight experiments by availing the Diamond Air Service (DAS). Figure 2 shows the schematic of the test chamber used for these flight experiments. This test chamber was also 35 L in volume, in which a rolled PMMA sheet was placed, which is similar to the setup in the work of Ferkul et al. [23]. The chamber had a suction fan for creating a flow ranging from 0 to 20 cm/s in the test section. The dimensions of the test section were 14 cm 14 cm 13 cm, and honeycomb plates were installed on both the upstream side and the downstream side of the test section. The PMMA sheet in the test section was 8 cm in length and 2 cm in width. The downstream end of the sample was ignited by the Ni–Cr wire 10 s before the onset of microgravity, and the flame that spread upstream was recorded with a CCD camera and IR camera to capture the flame behavior and the preheat zone on the sample, respectively. Under the conditions in which the initial oxygen concentration was lower than the LOI, we could not
Fig. 2. Schematic of experimental apparatus for parabolic flight experiments.
S. Takahashi et al. / Proceedings of the Combustion Institute 35 (2015) 2535–2543
N2 Ar CO2
Cp [J/mol K]
kg [W/m K]
ag [mm2/s]
aabs
30.47 20.78 48.94
0.0444 0.0312 0.0396
80.1 82.7 44.5
0.0 0.0 0.8
ignite the sample before the onset of microgravity. Hence, under such conditions, we ignited the sample at the onset of microgravity. When the sample was ignited right at the onset of microgravity, the time remained for flame spread was 10 s because the ignition procedure took about 10 s. If the flame survived until the end of the microgravity environment, we judged it as being flammable; else, we judged it as being extinct. Then, we defined the MLOC as the minimum LOC at which the flame survived. The spread rate Vf was defined as the average spread rate in 5 s. The flame near the extinction limit was blue and faint. Therefore, it might become extinct if the microgravity duration was longer, but the obtained extinction limit was considered as conservative. Molecular sieves and zeolites were packed inside the test chamber to absorb the water and carbon dioxide generated during the combustion process. A pressure transducer, a thermocouple, and an oxygen sensor were also installed to monitor the pressure, temperature, and oxygen concentration, respectively. We wound the rolled sheet to feed a new sample area after the completion of combustion. After the complete combustion of the 8-cm-long PMMA sheet, the oxygen concentration in the chamber decreased by 0.8%, but the actual decreased concentration of oxygen depended on the consumed length of the sample in the experiment. After filling an oxygen/nitrogen mixture in the chamber, we repeated the combustion test without adding consumed oxygen, and so, the oxygen concentration in the chamber decreased gradually during the experiment. We conducted four flight experiments for a N2 balance condition, and the initial oxygen concentrations in these four experiments were 20%, 19%, 17%, and 15%. The initial pressure was 101 kPa; it decreased to 97 kPa after a series of parabolic flight experiments. For the CO2 balance condition, we replaced the molecular sieves with glass beads and conducted two flight experiments in which the initial oxygen concentrations were set as 25.5% and 20%, respectively.
measured, as shown in Fig. 3. At higher oxygen concentrations, the spread rates in the N2 balance and Ar balance were almost the same; that in the N2 balance was slightly higher. As shown in Table 2, the flame temperature in the Ar balance is expected to be higher than that in the N2 balance, but the heat conductivity of N2 is larger than that of Ar. Therefore, the effect of Tf depending on cg canceled the effect of kg in Eq. (2). The spread rate in the CO2 balance was lowest owing to a large cg and small ag, which were the advantageous features of CO2 as an extinguishing agent. The oxygen concentration at which extinction occurred was lowest when Ar was used as the balance gas, owing to its small cg. In contrast, the oxygen concentration at which extinction occurred was highest when CO2 was used as the balance gas. Upon conducting more detailed downward spread tests near the extinction limit, we obtained the LOIs for each balance gas, which are presented in Table 3 (LOI: Measured). The obtained results are well-known facts and are consistent with the results of a large number of conducted ground flammability tests [24]. 3.2. Flammability maps by scale modeling In order to draw the flammability map by using the nondimensional factors in Eqs. (4) and (5), we first attempted to determine the empirical constants for Da and Rrad to make them quantitative variables. In downward spread tests, extinction was observed when the oxygen concentration was 17.2%. This extinction is thought to be caused by a kinetic limit; therefore, the Damko¨hler number,
7
Flame spread rate (mm/sec)
Table 2 Properties of balance gases at Tv = 670 K and 1 atm.
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6
N2 Ar CO2
5 4 3 2 1 0 10 12 14 16 18 20 22 24 26 28 30
3. Results and discussion 3.1. Downward spread in normal gravity First, the downward spread rates in normal gravity under varying ambient oxygen concentrations for N2, CO2, and Ar balances were
Oxygen level (%) Fig. 3. Downward flame spread rates in normal gravity under varying oxygen concentrations in N2, Ar, and CO2 balances. The oxygen concentration at which extinction occurs corresponds to the limiting oxygen index (LOI).
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Table 3 Limiting oxygen index (LOI) in downward spread and minimum limiting oxygen concentration (MLOC) in microgravity for each balance gas. Balance gas
N2
Ar
CO2
LOI
17% 17.0% 11% 14.7% 6% 2.3% 6 cm/s 10 cm/s
11% 12.9% 8% N/A 3% N/A 8 cm/s N/A
24% 24.3% 12% 19.2% 12% 5.1% 1.4 cm/s 2 cm/s
MLOC DO2 Vcr
Predicted Measured Predicted Measured Predicted Measured Predicted Measured
expressed in Eq. (5), should be unity under this condition. In our previous scale analysis [25], the buoyant flow velocity VBC was estimated as 1=3 ag gðT v T 1 Þ V BC ¼ cBC ; ð6Þ T1 where {cBC}= 5.32. The constant cBC was determined by assuming that VBC, which corresponded to Vg in the model, was 35 cm/s for the N2 balance condition, which is a typical value observed in practice. By using the properties of PMMA listed in Table 1 and by calculating the adiabatic temperature under the considered condition, Tf, we derived an empirical constant, B1, for Da: ag Da ¼ B1 2 qg Y O A expðE=RT f Þ; ð7Þ Vr where B1 = 0.131. The thermodynamic properties in the gas phase were estimated at Tv by using the Chapman–Enskog theory; Yo is the value of the ambient gas in the chamber. The thermodynamic properties in the reaction zone can be varied by Tf. which is a function of Yo, but ag qg kg =cg has a relatively temperature dependence pffiffiffiffiffismall ffi because kg T f and cg increases with increasing Tf. Hence, for simplicity, we used Eq. (7) to discuss the blow-off limit. Then, we derived the empirical constant for Rrad. From our previous experiments with a drop tower, we had found that when the opposed-flow velocity was 3 cm/s or less, radiative extinction occurred at an oxygen level of 21% for a PMMA sample that was almost identical to that used in the present study, the only difference being its width of 1 cm [20,26]. Therefore, in our model, the radiative loss factor Rrad should be unity under this condition, i.e., Vg = 3 cm/s. We similarly obtained the empirical constant B2 for Rrad: Rrad ¼ B2
eð1 aabs ÞrðT 4m T 41 Þ ; qg cg V r ðT f T m Þ
where B2 = 2.67.
ð8Þ
Using the obtained empirical constants B1 and B2 and the properties listed in Table 2, we calculated the condition of the opposed-flow velocity and the oxygen concentration at which Rrad = 1 or Da = 1 is achieved. The kinetic and radiative limits predicted using the constants in Eqs. (7) and (8), respectively, are shown in Fig. 4. for N2, Ar, and CO2 balances. The properties of the balance gases were estimated at Tv, and the parameters for the Arrhenius equation listed in Table 1 were used. The vertical dotted lines in the figure indicate the buoyant flow velocity, which is estimated using Eq. (6) for each balance gas condition. The constants cBC, B1, and B2 have the same values as those mentioned under Eqs. (6)–(8), respectively, for all balance gas conditions. The intersections of the dotted line and the kinetic limit correspond to the blow-off limits, which are 11% and 24% for the Ar and CO2 balance conditions, respectively. The experimental LOIs listed in Table 3 are superimposed in the plot of Fig. 4. As mentioned earlier, the constants B1 and cBC were evaluated with the N2 balance condition at a 21% oxygen level, but it was found that these constants are also valid for quantitatively estimating the LOIs under different balance conditions. The predicted LOIs are presented in Table 3 (LOI: Predicted). The predicted values agree well with the measured LOIs even for diluents gases other than N2. The developed model for the blow-off limit is a simplified one, but it can accurately predict the effect of a change in thermal properties. The intersection of the kinetic and radiative limits implies the condition of the MLOC for a PMMA sheet under each balance condition. The predicted MLOCs are 11%, 8%, and 12% for N2, Ar, and CO2 balances, respectively, which are listed in Table 3 (MLOC: Predicted). These values are lower than the corresponding LOIs, but the difference between the LOI and MLOC, DO2, is different for the three diluent gases (see Table 3, DO2: Predicted). Under each condition, there exists a region on the flammability map where the flame can survive even below the LOI. From among all the gas balance conditions, the LOI is lowest under the Ar balance condition, and the risk of a fire hazard is most severe for this diluent gas. However, the DO2 value for this gas is only 4%, which is the smallest among all three diluent gases, and the information obtained in these ground tests is relatively reliable. However, the DO2 value for the CO2 balance is 12%; this value is so large that the flammability data obtained in the ground tests are not sufficiently reliable. The difference in the values of DO2 among the diluent gases was attributed to the difference in their properties, but a similar difference could be caused by differences in the properties of the solid material, such as DHr, A, and E.
S. Takahashi et al. / Proceedings of the Combustion Institute 35 (2015) 2535–2543
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Fig. 4. Flammability map of a thin PMMA sheet with the kinetic limit and radiative limit predicted by Eqs. (7) and (8), respectively: (a) in N2 balance, (b) in Ar balance, and (c) in CO2 balance. The kinetic limit corresponds to Da = 1, and the radiative limit corresponds to Rrad = 1. In all flammability maps, identical constants, B1, B2, and CBC were used. The symbol “G.C.” refers to the ground condition, which corresponds to Vg = VBC in Eq. (6) and an oxygen concentration of 21%.
21
3.3. Flammability test below LOI
20
2.09
1.70 1.62
19
Oxygen level (%)
Figure 5 shows the flammability map with the N2 balance as obtained from the parabolic flight experiments. The data obtained in the downward spread tests are superimposed on the flammability map by assuming that the buoyant flow velocity is 35 cm/s. The preheat zone length observed by the IR camera is inversely proportional to the opposed-flow velocity (not shown in the figure); this trend is consistent with the prediction of the scale analysis. We observed the flame spread below the LOI, and the MLOC in the experiments was 14.7%, which was 2.3% lower than the LOI. The measured MLOC was 14.7%, whereas that predicted by the model was 11%. Therefore, the simplified model underestimated the flammability limit. This is because the model takes into account either the radiation effect or the kinetic effect. In reality, near the flammability limit, both these effects suppress the flame spread. Therefore, the actual curve of the flammability limit is U-shaped (shown in Fig. 5. by the dotted line), and not V-shaped as predicted. However, the predicted MLOC can be considered “conservative,” and the sharp bottom of the model illustrates the MLOC as well as the critical opposed-flow velocity Vcr. Figure 6 shows the spread rate calculated by the values mentioned beside the symbols in Fig. 5. by using an interpolation method. The curve of the spread rate versus the opposed flow velocity has a peak near Vg10 cm/s, which is consistent with the observations in our previous work [31] and other previous works [6,7]. In particular, it is found that at the 16% oxygen level, steady spread can be observed only under the microgravity condition or a reduced gravity
1.10
1.00
18
0.49
LOI
17
1.15
0.26
0.81 0.67
16
0.50 0.45
15
0.38
0.79 0.78 0.80 0.63 0.50
1.19
0.83 0.83 0.63
14 13 12
Flammable Extinct
MLOC
11 2
4
6
8 10
20
40
Opposed flow velocity, Vg (cm/sec) Fig. 5. Flame spread rates obtained by parabolic flight experiments under N2 balance condition. The open symbols indicate the results of downward spread tests. The numbers beside the symbols are the spread rates in mm/s.
condition. It is difficult to identify the opposedflow velocity at which the flame is strongest from just the flammability map, but this velocity is obvious from Fig. 6. The peak velocity should correspond to Vcr. The measured Vcr was close to 10 cm/s, which is comparable to the predicted Vcr of 6 cm/s. When the opposed flow velocity was 2 cm/s, we could not observe the flame spread in the N2 balance. The parabolic flight had a G-jitter [27,28] of 102 g (0.51 Hz), and consequently, a mild flow of around 3 cm/s was expected. Therefore, the data obtained with the
S. Takahashi et al. / Proceedings of the Combustion Institute 35 (2015) 2535–2543
Flame spread rate (mm/s)
2
1.5
28
O2: 18% O2: 17% O2: 16%
26
Oxygen level (%)
2542
1
1.44 1.88 1.42
LOI
24
1.17
1.13
1.06
22
1.17 1.13 0.80
0.97
0.65
0.75 0.46
0.48
20
0.35
0.56 0.48
0.46
0.31
18 16
0.5
Flammable Extinct
14 MLOC
12
0
0.96 0.88
10
20
30
1
40
Opposed flow velocity (cm/s)
opposed flow of 2 cm/s may include some error; however, the drastic weakening of the flame at a low opposed-flow velocity was the characteristic behavior of the flame in the N2 balance, which was quite different from that in the CO2 balance, as explained later. Then, we drew the flammability map in the CO2 balance, as shown in Fig. 7. The measured and predicted LOIs in the CO2 balance were 24.3% and 25%, as shown in Figs. 4 and 6, respectively. It was found that the flammable condition expanded further below the LOI, which was consistent with the results shown in Fig. 4c. The MLOC was 19.2%, which was 5.1% lower than the LOI (see Table 3, DO2: Measured). The actual DO2 value was smaller than the predicted value of 12%, for the same reason as that mentioned earlier in the discussion of Fig. 5. However, the trend of the DO2 value in the CO2 balance being much larger than that in the N2 balance agreed with the prediction. It is interesting that the flame survived in a slow opposed flow of 2 cm/s, but the flame was unable to spread in this same flow in the N2 balance. The fact that the flame survived much below the LOI with very slow opposed flow in the CO2 balance is attributed to the lower Rrad resulting from the reabsorption effect of CO2, as has also been pointed out by the other researchers. [29–31] As shown in Fig. 4c, Vcr in this case was predicted at Vg = 1.4 cm/s, which was much lower than the Vcr value in the N2 balance (6 cm/s). Fig. 8. shows the flame spread rate in the CO2 balance obtained in the same manner as the data plotted in Fig. 6. When the oxygen level was close to the MLOC, the opposed-flow velocity at which the spread rate showed a peak shifted from 10 cm/ s to 2 cm/s. Even under a quiescent condition, the
4
6 8 10
20
40
Fig. 7. Flame spread rates obtained by parabolic flight experiments under CO2 balance condition. The open symbols indicate the results of downward spread tests. The numbers beside the symbols are the spread rates in mm/s.
flame spread could be observed in the CO2 balance. However, as mentioned earlier, the G-jitter could have caused mild flow around the flame. Therefore, the obtained result was rather qualitative, but the observed trend that the flame could survive in a low opposed flow was consistent with the prediction. According to Eq. (6), a buoyant flow of 1.43.0 cm/s corresponds to G-level of 104–103 g. Therefore, this means, for example, that the PMMA in a CO2 balance is more hazardous at a much lower gravity level, as is the case in the ISS. The predicted DO2 and Vcr correspond to
2
Flame spread rate (mm/s)
Fig. 6. Flame spread rates under N2 balance condition as estimated from the data in Fig. 5. by the interpolation method.
2
Opposed flow velocity, Vg (cm/sec)
1.5
O2: 24% O2: 22% O2: 20%
1
0.5
0
10
20
30
Opposed flow velocity (cm/s) Fig. 8. Flame spread rates under CO2 balance condition as estimated from the data in Fig. 7. by the interpolation method.
S. Takahashi et al. / Proceedings of the Combustion Institute 35 (2015) 2535–2543
the behavior of the flame for each the N2 and CO2 balances in a microgravity environment. These trends can be predicted by the simplified model, and the results are helpful in judging the risk involved in applying the data obtained in ground tests to the evaluation of the flammability of a material in space. In this paper, we discussed the effect of diluent-gas properties on the developed model. As future work, we will validate the model with different materials, and accordingly discuss the effects of various solid properties on the model. 4. Conclusions By introducing nondimensional factors, Da and Rrad, we developed a simplified model for the spread of an opposed-flow flame in order to predict the kinetic and radiative limits for the flammability of a thermally thin material. Empirical constants were obtained via downward spread tests in normal gravity and via extinction tests near a quiescent condition in microgravity. The expression of the kinetic limit successfully predicted the blowoff condition irrespective of the balance gas used (N2, Ar, or CO2). Using the kinetic limit and radiative limit, we could successfully estimate the margin between the LOI and the MLOC, which is a measure of the risk involved in applying ground data to the evaluation of fire safety of a material in space. The developed model underestimated the MLOC owing to the lack of a coupling effect between the radiation and the kinetics, but the predicted flammability map under the LOI was found to well describe the behavior of the flame spread with a slow or mild opposed flow. Additionally, the developed model can predict the critical flow velocity at which the flame spread becomes most intensive. The model can also be used to determine the most hazardous gravity level for the material under consideration.
Acknowledgments This study was conducted as part of the SOLID COMBUSTION project and FLARE project supported by JAXA and the working group supported by the Japan Space Forum. We are thankful to the staff of DAS for their excellent technical support.
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