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Radiation attenuation characteristics of pyrolysis volatiles of solid fuels and their effect for radiant ignition model
Combustion and Flame 157 (2010) 167–175
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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Radiation attenuation characteristics of pyrolysis volatiles of solid fuels and their effect for radiant ignition model Yupeng Zhou, Lizhong Yang *, Jiakun Dai, Yafei Wang, Zhihua Deng State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, Anhui Province, China
a r t i c l e
i n f o
Article history: Received 30 March 2009 Received in revised form 21 May 2009 Accepted 15 June 2009 Available online 7 August 2009 Keywords: Radiation attenuation Incident heat flux Pyrolysis volatiles Radiation absorptivity Ignition model
a b s t r a c t Radiation attenuation characteristics of pyrolysis volatiles from heated solid fuels, a neglected physical effect in radiant ignition process, are studied by simulated experiment and mathematical models. Firstly, it is experimentally found the radiation attenuation of an incident heat flux when pine or Polymethyl Methacrylate (PMMA) is heated occurs before flaming ignition (6–14%), especially for the one in the experiment of the Cone Calorimeter style apparatus with a shorter test radiation distance (D < 100 mm). Then, a more reasonable parameter using Beer’s law for determining the radiation absorptivity of pyrolysis volatiles of different fuels is presented. It is found the radiation absorptivity of pyrolysis volatiles of PMMA is actually larger than the one of pine and the ignition of PMMA more depends on the gas-phase heating by radiation absorption. Finally, the calculated results with the experimental radiation attenuation data illustrates that consideration of the radiation attenuation by pyrolysis volatiles in radiant ignition models is necessary. A constant radiation attenuation coefficient G = 0.1 is approximately accepted for the general calculation of radiant ignition model. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Radiant heating by the fire, smoke, and heated surfaces is the primary driving force for fire growth on materials [1]. Because the radiant ignition of fuels is the first step in all fire prevention strategies and is closely connected with other important fire process, e.g. fire spread over fuels, room fire flashover, and the jump of a forest fire across a firebreak [2], it is always an interesting subject in fire research [1–11]. In the radiant ignition process, there is a gas-phase effect which has been studied by some researchers before [2,3,12–16]. The incident radiant heat flux for heating solid combustible will be selectively absorbed and attenuated by the pyrolysis volatiles in the boundary layer so that the irradiance practically available is substantially less than that without the absorbing gas. The attenuation will retard the time to full thermal decomposition of the solid fuel, and consequently delay the attainment of the sufficient amount of ignitable pyrolysis volatiles. Especially for the condition with the horizontal materials irradiated vertically, which is the most test condition in Cone Calorimeter, the incident radiant heat flux passes through a rising plume by the pyrolysis volatiles and its intensity may be significantly attenuated [12], which is confirmed by Park with a numerical simulation [14].
* Corresponding author. Fax: +86 551 3601 669. E-mail address: [email protected] (L. Yang).
Despite years of experimental and theoretical research, the neglected physical effect is still not studied adequately, and whether it is significant in real fire situations is not known [2,3,12,13]. In current radiant ignition models, the boundary condition usually only includes the radiation and convection heat loss from sample surface, see in Eq. (1) [1,10].
@T ks ¼ esur q_ 00 jsur ðT sur T 1 Þ esur rðT 4sur T 41 Þ @x x¼0
ð1Þ
In Kashiwagi’s experiment with a laser radiant heater, a very large attenuation percentage (50–80%) was observed before the ignition [13]. The calculated surface temperature result in Kashiwagi’s work presented a better agreement with the experimental one by considering a time-dependent attenuation of incident radiant heat flux. However, the wavelength of the laser radiant heater (10.6 lm) and the range of radiant heat flux (70–174 kW/m2) in Kashiwagi’s experiment are both not consistent with the ones (20–80 kW/m2) in the typical experimental condition in Cone Calorimeter with a resistance element radiant heater [12], which could not support the adequate results for the improvement of the current commonly used radiant ignition model. The attenuation of the incident radiation by pyrolysis volatiles also was considered by Nelson, but the attenuation, which is time-dependent, was set as an arbitrary constant coefficient without experimental validation [17]. There is lack of a corresponding study on the attenuation characteristics for heating under a resistance element radiant heater which is closer to real fire conditions [3,18]. Furthermore, although it is qualitatively
0010-2180/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2009.06.020
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Nomenclature A b C D E f G h k L m00 M N q_ 00 Q R s(t) T t
vg x
pre-exponential factor, s1 absorbing path length of incident heat flux, m thermal capacity at constant pressure, J/kg K radiation distance, m reaction activation energy, J/mol mass concentration of absorbing species, kg L1 constant radiation attenuation coefficient specific enthalpy, J/kg thermal conductivity, W/m K sample thickness, m mass flux of volatiles, kg/m2s normalized radiation absorption normalized transmission of incident radiant flux external heat flux, kW/m2 heat of reaction, J/kg gas constant, J/mol K distance moved by upper surface from its initial location, m temperature, K time, s vertical releasing velocity of pyrolysis volatiles, m/s distance from the initial location of the upper surface, m
known that the degree of radiation attenuation is related directly with the concentration of pyrolysis volatiles, a quantitative study on this subject is still not known. As for Kashiwagi’s experiment conclusion, it reported that the degree of radiation attenuation for pine is larger than PMMA [12]. However, if determined the radiation attenuation capability of per unit pyrolysis volatiles by coupling with the corresponding mass loss rate together, which is related directly with the yield rate of pyrolysis volatiles, the conclusion above may be different. In this paper, the radiation attenuation characteristics of two classic solid combustibles (pine and PMMA) are investigated experimentally with a resistance element radiant heater firstly. Then the quantitative relationship between the degree of radiation attenuation and the concentration of pyrolysis volatiles is obtained by coupling with the synchronous mass loss rate. The radiation absorptivity of pyrolysis volatiles of different solid fuels is discussed using Beer’s law. Finally, a radiant ignition model with different incident heat flux boundary conditions (none, constant and time-dependent radiation attenuation) is used to present a comprehensive comparison of the effect of radiation attenuation, and to investigate how to reasonably consider the effect of radiation attenuation in radiant ignition model. 2. Theory Although the detailed components of pyrolysis volatiles are still not very clear due to its complexity, several researchers have reported the primary pyrolysis volatiles components of pine and PMMA, which include CO2, CO, H2O, and relatively smaller amounts of low molecular weight alkanes and alkenes like CH4, C3H6, some aromatics like methanol, ethanol, benzene [19–22]. These primary pyrolysis volatiles components all have the specific infrared absorbing wave band within wavelength area 2.5–25 lm. For example, the peak absorption of water is around 3 lm and 6 lm, the CO2 is 4.26 lm, the CO is around 4.5 lm, CH4 is around 3.4 lm, C3H6 is around 8.3 lm, methanol is around 3 lm and 10 lm [23,24]. The infrared absorbing wave band of the primary
Greek symbols c mass radiation absorptivity, L kg1 m1 q density, kg/m3 j convection coefficient, W/m K c* mass radiation absorptivity with absolute value of radiation attenuation, kW/kg e emissivity Subscripts a attenuation ac constant coefficient radiation attenuation add added at time-dependent radiation attenuation c char e experiment g gas in incident ig ignition p pyrolyzing part s pyrolyzed area sur surface w virgin wood 1 surround 0 initial
pyrolysis volatiles components of pine and PMMA is within the emission wave band of a resistance element radiant heater (2– 15 lm) [25], which could illustrate the possibility of radiation absorption by pyrolysis volatiles in the experiment of this paper. 3. Experiment details The experimental work was conducted in an apparatus for studying the radiant ignition of fuels, as shown in Fig. 1. The radiant heater consists of silicon carbide heating elements, which tends to have a near-grey-body characteristic, and has a high emissivity (0.8–0.9) with a little variability between wavelength 2–15 lm [25]. The size of the heating area of radiant heater is 0.4 m 0.4 m. The working temperature of radiant heater ranges from 600 to 1100 °C, which is consistent with the hot gas layer temperature in typical fires [18] and hence can effectively simulate the radiant heating within the infrared wavelength range seen in fires. The top of the radiant heater has four smoke ventilation slots which could let the pyrolysis volatiles pass through it without accumulation. Two classic solid combustibles are tested: pine and PMMA. The samples sizes of pine and PMMA are 0.15 m 0.15 m 0.02 m and 0.15 m 0.15 m 0.015 m, respectively. Prior to tests, the pine sample is dried in an oven with a temperature 60 °C for 24 h. The unexposed surface and edges of each sample are wrapped in a double-layer of fiberglass fabric (20 mm thick) and aluminum foil to promote one-dimensional heat transfer. Pine is tested at radiation distance (D) both 0.1 m and 0.2 m. PMMA is just tested at radiation distance 0.1 m. The sample surface temperature is measured by 0.5 mm diameter type-K thermocouples which are mounted onto the sample surface. The auto-ignition is conducted in all the experimental conditions with the measure of radiation attenuation. In order to obtain a more comprehensive comparison of the effect of radiation attenuation in radiant ignition model, the piloted-ignition is also conducted with pine at radiation distance 0.1 m. The detailed measurement process of the attenuated radiant heat flux by pyrolysis volatiles is shown in Fig. 1. There is a
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169
Fig. 1. Schematics of the experiment apparatus and the measurement settings of the attenuated incident radiant heat flux.
0.03 m diameter hole through the center of test sample. The hole takes up only 3% of the whole area of the sample, so that its effect could be ignored. A Gardon-type water-cooled heat flux gauge (U0.025 m) with an uncertainty 2%, which is produced and calibrated by the 102nd research institute of China Aerospace Corporation, is fixed on a trestle table before the radiant heater is opened and is used to measure if the setting incident heat flux (q_ 00in ) is achieved after the radiant heater is opened and to measure the radiation (q_ 00 ðtÞ) reaches the sample surface through the plume of the pyrolysis volatiles during a test. The gauge is cooled with 65 °C water during the test to prevent condensation from forming on the gauge face, which is referred to Beaulieua’s method in a similar heat flux measurement [26]. The trestle table is settled on the firebrick board below and not contact with the sample platform which is settled on the electronic load cell (METTLER TOLEDO, made in Switzerland). When the setting incident heat flux is achieved and stays steady, the radiant heater is insulated with a fireproof shutter and then the test sample is mounted horizontally together with the heat flux gauge without contact. The heat flux gauge is also not contacted with the bottom of the sample. These configurations ensure the measurements of radiation attenuation and mass loss rate could be conducted simultaneously without the influence of water cooling circulation, which is not fulfilled in Kashiwagi’s experiment [12,13], and then to determine the radiation attenuation capability of per unit pyrolysis volatiles by coupling with the corresponding mass loss rate together. Once the checking for the uniformity of the top position of test sample and heat flux gauge is finished, the fireproof shutter is removed swiftly, leaving the sample exposed to the heat flux. Two runs are carried out for each test condition. If the runs are obviously different, a third or a fourth run is carried out. The incident radiant heat flux, the mass loss and the surface temperature are continuously recorded at intervals of 1 s. A CCD camera is used to record time to ignition. The test is terminated when the flaming ignition occurs.
4. Results and discussion 4.1. Radiation attenuation of incident radiant flux 4.1.1. Normalized transmission of incident radiant flux The normalized transmission of incident radiant flux (N), see in Eq. (2), is shown in Fig. 2. The data shown in figures is taken before the ignition occurs, as it is what this paper focuses on. The fluctuation in the curves is mainly caused by the wandering of the pyrolysis volatiles plume. The N at the moment of ignition of pine sample in D = 0.1 m is between 0.86 and 0.90, and the one of PMMA sample in D = 0.1 m is between 0.91 and 0.96, as shown in Fig. 2. Because the faster yield rate of pyrolysis volatiles at the higher incident radiant flux, the attenuation rate of N increases with the rise in the incident radiant flux.
N ¼ q_ 00 ðtÞ=q_ 00in
ð2Þ
The N of PMMA sample is smaller than that of pine at a uniform incident heat flux, as shown in Fig. 3, which is consistent with Kashiwagi’s relative result [12]. This result is because that the faster yield period of pyrolysis volatiles of PMMA is delayed by its larger thermal inertia (kqC) which is roughly twice that of pine. However, the analysis above could only be used to explain the delay of radiation attenuation of PMMA, but should not be used to draw the conclusion that the radiation absorbability of PMMA is weaker than pine, which will be further demonstrated together with the mass flux (m00 ) in the chapter followed. The N at the moment of ignition of pine sample in D = 0.2 m is 0.91–0.94, as shown in Fig. 2c, which is smaller than the one of pine sample in D = 0.1 m (0.86–0.90) at a same intensity of incident heat flux. Although the radiation attenuation layer thickness is larger for D = 0.2 m, the concentration of pyrolysis volatiles plume under the same heating condition is thinner because of more intense dilution effect, which causes the degree of radiation attenuation is relatively lower. This result indicates that the radiation attenuation effect in the apparatus with shorter radiation distance,
170
a
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1.00
1.00
2
2
57kw/m 2 43kw/m 2 32kw/m
26kw/m 2 26kw/m 2 53kw/m 2 53kw/m
0.95
N
N
0.95
53kw/m 2 37kw/m 2 26kw/m
2
PMMA Pine PMMA Pine
0.90
0.90
0.85
0.85 0
50
100
150
0
200
50
100
150
t (s)
b
250
300
Fig. 3. Comparison of radiation attenuation between pine and PMMA, D = 0.1 m.
1.00
a 0.95
6
2
2
57kw/m 2 48kw/m 2 32kw/m
53kw/m 2 37kw/m 2 26kw/m
q"a ( kw/m2)
N
5
0.90
4 3 2 1
2
57 kw/m 2 43 kw/m 2 32 kw/m
0.85 0
50
100
150
200
250
0
t (s)
c
200
t (s)
0
30
60
90
120
150
2
53 kw/m 2 37 kw/m 2 26 kw/m 180
210
t (s) 1.00
b 0.95
5
57 kw/m2 48 kw/m2 32 kw/m2
0.90 2
2
62kw/m 2 47kw/m 2 33kw/m
55kw/m 2 41kw/m 2 28kw/m
q"a ( kw/m2)
N
4
53 kw/m2 37 kw/m2 26 kw/m2
3
2
1
0.85 0
50
100
150
200
250
t (s) Fig. 2. Normalized transmission of incident radiant flux (N): (a) pine, D = 0.1 m; (b) PMMA, D = 0.1 m; and (c) pine, D = 0.2 m.
e.g. Cone Calorimeter type (D < 0.1 m), is more obvious and needs more attention. 4.1.2. Absolute value of radiation attenuation of incident radiant flux The absolute values of radiation attenuation of incident radiant flux (q_ 00a ) at the moment of ignition of pine and PMMA are rising with the increase of incident radiant flux, as shown in Fig. 4. The increase trend of q_ 00a corresponds with the nonlinear relation be-
0 0
50
100
150
200
250
300
t (s) Fig. 4. Absolute value of radiation attenuation (q_ 00a ): (a) pine, D = 0.1 m; and (b) PMMA, D = 0.1 m.
tween the amount of radiation attenuation and the concentration of absorbing components in Beer’s law [27]. So, the expressions of time-dependent q_ 00a at different incident heat fluxes are gained with an exponential decay fitting, which are applied in a radiant ignition model with different incident heat flux boundary
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171
conditions in the next chapter, as shown in Table 1 and Fig. 4 (see the black solid line).
value of incident radiant heat fluxes by pyrolysis volatiles could be obtained indirectly by the mass flux.
4.2. Radiation absorptivity of pyrolysis volatiles
4.2.2. Mass radiation absorptivity of pyrolysis volatiles Beer’s law, see in Eq. (3), is an empirical relationship that indicates the degree of monochromatic radiation absorption (M) depends on the thickness of the absorbing medium (b) and the concentration of the absorbing species (f) [27], and has been applied by several people [2,4,16] in their work concerning the radiation absorption by pyrolysis volatiles before.
4.2.1. Relationship between absolute value of radiation attenuation and mass flux The absolute value of radiation attenuation coupled with the mass flux of pine and PMMA is shown in Fig. 5, whose corresponding trend in the range of test incident heat fluxes is consistent. It is found that the relationship between the absolute value of radiation attenuation and the mass flux follows Beer’s law which is suited for thin liquor. The increase of the absolute value of radiation attenuation is proportional to the increase of the mass flux, namely the increase of the concentration of pyrolysis volatiles above sample surface. It is a very useful conclusion which means the attenuation Table 1 Exponential decay fitting of the time-dependent q00a .
Pine
PMMA
a
q00in
Expression of exponential decay fitting
R2
26 32 37 43 53 57
q00a q00a q00a q00a q00a q00a
¼ 7:04 expðt=330:59Þ þ 6:99 ¼ 7:37 expðt=222:56Þ þ 7:24 ¼ 8:47 expðt=140:27Þ þ 8:27 ¼ 9:90 expðt=114:26Þ þ 9:62 ¼ 11:45 expðt=77:01Þ þ 11:17 ¼ 12:62 expðt=54:64Þ þ 12:33
0.95517 0.97216 0.98137 0.98109 0.97692 0.97269
26 32 37 48 53 57
q00a q00a q00a q00a q00a q00a
¼ 1:85 expðt=75:60Þ þ 1:73 ¼ 3:46 expðt=86:05Þ þ 3:24 ¼ 6:67 expðt=89:95Þ þ 6:30 ¼ 11:95 expðt=122:75Þ þ 11:63 ¼ 14:38 expðt=140:65Þ þ 14:09 ¼ 37:12 expðt=234:18Þ þ 37:37
0.98539 0.99056 0.98955 0.98214 0.98219 0.93139
0.003
4
m" 3
2 0.002 1
q"a ( kw/m2)
m" ( kg/m2.s)
q"a
0 20
40
60
80
100
120
140
160
t (s)
b
3
m" q"a
2
1
0.001
q"a ( kw/m2)
m" ( kg/m2.s)
0.002
0 0.000 -1 0
20
40
60
80
100
120
140
t (s) Fig. 5. Absolute value of radiation attenuation coupled with mass flux (D = 0.1 m ðq_ 00in ¼ 32 kW=m2 Þ: (a) pine and (b) PMMA.
ð3Þ
The mass radiation absorptivity c, which has the units of L kg1 m1 and is used when b is in cm and f is in kg L1, is independent of the concentration of absorbing species. b is the absorbing path length of incident heat flux. f is the mass concentration of absorbing species. The parameter c represents the specific radiation absorptivity per unit mass concentration of absorbing components when radiant heat flux passes through per unit length of absorbing species in physics, see in Eq. (4).
c ¼ M=b f
ð4Þ
f ¼ m00 ðtÞ=v g
ð5Þ
It is assumed that the vertical releasing velocity of pyrolysis volatiles (vg) is a constant (vg = 0.25 m/s), which is observed and determined by experiment video, on the absorbing path of incident heat flux. Because of the absorbing path of pyrolysis volatiles is comparatively short (b = 0.1 m), it is assumed that the concentration of pyrolysis volatiles in every second period is uniform in the whole absorbing area and is determined by the time-dependent mass flux, see in Eq. (5). Then, the mass radiation absorptivity (c) is obtained by substituting the time-dependent mass concentration of pyrolysis volatiles (f) in Eq. (4) with the one in Eq. (5), see in Eq. (6). The mass radiation absorptivity with the relative value of radiation attenuation in Eq. (6) is based on one single degree of radiant heat fluxes in Beer’s law. Considering the different degree of radiant heat fluxes selected in experiment, the mass radiation absorptivity with the absolute value of radiation attenuation (c*, kW/kg) is applied in the analysis that followed, which can represent the difference of mass radiation absorptivity caused by different incident heat fluxes better, see in Eq. (7).
c ¼ M=½b ðm00 ðtÞ=v g Þ c ¼ ðM q_ 00in Þ=½b ðm00 ðtÞ=v g Þ
0.001 0
M ¼1N ¼cbf
ð6Þ ð7Þ
The c* of pine and PMMA both increase with time, as shown in Fig. 6. It may be because of that, as the increase of the temperature of test sample caused by external heating, the pyrolysis products potentially crack to gas components in the higher temperature [9] and the amount of gas components with the stronger radiation absorptivity in infrared wavelengths becomes larger. The increase rates of c* of pine and PMMA at different incident heat fluxes appreciably rise with the increase of incident heat flux, as the arrow shown in Fig. 6. The explanation above about the larger generation rate of the gas components with stronger radiation absorptivity at the larger incident heat flux can also be applied in here. So, for the result before concerning the attenuation rate of N increases with a rise of the incident radiant flux, the corresponding explanations of Kashiwagi and this paper before with a faster yield rate of pyrolysis volatiles are both not sufficient, and the contribution by the faster increase of c* at the larger incident heat flux also needs to consider. Furthermore, it is also found that the increase of the c* of pine and PMMA tends to be small, which may be ascribed to the saturation of radiation absorptivity [27]. In order to compare the mass radiation absorptivity of pyrolysis volatiles of pine and PMMA, the mean and the fitted mean of c* of
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a
0.8
0.5 0.4 0.3 (kW/kg)
(kW/kg)
0.6
0.2
26 kw/m2 37 kw/m2 53 kw/m2 Mean
0.1 0.0
32 kw/m2 43 kw/m2 57 kw/m2
0.4
0.2 Pine Mean Pine Mean Fitted PMMA Mean PMMA Mean Fitted
0.0 0
50
100
150
200
0
t (s)
50
100
150
200
t (s)
b
Fig. 7. Comparison of the mass radiation absorptivity of pine and PMMA.
1.0
(kW/kg)
0.8
Table 2 Exponential decay fitting of the mass radiation absorptivity of pine and PMMA.
0.6
Expression of exponential decay fitting
0.4
2
2
26 kw/m 37 kw/m2 53 kw/m2 Mean
0.2
32 kw/m 48 kw/m2 57 kw/m2
0.0 0
50
100
150
200
t (s) Fig. 6. Mass radiation absorptivity with absolute value of radiation attenuation: (a) pine, D = 0.1 m and (b) PMMA, D = 0.1 m.
them are processed, as shown in Figs. 6 and 7 and Table 2. It is found that the c* of pyrolysis volatiles of PMMA is actually larger than the one of pine. For heating under a uniform condition, the pyrolysis volatiles of PMMA may comprise more amounts of gas components with stronger radiation absorptivity in infrared wavelengths. This conclusion is different from the one in Section 3.2 which the q_ 00a of pine is larger. Because the analysis in Section 3.2 did not take the radiation attenuation with the mass flux together into account, compared with the more reasonable parameter c*, it is one-sided for determining the radiation absorptivity of pyrolysis volatiles of different fuels. Park and Blasi both pointed out the absorbed radiant energy played an important role in the induction of the gas-phase ignition [14,16]. Due to the in-depth radiation absorption of PMMA: (1) the rising rate of surface temperature of PMMA is smaller than the one of pine, the convection heating effect from sample surface is smaller for PMMA; (2) the mass flux of PMMA is also smaller than the one of pine. However, because the radiation absorptivity per unit mass concentration of pyrolysis volatiles of PMMA is larger than the one of pine; the proportion of induced heating by gas-phase radiation absorption for the ignition of PMMA is larger. It also means the ignition of PMMA more depends on the gas-phase heating by radiation absorption which is consistent with Kashiwagi’s relative conclusion [12].
Pine, D = 0.1 m PMMA, D = 0.1 m
*
c = 0.3581exp(t/64.7045) + 0.3767 c* = 0.7689exp(t/12.369) + 0.6698
R2 0.93534 0.89229
introduced briefly together with the new improved part of the model. The energy equation for the test sample on s(t) 6 x 6 L is,
qs C s
@T @ @T @T _ 00 C g ¼ ks þm @t @x @x @x @ qs hc q s hc q w þ Q þ hg þ @t qw qc qw qc
ð8Þ
The boundary conditions which include the time-dependent incident heat flux term (q_ 00in ðtÞ) with the fitted expressions in Table 1 and the invariable incident heat flux term ðð1 GÞq_ 00in Þ with the constant radiation attenuation coefficient referred to Nelson’s work [17] on the moving boundary x = s(t) are:
@T ks ¼ esur q_ 00in ðtÞ jsur ðT sur T 1 Þ esur rðT 4sur T 41 Þ ð9Þ @x x¼0 @T ks ¼ esur ð1 GÞq_ 00in jsur ðT sur T 1 Þ esur rðT 4sur T 41 Þ ð10Þ @x x¼0 The rate of pyrolysis is:
@ qs qs qc E qw exp ¼ A RT @t qw qc
ð11Þ
The conservation equation for the mass of gas is:
_ 00 @ qs @m ¼ @x @t
ð12Þ
The initial condition is:
t ¼ 0;
T ¼ T1;
q ¼ qw ; m00 ¼ 0
ð13Þ
5. Effect of radiation attenuation in radiant ignition model
The selected fuel for calculation is pine. The selected values of the parameters in model are shown in Table 3. Considering the radiation attenuation term in the boundary condition is related directly with the surface emissivity (esur), the different surface emissivities are selected in the numerical calculation for a comprehensive comparison of the effect of radiation attenuation in model.
5.1. Radiant ignition model
5.2. Comparison of calculation results
The model used in this paper to study the effect of radiation attenuation has been published in our work before [7]. So it is only
For current radiant ignition model, the critical surface temperature and the critical mass flux are the most commonly used
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ignition criteria [2], so these two parameters are focused on in the followed numerical calculation concerning the effect of radiation attenuation.
a
500
400
Tsur (ºC)
300
200
100
0
b
Table 3 Selected values of the parameters in the model. Symbol
Value
Symbol
Value
Cp [5] Cc [5] Cg [5] kp [5] kc [5] Q [5] qc [5] G [17]
2140 J/kg K 1928 J/kg K 0 J/kg K 0.157 W/m K 0.084 W/m K 300000 J/kg 125 kg/m3 0.1
esur [5] esur [19] jsur [19]
0.98 0.72 10 J/m2 s K 150 kJ/mol 1.4 1010 s1 300 K 530 kg/m3 0.02 m
E [28] A [28] T1 [measured] qw [measured] L [measured]
Tac ( ε sur =0.72)
Tat (ε sur =0.98)
Tat ( ε sur =0.72)
100
t (s)
150
200
250
700 600 500 400 300 200 100
T0 ( ε sur=0.98)
T0 ( ε sur=0.72)
Tac ( ε sur=0.98)
Tac (ε sur=0.72)
Tat ( ε sur=0.98)
Tat (ε sur=0.72)
Te
0 20
40
60
t (s)
Fig. 8. Comparison of surface temperature history: (a) q_ 00in ¼ 26 kW=m2 and (b) q_ 00in ¼ 57 kW=m2 .
70 60
Δ Tsur ( ºC )
50 40 30 20
2
26kw/m 2 57kw/m 2 26kw/m 2 57kw/m
10 0 0
5.2.3. Time to ignition The critical auto-ignition and piloted-ignition surface temperature are selected to be 420 °C and 350 °C, respectively, for the mod-
T0 ( ε sur =0.72)
Tac ( ε sur =0.98)
50
0
5.2.2. Mass flux The calculated mass flux (m00 ) with ðm00a Þ: time-dependent ðm00at Þ, constant coefficient ðm00ac Þ and without ðm000 Þ the radiation attenuation by pyrolysis volatiles and the experimental one ðm00e Þ are shown in Fig. 10. Although there is still a certain difference between the m00a and the m00e , which is ascribed to the effect of the inner moisture and the simple one step global pyrolysis sub-model applied, compared to the m000 , the m00a is closer to the m00e . The radiation attenuation significantly reduces the mass flux peak and delays the time it is achieved. The peak value of the m00ac with the constant radiation attenuation coefficient G = 0.1 is close to the one of the m00at , and the time to peak of the m00ac is a little later than the one of the m00at . Fig. 10 also shows that there is an obvious area with large difference in mass flux ðDm0ac ; Dm0at Þ during the early stages of mass flux when the radiation attenuation is considered. The relative effect of radiation attenuation on the predicted time to ignition using a critical ignition mass flux will be presented in the chapter followed.
T0 ( ε sur =0.98)
Te
0
Tsur (ºC)
5.2.1. Surface temperature The calculated surface temperature (Tsur) history with ((Ta): time-dependent (Tat), constant coefficient (Tac)) and without (T0) the radiation attenuation by pyrolysis volatiles and the experimental one (Te) are shown in Fig. 8. Compared to the calculated Tsur with a surface emissivity esur = 0.98, the one with a surface emissivity esur = 0.72 is closer to the Te. It is indicated that the surface emissivity with a value esur = 0.98 is overestimated and the one with a value esur = 0.72 is more reasonable. So, a value esur = 0.72 is chose as the sample surface emissivity selected in all the followed numerical calculation conditions. Compared to the T0, the Ta is closer to the Te, which means the consideration of the radiation attenuation is resultful. It is also shown that the Tac with the coefficient G = 0.1 is close to the Tat, which means the selected value G = 0.1 is approximately accepted for the general calculation of radiant ignition model. The curves in Fig. 9 present the detailed difference in surface temperature history (DTsur) with and without the radiation attenuation. There is no obvious difference for the DTsur with different surface emissivity. The DTsur with the time-dependent radiation attenuation increases with time and can exceed 60 °C. The DTsur is larger in the early heating period (t < 150 s) at high incident heat fluxes (e.g. q_ 00in ¼ 57 kW=m2 ) for both time-dependent and constant radiation attenuation conditions. The relative effect of radiation attenuation on the predicted time to ignition using a critical ignition surface temperature will be presented in the chapter followed.
100
200
300
2
26kw/m 2 57kw/m 2 26kw/m 2 57kw/m
400
t (s) Fig. 9. Difference in surface temperature history with and without radiation attenuation: solid point, DTsur-ac; virtual point, DTsur-at; square point, esur = 0.98; circinal point, esur = 0.72.
el in this paper, which is referred to the species and size of wood sample [6]. The critical piloted-ignition mass flux is selected to be 2.5 g/m2 s, which is a widely applied value [2] and originally from Bamford’s work [29]. The calculated time to ignition (tig) with (time-dependent (tig-at), constant coefficient (tig-ac)) and without (tig-0) the radiation attenuation by pyrolysis volatiles and the experimental time to ignition (tig-e) are shown in Fig. 11. The difference between the experimental auto-ignition results and the predicted ones at high incident heat fluxes, as shown in Fig. 11a, is mainly ascribed to the selected critical auto-ignition surface temperature actually has a comparatively larger range [1,6] and a
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a
0.007 Δ m"o-at
0.006
tig-e tig-ac
0.20
Δ m"o-ac
0.000
0.004 0
50
100
150
tig-o tig-at
tig -0.5( s-0.5)
0.002
0.005
m“ ( kg/m2.s)
0.004
0.15
200
0.003
0.10
0.002 0.001
m“0
m“at
0.000
m“e
m“ac
0
20
40
60
80
100
0.05 25
120
30
single value could not be appropriate for both high and low incident heat flux ranges. It could be seen in Fig. 11 that the time to ignition considered the radiation attenuation is closer to the experimental results for all the calculated conditions with different ignition criteria, which reflects the retardation effect for the pyrolysis and the attainment of an ignitable boundary layer mixture by the radiation attenuation, and illustrates that the consideration of the radiation attenuation by pyrolysis volatiles in radiant ignition models is necessary. It could also be seen that the tig-ac with the coefficient G = 0.1 is close with the tig-at, which also means the selected value G = 0.1 is approximately accepted for the general calculation of radiant ignition model.
b
40
45
50
55
60
50
55
60
50
55
60
0.30
tig-e tig-ac
0.25
tig -0.5( s-0.5)
Fig. 10. Mass flux with and without radiation attenuation: q_ 00in ¼ 37 kW=m2 , esur = 0.72.
35
q"in ( kw/m2)
t (s)
tig-o tig-at
0.20
0.15
0.10
0.05 25
30
35
40
45
q"in ( kw/m2)
In this paper, the radiation attenuation characteristics of pyrolysis volatiles of pine and PMMA when heated under a resistance element type radiant heater are experimentally studied by coupling with the synchronously measured mass loss rate. A radiant ignition model with different incident heat flux boundary conditions (none, constant and time-dependent radiation attenuation) is used to investigate how to reasonably consider the effect of radiation attenuation in radiant ignition model. The main conclusions include:
c 0.25
tig -0.5( s-0.5)
6. Conclusions
tig-e tig-ac
0.20
tig-o tig-at
0.15
0.10
1. The degree of radiation attenuation of incident heat flux of pine and PMMA (6–14%) is evident before ignition, although not as large as the Kashiwagi’s reported result (50–80%) with a laser radiant heater. 2. The radiation attenuation in the apparatus with the shorter radiation distance (D < 0.1 m), e.g. Cone Calorimeter type, is more obvious and needs more attention. 3. The increase trend of q_ 00a of pine and PMMA corresponds with the nonlinear relation between the amount of radiation attenuation and the concentration of absorbing components in Beer’s law. 4. For the attenuation rate of N increases with a rise of the incident radiant flux, it is not only caused by the faster concentration rise of pyrolysis volatiles, but also ascribed to the faster increase of the mass radiation absorptivity. 5. The c* of pyrolysis volatiles of PMMA is larger than the one of pine. The ignition of PMMA more depends on the gas-phase heating by radiation absorption. Compared to the M, the c* is more reasonable for determining the radiation absorptivity of pyrolysis volatiles of different fuels. 6. By comparing the calculated results with and without radiation attenuation, it illustrates that consideration of the radiation attenuation by pyrolysis volatiles in radiant ignition models
0.05 25
30
35
40
45
q"in ( kw/m2) Fig. 11. Comparison of time to ignition: esur = 0.72, (a) auto-ignition, critical ignition surface temperature; (b) piloted-ignition, critical ignition surface temperature; and (c) piloted-ignition, critical ignition mass flux.
for resistance element radiant heater heating condition is necessary. A constant radiation attenuation coefficient G = 0.1 is approximately accepted for the general calculation of radiant ignition model.
Acknowledgments This research was supported by National Natural Science Foundation of China (Grant No.: 50536030) and Program for New Century Excellent Talents in University (NCET-05-0551). The authors deeply appreciate the support.
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References [1] J.G. Quintiere, Fire Mater. 30 (2006) 175–214. [2] A.M. Kanury, Flaming ignition of solid fuels, in: The SFPE Handbook of Fire Protection Engineering, third ed., 1999 (Section 2/Chapter 11). [3] D. Drysdale, An Introduction to Fire Dynamics, second ed., Wiley, Chichester, UK, 1999. [4] T. Kashiwagi, Combust. Sci. Technol. 8 (1974) 225–236. [5] H.C. Kung, Combust. Flame 18 (1972) 185–195. [6] V. Babrauskas, J. Fire Protection Eng. 12 (2002) 163–189. [7] L. Yang, Combust. Flame 133 (2003) 407–413. [8] J.T. Kuo, C. His, Combust. Flame 142 (2005) 401–412. [9] C.D. Blasi, Prog. Energy Combust. Sci. 19 (1993) 71–104. [10] B. Moghtaderi, Fire Mater. 30 (2006) 1–34. [11] M. Delichatsios, Fire Safety J. 38 (2003) 219–228. [12] T. Kashiwagi, Combust. Flame 34 (1979) 231–244. [13] T. Kashiwagi, Combust. Sci. Technol. 20 (1979) 225–234. [14] S.H. Park, C.L. Tien, Int. J. Heat Mass Transfer 33 (1990) 1511–1520. [15] B. Amos, A.C. Fernandez-Pello, Combust. Sci. Technol. 62 (1988) 331–343. [16] C.D. Blasi, Combust. Flame 83 (1991) 333–344. [17] M.I. Nelson, Fire Safety J. 24 (1995) 107–130.
175
[18] V. Babrauskas, The Cone Calorimeter, The SFPE Handbook of Fire Protection Engineering, third ed., 1999 (Section 3/Chapter 3). [19] C.D. Blasi, Prog. Energy Combust. Sci. 34 (2008) 47–90. [20] E.M. Suuberg, Behavior of Charring Materials in Simulated Fire Environments, National Institute of Standards and Technology, Gaithersburg, MD, NIST-GCR94-645, 1994, p p. 75–79/p. 487. [21] B. Bodzay, J. Anal. Appl. Pyrol. 85 (2009) 313–320. [22] M. Stanislav, Polym. Degrad. Stabil. 64 (1999) 379–385. [23] G.W. Gokel, Dean’s Handbook of Organic Chemistry, second ed., McGraw-Hill Companies, Inc., 2004. [24] K. Wakatsuki, Proc. Combust. Inst. 30 (2005) 1565–1573. [25] M.L. Toison, Infrared and its Thermal Applications, Philips Technical Library, Centrex, Eindhoven, 1964. [26] P.A. Beaulieua, N.A. Dembseyb, Fire Safety J. 43 (2008) 410–428. [27] J.D.J. Ingle, S.R. Crouch, Spectrochemical Analysis, Prentice Hall, New Jersey, 1988. [28] B.M. Wagenaar, Fuel Process. Technol. 36 (1993) 291–298. [29] C.H. Bamford, On the combustion of wood. Part I. Proc. Cambridge Philos. Soc., 1946, pp. 166–182.
Contents lists available at ScienceDirect
Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Radiation attenuation characteristics of pyrolysis volatiles of solid fuels and their effect for radiant ignition model Yupeng Zhou, Lizhong Yang *, Jiakun Dai, Yafei Wang, Zhihua Deng State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, Anhui Province, China
a r t i c l e
i n f o
Article history: Received 30 March 2009 Received in revised form 21 May 2009 Accepted 15 June 2009 Available online 7 August 2009 Keywords: Radiation attenuation Incident heat flux Pyrolysis volatiles Radiation absorptivity Ignition model
a b s t r a c t Radiation attenuation characteristics of pyrolysis volatiles from heated solid fuels, a neglected physical effect in radiant ignition process, are studied by simulated experiment and mathematical models. Firstly, it is experimentally found the radiation attenuation of an incident heat flux when pine or Polymethyl Methacrylate (PMMA) is heated occurs before flaming ignition (6–14%), especially for the one in the experiment of the Cone Calorimeter style apparatus with a shorter test radiation distance (D < 100 mm). Then, a more reasonable parameter using Beer’s law for determining the radiation absorptivity of pyrolysis volatiles of different fuels is presented. It is found the radiation absorptivity of pyrolysis volatiles of PMMA is actually larger than the one of pine and the ignition of PMMA more depends on the gas-phase heating by radiation absorption. Finally, the calculated results with the experimental radiation attenuation data illustrates that consideration of the radiation attenuation by pyrolysis volatiles in radiant ignition models is necessary. A constant radiation attenuation coefficient G = 0.1 is approximately accepted for the general calculation of radiant ignition model. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Radiant heating by the fire, smoke, and heated surfaces is the primary driving force for fire growth on materials [1]. Because the radiant ignition of fuels is the first step in all fire prevention strategies and is closely connected with other important fire process, e.g. fire spread over fuels, room fire flashover, and the jump of a forest fire across a firebreak [2], it is always an interesting subject in fire research [1–11]. In the radiant ignition process, there is a gas-phase effect which has been studied by some researchers before [2,3,12–16]. The incident radiant heat flux for heating solid combustible will be selectively absorbed and attenuated by the pyrolysis volatiles in the boundary layer so that the irradiance practically available is substantially less than that without the absorbing gas. The attenuation will retard the time to full thermal decomposition of the solid fuel, and consequently delay the attainment of the sufficient amount of ignitable pyrolysis volatiles. Especially for the condition with the horizontal materials irradiated vertically, which is the most test condition in Cone Calorimeter, the incident radiant heat flux passes through a rising plume by the pyrolysis volatiles and its intensity may be significantly attenuated [12], which is confirmed by Park with a numerical simulation [14].
* Corresponding author. Fax: +86 551 3601 669. E-mail address: [email protected] (L. Yang).
Despite years of experimental and theoretical research, the neglected physical effect is still not studied adequately, and whether it is significant in real fire situations is not known [2,3,12,13]. In current radiant ignition models, the boundary condition usually only includes the radiation and convection heat loss from sample surface, see in Eq. (1) [1,10].
@T ks ¼ esur q_ 00 jsur ðT sur T 1 Þ esur rðT 4sur T 41 Þ @x x¼0
ð1Þ
In Kashiwagi’s experiment with a laser radiant heater, a very large attenuation percentage (50–80%) was observed before the ignition [13]. The calculated surface temperature result in Kashiwagi’s work presented a better agreement with the experimental one by considering a time-dependent attenuation of incident radiant heat flux. However, the wavelength of the laser radiant heater (10.6 lm) and the range of radiant heat flux (70–174 kW/m2) in Kashiwagi’s experiment are both not consistent with the ones (20–80 kW/m2) in the typical experimental condition in Cone Calorimeter with a resistance element radiant heater [12], which could not support the adequate results for the improvement of the current commonly used radiant ignition model. The attenuation of the incident radiation by pyrolysis volatiles also was considered by Nelson, but the attenuation, which is time-dependent, was set as an arbitrary constant coefficient without experimental validation [17]. There is lack of a corresponding study on the attenuation characteristics for heating under a resistance element radiant heater which is closer to real fire conditions [3,18]. Furthermore, although it is qualitatively
0010-2180/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2009.06.020
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Nomenclature A b C D E f G h k L m00 M N q_ 00 Q R s(t) T t
vg x
pre-exponential factor, s1 absorbing path length of incident heat flux, m thermal capacity at constant pressure, J/kg K radiation distance, m reaction activation energy, J/mol mass concentration of absorbing species, kg L1 constant radiation attenuation coefficient specific enthalpy, J/kg thermal conductivity, W/m K sample thickness, m mass flux of volatiles, kg/m2s normalized radiation absorption normalized transmission of incident radiant flux external heat flux, kW/m2 heat of reaction, J/kg gas constant, J/mol K distance moved by upper surface from its initial location, m temperature, K time, s vertical releasing velocity of pyrolysis volatiles, m/s distance from the initial location of the upper surface, m
known that the degree of radiation attenuation is related directly with the concentration of pyrolysis volatiles, a quantitative study on this subject is still not known. As for Kashiwagi’s experiment conclusion, it reported that the degree of radiation attenuation for pine is larger than PMMA [12]. However, if determined the radiation attenuation capability of per unit pyrolysis volatiles by coupling with the corresponding mass loss rate together, which is related directly with the yield rate of pyrolysis volatiles, the conclusion above may be different. In this paper, the radiation attenuation characteristics of two classic solid combustibles (pine and PMMA) are investigated experimentally with a resistance element radiant heater firstly. Then the quantitative relationship between the degree of radiation attenuation and the concentration of pyrolysis volatiles is obtained by coupling with the synchronous mass loss rate. The radiation absorptivity of pyrolysis volatiles of different solid fuels is discussed using Beer’s law. Finally, a radiant ignition model with different incident heat flux boundary conditions (none, constant and time-dependent radiation attenuation) is used to present a comprehensive comparison of the effect of radiation attenuation, and to investigate how to reasonably consider the effect of radiation attenuation in radiant ignition model. 2. Theory Although the detailed components of pyrolysis volatiles are still not very clear due to its complexity, several researchers have reported the primary pyrolysis volatiles components of pine and PMMA, which include CO2, CO, H2O, and relatively smaller amounts of low molecular weight alkanes and alkenes like CH4, C3H6, some aromatics like methanol, ethanol, benzene [19–22]. These primary pyrolysis volatiles components all have the specific infrared absorbing wave band within wavelength area 2.5–25 lm. For example, the peak absorption of water is around 3 lm and 6 lm, the CO2 is 4.26 lm, the CO is around 4.5 lm, CH4 is around 3.4 lm, C3H6 is around 8.3 lm, methanol is around 3 lm and 10 lm [23,24]. The infrared absorbing wave band of the primary
Greek symbols c mass radiation absorptivity, L kg1 m1 q density, kg/m3 j convection coefficient, W/m K c* mass radiation absorptivity with absolute value of radiation attenuation, kW/kg e emissivity Subscripts a attenuation ac constant coefficient radiation attenuation add added at time-dependent radiation attenuation c char e experiment g gas in incident ig ignition p pyrolyzing part s pyrolyzed area sur surface w virgin wood 1 surround 0 initial
pyrolysis volatiles components of pine and PMMA is within the emission wave band of a resistance element radiant heater (2– 15 lm) [25], which could illustrate the possibility of radiation absorption by pyrolysis volatiles in the experiment of this paper. 3. Experiment details The experimental work was conducted in an apparatus for studying the radiant ignition of fuels, as shown in Fig. 1. The radiant heater consists of silicon carbide heating elements, which tends to have a near-grey-body characteristic, and has a high emissivity (0.8–0.9) with a little variability between wavelength 2–15 lm [25]. The size of the heating area of radiant heater is 0.4 m 0.4 m. The working temperature of radiant heater ranges from 600 to 1100 °C, which is consistent with the hot gas layer temperature in typical fires [18] and hence can effectively simulate the radiant heating within the infrared wavelength range seen in fires. The top of the radiant heater has four smoke ventilation slots which could let the pyrolysis volatiles pass through it without accumulation. Two classic solid combustibles are tested: pine and PMMA. The samples sizes of pine and PMMA are 0.15 m 0.15 m 0.02 m and 0.15 m 0.15 m 0.015 m, respectively. Prior to tests, the pine sample is dried in an oven with a temperature 60 °C for 24 h. The unexposed surface and edges of each sample are wrapped in a double-layer of fiberglass fabric (20 mm thick) and aluminum foil to promote one-dimensional heat transfer. Pine is tested at radiation distance (D) both 0.1 m and 0.2 m. PMMA is just tested at radiation distance 0.1 m. The sample surface temperature is measured by 0.5 mm diameter type-K thermocouples which are mounted onto the sample surface. The auto-ignition is conducted in all the experimental conditions with the measure of radiation attenuation. In order to obtain a more comprehensive comparison of the effect of radiation attenuation in radiant ignition model, the piloted-ignition is also conducted with pine at radiation distance 0.1 m. The detailed measurement process of the attenuated radiant heat flux by pyrolysis volatiles is shown in Fig. 1. There is a
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169
Fig. 1. Schematics of the experiment apparatus and the measurement settings of the attenuated incident radiant heat flux.
0.03 m diameter hole through the center of test sample. The hole takes up only 3% of the whole area of the sample, so that its effect could be ignored. A Gardon-type water-cooled heat flux gauge (U0.025 m) with an uncertainty 2%, which is produced and calibrated by the 102nd research institute of China Aerospace Corporation, is fixed on a trestle table before the radiant heater is opened and is used to measure if the setting incident heat flux (q_ 00in ) is achieved after the radiant heater is opened and to measure the radiation (q_ 00 ðtÞ) reaches the sample surface through the plume of the pyrolysis volatiles during a test. The gauge is cooled with 65 °C water during the test to prevent condensation from forming on the gauge face, which is referred to Beaulieua’s method in a similar heat flux measurement [26]. The trestle table is settled on the firebrick board below and not contact with the sample platform which is settled on the electronic load cell (METTLER TOLEDO, made in Switzerland). When the setting incident heat flux is achieved and stays steady, the radiant heater is insulated with a fireproof shutter and then the test sample is mounted horizontally together with the heat flux gauge without contact. The heat flux gauge is also not contacted with the bottom of the sample. These configurations ensure the measurements of radiation attenuation and mass loss rate could be conducted simultaneously without the influence of water cooling circulation, which is not fulfilled in Kashiwagi’s experiment [12,13], and then to determine the radiation attenuation capability of per unit pyrolysis volatiles by coupling with the corresponding mass loss rate together. Once the checking for the uniformity of the top position of test sample and heat flux gauge is finished, the fireproof shutter is removed swiftly, leaving the sample exposed to the heat flux. Two runs are carried out for each test condition. If the runs are obviously different, a third or a fourth run is carried out. The incident radiant heat flux, the mass loss and the surface temperature are continuously recorded at intervals of 1 s. A CCD camera is used to record time to ignition. The test is terminated when the flaming ignition occurs.
4. Results and discussion 4.1. Radiation attenuation of incident radiant flux 4.1.1. Normalized transmission of incident radiant flux The normalized transmission of incident radiant flux (N), see in Eq. (2), is shown in Fig. 2. The data shown in figures is taken before the ignition occurs, as it is what this paper focuses on. The fluctuation in the curves is mainly caused by the wandering of the pyrolysis volatiles plume. The N at the moment of ignition of pine sample in D = 0.1 m is between 0.86 and 0.90, and the one of PMMA sample in D = 0.1 m is between 0.91 and 0.96, as shown in Fig. 2. Because the faster yield rate of pyrolysis volatiles at the higher incident radiant flux, the attenuation rate of N increases with the rise in the incident radiant flux.
N ¼ q_ 00 ðtÞ=q_ 00in
ð2Þ
The N of PMMA sample is smaller than that of pine at a uniform incident heat flux, as shown in Fig. 3, which is consistent with Kashiwagi’s relative result [12]. This result is because that the faster yield period of pyrolysis volatiles of PMMA is delayed by its larger thermal inertia (kqC) which is roughly twice that of pine. However, the analysis above could only be used to explain the delay of radiation attenuation of PMMA, but should not be used to draw the conclusion that the radiation absorbability of PMMA is weaker than pine, which will be further demonstrated together with the mass flux (m00 ) in the chapter followed. The N at the moment of ignition of pine sample in D = 0.2 m is 0.91–0.94, as shown in Fig. 2c, which is smaller than the one of pine sample in D = 0.1 m (0.86–0.90) at a same intensity of incident heat flux. Although the radiation attenuation layer thickness is larger for D = 0.2 m, the concentration of pyrolysis volatiles plume under the same heating condition is thinner because of more intense dilution effect, which causes the degree of radiation attenuation is relatively lower. This result indicates that the radiation attenuation effect in the apparatus with shorter radiation distance,
170
a
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1.00
1.00
2
2
57kw/m 2 43kw/m 2 32kw/m
26kw/m 2 26kw/m 2 53kw/m 2 53kw/m
0.95
N
N
0.95
53kw/m 2 37kw/m 2 26kw/m
2
PMMA Pine PMMA Pine
0.90
0.90
0.85
0.85 0
50
100
150
0
200
50
100
150
t (s)
b
250
300
Fig. 3. Comparison of radiation attenuation between pine and PMMA, D = 0.1 m.
1.00
a 0.95
6
2
2
57kw/m 2 48kw/m 2 32kw/m
53kw/m 2 37kw/m 2 26kw/m
q"a ( kw/m2)
N
5
0.90
4 3 2 1
2
57 kw/m 2 43 kw/m 2 32 kw/m
0.85 0
50
100
150
200
250
0
t (s)
c
200
t (s)
0
30
60
90
120
150
2
53 kw/m 2 37 kw/m 2 26 kw/m 180
210
t (s) 1.00
b 0.95
5
57 kw/m2 48 kw/m2 32 kw/m2
0.90 2
2
62kw/m 2 47kw/m 2 33kw/m
55kw/m 2 41kw/m 2 28kw/m
q"a ( kw/m2)
N
4
53 kw/m2 37 kw/m2 26 kw/m2
3
2
1
0.85 0
50
100
150
200
250
t (s) Fig. 2. Normalized transmission of incident radiant flux (N): (a) pine, D = 0.1 m; (b) PMMA, D = 0.1 m; and (c) pine, D = 0.2 m.
e.g. Cone Calorimeter type (D < 0.1 m), is more obvious and needs more attention. 4.1.2. Absolute value of radiation attenuation of incident radiant flux The absolute values of radiation attenuation of incident radiant flux (q_ 00a ) at the moment of ignition of pine and PMMA are rising with the increase of incident radiant flux, as shown in Fig. 4. The increase trend of q_ 00a corresponds with the nonlinear relation be-
0 0
50
100
150
200
250
300
t (s) Fig. 4. Absolute value of radiation attenuation (q_ 00a ): (a) pine, D = 0.1 m; and (b) PMMA, D = 0.1 m.
tween the amount of radiation attenuation and the concentration of absorbing components in Beer’s law [27]. So, the expressions of time-dependent q_ 00a at different incident heat fluxes are gained with an exponential decay fitting, which are applied in a radiant ignition model with different incident heat flux boundary
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171
conditions in the next chapter, as shown in Table 1 and Fig. 4 (see the black solid line).
value of incident radiant heat fluxes by pyrolysis volatiles could be obtained indirectly by the mass flux.
4.2. Radiation absorptivity of pyrolysis volatiles
4.2.2. Mass radiation absorptivity of pyrolysis volatiles Beer’s law, see in Eq. (3), is an empirical relationship that indicates the degree of monochromatic radiation absorption (M) depends on the thickness of the absorbing medium (b) and the concentration of the absorbing species (f) [27], and has been applied by several people [2,4,16] in their work concerning the radiation absorption by pyrolysis volatiles before.
4.2.1. Relationship between absolute value of radiation attenuation and mass flux The absolute value of radiation attenuation coupled with the mass flux of pine and PMMA is shown in Fig. 5, whose corresponding trend in the range of test incident heat fluxes is consistent. It is found that the relationship between the absolute value of radiation attenuation and the mass flux follows Beer’s law which is suited for thin liquor. The increase of the absolute value of radiation attenuation is proportional to the increase of the mass flux, namely the increase of the concentration of pyrolysis volatiles above sample surface. It is a very useful conclusion which means the attenuation Table 1 Exponential decay fitting of the time-dependent q00a .
Pine
PMMA
a
q00in
Expression of exponential decay fitting
R2
26 32 37 43 53 57
q00a q00a q00a q00a q00a q00a
¼ 7:04 expðt=330:59Þ þ 6:99 ¼ 7:37 expðt=222:56Þ þ 7:24 ¼ 8:47 expðt=140:27Þ þ 8:27 ¼ 9:90 expðt=114:26Þ þ 9:62 ¼ 11:45 expðt=77:01Þ þ 11:17 ¼ 12:62 expðt=54:64Þ þ 12:33
0.95517 0.97216 0.98137 0.98109 0.97692 0.97269
26 32 37 48 53 57
q00a q00a q00a q00a q00a q00a
¼ 1:85 expðt=75:60Þ þ 1:73 ¼ 3:46 expðt=86:05Þ þ 3:24 ¼ 6:67 expðt=89:95Þ þ 6:30 ¼ 11:95 expðt=122:75Þ þ 11:63 ¼ 14:38 expðt=140:65Þ þ 14:09 ¼ 37:12 expðt=234:18Þ þ 37:37
0.98539 0.99056 0.98955 0.98214 0.98219 0.93139
0.003
4
m" 3
2 0.002 1
q"a ( kw/m2)
m" ( kg/m2.s)
q"a
0 20
40
60
80
100
120
140
160
t (s)
b
3
m" q"a
2
1
0.001
q"a ( kw/m2)
m" ( kg/m2.s)
0.002
0 0.000 -1 0
20
40
60
80
100
120
140
t (s) Fig. 5. Absolute value of radiation attenuation coupled with mass flux (D = 0.1 m ðq_ 00in ¼ 32 kW=m2 Þ: (a) pine and (b) PMMA.
ð3Þ
The mass radiation absorptivity c, which has the units of L kg1 m1 and is used when b is in cm and f is in kg L1, is independent of the concentration of absorbing species. b is the absorbing path length of incident heat flux. f is the mass concentration of absorbing species. The parameter c represents the specific radiation absorptivity per unit mass concentration of absorbing components when radiant heat flux passes through per unit length of absorbing species in physics, see in Eq. (4).
c ¼ M=b f
ð4Þ
f ¼ m00 ðtÞ=v g
ð5Þ
It is assumed that the vertical releasing velocity of pyrolysis volatiles (vg) is a constant (vg = 0.25 m/s), which is observed and determined by experiment video, on the absorbing path of incident heat flux. Because of the absorbing path of pyrolysis volatiles is comparatively short (b = 0.1 m), it is assumed that the concentration of pyrolysis volatiles in every second period is uniform in the whole absorbing area and is determined by the time-dependent mass flux, see in Eq. (5). Then, the mass radiation absorptivity (c) is obtained by substituting the time-dependent mass concentration of pyrolysis volatiles (f) in Eq. (4) with the one in Eq. (5), see in Eq. (6). The mass radiation absorptivity with the relative value of radiation attenuation in Eq. (6) is based on one single degree of radiant heat fluxes in Beer’s law. Considering the different degree of radiant heat fluxes selected in experiment, the mass radiation absorptivity with the absolute value of radiation attenuation (c*, kW/kg) is applied in the analysis that followed, which can represent the difference of mass radiation absorptivity caused by different incident heat fluxes better, see in Eq. (7).
c ¼ M=½b ðm00 ðtÞ=v g Þ c ¼ ðM q_ 00in Þ=½b ðm00 ðtÞ=v g Þ
0.001 0
M ¼1N ¼cbf
ð6Þ ð7Þ
The c* of pine and PMMA both increase with time, as shown in Fig. 6. It may be because of that, as the increase of the temperature of test sample caused by external heating, the pyrolysis products potentially crack to gas components in the higher temperature [9] and the amount of gas components with the stronger radiation absorptivity in infrared wavelengths becomes larger. The increase rates of c* of pine and PMMA at different incident heat fluxes appreciably rise with the increase of incident heat flux, as the arrow shown in Fig. 6. The explanation above about the larger generation rate of the gas components with stronger radiation absorptivity at the larger incident heat flux can also be applied in here. So, for the result before concerning the attenuation rate of N increases with a rise of the incident radiant flux, the corresponding explanations of Kashiwagi and this paper before with a faster yield rate of pyrolysis volatiles are both not sufficient, and the contribution by the faster increase of c* at the larger incident heat flux also needs to consider. Furthermore, it is also found that the increase of the c* of pine and PMMA tends to be small, which may be ascribed to the saturation of radiation absorptivity [27]. In order to compare the mass radiation absorptivity of pyrolysis volatiles of pine and PMMA, the mean and the fitted mean of c* of
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a
0.8
0.5 0.4 0.3 (kW/kg)
(kW/kg)
0.6
0.2
26 kw/m2 37 kw/m2 53 kw/m2 Mean
0.1 0.0
32 kw/m2 43 kw/m2 57 kw/m2
0.4
0.2 Pine Mean Pine Mean Fitted PMMA Mean PMMA Mean Fitted
0.0 0
50
100
150
200
0
t (s)
50
100
150
200
t (s)
b
Fig. 7. Comparison of the mass radiation absorptivity of pine and PMMA.
1.0
(kW/kg)
0.8
Table 2 Exponential decay fitting of the mass radiation absorptivity of pine and PMMA.
0.6
Expression of exponential decay fitting
0.4
2
2
26 kw/m 37 kw/m2 53 kw/m2 Mean
0.2
32 kw/m 48 kw/m2 57 kw/m2
0.0 0
50
100
150
200
t (s) Fig. 6. Mass radiation absorptivity with absolute value of radiation attenuation: (a) pine, D = 0.1 m and (b) PMMA, D = 0.1 m.
them are processed, as shown in Figs. 6 and 7 and Table 2. It is found that the c* of pyrolysis volatiles of PMMA is actually larger than the one of pine. For heating under a uniform condition, the pyrolysis volatiles of PMMA may comprise more amounts of gas components with stronger radiation absorptivity in infrared wavelengths. This conclusion is different from the one in Section 3.2 which the q_ 00a of pine is larger. Because the analysis in Section 3.2 did not take the radiation attenuation with the mass flux together into account, compared with the more reasonable parameter c*, it is one-sided for determining the radiation absorptivity of pyrolysis volatiles of different fuels. Park and Blasi both pointed out the absorbed radiant energy played an important role in the induction of the gas-phase ignition [14,16]. Due to the in-depth radiation absorption of PMMA: (1) the rising rate of surface temperature of PMMA is smaller than the one of pine, the convection heating effect from sample surface is smaller for PMMA; (2) the mass flux of PMMA is also smaller than the one of pine. However, because the radiation absorptivity per unit mass concentration of pyrolysis volatiles of PMMA is larger than the one of pine; the proportion of induced heating by gas-phase radiation absorption for the ignition of PMMA is larger. It also means the ignition of PMMA more depends on the gas-phase heating by radiation absorption which is consistent with Kashiwagi’s relative conclusion [12].
Pine, D = 0.1 m PMMA, D = 0.1 m
*
c = 0.3581exp(t/64.7045) + 0.3767 c* = 0.7689exp(t/12.369) + 0.6698
R2 0.93534 0.89229
introduced briefly together with the new improved part of the model. The energy equation for the test sample on s(t) 6 x 6 L is,
qs C s
@T @ @T @T _ 00 C g ¼ ks þm @t @x @x @x @ qs hc q s hc q w þ Q þ hg þ @t qw qc qw qc
ð8Þ
The boundary conditions which include the time-dependent incident heat flux term (q_ 00in ðtÞ) with the fitted expressions in Table 1 and the invariable incident heat flux term ðð1 GÞq_ 00in Þ with the constant radiation attenuation coefficient referred to Nelson’s work [17] on the moving boundary x = s(t) are:
@T ks ¼ esur q_ 00in ðtÞ jsur ðT sur T 1 Þ esur rðT 4sur T 41 Þ ð9Þ @x x¼0 @T ks ¼ esur ð1 GÞq_ 00in jsur ðT sur T 1 Þ esur rðT 4sur T 41 Þ ð10Þ @x x¼0 The rate of pyrolysis is:
@ qs qs qc E qw exp ¼ A RT @t qw qc
ð11Þ
The conservation equation for the mass of gas is:
_ 00 @ qs @m ¼ @x @t
ð12Þ
The initial condition is:
t ¼ 0;
T ¼ T1;
q ¼ qw ; m00 ¼ 0
ð13Þ
5. Effect of radiation attenuation in radiant ignition model
The selected fuel for calculation is pine. The selected values of the parameters in model are shown in Table 3. Considering the radiation attenuation term in the boundary condition is related directly with the surface emissivity (esur), the different surface emissivities are selected in the numerical calculation for a comprehensive comparison of the effect of radiation attenuation in model.
5.1. Radiant ignition model
5.2. Comparison of calculation results
The model used in this paper to study the effect of radiation attenuation has been published in our work before [7]. So it is only
For current radiant ignition model, the critical surface temperature and the critical mass flux are the most commonly used
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Y. Zhou et al. / Combustion and Flame 157 (2010) 167–175
ignition criteria [2], so these two parameters are focused on in the followed numerical calculation concerning the effect of radiation attenuation.
a
500
400
Tsur (ºC)
300
200
100
0
b
Table 3 Selected values of the parameters in the model. Symbol
Value
Symbol
Value
Cp [5] Cc [5] Cg [5] kp [5] kc [5] Q [5] qc [5] G [17]
2140 J/kg K 1928 J/kg K 0 J/kg K 0.157 W/m K 0.084 W/m K 300000 J/kg 125 kg/m3 0.1
esur [5] esur [19] jsur [19]
0.98 0.72 10 J/m2 s K 150 kJ/mol 1.4 1010 s1 300 K 530 kg/m3 0.02 m
E [28] A [28] T1 [measured] qw [measured] L [measured]
Tac ( ε sur =0.72)
Tat (ε sur =0.98)
Tat ( ε sur =0.72)
100
t (s)
150
200
250
700 600 500 400 300 200 100
T0 ( ε sur=0.98)
T0 ( ε sur=0.72)
Tac ( ε sur=0.98)
Tac (ε sur=0.72)
Tat ( ε sur=0.98)
Tat (ε sur=0.72)
Te
0 20
40
60
t (s)
Fig. 8. Comparison of surface temperature history: (a) q_ 00in ¼ 26 kW=m2 and (b) q_ 00in ¼ 57 kW=m2 .
70 60
Δ Tsur ( ºC )
50 40 30 20
2
26kw/m 2 57kw/m 2 26kw/m 2 57kw/m
10 0 0
5.2.3. Time to ignition The critical auto-ignition and piloted-ignition surface temperature are selected to be 420 °C and 350 °C, respectively, for the mod-
T0 ( ε sur =0.72)
Tac ( ε sur =0.98)
50
0
5.2.2. Mass flux The calculated mass flux (m00 ) with ðm00a Þ: time-dependent ðm00at Þ, constant coefficient ðm00ac Þ and without ðm000 Þ the radiation attenuation by pyrolysis volatiles and the experimental one ðm00e Þ are shown in Fig. 10. Although there is still a certain difference between the m00a and the m00e , which is ascribed to the effect of the inner moisture and the simple one step global pyrolysis sub-model applied, compared to the m000 , the m00a is closer to the m00e . The radiation attenuation significantly reduces the mass flux peak and delays the time it is achieved. The peak value of the m00ac with the constant radiation attenuation coefficient G = 0.1 is close to the one of the m00at , and the time to peak of the m00ac is a little later than the one of the m00at . Fig. 10 also shows that there is an obvious area with large difference in mass flux ðDm0ac ; Dm0at Þ during the early stages of mass flux when the radiation attenuation is considered. The relative effect of radiation attenuation on the predicted time to ignition using a critical ignition mass flux will be presented in the chapter followed.
T0 ( ε sur =0.98)
Te
0
Tsur (ºC)
5.2.1. Surface temperature The calculated surface temperature (Tsur) history with ((Ta): time-dependent (Tat), constant coefficient (Tac)) and without (T0) the radiation attenuation by pyrolysis volatiles and the experimental one (Te) are shown in Fig. 8. Compared to the calculated Tsur with a surface emissivity esur = 0.98, the one with a surface emissivity esur = 0.72 is closer to the Te. It is indicated that the surface emissivity with a value esur = 0.98 is overestimated and the one with a value esur = 0.72 is more reasonable. So, a value esur = 0.72 is chose as the sample surface emissivity selected in all the followed numerical calculation conditions. Compared to the T0, the Ta is closer to the Te, which means the consideration of the radiation attenuation is resultful. It is also shown that the Tac with the coefficient G = 0.1 is close to the Tat, which means the selected value G = 0.1 is approximately accepted for the general calculation of radiant ignition model. The curves in Fig. 9 present the detailed difference in surface temperature history (DTsur) with and without the radiation attenuation. There is no obvious difference for the DTsur with different surface emissivity. The DTsur with the time-dependent radiation attenuation increases with time and can exceed 60 °C. The DTsur is larger in the early heating period (t < 150 s) at high incident heat fluxes (e.g. q_ 00in ¼ 57 kW=m2 ) for both time-dependent and constant radiation attenuation conditions. The relative effect of radiation attenuation on the predicted time to ignition using a critical ignition surface temperature will be presented in the chapter followed.
100
200
300
2
26kw/m 2 57kw/m 2 26kw/m 2 57kw/m
400
t (s) Fig. 9. Difference in surface temperature history with and without radiation attenuation: solid point, DTsur-ac; virtual point, DTsur-at; square point, esur = 0.98; circinal point, esur = 0.72.
el in this paper, which is referred to the species and size of wood sample [6]. The critical piloted-ignition mass flux is selected to be 2.5 g/m2 s, which is a widely applied value [2] and originally from Bamford’s work [29]. The calculated time to ignition (tig) with (time-dependent (tig-at), constant coefficient (tig-ac)) and without (tig-0) the radiation attenuation by pyrolysis volatiles and the experimental time to ignition (tig-e) are shown in Fig. 11. The difference between the experimental auto-ignition results and the predicted ones at high incident heat fluxes, as shown in Fig. 11a, is mainly ascribed to the selected critical auto-ignition surface temperature actually has a comparatively larger range [1,6] and a
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Y. Zhou et al. / Combustion and Flame 157 (2010) 167–175
a
0.007 Δ m"o-at
0.006
tig-e tig-ac
0.20
Δ m"o-ac
0.000
0.004 0
50
100
150
tig-o tig-at
tig -0.5( s-0.5)
0.002
0.005
m“ ( kg/m2.s)
0.004
0.15
200
0.003
0.10
0.002 0.001
m“0
m“at
0.000
m“e
m“ac
0
20
40
60
80
100
0.05 25
120
30
single value could not be appropriate for both high and low incident heat flux ranges. It could be seen in Fig. 11 that the time to ignition considered the radiation attenuation is closer to the experimental results for all the calculated conditions with different ignition criteria, which reflects the retardation effect for the pyrolysis and the attainment of an ignitable boundary layer mixture by the radiation attenuation, and illustrates that the consideration of the radiation attenuation by pyrolysis volatiles in radiant ignition models is necessary. It could also be seen that the tig-ac with the coefficient G = 0.1 is close with the tig-at, which also means the selected value G = 0.1 is approximately accepted for the general calculation of radiant ignition model.
b
40
45
50
55
60
50
55
60
50
55
60
0.30
tig-e tig-ac
0.25
tig -0.5( s-0.5)
Fig. 10. Mass flux with and without radiation attenuation: q_ 00in ¼ 37 kW=m2 , esur = 0.72.
35
q"in ( kw/m2)
t (s)
tig-o tig-at
0.20
0.15
0.10
0.05 25
30
35
40
45
q"in ( kw/m2)
In this paper, the radiation attenuation characteristics of pyrolysis volatiles of pine and PMMA when heated under a resistance element type radiant heater are experimentally studied by coupling with the synchronously measured mass loss rate. A radiant ignition model with different incident heat flux boundary conditions (none, constant and time-dependent radiation attenuation) is used to investigate how to reasonably consider the effect of radiation attenuation in radiant ignition model. The main conclusions include:
c 0.25
tig -0.5( s-0.5)
6. Conclusions
tig-e tig-ac
0.20
tig-o tig-at
0.15
0.10
1. The degree of radiation attenuation of incident heat flux of pine and PMMA (6–14%) is evident before ignition, although not as large as the Kashiwagi’s reported result (50–80%) with a laser radiant heater. 2. The radiation attenuation in the apparatus with the shorter radiation distance (D < 0.1 m), e.g. Cone Calorimeter type, is more obvious and needs more attention. 3. The increase trend of q_ 00a of pine and PMMA corresponds with the nonlinear relation between the amount of radiation attenuation and the concentration of absorbing components in Beer’s law. 4. For the attenuation rate of N increases with a rise of the incident radiant flux, it is not only caused by the faster concentration rise of pyrolysis volatiles, but also ascribed to the faster increase of the mass radiation absorptivity. 5. The c* of pyrolysis volatiles of PMMA is larger than the one of pine. The ignition of PMMA more depends on the gas-phase heating by radiation absorption. Compared to the M, the c* is more reasonable for determining the radiation absorptivity of pyrolysis volatiles of different fuels. 6. By comparing the calculated results with and without radiation attenuation, it illustrates that consideration of the radiation attenuation by pyrolysis volatiles in radiant ignition models
0.05 25
30
35
40
45
q"in ( kw/m2) Fig. 11. Comparison of time to ignition: esur = 0.72, (a) auto-ignition, critical ignition surface temperature; (b) piloted-ignition, critical ignition surface temperature; and (c) piloted-ignition, critical ignition mass flux.
for resistance element radiant heater heating condition is necessary. A constant radiation attenuation coefficient G = 0.1 is approximately accepted for the general calculation of radiant ignition model.
Acknowledgments This research was supported by National Natural Science Foundation of China (Grant No.: 50536030) and Program for New Century Excellent Talents in University (NCET-05-0551). The authors deeply appreciate the support.
Y. Zhou et al. / Combustion and Flame 157 (2010) 167–175
References [1] J.G. Quintiere, Fire Mater. 30 (2006) 175–214. [2] A.M. Kanury, Flaming ignition of solid fuels, in: The SFPE Handbook of Fire Protection Engineering, third ed., 1999 (Section 2/Chapter 11). [3] D. Drysdale, An Introduction to Fire Dynamics, second ed., Wiley, Chichester, UK, 1999. [4] T. Kashiwagi, Combust. Sci. Technol. 8 (1974) 225–236. [5] H.C. Kung, Combust. Flame 18 (1972) 185–195. [6] V. Babrauskas, J. Fire Protection Eng. 12 (2002) 163–189. [7] L. Yang, Combust. Flame 133 (2003) 407–413. [8] J.T. Kuo, C. His, Combust. Flame 142 (2005) 401–412. [9] C.D. Blasi, Prog. Energy Combust. Sci. 19 (1993) 71–104. [10] B. Moghtaderi, Fire Mater. 30 (2006) 1–34. [11] M. Delichatsios, Fire Safety J. 38 (2003) 219–228. [12] T. Kashiwagi, Combust. Flame 34 (1979) 231–244. [13] T. Kashiwagi, Combust. Sci. Technol. 20 (1979) 225–234. [14] S.H. Park, C.L. Tien, Int. J. Heat Mass Transfer 33 (1990) 1511–1520. [15] B. Amos, A.C. Fernandez-Pello, Combust. Sci. Technol. 62 (1988) 331–343. [16] C.D. Blasi, Combust. Flame 83 (1991) 333–344. [17] M.I. Nelson, Fire Safety J. 24 (1995) 107–130.
175
[18] V. Babrauskas, The Cone Calorimeter, The SFPE Handbook of Fire Protection Engineering, third ed., 1999 (Section 3/Chapter 3). [19] C.D. Blasi, Prog. Energy Combust. Sci. 34 (2008) 47–90. [20] E.M. Suuberg, Behavior of Charring Materials in Simulated Fire Environments, National Institute of Standards and Technology, Gaithersburg, MD, NIST-GCR94-645, 1994, p p. 75–79/p. 487. [21] B. Bodzay, J. Anal. Appl. Pyrol. 85 (2009) 313–320. [22] M. Stanislav, Polym. Degrad. Stabil. 64 (1999) 379–385. [23] G.W. Gokel, Dean’s Handbook of Organic Chemistry, second ed., McGraw-Hill Companies, Inc., 2004. [24] K. Wakatsuki, Proc. Combust. Inst. 30 (2005) 1565–1573. [25] M.L. Toison, Infrared and its Thermal Applications, Philips Technical Library, Centrex, Eindhoven, 1964. [26] P.A. Beaulieua, N.A. Dembseyb, Fire Safety J. 43 (2008) 410–428. [27] J.D.J. Ingle, S.R. Crouch, Spectrochemical Analysis, Prentice Hall, New Jersey, 1988. [28] B.M. Wagenaar, Fuel Process. Technol. 36 (1993) 291–298. [29] C.H. Bamford, On the combustion of wood. Part I. Proc. Cambridge Philos. Soc., 1946, pp. 166–182.