Energy Fuels 2010, 24, 609–615 Published on Web 10/26/2009
: DOI:10.1021/ef900781m
Experimental and Modeling Study of Atmospheric Pressure Effects on Ignition of Pine Wood at Different Altitudes Jiakun Dai, Lizhong Yang,* Xiaodong Zhou, Yafei Wang, Yupeng Zhou, and Zhihua Deng State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, 230026, Anhui Province, China Received July 23, 2009. Revised Manuscript Received October 13, 2009
The pyrolysis and ignition characteristics of wood in different atmospheric pressure are investigated experimentally and theoretically. A set of contrast experiments is carried out to study the effects of atmospheric pressure on the ignition characteristics of pine in the Tibetan plateau and Hefei, respectively. The experimental location pressure is 0.66 atm in the Tibetan plateau and 1.0 atm in Hefei. An extended model considering the atmospheric pressure and unsteady gas-phase processes is developed to predict the pyrolysis of wood. A comparison to experimental data shows that the predicted change trend of the mass loss rate using the model is relatively in good agreement with experiments. The results indicate that a lower atmospheric pressure can result in higher mass loss rates under the same external heat flux and the ignition time of wood in the Tibetan plateau is much earlier than that in Hefei. Further analysis is directed to assess a new relationship between the pressure and critical heat flux of flaming ignition, which confirms that the atmospheric pressure plays a vital role in pyrolysis and ignition of wood.
describe the pyrolysis process of charring materials,1-17 in which several parameters, such as wood porosity,2-4 moisture content,5-8 the orientation of the sample with an external heat source,9,10 ambient oxygen concentration,5,11-14 and wood shrinkage and crack formation,15,16 were taken into account. These comprehensive models are reasonable to predict the surface temperature, mass loss rate, and critical heat flux. However, the primary focus of these previous models is often not pressure-driven gas transport because the assumption of a one-dimensional model usually obviates the need. In subsequent studies, more realistic models were taken by other authors,18,19 who added a number of new features to the relatively simple model, including the effects of unsteady gasphase processes, velocity variation, and convective transport of volatile species. Nevertheless, up to now, it is depressing that ambient pressure is not identified as a key factor affecting the ignition and pyrolysis process of wood. In this study, aiming at the fire safety in the Tibetan plateau, the pressure effect is highlighted as an important controlling parameter of ignition. The contrast experimental investigations are carried out in Lhasa and Hefei, respectively, in which the ignition and mass loss rate of pine were measured. On the basis of Kung’s model, an extended model considering unsteady gas-phase processes is developed in detail to predict the pyrolysis of timber materials. The comparisons between the
1. Introduction Most societies recognize that the work of previous generations is an important part of their culture. Especially for the Tibetan culture or custom, historic buildings are a valuable part of this environment. In the Tibetan plateau, the number of listed or designated historic buildings over 100 years is thousands. However, historic buildings are exposed to the same fire threats as other buildings, including arson, lighting, construction operations, faulty equipment, and inadequate maintenance. Many specific aspects of the fire problem on the plateau are unknown, because the research of fire science in lower atmospheric pressure (0.66 atm in Tibet) is almost nonexistent. There is usually no accurate experimental data to study plateau fire dynamics. Indeed, pyrolysis of charring materials plays an important role in the early stage of building fire, which controls the production rate of fuel and the heat release rate. Thus, the capability to predict the ignition and burning rate of charring materials has become increasingly important as fire safety engineering moves toward a performance-based approach to wooden building design. There is a substantial volume of work in the literature dealing with the ignition, pyrolysis, and charring behavior of wood. As for the previous investigations, a large number of comprehensive models have been used to *To whom correspondence should be addressed. Telephone: þ86551-3606-416. Fax: þ86-551-3601-669. E-mail:
[email protected]. (1) Kung, H. C. Combust. Flame 1972, 18, 185–195. (2) Kansa, E.; Perlee, H.; Chaiken, R. Combust. Flame 1977, 29, 311– 324. (3) Blasi, D. C. Combust. Sci. Technol. 1993, 90, 315–340. (4) Melaaen, M. C. Numer. Heat Transfer, Part A 1996, 29, 331–355. (5) Lu, H.; Robert, W.; Peirce, G.; Ripa, B.; Baxter, L. L. Energy Fuels 2008, 22, 2826–2839. (6) Moghtaderi, B.; Dlugogorski, B. Z.; Kennedy, E. M.; Fletcher, D. F. Fire Mater. 1998, 22, 155–165. (7) Bryden, K. M.; Ragland, K. M.; Rutland, C. J. Biomass Bioenergy 2002, 22, 41–53. (8) de Diego, L. F.; Carcia-Labiano, F.; Abad, A.; Gayan, P.; Adanez, J. Energy Fuels 2003, 17, 285–290. r 2009 American Chemical Society
(9) Spearpoint, M. J.; Quintiere, J. G. Fire Saf. J. 2001, 36, 391–415. (10) Janssens, M. Interflam, 1993; pp 549-555. (11) Delichatsios, M. A. Fire Saf. J. 2005, 40, 197–212. (12) Weng, W. G.; Hasemi, Y.; Fan, W. C. Combust. Flame 2006, 145, 723–729. (13) Moghtaderi, B. Fire Mater. 2000, 24, 303–304. (14) Kashiwagi, T.; Ohlemiller, T. J.; Werner, K. Combust. Flame 1987, 69, 331–345. (15) Shen, D. K.; Gu, S.; Luo, K. H.; Bridgwater, A. V. Energy Fuels 2009, 23, 1081–1088. (16) Gronli, M. C.; Melaaen, M. C. Energy Fuels 2000, 14, 791–800. (17) Liang, X. H.; Kozinski, J. A. Fuel 2000, 79, 1477–1486. (18) Blasi, C. D. Prog. Energy Combust. Sci. 1993, 19, 71–104. (19) Moghtaderi, B.; Dlugogorski, B. Z.; Kennedy, E. M.; Fletcher, D. F. Fire Mater. 1998, 22, 155–165.
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: DOI:10.1021/ef900781m
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occurs. (6) Gases behave according to the ideal gas law. (7) Concerning the assumption of thermal conduction, it mainly refers to Kung’s work. The energy, volatiles mass, Darcy’s law, and ideal gas law equation constitute the mathematical description of the problem. Energy conservation: DT D kDT DT DF DðFcp Þ ¼ þ m_ 00 cp;mix þ a Qp - T Fcp Dt Dx Dx Dx Dt Dt ð1Þ Boundary conditions: DT -k Dx
Figure 1. Schematics of the experimental apparatus.
:00 ¼ q0 - σðT 4 - T¥ 4 Þ
ð2Þ
x¼0
predicted results and experimental data for pine are given. In the Modeling Section, basic equations and boundary conditions controlling the gas transport are derived and used to obtain the relationship between the atmospheric pressure and critical heat flux of ignition.
Tjx ¼ ¥ ¼ T¥
ð3Þ
Initial conditions: Tðx, 0Þ ¼ T¥
2. Experimental Section
Fðx, 0Þ ¼ Fw
For dimensions of the specimen, the heated surface area is 50 50 mm and the thickness is 20 mm. The specimen is tested in the horizontal orientation and placed in the specimen holder. The distance between the heated surface of the specimen and the rectangle radiator is 100 mm. There is no spark igniter above the sample surface, the way that spontaneous ignition is introduced. Samples are wrapped by low-density asbestos fiber insulation material, with only one surface exposed to radiation. Simultaneously, a layer of aluminum foil enwraps the asbestos fiber insulation material to prevent radiation heat loss. A schematic diagram is shown in Figure 1 to illustrate the experiment. The experiments are separately carried out in Lhasa (the capital of China’s Tibet Autonomous Region) and Hefei (the capital of the Anhui Province in eastern China). The atmospheric pressure in Lhasa is 0.66 atm, and the atmospheric pressure in Hefei is 1.0 atm. The tests include the measurements of the ignition time, mass loss percentage, and surface temperature, which are conducted under incident heat fluxes of 18-47 kw/m2. Every group experiment is performed until the flaming ignition of pine occurred, but the measure time is no more than 10 min. Under one incident heat flux level, two or three runs are performed with the same experimental conditions. Before each sample is placed in the specimen holder, the incident heat flux is measured to prevent error.
Fa ðx, 0Þ ¼ Fw - Fc
ð4Þ
where the values of k, F, and c are taken from the following relationships and the subscripts a, w, and c refer to the active material, wood, and char, respectively: 0 ! !1 F F a a A þ Fmix cp;mix 1 Fcp ¼ ε@Fw cp;w Fw - Fc Fw - Fc þ ð1 - εÞFc cp;c 0 k ¼ ε@kw
ð5Þ
! !1 Fa Fa A þ ð1 - εÞkc þ kmix 1 Fw - Fc Fw - Fc ð6Þ
The conservation of mass for the active solid phase gives DFa E ¼ - AFa exp ð7Þ RT Dt In eq 7, the specific solution presented here is for a single firstorder Arrhenius reaction. Blasi and Moghtaderi et al.18,19 have considered the porous structure of the solid, and the velocity of the gas phase is obtained from Darcy’s law kD dp ð8Þ uBmix ¼ μ dx
3. Modeling Section 3.1. Extended Model To Predict the Mass Loss Rate. On the basis of Kung’s model,1 a new one-dimensional pyrolysis model applicable to semi-infinite slabs can be formulated, in which features of gas transport and atmospheric pressure are taken into account. The model is mainly based on the following assumptions: (1) The wood consists of char and active materials, where the framework of the porous medium is made of char and the space is occupied by active wood. The wood is assumed to be initially nonporous. (2) The fuel volatiles are not regarded as flowing out of the solid immediately after their generation, and the mass flux of gas is related to the pressure gradient by Darcy’s law. (3) The volume occupied by active wood does not change as the solid undergoes pyrolysis. (4) The temperature of the volatile mixture is the same as the local char temperature, and the convective heat transfer between the volatile mixture and char is ignored. (5) No diffusive transport of volatile species
with the boundary condition pð0, tÞ ¼ p¥
ð9Þ
Using the ideal gas law, the density of mixture volatiles can be related to pressure and temperature R ð10Þ p ¼ Fmix T ¼ Fmix Rmix T M The conservation of the mass equation for the gas phase gives DFmix ε DF þ rðFmix uBmix Þ ¼ - a ð11Þ Dt Dt The set of equations from eqs 1 to 11 describe the heat- and mass-transfer processes for the pyrolysis of charring materials. 610
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with the boundary condition of the heated surface ð14Þ
pð0, tÞ ¼ p¥
Using conservation of mass on the pyrolysis front control volume, the other boundary condition is established kD p dx ðF - F Þ rp ¼ ð15Þ c Bi w εμRmix T dt x ¼ δc Concerning the parameters in eq 15, the functions p(x, t) and T(x, t) in the char layer are still unknown. 3.2.2. Temperature and Pressure Distribution in the Charring Layer. On the basis of the idealized scenarios as provided above in section 3.2.1, there are no chemical reactions in the charring layer and no heat transfer between the volatile species and the char. The temperature T(x) satisfies the following equations:
Figure 2. Schematic of the model for decomposition.
The unknowns are temperature (T), density of the active material (Fa), density of the control volume (F), mixture mass average velocity (umix), pressure (p), and density of the gas phase (Fmix). The governing equations in the section above form a set of nonlinear parabolic partial differential equations (PDEs), which can be solved numerically. Using a discrete method, the specific finite difference equations are obtained. The Crank-Nicolson method, which is stable regardless of the time step size for the linear problem, is used for calculations. 3.2. Theoretical Analysis about the Effect of the Pressure on the Critical Heat Flux. In a previous study,12 the fuel mass flux at ignition is nearly independent of the oxygen concentration. Therefore, a reduced oxygen atmosphere has relatively no influence on the ignition time and the critical heat flux. Rather than the effect of the oxygen concentration, the influence of the atmospheric pressure on the ignition of wood receives more attention in this study. 3.2.1. Transport Modeling of Volatile Species. According to the previous work by Spearpoint and Quintiere20 and Baum and Atreya,21 the following specific assumptions are included: (1) The wood decomposes to volatile species and char in an infinitesimal pyrolysis front at a fixed vaporization temperature. (2) The solid is semi-infinitely thick. (3) The virgin wood is inert and nonporous up to decomposition. (4) The char material is also inert but assumed to be porous. (5) The volatile species evolved by thermal degradation are transported by pressure differences through the porous char. (6) The temperature of volatiles is the same as the local char temperature, and the convective heat transfer between the volatiles species and the char is ignored. The physics of the thermal pyrolysis of wood is portrayed in Figure 2. On the basis of the assumptions above, the fuel volatiles will fill in the porous medium after their generation. Because the fuel decomposes to volatiles in an infinitesimal pyrolysis front at a predefined temperature, no volatile generation term in the porous char matrix exists. Thus, the mass conservation equation for the evolved gas takes the form DðFmix εÞ þ rðFmix uBmix Þ ¼ 0 ð12Þ Dt Substituting eqs 8 and 10 into eq 12 D p kD p ¼ r rp Dt T εμT
Fc cp;c
DTc D2 Tc ¼ kc 2 Dt Dx
0 e x e δc
ð16Þ
with boundary conditions dTc - kc dx dx Fw ½Hp ¼ dt
:00 ¼ q0
ð17Þ
x¼0
DTw DTc - kc kw Dx Dx
ð18Þ x ¼ δc
Tc jx ¼ δc ¼ Tp
ð19Þ
A similarity variable η is introduced into the PDE above x kc ηc pffiffiffiffiffiffiffiffiffi , Rc ¼ F 4Rc t c cp;c
ð20Þ
In previous work,21 it was indicated that the interface position (x = δc) is related to a constant value of η, with defining η = C. Then, eq 16 becomes - 2ηc
dTc d2 Tc ¼ dηc dη2c
0 e ηc e C
ð21Þ
Combining boundary conditions, the solution satisfying eq 21 can be written in the form pffiffiffiffiffiffiffiffiffiffi :00 Rc πt q0 ½erfðηc Þ - erfðCÞ þ Tp ð22Þ Tðηc Þ ¼ kc Considering the function of pressure in the char layer p(x, t), the derivation starts from eq 13. The similarity variable η is similarly introduced into eqs 13 and 15. The particular procedure of derivation refers to the study by Baum and Atreya21 Z ηc pðηc Þ ¼ p¥ ð1 þ 2N ðGðuÞ2 ÞduÞ1=2 ð23Þ 0
where N was defined as in a previous work dðp=p¥ Þ ðp=p¥ Þ N dη
ð13Þ
ð24Þ
ηc ¼ C
(21) Baum, H. R.; Atreya, A. Proc. Combust. Inst. 2007, 31, 2633– 2641.
(20) Spearpoint, M. J.; Quintiere, J. G. Combust. Flame 2000, 123, 308–324.
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Table 1. Values of Properties and Parameters Used in Numerical Calculation parameter log A E Fw cp,w kw Fc cp,c kc
value
reference
-1
parameter
25 25
6.7 s 114.5 kJ/mol 500 kg/m3 2520 J kg-1 K-1 0.126 W m-1 K-1 125 kg/m3 2520 J kg-1 K-1 0.08 W m-1K-1
cp,mix Qp L σ kD q000 T0
1 1 1 1 1
value -1
1008 J kg K 300000 0.02 m 5.67 10-8 3.12 10-10 30 kW/m2 300 K
reference -1
1 1 assumed
Figure 3. Calculated values of the mass percentage in different atmospheric pressures under 37 kW/m2.
Figure 4. Comparison of residual errors with polynomial orders 5 and 7.
and G(u) is obtained from eq 22 TðuÞ GðuÞ ¼ Tp
Substituting eq 29 into eq 30 :00 :00 1 q0 - β qcr std pffiffiffiffiffiffiffi ¼ 00 00 : tign C1 ð q0 =m_ ign Þðp¥ =pstd Þ2 þ C2
ð25Þ
3.2.3. Evaluation of the Critical Heat Flux. The mass flux vector is related to the pressure gradient through the equation ! 2 0:5rp ð26Þ m_ 00 ¼ Fmix uBmix jx ¼ 0 ¼ - kD εμRmix T
where subscript std refers to standard atmospheric pressure and constants C1 and C2 correspond, respectively, to C1 ¼
x¼0
Substituting eqs 22 and 23 into eq 26 kD Np¥ 2 m_ 00 ¼ - pffiffiffiffiffiffiffi 2ε Rc tμp Tp Rmix
ð31Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi kD Nπpstd 2 Fc cp;c kc Fc cp;c πðTp - T¥ Þ pffiffiffiffiffi erfðCÞ, C2 ¼ 2 4εμp Tp Rmix kc 4. Results and Discussion
ð27Þ
At the ignition time, eq 27 can be rearranged as pffiffiffiffiffiffiffiffiffiffiffiffi kD Np¥ 2 Rc tign ¼ 00 2εμp Tp m_ ign Rmix
4.1. Validation of the Model. The properties of pine used in this simulation are taken from the literature and shown in Table 1, where the specific heat of char is assumed to be the same as that of the virgin material.1 The calculation mass loss curves are shown in Figure 3. However, possibly because of errors of the computer, some singular points exist in the calculated data. The first-order derivation of the curves in Figure 3 is difficult to perform as a result of these bad points. Therefore, it is necessary to smooth these curves using polynomial fitting. In this case, the smoothing quality should be characterized in mathematical senses. We choose two orders (5 and 7) to carry out the polynomial fitting, and the polynomial order corresponding to the better smoothing quality is selected using residual errors analysis. As shown in Figure 4, the residual errors with respect to 7-order polynomial fitting present a Gaussian distribution, which implies that a higher quality of smoothing can be achieved using 7-order polynomial fitting. Similarly, the smoothing results of other curves in Figure 3 are also given through the same procedure above. After the derivation of smoothing curves, the calculated mass loss rates in different atmospheric pressure are shown in Figure 5. According to the calculated results, the influence of the atmospheric pressure is quite evident. The lower the atmospheric pressure, the higher the mass loss rate.
ð28Þ
Adding eqs 22 and 28 with respect to the surface temperature at ignition time is pffiffiffi :00 kD Np¥ 2 π q0 erfðCÞ þ Tp ð29Þ Tign ¼ 00 2εμp Tp m_ ign Rmix kc x¼0
For the thermal thick material, the ignition time is given by the following formula:22,23 :00 :00 q0 - β qcr std 1 2 ð30Þ pffiffiffiffiffiffiffi ¼ pffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tign π kc Fc cp;c ðTign - T¥ Þ Here, β is a correction coefficient, and q_ 00cr_std is defined as the critical ignition time in standard atmospheric pressure. (22) Delichatsios, M. A. Proceedings of the 6th International Symposium Fire Safety Science, International Association of Fire Safety Science (IAFSS), 1999; pp 233-244. (23) Delichatsiosa, M.; Parozb, B.; Bhargavac, A. Fire Saf. J. 2003, 28, 219–228.
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: DOI:10.1021/ef900781m
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Figure 5. Calculated mass loss rates in different atmospheric pressures under 37 kW/m2.
Figure 7. Experimental mass loss rates in Lhasa (atmospheric pressure of 0.66 atm) under different heat fluxes.
Figure 6. Experimental mass loss rates in Hefei (atmospheric pressure of 1.0 atm) under different heat fluxes. Figure 8. Comparison of the calculated and experimental mass loss rates under 37 kW/m2 in Lhasa and Hefei.
To evaluate the accuracy of the extended pyrolysis model in this study, the predicted mass loss rates should be compared to two sets of experimental results in Lhasa and Hefei. The experimental mass loss rates of pine under different incident heat fluxes are shown in Figures 6 and 7, which are carried out in Hefei and Lhasa, respectively. As shown in Figures 6 and 7, it is clear that higher heat flux brings about a larger mass loss rate. Whereas, as shown in Figure 8, the mass loss rate in Lhasa is far more than that in Hefei under external heat flux of 37.0 kW/m2. It is indicated that, at the same heat flux, a higher mass loss rate is present in Lhasa with a lower atmospheric pressure. As can be seen from Figure 8, the calculated and measured mass loss rates in Lhasa (after 20 s) and in Hefei (after 60 s) are in good agreement. However, with a comparison of the experimental data, the predicted mass loss rates are still null in the initial stage (0-20 s in Lhasa and 0-60 s in Hefei). The differences are thought to be due to several simplifications within the pyrolysis model. In the actual process of pyrolysis, the moisture evaporation mainly contributes to the mass loss in the initial stage, but in the current pyrolysis model, the effect of moisture is neglected. Meanwhile, with a remarkable increase of the surface temperature, the boundary condition p(0, t) may be less than the initial ambient pressure. Thus, the moisture or pyrolysis volatiles are easier to release from the charring layer. However, ignoring the effect of the temperature, the ambient pressure is constant and the onset of the mass loss is delayed evidently. Therefore, no diffusive transport of moisture and pyrolysis volatiles occurs, and there is no mass loss in the initial stage. As for the Hefei experimental curve, the mass loss rate gradually increases after about 90 s, but the corresponding calculated curve has a
decreasing trend. This discrepancy may be due to the simplified boundary condition. In reference to Boonmee and Quintiere’s work,24 char surface oxidation plays a significant role in the onset of glowing ignition; therefore, it is necessary to consider the char oxidation in the surface boundary condition for the energy equation. Meanwhile, the decrease of char because of oxidation may mainly contribute to the overall mass loss. However, in our model, the influence of charring oxidation is ignored, which may lead to the discrepant change trend after 90 s between the experimental and calculated curves. Except for these discrepancies presented above, the comparison between the calculated and experimental results (Figure 8) still denotes that the extended model with its more sophisticated mass-transport scheme is relatively successful to predict the change trend of the experimental data. It is implied that the ambient pressure may play an important role in the ignition of pine wood. 4.2. Discussion of the Ignition Time and Critical Heat Flux. Table 2 exhibits the experimental data of the ignition time and mass loss rate in Lhasa and Hefei. The symbol “-” represents no experiment, and the experimental data is supplied with the method of interpolation. For example, under heat flux of 32.8 and 35.2 kW/m2, it is forecasted that the range of the ignition time is 21-48 s in Lhasa. When incident heat flux is 40.0-46.4 kW/m2, ignition time in Lhasa is approximately 0-31 s, which is much shorter than that in Hefei. If spontaneous ignition cannot occur, the ignition (24) Boonbee, N.; Quintiere, J. G. Proc. Combust. Inst. 2005, 30, 2303–2310. (25) Branca, C.; Blasi, C. D. Energy Fuels 2003, 17, 1609–1615.
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Table 2. Ignition Times for Pine in Different Atmospheric Pressures under Heat Fluxes of 18-47 kW/m2 incident heat flux (kW/m2) 18.3 24.7 30.0-30.3 32.8 35.2-35.5 37.0 40.5-41.0 44.1 45.4 46.4
ignition time in Lhasa (s)
mass loss rate (%/s)
180, 250, 280 83, 90 40, 48 21, 31 -
ignition time in Hefei (s)
0.045 0.071 0.081 0.09 -
mass loss rate (%/s) 0.049 0.070 0.063 0.069 0.081 0.095
no ignition no ignition no ignition 170 128, 110, 122 104, 109 72, 91 74, 64, 67, 62 56 48, 49
Figure 10. Plotting ignition time raised to the -0.55 power on the y axis and the irradiance on the x axis.
Figure 9. Plotting ignition time raised to the -0.5 power on the y axis and the irradiance on the x axis.
Table 3. Parameters To Describe the Data Fit in Figure 1
time is defined as infinite. Therefore, as displayed in Table 2, under the same incident heat flux, the ignition time in Lhasa is much shorter than that in Hefei obviously. According to our experimental data, the lowest heat flux under which ignition occurrs is 18.3 kW/m2 in Lhasa and 32.8 kW/m2 in Hefei, with no ignition at 16.0 and 30.0 kw/m2. The critical incident heat fluxes in two altitudes are estimated to be 17.2 and 31.4 kw/m2, respectively. A lower critical incident heat flux is measured in the plateau, and the ignition of pine wood occurs much easier at lower atmospheric pressure. Consequently, in Lhasa with lower pressure, the predicted ignition time becomes earlier than that in Hefei under the same external heat flux. In section 3.2.3, it has been concluded that the critical heat flux of ignition can be related to the atmospheric pressure by eq 31. From Table 2, the higher the applied external heat flux, the more mass flux is measured at ignition time, which indicates that m_ 00ign has an approximate linear relationship with q_ 000 . Thus, a simple assumption is established :00 q0 ¼ C3 00 m_ ign
ð32Þ
intercept on the x axis 11.1 21.4
A more accurate value of the critical heat flux can be estimated using eq 35. Simultaneously, it is convenient to obtain the slope and intercept from the straight line in Figure 10. These results are listed in Table 3. As shown in Figure 10, the intercept at the x axis of the two fit lines is not equal, which implies that the atmospheric pressure plays a different role in the slope and intercept. Thereby, eq 35 is more reasonable to rewrite as
ð33Þ
where C4 = C1C3. Considering that C2 and C4, independent of atmospheric pressure, are both constants, eq 33 becomes :00 :00 q - β qcr std 1 pffiffiffiffiffiffiffi ¼ 0 tign Cign ðp¥ =pstd Þn
slope λ 0.00665 0.0045
approximations to an inert-body model of an igniting solid, plotting the ignition time raised to the -0.5 power on the y axis and the external heat flux on the x axis, which is illustrated with the experimental data in Figure 9. When the data are plotted in this way, the x axis intercept is obtained using linear fitting. For well-insulated samples, the intercept is 64% of the critical heat flux22,23 and the correction coefficient β = 0.64. In the example, the critical heat flux is evaluated to be 15.2 kW/m2 in Lhasa and 28.1 kW/m2 in Hefei. In comparison to experimental results (17.2 kw/m2 in Lhasa and 31.4 kw/m2 in Hefei), the calculation results are relatively small. Previous work26,27 entails plotting the ignition time raised to the -0.55 power on the y axis. Thus, eq 34 is rewritten as :00 :00 q - β qcr std ð35Þ tign - 0:55 ¼ 0 Cign ðp¥ =pstd Þn
On the basis of eq 32, eq 31 can be rearranged as :00 :00 q0 - β qcr std 1 ¼ pffiffiffiffiffiffiffi tign C4 ðp¥ =pstd Þ2 þ C2
experimental location Lhasa Hefei
tign
ð34Þ
In eq 34, the constant Cign and order n need to be confirmed using experimental data. This equation is based on numeric
- 0:55
1 ¼ Cign
! :00 :00 β qcr std q0 ðp¥ =pstd Þn1 ðp¥ =pstd Þn2
(26) Janssens, M. L. Fire Mater. 1991, 15, 151–167. (27) Babrauskas, V. J. Fire Prot. Eng. 2002, 12, 163–188.
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ð36Þ
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: DOI:10.1021/ef900781m
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Using of the results in Table 3, the parameters n1 and n2 in eq 36 are n1 ¼ lnðλLhasa =λHefei Þ=lnðp¥ :00 n2 ¼ n1 þ lnð qcr lnðp¥
Hefei =p¥ Lhasa Þ
≈1
Acknowledgment. The authors deeply appreciate the financial support from the National Natural Science Foundation of China (50976111).
ð37Þ
Nomenclature A = pre-exponential factor (s-1) C = constant cp = specific heat (J K-1 kg-1) E = activation energy (kJ mol-1) H = enthalpy (J kg-1) k = thermal conductivity (W m-1 K-1) kD = Darcy’s coefficient (m3 s kg-1) L = thickness (m) M = molar mass (kg mol-1) m_ 00 = mass flux of volatile material (kg m-2 s-1) n = order p = pressure (Pa) q_ 000 = incident heat flux (kW m-2) q_ 00cr = critical incident heat flux of ignition (kW m-2) Q = endothermicity (J kg-1) R = gas content (8.314 J mol-1 K-1) t = time (s) T = temperature (K) u = velocity (m s-1) R = thermal diffusion coefficient (m2 s-1) β = correction coefficient F = density (kg m-3) ε = porosity η = progress variable μ = gas viscosity coefficient (N s m-2) λ = slope σ = Stefan-Boltzmann constant (5.67 10-8 W m-2 K-4) δ = depth (m)
:00
Lhasa = qcr Hefei Þ=
Hefei =p¥ Lhasa Þ
≈ - 0:6
ð38Þ
Finally, substituting eqs 37 and 38 into eq 36 tign
- 0:55
1 ¼ Cign
:00 q0 ðp¥ =pstd Þ1
-
:00 β qcr
std ðp¥ =pstd Þ- 0:6
! ð39Þ
Under the critical heat flux, tign-0.55 = 0. Therefore, the relationship between the atmospheric pressure and critical external heat flux of ignition is :00 :00 ð qcr 1 = qcr 2 Þ ¼ ðp¥ 1 =p¥ 2 Þ1:6
ð40Þ
From eq 40, it is clear that higher atmospheric pressure can result in a larger critical heat flux for flaming ignition. 5. Conclusion In this paper, the contrast experiments in Lhasa and Hefei have significantly advanced our understanding of the ambient pressure influence on ignition characteristics of pine. With a comparison to experimental results in Hefei, a lower critical heat flux was measured in Lhasa with a pressure of only 0.66 atm. Therefore, the ignition of pine occurs much easier in lower ambient pressure. A new model considering factors of gas transport and pressure is relatively successful in predicting the trend of the mass loss rate in different atmospheric pressures, which agrees with the experiments reasonably well. It is indicated that this model can give a simple description of the atmospheric pressure effects on the mechanism of wood pyrolysis. In theoretical analysis, the relationship between the atmospheric pressure and critical external heat flux of ignition is established, and it is concluded that the increase of the atmospheric pressure results in a higher critical heat flux for flaming ignition.
Subscripts 0 = initial condition ¥ = ambient a = active material c = char w = wood mix = gas-phase mixture ign = at ignition time p = pyrolysis
615
