- Email: [email protected]
A modified model of pyrolysis for charring materials in fire
International Journal of Engineering Science 40 (2002) 1011–1021 www.elsevier.com/locate/ijengsci
A modified model of pyrolysis for charring materials in fire Yang Lizhong *, Chen Xiaojun, Zhou Xiaodong, Fan Weicheng State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui Province 230026, People’s Republic of China Received 13 June 2001; accepted 13 August 2001
Abstract A modified model of pyrolysis for charring materials in fire has been proposed in this paper. In this model some special factors which show the effect on pyrolysis are considered, i.e., heat loss by convection and radiation caused by surface temperature rise and shrinkage of char surface are considered. Experimental device is designed specially for validating the reliability of the model. Effects of density of materials and heat radiation on pyrolysis of materials have also been investigated. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Charring materials; Pyrolysis; Fire; Thermal radiation; Model
1. Introduction The pyrolysis behavior of solid materials can be divided into two types: noncharring and charring [1,2]. Noncharring materials such as PMMA burn away completely, leaving no residue, and can be modeled using a theory similar to flammable liquids. In contrast, charring materials leave relatively significant amounts of residue when they burn. The pyrolysis of charring materials such as wood is a complex interplay of chemistry, heat, and mass transfer. Charring materials must be modeled in terms of a pyrolysis front penetrating into the materials with an increasing surface temperature and without a well-defined steady state. The char layer forms an increasing thermal resistance between the exposed surface and the pyrolysis front, resulting in a continuously decreasing rate of heat release after the first peak. Combustion is a complex interplay of chemical reaction, heat, and mass transfer, and combustion of solid materials becomes more complex because of the existing solid phase. Main combustible materials appearing in building fire are wood and other cellulosic materials, thus a *
Corresponding author. Tel.: +86-551-360-6416; fax: +86-551-360-1669. E-mail address: [email protected] (Y. Lizhong).
0020-7225/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 0 - 7 2 2 5 ( 0 2 ) 0 0 0 0 2 - 2
1012
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
study on their combustion characteristics during fire shows an important role. Maybe it is the key for a study on the ignition of solid materials and fire spreading to the research on pyrolysis of solid materials. Consider a ‘‘thick’’ sample of wood with its surface uniformly exposed to a constant external heat flux. So the heat and mass transfer through the sample can be considered one-dimensional. Ignition can occur at surface temperature anywhere from 200 to 400 °C. At the instant of ignition, the heat flux to the surface of the wood is a combination of the external flux plus the flux from the flame. The rate of heat release rapidly rises to a maximum, then a char layer gradually builds up as the pyrolysis front moves inward. Its rate of heat release eventually reaches a more or less steady value [3]. At temperature above around 300 °C the char layer begins to break down rapidly. The char layer also shrinks and pressure gradients are set up within the materials. Small cracks appear on the surface, and these cracks allow volatiles to escape more easily. The cracks gradually widen as the char layer deepens [3]. Owing to its importance and complexity of pyrolysis of charring materials, there is a substantial volume of work regarding the ignition, pyrolysis, burning, and charring behavior of wood and cellulosic materials experimentally and theoretically [4–12]. A thorough review on this work has been described by other researchers [1] and it is not the intent of the work. We will present a brief summary. Several models for the burning rate of solid materials, both charring and noncharring, have been developed. Examples include the studies by Hsiang-Cheng Kung [9], Indreks Wichman et al. [10] and Ellen et al. [11]. These models range from simple treatments of the ignition and burning process using pure heat conduction models to the use of complex chemical kinetics for the pyrolysis of charring materials. However, each model has its restrictions. In this paper, a modified one-dimensional pyrolysis model, which considers transient conduction, gas convection, endothermic effect of process, non-linear boundary condition and shrinkage of the slab, is proposed. The model is also compared against experimental data obtained from our research on white pine.
2. Theory The model proposed in this paper considers some factors that have a strong influence on pyrolysis of solid materials such as: transient heat conduction inside solid materials; the effect of gas convection on heat transfer; thermal effect of pyrolysis process. Moreover, thermal properties of materials are permitted to vary with temperature. 2.1. Assumptions It is a complex process for wood pyrolysis and combustion. Thus it is very difficult to consider all factors affecting the process in numerical simulation. Specific assumptions are needed to establish the mathematical model: (1) The volatiles do not accumulate within the char layer but are produced and leave the surface of the solid immediately. Actually, most volatiles exit immediately, while others penetrate into the inner of solid.
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1013
(2) Moisture content of solid is neglected. Actually, water affects mainly mass loss at early stage of heating and postpones surface temperature rise. (3) Chemical reaction between volatile and char layer, char and air is ignored. (4) Materials properties are assumed to be linear with the range of temperatures considered. 2.2. Controlling equation The surface and inner temperatures of wood will increase at external heat flux. When the temperature reaches the vaporization temperature, water begins to vaporize. Most water vapor produced exits from the upper surface, while a little penetrates into the surround. In case all water exits, the surface temperature of wood rises more and pyrolysis rate begins to increase and to form a pyrolysis reaction zone. Along with propagation of the reaction zone, different wood layers decompose simultaneously at different temperatures because of temperature field of the inner of wood and different product forms. Features of the model and the physics of the thermal decomposition of wood are portrayed in Fig. 1. Density of the decomposed wood is given as qf ð1Þ qa þ qf ; qs ¼ 1 qw where qs is the density of decomposed wood, qf is the density of the char, qa is the density of decomposing wood and qw is the density of the virgin wood. Arrhenius equation is chosen to describe the reaction rate, oqs Ea n ws ¼ ¼ qa A exp ; ð2Þ ot RT where n is the reaction index, Ea is the reaction active energy and A is the pre-exponential factor. Based on the above two equations, we obtain n dqs qs qc Ea ¼ A q exp : ð3Þ dt qw qc w RT
Fig. 1. Schematic of model for decomposition.
1014
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
Gas mass conservation equation is given as oMg oqs ¼ ; ox ot
ð4Þ
where Mg is the mass of volatiles. Energy conservation equation is given by oðqs hs Þ o oT o oq ¼ ks þ ðMg hg Þ Q s ; ð5Þ ot ox ox ox ot RT where qs hs ¼ qa ha þ qg hg , h ¼ T0 Cp dT , subscript g refers to gas and Q is the reaction heat of pyrolysis process. ha ¼
Z
T
Cpa dT ;
hc ¼
T0
Z
T
Cpc dT ; T0
hg ¼
Z
T
Cpg dT :
ð6Þ
T0
Combining Eqs. (4) and (5), we obtain oT o oT oT oq hc qc ha qw ¼ ks þ Q þ hg þ qs Cps : þ Mg Cpg ot ox ox ox ot qw qc qw qc Boundary condition is oT ¼ q00 hðTs T0 Þ erðTs4 T04 Þ: ks ox x¼0
ð7Þ
ð8Þ
Initial condition is T ¼ T0 ;
q ¼ q0 ;
Mg ¼ 0
ðt ¼ 0Þ:
ð9Þ
Material properties are assumed to be linear functions of temperature, i.e., k ¼ k 0 þ k ðT T0 Þ;
ð10Þ
Cp ¼ Cp0 þ Cp ðT T0 Þ;
ð11Þ
where k 0 is the thermal conductivity at constant temperature, k and Cp are the linear coefficients with temperature and Cp0 is the thermal capacity at constant temperature. Three unknown parameters, i.e., qs ðx; tÞ, Mg ðx; tÞ, T ðx; tÞ, can be solved according to Eqs. (3), (4) and (7). 2.3. Modifications on the formers’ model Main modifications of the model are as follows: (1) Generally, equal thermal flux density was applied and heat loss via convection and radiation caused by rise of surface temperature of wood
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1015
was not considered for the existed models. The heat loss is considered in the model presented in this paper. It is described in Eq. (8). (2) Actually, the surface of wood shrinks along with wood decomposition. This situation is considered in the model. 2.4. Dimensionless analysis and solution The following dimensionless variables are selected to consolidate the variables: qa q q T Ea ; qs ¼ s ; qc ¼ c ; T ¼ ; T E ¼ ; T0 qw qw qw RT0 Cps Cpa Cpc Cpg C ps ¼ ; C pa ¼ ; C pc ¼ ; C pg ¼ ; Cpw Cpw Cpw Cpw qa ¼
x x¼ ; l
t¼
tkw ; Cpw qw l2
k¼
ks ; kw
Q¼
Q ; Cpw T0
A¼
Ts ¼
Ts ; T0
ACpw qw l2 ; kw ð1 qc Þ
Mg ¼
Mg Cpw l kw
Substituting for the dimensionless variables in the above equations: Eqs. (3), (4), (7)–(9), oqs n ¼ Aðqs qc Þ exp ot
TE ; T
ð12Þ
oM g oqs ¼ ; ox ot
ð13Þ
o2 T qs C ps oT 1 oqs Q ¼ þ ox k ot k ot
Z
T
1
! C pa qc C pc M g C pg oT 1 oT C pg dt ; ox k ox 1 qc 1 qc k
ð14Þ
oT q00 l hl erl 4 ¼ ðT s 1Þ ðT 1Þ k s ox x¼0 kw T0 kw kw s
ð15Þ
T ¼ 1;
ð16Þ
qs ¼ 1;
Mg ¼ 0
ðt ¼ 0Þ:
Crank–Nicolson method is used to solve these dimensionless equations [9]. Numerical modeling description can be also found in Hsiang-Cheng Kung’s paper [9]. The values of some parameters are chosen according to Table 1. By the way, moisture content is not considered in the model proposed in this paper.
3. Description of experiments A device to study characteristics of fire at an early stage has been developed by State Key Laboratory of Fire Science (SKLFS). It is schematically shown in Fig. 2. The device is made of stainless steel. Its outer dimension is 1.5 m long by 1.5 m wide by 2.0 m high. Actually, there exists a specimen holder (550 mm long by 550 mm wide) on the rack. The device can mainly be used to
1016
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
Table 1 The selected value of some parameters A E T0 Q h1 h2 0 Cpa 0 Cpc 0 Cpg Cpa Cpc Cpg 0 ka kc0 ka kc
7.4E9 s1 1.45E8 J/(mol K) 300 K 3.0E5 J/kg 10 W=ðm2 KÞ 10 W=ðm2 KÞ 2140 J/(kg K) 1928 J/(kg K) 2000 J/(kg K) 4.19 J=ðkg K2 Þ 1.98 J=ðkg K2 Þ 0 J=ðkg K2 Þ 0.157 W/(m K) 0.084 W/(m K) 0.0003 W=ðm K2 Þ 0.0002 W=ðm K2 Þ
Fig. 2. Schematic of the device: (1) elevator; (2) load cells; (3) heat insulation; (4) rack; (5) sample; (6) electrical radiator; (7) exhaust hood; (8) sampling position; (9) smoke duct.
measure parameters such as flame temperature, flame image area, smoke components, smoke temperature, smoke flux, weight loss of sample, ignition temperature of sample, ignition time, etc. The sample is dried before experiment. The distance between sample and rectangle radiator may change from 300 to 800 mm. The sample is ignited using an electrical radiator. Power of the
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1017
radiator is 0–110 kW and can be adjusted continuously. The cross-section of the radiator is 450 mm 450 mm. Sample is placed on the holder and ignited by the electrical radiator. A minimum of two runs is carried out for each material at each heat flux. If the runs are significantly different, a third run is made.
4. Results and discussions As described in the above analysis, surface temperature and mass loss rate of sample are the two key parameters during thermal decomposition of solid materials. Usually, surface temperature of sample is the controlling factor to determine if materials can be ignited or not when there is no pilot ignition source. Mass loss rate is related with combustion rate and heat release rate is calculated based on the mass loss rate [13], Q_ ðtÞ ¼ mloss ðtÞ vA ðtÞ Hc ;
ð17Þ
where Hc is the combustion heat of volatiles and vA ðtÞ is the combustion efficiency (<1.0). Fig. 3 gives the experimental and theoretical values of mass loss rate of white pine under thermal radiation. Fig. 4 is a comparison of the theoretical value and TG experiments. As shown in Fig. 3, calculation value is little higher than the experimental value at early stage. As a whole, they match well. These results have shown that the model presented in this paper is reasonable. But as shown in Fig. 4, little discrepancy exists between theoretical and experimental value. This may be due to different environments between TG experiments and pyrolysis of solid materials at real fire. Figs. 5–8 give some calculation results based on the model. Figs. 5 and 6 indicate the dependence of decomposition and surface temperature on the density of solid materials at fixed thermal radiation, respectively. As shown in these two figures, mass loss increases with decreasing density of materials, however, variation of surface temperature shows a little complexity. It increases with the decreasing density first, then decreases.
Fig. 3. Comparison between experiments and decomposition.
1018
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
Fig. 4. Comparison between calculated values and TG experiments.
Fig. 5. Effect of density on decomposition ð50 kW=m2 Þ.
Fig. 6. Effect of density on surface temperature rise ð40 kW=m2 Þ.
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1019
Fig. 7. Effect of external thermal flux on decomposition.
Fig. 8. Effect of external thermal flux on surface temperature.
Figs. 7 and 8 show the dependence of mass loss and surface temperature of materials on external thermal radiation. As can be seen from these two figures, mass loss and surface temperature of solid materials increase with the increase of thermal radiation. Generally, fire risk of materials can be assessed using two parameters: heat release rate and ignition time. The former is related to fire development and the latter affects fire occurrence. The bigger the heat release rate of materials and the shorter the ignition time, the more dangerous the materials. Consider the following equation [14]: 2 ðTig T0 Þ2 ; tig ¼ ðkqcÞ 3 ðq_ 00 Þ2
ð18Þ
1020
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
where q_ 00 is the net heat obtained, kqc is the thermal inertia of materials, Tig is the surface ignition temperature, tig is ignition time and T0 is the environmental temperature, q_ 00 ¼ q_ 00i q_ 00cr ;
ð19Þ
where q_ 00i is the thermal flux and q_ 00cr is the critical thermal flux needed to ignited the materials. As shown in Fig. 7, the bigger the external thermal flux, the bigger the mass loss, then the bigger the heat loss rate; As can be seen from Fig. 8, the bigger the external thermal flux, the shorter the ignition time. Summarizing the above analysis, we can draw a conclusion. With the increase of materials density and external thermal flux, mass loss and heat release rates also increase, ignition time becomes shorter, thus fire risk of materials shows the tendency of increase. The result matches well with the experiments [15]. 5. Remarks A modified model has been presented in this paper. Some important factors affecting thermal decomposition are considered in the model, i.e., heat loss by convection and radiation caused by surface temperature rise and shrinkage of the char layer are considered and any n can be applied to the Arrhenius equation. Mass loss rate of thermal decomposition of white pine is calculated based on the model. The results show a good agreement with the experimental results. In addition, effects of density of materials and external thermal flux on decomposition have been studied theoretically using the model under large size sample condition. Main conclusions are as follows: (1) Density of materials shows a large effect on fire risk. Generally, the smaller the density, the more the fire risk of materials. This conclusion means that materials of bigger density should be used to decrease the possibility of fire occurrence. However, it is needed to note that this conclusion has only considered the effect of density on fire risk of materials. Actually other parameters, such as thermal conductivity, etc., should be considered. (2) External heat flux also shows a large effect on fire risk of materials. Generally speaking, with the increase of external thermal flux, mass loss and heat release rates also increase, ignition time becomes shorter, thus fire risk of materials shows the tendency to increase.
Acknowledgements This paper was supported by National Natural Science Foundation of China (grant no. 59936140 and 50006012). The authors deeply appreciate the support.
References [1] M.J. Spearpoint, J.G. Quintiere, Combust. Flame 123 (2000) 308. [2] G.W. Anderson, A burning rate model for charring materials, NIST-GCR-97-725, National Institute of Standards and Technology, Gaitherburg, MD, 1997.
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1021
[3] M. Janssens, Ph.D. thesis, University of Gent, Belgium, 1991. [4] A.M. Kanury, in: SFPE Handbook of Fire Protection Engineering, 2nd ed., Society of Fire Protection Engineers, Boston, MA, 1995, pp. 2–190. [5] A.M. Kanury, Rate of charring combustion in a fire, in: Proceedings of the 14th International Symposium on Combustion, Pennsylvania State University, 1974. [6] A.F. Roberts, Combust. Flame 14 (1970) 261. [7] D.L. Simms, Combust. Flame 6 (1962) 303. [8] E.M. Suuberg, I. Milosavljevic, W.D. Lilly, Behavior of charring materials in simulated fire environments, NISTGCR-94-645, Gaithersburg, MD, 1994. [9] Hsiang-Cheng Kung, Combust. Flame 18 (1972) 185. [10] I.S. Wichma, A. Atreya, Combust. Flame 68 (1987) 231. [11] E.G. Brehob, A.K. Kulkarni, Fire Mater. 17 (1991) 249. [12] T.J. Ohlemiller, T. Kashiwagi, K. Werner, Combust. Flame 69 (1987) 155. [13] D. Drysdale, An Introduction to Fire Dynamics, Wiley, New York, 1987. [14] A. Tewarson, J. Fire Sci. 12 (1994) 329. [15] Yang Lizhong, Deng Zhihua, Chen Xiaojun, Fire Sci. 9 (2000) 32 (in Chinese).
A modified model of pyrolysis for charring materials in fire Yang Lizhong *, Chen Xiaojun, Zhou Xiaodong, Fan Weicheng State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui Province 230026, People’s Republic of China Received 13 June 2001; accepted 13 August 2001
Abstract A modified model of pyrolysis for charring materials in fire has been proposed in this paper. In this model some special factors which show the effect on pyrolysis are considered, i.e., heat loss by convection and radiation caused by surface temperature rise and shrinkage of char surface are considered. Experimental device is designed specially for validating the reliability of the model. Effects of density of materials and heat radiation on pyrolysis of materials have also been investigated. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Charring materials; Pyrolysis; Fire; Thermal radiation; Model
1. Introduction The pyrolysis behavior of solid materials can be divided into two types: noncharring and charring [1,2]. Noncharring materials such as PMMA burn away completely, leaving no residue, and can be modeled using a theory similar to flammable liquids. In contrast, charring materials leave relatively significant amounts of residue when they burn. The pyrolysis of charring materials such as wood is a complex interplay of chemistry, heat, and mass transfer. Charring materials must be modeled in terms of a pyrolysis front penetrating into the materials with an increasing surface temperature and without a well-defined steady state. The char layer forms an increasing thermal resistance between the exposed surface and the pyrolysis front, resulting in a continuously decreasing rate of heat release after the first peak. Combustion is a complex interplay of chemical reaction, heat, and mass transfer, and combustion of solid materials becomes more complex because of the existing solid phase. Main combustible materials appearing in building fire are wood and other cellulosic materials, thus a *
Corresponding author. Tel.: +86-551-360-6416; fax: +86-551-360-1669. E-mail address: [email protected] (Y. Lizhong).
0020-7225/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 0 - 7 2 2 5 ( 0 2 ) 0 0 0 0 2 - 2
1012
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
study on their combustion characteristics during fire shows an important role. Maybe it is the key for a study on the ignition of solid materials and fire spreading to the research on pyrolysis of solid materials. Consider a ‘‘thick’’ sample of wood with its surface uniformly exposed to a constant external heat flux. So the heat and mass transfer through the sample can be considered one-dimensional. Ignition can occur at surface temperature anywhere from 200 to 400 °C. At the instant of ignition, the heat flux to the surface of the wood is a combination of the external flux plus the flux from the flame. The rate of heat release rapidly rises to a maximum, then a char layer gradually builds up as the pyrolysis front moves inward. Its rate of heat release eventually reaches a more or less steady value [3]. At temperature above around 300 °C the char layer begins to break down rapidly. The char layer also shrinks and pressure gradients are set up within the materials. Small cracks appear on the surface, and these cracks allow volatiles to escape more easily. The cracks gradually widen as the char layer deepens [3]. Owing to its importance and complexity of pyrolysis of charring materials, there is a substantial volume of work regarding the ignition, pyrolysis, burning, and charring behavior of wood and cellulosic materials experimentally and theoretically [4–12]. A thorough review on this work has been described by other researchers [1] and it is not the intent of the work. We will present a brief summary. Several models for the burning rate of solid materials, both charring and noncharring, have been developed. Examples include the studies by Hsiang-Cheng Kung [9], Indreks Wichman et al. [10] and Ellen et al. [11]. These models range from simple treatments of the ignition and burning process using pure heat conduction models to the use of complex chemical kinetics for the pyrolysis of charring materials. However, each model has its restrictions. In this paper, a modified one-dimensional pyrolysis model, which considers transient conduction, gas convection, endothermic effect of process, non-linear boundary condition and shrinkage of the slab, is proposed. The model is also compared against experimental data obtained from our research on white pine.
2. Theory The model proposed in this paper considers some factors that have a strong influence on pyrolysis of solid materials such as: transient heat conduction inside solid materials; the effect of gas convection on heat transfer; thermal effect of pyrolysis process. Moreover, thermal properties of materials are permitted to vary with temperature. 2.1. Assumptions It is a complex process for wood pyrolysis and combustion. Thus it is very difficult to consider all factors affecting the process in numerical simulation. Specific assumptions are needed to establish the mathematical model: (1) The volatiles do not accumulate within the char layer but are produced and leave the surface of the solid immediately. Actually, most volatiles exit immediately, while others penetrate into the inner of solid.
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1013
(2) Moisture content of solid is neglected. Actually, water affects mainly mass loss at early stage of heating and postpones surface temperature rise. (3) Chemical reaction between volatile and char layer, char and air is ignored. (4) Materials properties are assumed to be linear with the range of temperatures considered. 2.2. Controlling equation The surface and inner temperatures of wood will increase at external heat flux. When the temperature reaches the vaporization temperature, water begins to vaporize. Most water vapor produced exits from the upper surface, while a little penetrates into the surround. In case all water exits, the surface temperature of wood rises more and pyrolysis rate begins to increase and to form a pyrolysis reaction zone. Along with propagation of the reaction zone, different wood layers decompose simultaneously at different temperatures because of temperature field of the inner of wood and different product forms. Features of the model and the physics of the thermal decomposition of wood are portrayed in Fig. 1. Density of the decomposed wood is given as qf ð1Þ qa þ qf ; qs ¼ 1 qw where qs is the density of decomposed wood, qf is the density of the char, qa is the density of decomposing wood and qw is the density of the virgin wood. Arrhenius equation is chosen to describe the reaction rate, oqs Ea n ws ¼ ¼ qa A exp ; ð2Þ ot RT where n is the reaction index, Ea is the reaction active energy and A is the pre-exponential factor. Based on the above two equations, we obtain n dqs qs qc Ea ¼ A q exp : ð3Þ dt qw qc w RT
Fig. 1. Schematic of model for decomposition.
1014
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
Gas mass conservation equation is given as oMg oqs ¼ ; ox ot
ð4Þ
where Mg is the mass of volatiles. Energy conservation equation is given by oðqs hs Þ o oT o oq ¼ ks þ ðMg hg Þ Q s ; ð5Þ ot ox ox ox ot RT where qs hs ¼ qa ha þ qg hg , h ¼ T0 Cp dT , subscript g refers to gas and Q is the reaction heat of pyrolysis process. ha ¼
Z
T
Cpa dT ;
hc ¼
T0
Z
T
Cpc dT ; T0
hg ¼
Z
T
Cpg dT :
ð6Þ
T0
Combining Eqs. (4) and (5), we obtain oT o oT oT oq hc qc ha qw ¼ ks þ Q þ hg þ qs Cps : þ Mg Cpg ot ox ox ox ot qw qc qw qc Boundary condition is oT ¼ q00 hðTs T0 Þ erðTs4 T04 Þ: ks ox x¼0
ð7Þ
ð8Þ
Initial condition is T ¼ T0 ;
q ¼ q0 ;
Mg ¼ 0
ðt ¼ 0Þ:
ð9Þ
Material properties are assumed to be linear functions of temperature, i.e., k ¼ k 0 þ k ðT T0 Þ;
ð10Þ
Cp ¼ Cp0 þ Cp ðT T0 Þ;
ð11Þ
where k 0 is the thermal conductivity at constant temperature, k and Cp are the linear coefficients with temperature and Cp0 is the thermal capacity at constant temperature. Three unknown parameters, i.e., qs ðx; tÞ, Mg ðx; tÞ, T ðx; tÞ, can be solved according to Eqs. (3), (4) and (7). 2.3. Modifications on the formers’ model Main modifications of the model are as follows: (1) Generally, equal thermal flux density was applied and heat loss via convection and radiation caused by rise of surface temperature of wood
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1015
was not considered for the existed models. The heat loss is considered in the model presented in this paper. It is described in Eq. (8). (2) Actually, the surface of wood shrinks along with wood decomposition. This situation is considered in the model. 2.4. Dimensionless analysis and solution The following dimensionless variables are selected to consolidate the variables: qa q q T Ea ; qs ¼ s ; qc ¼ c ; T ¼ ; T E ¼ ; T0 qw qw qw RT0 Cps Cpa Cpc Cpg C ps ¼ ; C pa ¼ ; C pc ¼ ; C pg ¼ ; Cpw Cpw Cpw Cpw qa ¼
x x¼ ; l
t¼
tkw ; Cpw qw l2
k¼
ks ; kw
Q¼
Q ; Cpw T0
A¼
Ts ¼
Ts ; T0
ACpw qw l2 ; kw ð1 qc Þ
Mg ¼
Mg Cpw l kw
Substituting for the dimensionless variables in the above equations: Eqs. (3), (4), (7)–(9), oqs n ¼ Aðqs qc Þ exp ot
TE ; T
ð12Þ
oM g oqs ¼ ; ox ot
ð13Þ
o2 T qs C ps oT 1 oqs Q ¼ þ ox k ot k ot
Z
T
1
! C pa qc C pc M g C pg oT 1 oT C pg dt ; ox k ox 1 qc 1 qc k
ð14Þ
oT q00 l hl erl 4 ¼ ðT s 1Þ ðT 1Þ k s ox x¼0 kw T0 kw kw s
ð15Þ
T ¼ 1;
ð16Þ
qs ¼ 1;
Mg ¼ 0
ðt ¼ 0Þ:
Crank–Nicolson method is used to solve these dimensionless equations [9]. Numerical modeling description can be also found in Hsiang-Cheng Kung’s paper [9]. The values of some parameters are chosen according to Table 1. By the way, moisture content is not considered in the model proposed in this paper.
3. Description of experiments A device to study characteristics of fire at an early stage has been developed by State Key Laboratory of Fire Science (SKLFS). It is schematically shown in Fig. 2. The device is made of stainless steel. Its outer dimension is 1.5 m long by 1.5 m wide by 2.0 m high. Actually, there exists a specimen holder (550 mm long by 550 mm wide) on the rack. The device can mainly be used to
1016
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
Table 1 The selected value of some parameters A E T0 Q h1 h2 0 Cpa 0 Cpc 0 Cpg Cpa Cpc Cpg 0 ka kc0 ka kc
7.4E9 s1 1.45E8 J/(mol K) 300 K 3.0E5 J/kg 10 W=ðm2 KÞ 10 W=ðm2 KÞ 2140 J/(kg K) 1928 J/(kg K) 2000 J/(kg K) 4.19 J=ðkg K2 Þ 1.98 J=ðkg K2 Þ 0 J=ðkg K2 Þ 0.157 W/(m K) 0.084 W/(m K) 0.0003 W=ðm K2 Þ 0.0002 W=ðm K2 Þ
Fig. 2. Schematic of the device: (1) elevator; (2) load cells; (3) heat insulation; (4) rack; (5) sample; (6) electrical radiator; (7) exhaust hood; (8) sampling position; (9) smoke duct.
measure parameters such as flame temperature, flame image area, smoke components, smoke temperature, smoke flux, weight loss of sample, ignition temperature of sample, ignition time, etc. The sample is dried before experiment. The distance between sample and rectangle radiator may change from 300 to 800 mm. The sample is ignited using an electrical radiator. Power of the
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1017
radiator is 0–110 kW and can be adjusted continuously. The cross-section of the radiator is 450 mm 450 mm. Sample is placed on the holder and ignited by the electrical radiator. A minimum of two runs is carried out for each material at each heat flux. If the runs are significantly different, a third run is made.
4. Results and discussions As described in the above analysis, surface temperature and mass loss rate of sample are the two key parameters during thermal decomposition of solid materials. Usually, surface temperature of sample is the controlling factor to determine if materials can be ignited or not when there is no pilot ignition source. Mass loss rate is related with combustion rate and heat release rate is calculated based on the mass loss rate [13], Q_ ðtÞ ¼ mloss ðtÞ vA ðtÞ Hc ;
ð17Þ
where Hc is the combustion heat of volatiles and vA ðtÞ is the combustion efficiency (<1.0). Fig. 3 gives the experimental and theoretical values of mass loss rate of white pine under thermal radiation. Fig. 4 is a comparison of the theoretical value and TG experiments. As shown in Fig. 3, calculation value is little higher than the experimental value at early stage. As a whole, they match well. These results have shown that the model presented in this paper is reasonable. But as shown in Fig. 4, little discrepancy exists between theoretical and experimental value. This may be due to different environments between TG experiments and pyrolysis of solid materials at real fire. Figs. 5–8 give some calculation results based on the model. Figs. 5 and 6 indicate the dependence of decomposition and surface temperature on the density of solid materials at fixed thermal radiation, respectively. As shown in these two figures, mass loss increases with decreasing density of materials, however, variation of surface temperature shows a little complexity. It increases with the decreasing density first, then decreases.
Fig. 3. Comparison between experiments and decomposition.
1018
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
Fig. 4. Comparison between calculated values and TG experiments.
Fig. 5. Effect of density on decomposition ð50 kW=m2 Þ.
Fig. 6. Effect of density on surface temperature rise ð40 kW=m2 Þ.
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1019
Fig. 7. Effect of external thermal flux on decomposition.
Fig. 8. Effect of external thermal flux on surface temperature.
Figs. 7 and 8 show the dependence of mass loss and surface temperature of materials on external thermal radiation. As can be seen from these two figures, mass loss and surface temperature of solid materials increase with the increase of thermal radiation. Generally, fire risk of materials can be assessed using two parameters: heat release rate and ignition time. The former is related to fire development and the latter affects fire occurrence. The bigger the heat release rate of materials and the shorter the ignition time, the more dangerous the materials. Consider the following equation [14]: 2 ðTig T0 Þ2 ; tig ¼ ðkqcÞ 3 ðq_ 00 Þ2
ð18Þ
1020
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
where q_ 00 is the net heat obtained, kqc is the thermal inertia of materials, Tig is the surface ignition temperature, tig is ignition time and T0 is the environmental temperature, q_ 00 ¼ q_ 00i q_ 00cr ;
ð19Þ
where q_ 00i is the thermal flux and q_ 00cr is the critical thermal flux needed to ignited the materials. As shown in Fig. 7, the bigger the external thermal flux, the bigger the mass loss, then the bigger the heat loss rate; As can be seen from Fig. 8, the bigger the external thermal flux, the shorter the ignition time. Summarizing the above analysis, we can draw a conclusion. With the increase of materials density and external thermal flux, mass loss and heat release rates also increase, ignition time becomes shorter, thus fire risk of materials shows the tendency of increase. The result matches well with the experiments [15]. 5. Remarks A modified model has been presented in this paper. Some important factors affecting thermal decomposition are considered in the model, i.e., heat loss by convection and radiation caused by surface temperature rise and shrinkage of the char layer are considered and any n can be applied to the Arrhenius equation. Mass loss rate of thermal decomposition of white pine is calculated based on the model. The results show a good agreement with the experimental results. In addition, effects of density of materials and external thermal flux on decomposition have been studied theoretically using the model under large size sample condition. Main conclusions are as follows: (1) Density of materials shows a large effect on fire risk. Generally, the smaller the density, the more the fire risk of materials. This conclusion means that materials of bigger density should be used to decrease the possibility of fire occurrence. However, it is needed to note that this conclusion has only considered the effect of density on fire risk of materials. Actually other parameters, such as thermal conductivity, etc., should be considered. (2) External heat flux also shows a large effect on fire risk of materials. Generally speaking, with the increase of external thermal flux, mass loss and heat release rates also increase, ignition time becomes shorter, thus fire risk of materials shows the tendency to increase.
Acknowledgements This paper was supported by National Natural Science Foundation of China (grant no. 59936140 and 50006012). The authors deeply appreciate the support.
References [1] M.J. Spearpoint, J.G. Quintiere, Combust. Flame 123 (2000) 308. [2] G.W. Anderson, A burning rate model for charring materials, NIST-GCR-97-725, National Institute of Standards and Technology, Gaitherburg, MD, 1997.
Y. Lizhong et al. / International Journal of Engineering Science 40 (2002) 1011–1021
1021
[3] M. Janssens, Ph.D. thesis, University of Gent, Belgium, 1991. [4] A.M. Kanury, in: SFPE Handbook of Fire Protection Engineering, 2nd ed., Society of Fire Protection Engineers, Boston, MA, 1995, pp. 2–190. [5] A.M. Kanury, Rate of charring combustion in a fire, in: Proceedings of the 14th International Symposium on Combustion, Pennsylvania State University, 1974. [6] A.F. Roberts, Combust. Flame 14 (1970) 261. [7] D.L. Simms, Combust. Flame 6 (1962) 303. [8] E.M. Suuberg, I. Milosavljevic, W.D. Lilly, Behavior of charring materials in simulated fire environments, NISTGCR-94-645, Gaithersburg, MD, 1994. [9] Hsiang-Cheng Kung, Combust. Flame 18 (1972) 185. [10] I.S. Wichma, A. Atreya, Combust. Flame 68 (1987) 231. [11] E.G. Brehob, A.K. Kulkarni, Fire Mater. 17 (1991) 249. [12] T.J. Ohlemiller, T. Kashiwagi, K. Werner, Combust. Flame 69 (1987) 155. [13] D. Drysdale, An Introduction to Fire Dynamics, Wiley, New York, 1987. [14] A. Tewarson, J. Fire Sci. 12 (1994) 329. [15] Yang Lizhong, Deng Zhihua, Chen Xiaojun, Fire Sci. 9 (2000) 32 (in Chinese).