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Flame radiation from polymer fires
Fire Safety Journal 30 (1998) 383—395 ( 1998 Published by Elsevier Science Ltd. All rights reserved. Printed in Great Britain 0379—7112/98/$19.00 PII: SO379–7112(97)000016–7
Flame Radiation from Polymer Fires Fenghui Jiang* State Key Laboratory of Fire Science, USTC, Hefei, Anhui, 230026, PR China (Received 6 November 1995; revised version received 14 January 1997; accepted 8 February 1997)
ABS¹RAC¹ Enclosure fires can be divided into two ventilation regimes: well-ventilated and under-ventilated combustion. ¹he influence of fire ventilation on flame radiation is very important in enclosure fires especially for under-ventilated conditions. An approximate model for predicting flame radiation for both well- and under-ventilated fires is proposed on the basis of the !-correlation, in which the role of flame sootiness and heat release is considered. ¹his paper is an extension of work performed earlier and reported in ¹ewarson et al. (Combustion and Flame, 95 (1993) 151-169)1. ¹he results are calculated for several typical polymers, and the relationship between the flame radiant fraction and the fuel’s smoke-point has been examined. Additionally, flame radiation is predicted by the slightly modified Global Flame Radiation (GFR) Model of de Ris and Orloff. ¹he comparisons between experimental and predicted data are satisfactory. ¹his study attempts to provide: (1) a deeper scientific understanding of the effect of ventilation conditions on flame radiation, and (2) available correlation, for the analysis of enclosure fires. ( 1998 Published by Elsevier Science ¸td. All rights reserved.
NOMENCLATURE A A & A 7 C C 0 C 2
Area of enclosure opening (m2) Flame area (m2) Burning area of fuel (m2) Enclosure constant (kg/sm5@2) Constant between 2 and 6 Planck’s second constant
* Present address: Factory Mutual International, Melbourne, Victoria, Australia. 383
384
D E f 7 H *H K k ! k 4 ¸ ¸ & ¸ SP m m !*3 Q ¹ & ¹ = » & a b ! e g 4 m o 4 p ' s
F. Jiang
Diameter of fuel bed (m) Entrainment coefficient Soot volume fraction Height of enclosure opening (m) Heat of combustion (kJ/g) Effective emission coefficient (1/m) Mass air-to-fuel stoichiometric ratio Stoichiometric yield of maximum fuel conversion to soot Mean beam length (m) Flame height (m) Smoke-point flame height (m) Mass burning rate of fuel (kg/s) Inlet air flow rate (kg/s) Heat release rate (kW) Mean flame radiative temperature (K) Ambient temperature (298.15 K) Flame volume (m3) General correlation coefficient Shift correlation coefficient Ventilation-controlled combustion parameter Flame emissivity Generation efficiency of soot Slope correlation coefficient Density of soot particles (kg/m3) Stefan—Boltzmann constant Equivalence ratio Combustion efficiencies
Subscripts A Total heat release C Convective R Radiative 0 Well-ventilated T Complete Polymers Nylon PE PMMA PP PS WC
Nylon Polyethylene Polymethylmethacrylate Polypropylene Polystyrene Wood crib
Flame radiation from polymer fires
385
1 INTRODUCTION With a few exceptions (e.g. methanol and paraformaldehyde), most liquid and solid fuels burn with luminous diffusion flames, as a result of emission from minute carbonaceous particles with diameters of the order of 10—100 nm. While within a flame, these soot particles attain high temperatures and each one acts as a minute black or grey body. It is well known that emission from the soot particles is much larger than emission from the molecular emitters, such as H O and CO . Generally speaking, the ‘‘sootier’’ the flame, the lower 2 2 its average temperature. It was found that the non-luminous methanol flame has an average temperature of 1200°C, while the luminous flames of kerosene and benzene were much cooler, 990°C and 921°C, respectively2. Thus, to a great extent, flame radiation and temperature depends on the flame sootiness because of the heat loss mechanism. The fuel’s smoke-point is defined as the critical flame height at which a laminar ‘‘candle-like’’ flame just emits smoke from its tip. With the assumption that the smoke-point globally describes flame chemistry, the correlation between flame radiant fraction and smoke point has been established by Tewarson3 for well-ventilated combustion (unlimited supply of oxidant), i.e. s "0.41!0.85¸ (1) R0 SP0 where ¸ is in meters. Meanwhile, the Global Flame Radiation Model was SP0 recently presented by de Ris and Orloff 1 on the basis of the smoke-point principle, which can be used to predict the flame radiant fraction and global flame temperature for fuels burning in air. It was found to be an excellent predictor of flame radiation for many common fuels for well-ventilated combustion. As a basic mechanism of heat transfer, flame radiation is very important in many combustion problems. It becomes the dominant mode of heat transfer in fires as the fuel bed diameter increases beyond about 0.3 m, and determines the growth and spread of fires in enclosures. During enclosure fires, the air supply is limited, and fire ventilation is one of the main determinants of fire processes in many cases4,5. In their early stages, enclosure fires are wellventilated, and easy to control and extinguish. However, if they are allowed to grow with limited ventilation and a large fuel surface area, flashover occurs, and the fires become under-ventilated. At this stage, heat release and soot formation are governed to a great extent by fire ventilation. Theoretically, with a decrease in ventilation, the combustion efficiency decreases, whereas the concentration of soot particles increases. Despite its importance, the effect of ventilation on flame radiation and temperature for under-ventilated fires has often been assumed or omitted in many combustion analyses due to a lack of available correlation and scientific understanding.
386
F. Jiang
In this study, an approximate model for predicting the flame radiant fraction and mean flame radiative temperature was proposed. Calculations were performed by using this model and the Global Flame Radiation Model for six typical polymers involved in both small-scale and large-scale fires. The relationship between the flame radiant fraction and the fuel smoke-point was examined for well-ventilated combustion. The goal of this study is to provide a simple model for the prediction of flame radiation and temperature, and a deeper scientific understanding of the effects of fire ventilation on polymer fire behaviour, for enclosure fire analysis.
2 MODEL FORMULATION If a flame is assumed to be a homogeneous soot—gas volume with welldistributed temperature ¹ , according to the Stefan—Boltzmann equation, the & total radiant power from the flame is proportional to ¹4, i.e. & (2) Q "A ep(¹4!¹4 ) = & R & 2.1 Equivalence ratio Fire ventilation is most commonly expressed in terms of the mass fuel-to-air or mass fuel-to-oxygen stoichiometric ratio:6 '"k m/Em (3) ! !*3 where E is the entrainment coefficient, and is assumed to be about 0.8 in the calculation of '. When '(1.0, fires are defined as well-ventilated fires, and when ''1.0, fires are defined as under-ventilated fires. A correlation for the inlet air flow rate during an enclosure fire, through an opening, was first formulated by Kawagoe:7 m "CAH1@2 (4) !*3 where the value of enclosure constant C ranges from 0.40 to 0.61 kg/sm5@2, depending on the flow coefficient of the opening. The commonly used value is 0.52 kg/sm5@2. 2.2 Flame size and shape For simplicity, flame shape is approximated to a cylinder for natural diffusion flames. The flame height is given by ¸ "0.23Q2@5!1.02D & A
(5)
Flame radiation from polymer fires
387
in the range of 7(Q2@5/D(700 kW2@5/m. Thus, the flame area and volume A are A "nD(¸ #D/2) & & » "nD2¸ /4 & &
(6) (7)
respectively. 2.3 Heat release and soot formation Heat release rate in flaming combustion (Q ) has convective and radiative A components (Q and Q ). They are directly proportional to the mass burning C R rate of fuel, m, and the combustion efficiencies s, i.e. Q "s m*H (8) A A Q "s m*H (9) C C Q "s m*H (10) R R Soot particles are produced as a result of incomplete combustion. It is assumed here that the particles are uniformly distributed within a flame, and few of them are consumed when they pass into the oxidative regions of the flame. Therefore, the soot volume fraction f is 7 f "g mk /o » (11) 7 4 4 4 & where o "1100 kg/m3 is used, as suggested in Newman and Steciak8. The 4 value of f is generally about 10~6. 7 In eqn (8), (9), (10) and (11), the combustion efficiencies s and its convective A and radiative components s and s , and the generation efficiency of soot g , C R 4 are functions of the equivalence ratio '. The effect of ventilation on these efficiencies, as shown in Fig. 1 and Fig. 2, was examined through a series of tests by using the Flammability Apparatus at the Factory Mutual Research Corporation (FMRC) and a 0.022 m3 enclosure at the Fire Research Institute, Mitaka, Tokyo, Japan1. These efficiencies can be expressed in terms of the !-correlation, i.e.1 s "s (1#! ) A A0 A s "s (1#! ) C C0 C s "s !s "s #s ! !s ! R A C R0 A0 A C0 C g "g (1#! ) S S0 S
(12) (13) (14) (15)
388
F. Jiang
Fig. 1. The effect of ventilation on s . A
Fig. 2. The effect of ventilation on s . C TABLE 1 Correlation Coefficients
! A ! C
a
b
m
!0.97 !0.97
2.5 1.8
1.2 1.8
where the s , s , s and g are the combustion efficiencies and generation A0 C0 R0 S0 efficiency of soot at well-ventilated conditions, respectively. !"a exp(!b * * '~m*) is defined as the ventilation-controlled combustion parameter, i"A, C, S. The coefficients a , b and m are constants, and are listed in Tables 1 * * *
Flame radiation from polymer fires
389
TABLE 2 Data Used in the Prediction PMMA Nylon as b 4 m 4 s A0 s C0 g S0 k ! k 4 ¸ (m) SP0 *H (kJ/g) T
1.6 2.5 0.6 0.95 0.65 0.031 8.24 0.600 0.105 25.2
1.7 2.5 0.8 0.89 0.55 0.048 11.19 0.634 0.060 30.8
PE
PP
2.2 2.5 1.0 0.88 0.54 0.060 14.72 0.857 0.045 43.6
2.2 2.5 1.0 0.87 0.52 0.060 14.72 0.868 0.050 43.4
¼C
PS
2.5 2.8 2.5 2.5 1.2 1.3 0.86 0.72 0.50 0.30 0.013 0.158 6.25 13.22 0.530 0.923 0.080 0.015 17.9 39.2
and 2. Substituting m and s from eqn (3) and (14) into eqn (10) gives the R relationship between Q and ', i.e. R Q "(Em *H/k )(s #s ! !s ! )' R !*3 ! R0 A0 A C0 C
(16)
2.4 Flame radiative properties If emission from the molecular emitters is ignored, the flame emissivity depends only on the concentration and characteristics of soot particles and on the mean beam length of the flame, and can be expressed as e"1!exp(!K¸)
(17)
where K is the effective emission coefficient, proportional to the concentration and radiative temperature of the soot particles. A mean effective emission coefficient is suggested as9 K"3.72C f ¹ /C 0 7 & 2
(18)
where C is a constant between 2 and 6, depending on the complex index of 0 refraction. C is the Planck’s second constant (1.4388]10~2 mK). The defini2 tion of the mean beam length for flame volumes is10 ¸"3.6» /A & &
(19)
If the inlet air flow rate m and burning area A (or diameter of fuel bed D) are !*3 7 given, by substituting A , Q and e from eqn (6), (16), and (17) into eqn (2), the & R functional relationship between ¹ and ' can be obtained. &
390
F. Jiang
3 RESULT AND DISCUSSION In order to compare with the experiments performed at FMRC, USA and the Fire Research Institute, Japan, the following polymers were selected in this study. (1) Carbon—hydrogen containing polymers: (1.1) aliphatic: polyethylene, M(C H ) N and polypropylene, M(C H ) N; 2 4n 3 6n (1.2) aromatic: polystyrene, M(C H ) N; 8 8n (2) Carbon—hydrogen—oxygen containing polymers (aliphatic only): polymethylmethacrylate, M(C H O ) N and pine wood crib, M(C H O ) N; 5 8 2n 6 10 5 n (3) Carbon—hydrogen—oxygen—nitrogen containing polymer (aliphatic only): nylon, M(C H O N ) N. 12 22 2 2 n Calculations were conducted in the following two cases. (1) For small-scale fires, m "1.36 g/s, A "70.88 cm2, per the experimental condition of the !*3 7 Flammability Apparatus at FMRC. (2) For large-scale fires, a real room with an opening of 1.2 m]1.5 m (height) and burning area of 3.6 m2 was considered; the inlet air flow rate may be given by eqn (4), i.e. m "1.146 kg/s. !*3 The other data used in the prediction are listed in Table 2. The results are shown in Figs 3—9. 3.1 The effect of fire ventilation The effects of ventilation on soot concentration within a flame and mean flame radiative temperature are shown in Figs 3 and 4, respectively. For wellventilated fires, the f and ¹ are almost independent of '. On the other 7 &
Fig. 3. Dependence of f on '. V
Flame radiation from polymer fires
391
Fig. 4. Dependence of ¹ on '. &
Fig. 5. Predicted ¹ for both scale fires. &
hand, for under-ventilated fires, the f increases and ¹ decreases steeply as 7 & ' increases, due to the incomplete combustion and heat loss from soot particles. It is suggested that fuels having sootier flames have lower flame temperatures. 3.2 The effect of the chemical structure of the polymers From Figs 1 and 2, and Table 1, it can be seen that the ! and ! have the A C same a, b and m values for all polymers in this study, therefore the ratios of s /s and s /s are expected to be independent of the chemical structures of A A0 C C0 the fuels. The ! , on the other hand, has different a, b and m values, and the S
392
F. Jiang
Fig. 6. s
R0
versus ¸ for well-ventilated fires. SP0
Fig. 7. Predicted ¹ and s for well-ventilated combustion. & R
ratios of g /g and s /s depend on the chemical structures of the polymers S S0 R R0 (see Table 2 and eqn (14)). 3.3 The effect of fire scale It was found that in large-scale fires the heat release rate and mass burning rate per unit surface area of fuel increase with fire size because of the increase in the flame radiative heat flux, and finally reach their asympotic values3,4. The prediction of ¹ for both scale fires in Fig. 5 shows that ¹ is almost & & independent of the fire size.
Flame radiation from polymer fires
393
Fig. 8. Comparison of predicted ¹ . &
Fig. 9. Comparison of predicted s with the experimental data. R
3.4 The effect of the fuel’s smoke-point It has been found that the flame radiant fraction for fuels burning in air is principally determined by the fuel’s smoke-point11. The flame radiant fractions of the polymers at well-ventilated conditions are shown in Fig. 6, as a function of the fuel’s smoke-point. For comparison, the experimental data of other fuels and eqn (1) are shown simultaneously. It can be seen that the relationship between the flame radiant fraction and smoke-point of the polymers is in good agreement with eqn (1).
394
F. Jiang
3.5 The GFR model and comparisons The Global Flame Radiation Model of de Ris and Orloff1 was also used to predict s and ¹ . The values predicted from the GFR Model for wellR & ventilated polymer fires are shown in Fig. 7, which are in excellent agreement with the prediction from the proposed model. With slight modification of the GFR Model1, s and ¹ can be predicted for under-ventilated combustion. R & The results from both models for wood crib fires are shown in Figs 8 and 9, compared with the experimental data reported in de Ris and Orloff1. In addition, the ¹ of PMMA suggested in Drysdale2 and Tien et al. 9 is 1573 and & 1538 K, respectively; the predicted value in this study is about 1480 K. This comparison indicates that the proposed approximate model is satisfactory for predicting s and ¹ for both well- and under-ventilated polymer fires. R & 4 SUMMARY Fire ventilation is an important factor affecting enclosure fire behaviour. For under-ventilated fires, the flame radiant fraction and temperature depend on the fire ventilation. On the other hand, for well-ventilated fires, they are almost independent of the ventilation. As discussed in this paper, flame radiation and its ventilation effects could be predicted by using the following two models: the slightly modified Global Flame Radiation (GFR) Model and the !- correlation based model proposed in this paper. In addition, flame radiation from well-ventilated polymer fires may, to a certain extent, simply be predicted from the correlation between the radiant fraction and the smoke point. The GFR Model as well as the correlation are based on the smoke point, which is sometimes quite difficult to measure for solid materials. However, the proposed approximate model is based on the combustion efficiencies, which can easily be measured, and is therefore expected to be used more extensively. REFERENCES 1. Tewarson, A., Jiang, F. H. & Morikawa, T., Combustion and Flame, 95 (1993) 151—69. 2. Drysdale, D., An Introduction to Fire Dynamics. Wiley-Interscience, New York, 1985. 3. Tewarson, A., Generation of heat and chemical compounds in fires. In SFPE Handbook of Fire Protection Engineering, Section 3, Chapter 4. National Fire Protection Association, Quincy, MA, USA, 1995, pp. 3-53—3-124. 4. Jiang, F. H., Proc. 1st Asian Conf. on Fire Science and ¹echnology. International Academic Publishers, 1992, pp. 404—409.
Flame radiation from polymer fires
395
5. Tewarson, A., Jiang, F. H. and Alpert, R., Non-thermal fire damage effect of ventilation. 12th Panel Meeting of the UJNR Panel on Fire Research and Safety, Tsukuba and Tokyo, Japan, 27 November—2 October 1992. 6. Tewarson, A., Proc. 20th Int. Symp. on Combustion. The Combustion Institute, Pittsburgh, PA, USA, 1984, pp. 1555—1566. 7. Kawagoe, K., Fire Behaviour in Rooms. Report No. 27, The Building Research Institute, Scuba, Japan, September 1958. 8. Newman, J. S. & Steciak, J., Combustion and Flame, 67 (1987) 55—64. 9. Tien, C. L., Lee, K. Y. and Stretton, A. J., SFPE Handbook of Fire Protection Engineering. National Fire Protection Association, Quincy, MA, USA, 1988, pp. 1-92—1-105. 10. Holman, J. P., Heat ¹ransfer. McGraw-Hill, Scarborough, CA, USA, 1976. 11. Markstein, G. H., 20th Int. Symp. on Combustion. The Combustion Institute, Pittsburgh, PA, USA, 1985, p. 1055.
Flame Radiation from Polymer Fires Fenghui Jiang* State Key Laboratory of Fire Science, USTC, Hefei, Anhui, 230026, PR China (Received 6 November 1995; revised version received 14 January 1997; accepted 8 February 1997)
ABS¹RAC¹ Enclosure fires can be divided into two ventilation regimes: well-ventilated and under-ventilated combustion. ¹he influence of fire ventilation on flame radiation is very important in enclosure fires especially for under-ventilated conditions. An approximate model for predicting flame radiation for both well- and under-ventilated fires is proposed on the basis of the !-correlation, in which the role of flame sootiness and heat release is considered. ¹his paper is an extension of work performed earlier and reported in ¹ewarson et al. (Combustion and Flame, 95 (1993) 151-169)1. ¹he results are calculated for several typical polymers, and the relationship between the flame radiant fraction and the fuel’s smoke-point has been examined. Additionally, flame radiation is predicted by the slightly modified Global Flame Radiation (GFR) Model of de Ris and Orloff. ¹he comparisons between experimental and predicted data are satisfactory. ¹his study attempts to provide: (1) a deeper scientific understanding of the effect of ventilation conditions on flame radiation, and (2) available correlation, for the analysis of enclosure fires. ( 1998 Published by Elsevier Science ¸td. All rights reserved.
NOMENCLATURE A A & A 7 C C 0 C 2
Area of enclosure opening (m2) Flame area (m2) Burning area of fuel (m2) Enclosure constant (kg/sm5@2) Constant between 2 and 6 Planck’s second constant
* Present address: Factory Mutual International, Melbourne, Victoria, Australia. 383
384
D E f 7 H *H K k ! k 4 ¸ ¸ & ¸ SP m m !*3 Q ¹ & ¹ = » & a b ! e g 4 m o 4 p ' s
F. Jiang
Diameter of fuel bed (m) Entrainment coefficient Soot volume fraction Height of enclosure opening (m) Heat of combustion (kJ/g) Effective emission coefficient (1/m) Mass air-to-fuel stoichiometric ratio Stoichiometric yield of maximum fuel conversion to soot Mean beam length (m) Flame height (m) Smoke-point flame height (m) Mass burning rate of fuel (kg/s) Inlet air flow rate (kg/s) Heat release rate (kW) Mean flame radiative temperature (K) Ambient temperature (298.15 K) Flame volume (m3) General correlation coefficient Shift correlation coefficient Ventilation-controlled combustion parameter Flame emissivity Generation efficiency of soot Slope correlation coefficient Density of soot particles (kg/m3) Stefan—Boltzmann constant Equivalence ratio Combustion efficiencies
Subscripts A Total heat release C Convective R Radiative 0 Well-ventilated T Complete Polymers Nylon PE PMMA PP PS WC
Nylon Polyethylene Polymethylmethacrylate Polypropylene Polystyrene Wood crib
Flame radiation from polymer fires
385
1 INTRODUCTION With a few exceptions (e.g. methanol and paraformaldehyde), most liquid and solid fuels burn with luminous diffusion flames, as a result of emission from minute carbonaceous particles with diameters of the order of 10—100 nm. While within a flame, these soot particles attain high temperatures and each one acts as a minute black or grey body. It is well known that emission from the soot particles is much larger than emission from the molecular emitters, such as H O and CO . Generally speaking, the ‘‘sootier’’ the flame, the lower 2 2 its average temperature. It was found that the non-luminous methanol flame has an average temperature of 1200°C, while the luminous flames of kerosene and benzene were much cooler, 990°C and 921°C, respectively2. Thus, to a great extent, flame radiation and temperature depends on the flame sootiness because of the heat loss mechanism. The fuel’s smoke-point is defined as the critical flame height at which a laminar ‘‘candle-like’’ flame just emits smoke from its tip. With the assumption that the smoke-point globally describes flame chemistry, the correlation between flame radiant fraction and smoke point has been established by Tewarson3 for well-ventilated combustion (unlimited supply of oxidant), i.e. s "0.41!0.85¸ (1) R0 SP0 where ¸ is in meters. Meanwhile, the Global Flame Radiation Model was SP0 recently presented by de Ris and Orloff 1 on the basis of the smoke-point principle, which can be used to predict the flame radiant fraction and global flame temperature for fuels burning in air. It was found to be an excellent predictor of flame radiation for many common fuels for well-ventilated combustion. As a basic mechanism of heat transfer, flame radiation is very important in many combustion problems. It becomes the dominant mode of heat transfer in fires as the fuel bed diameter increases beyond about 0.3 m, and determines the growth and spread of fires in enclosures. During enclosure fires, the air supply is limited, and fire ventilation is one of the main determinants of fire processes in many cases4,5. In their early stages, enclosure fires are wellventilated, and easy to control and extinguish. However, if they are allowed to grow with limited ventilation and a large fuel surface area, flashover occurs, and the fires become under-ventilated. At this stage, heat release and soot formation are governed to a great extent by fire ventilation. Theoretically, with a decrease in ventilation, the combustion efficiency decreases, whereas the concentration of soot particles increases. Despite its importance, the effect of ventilation on flame radiation and temperature for under-ventilated fires has often been assumed or omitted in many combustion analyses due to a lack of available correlation and scientific understanding.
386
F. Jiang
In this study, an approximate model for predicting the flame radiant fraction and mean flame radiative temperature was proposed. Calculations were performed by using this model and the Global Flame Radiation Model for six typical polymers involved in both small-scale and large-scale fires. The relationship between the flame radiant fraction and the fuel smoke-point was examined for well-ventilated combustion. The goal of this study is to provide a simple model for the prediction of flame radiation and temperature, and a deeper scientific understanding of the effects of fire ventilation on polymer fire behaviour, for enclosure fire analysis.
2 MODEL FORMULATION If a flame is assumed to be a homogeneous soot—gas volume with welldistributed temperature ¹ , according to the Stefan—Boltzmann equation, the & total radiant power from the flame is proportional to ¹4, i.e. & (2) Q "A ep(¹4!¹4 ) = & R & 2.1 Equivalence ratio Fire ventilation is most commonly expressed in terms of the mass fuel-to-air or mass fuel-to-oxygen stoichiometric ratio:6 '"k m/Em (3) ! !*3 where E is the entrainment coefficient, and is assumed to be about 0.8 in the calculation of '. When '(1.0, fires are defined as well-ventilated fires, and when ''1.0, fires are defined as under-ventilated fires. A correlation for the inlet air flow rate during an enclosure fire, through an opening, was first formulated by Kawagoe:7 m "CAH1@2 (4) !*3 where the value of enclosure constant C ranges from 0.40 to 0.61 kg/sm5@2, depending on the flow coefficient of the opening. The commonly used value is 0.52 kg/sm5@2. 2.2 Flame size and shape For simplicity, flame shape is approximated to a cylinder for natural diffusion flames. The flame height is given by ¸ "0.23Q2@5!1.02D & A
(5)
Flame radiation from polymer fires
387
in the range of 7(Q2@5/D(700 kW2@5/m. Thus, the flame area and volume A are A "nD(¸ #D/2) & & » "nD2¸ /4 & &
(6) (7)
respectively. 2.3 Heat release and soot formation Heat release rate in flaming combustion (Q ) has convective and radiative A components (Q and Q ). They are directly proportional to the mass burning C R rate of fuel, m, and the combustion efficiencies s, i.e. Q "s m*H (8) A A Q "s m*H (9) C C Q "s m*H (10) R R Soot particles are produced as a result of incomplete combustion. It is assumed here that the particles are uniformly distributed within a flame, and few of them are consumed when they pass into the oxidative regions of the flame. Therefore, the soot volume fraction f is 7 f "g mk /o » (11) 7 4 4 4 & where o "1100 kg/m3 is used, as suggested in Newman and Steciak8. The 4 value of f is generally about 10~6. 7 In eqn (8), (9), (10) and (11), the combustion efficiencies s and its convective A and radiative components s and s , and the generation efficiency of soot g , C R 4 are functions of the equivalence ratio '. The effect of ventilation on these efficiencies, as shown in Fig. 1 and Fig. 2, was examined through a series of tests by using the Flammability Apparatus at the Factory Mutual Research Corporation (FMRC) and a 0.022 m3 enclosure at the Fire Research Institute, Mitaka, Tokyo, Japan1. These efficiencies can be expressed in terms of the !-correlation, i.e.1 s "s (1#! ) A A0 A s "s (1#! ) C C0 C s "s !s "s #s ! !s ! R A C R0 A0 A C0 C g "g (1#! ) S S0 S
(12) (13) (14) (15)
388
F. Jiang
Fig. 1. The effect of ventilation on s . A
Fig. 2. The effect of ventilation on s . C TABLE 1 Correlation Coefficients
! A ! C
a
b
m
!0.97 !0.97
2.5 1.8
1.2 1.8
where the s , s , s and g are the combustion efficiencies and generation A0 C0 R0 S0 efficiency of soot at well-ventilated conditions, respectively. !"a exp(!b * * '~m*) is defined as the ventilation-controlled combustion parameter, i"A, C, S. The coefficients a , b and m are constants, and are listed in Tables 1 * * *
Flame radiation from polymer fires
389
TABLE 2 Data Used in the Prediction PMMA Nylon as b 4 m 4 s A0 s C0 g S0 k ! k 4 ¸ (m) SP0 *H (kJ/g) T
1.6 2.5 0.6 0.95 0.65 0.031 8.24 0.600 0.105 25.2
1.7 2.5 0.8 0.89 0.55 0.048 11.19 0.634 0.060 30.8
PE
PP
2.2 2.5 1.0 0.88 0.54 0.060 14.72 0.857 0.045 43.6
2.2 2.5 1.0 0.87 0.52 0.060 14.72 0.868 0.050 43.4
¼C
PS
2.5 2.8 2.5 2.5 1.2 1.3 0.86 0.72 0.50 0.30 0.013 0.158 6.25 13.22 0.530 0.923 0.080 0.015 17.9 39.2
and 2. Substituting m and s from eqn (3) and (14) into eqn (10) gives the R relationship between Q and ', i.e. R Q "(Em *H/k )(s #s ! !s ! )' R !*3 ! R0 A0 A C0 C
(16)
2.4 Flame radiative properties If emission from the molecular emitters is ignored, the flame emissivity depends only on the concentration and characteristics of soot particles and on the mean beam length of the flame, and can be expressed as e"1!exp(!K¸)
(17)
where K is the effective emission coefficient, proportional to the concentration and radiative temperature of the soot particles. A mean effective emission coefficient is suggested as9 K"3.72C f ¹ /C 0 7 & 2
(18)
where C is a constant between 2 and 6, depending on the complex index of 0 refraction. C is the Planck’s second constant (1.4388]10~2 mK). The defini2 tion of the mean beam length for flame volumes is10 ¸"3.6» /A & &
(19)
If the inlet air flow rate m and burning area A (or diameter of fuel bed D) are !*3 7 given, by substituting A , Q and e from eqn (6), (16), and (17) into eqn (2), the & R functional relationship between ¹ and ' can be obtained. &
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3 RESULT AND DISCUSSION In order to compare with the experiments performed at FMRC, USA and the Fire Research Institute, Japan, the following polymers were selected in this study. (1) Carbon—hydrogen containing polymers: (1.1) aliphatic: polyethylene, M(C H ) N and polypropylene, M(C H ) N; 2 4n 3 6n (1.2) aromatic: polystyrene, M(C H ) N; 8 8n (2) Carbon—hydrogen—oxygen containing polymers (aliphatic only): polymethylmethacrylate, M(C H O ) N and pine wood crib, M(C H O ) N; 5 8 2n 6 10 5 n (3) Carbon—hydrogen—oxygen—nitrogen containing polymer (aliphatic only): nylon, M(C H O N ) N. 12 22 2 2 n Calculations were conducted in the following two cases. (1) For small-scale fires, m "1.36 g/s, A "70.88 cm2, per the experimental condition of the !*3 7 Flammability Apparatus at FMRC. (2) For large-scale fires, a real room with an opening of 1.2 m]1.5 m (height) and burning area of 3.6 m2 was considered; the inlet air flow rate may be given by eqn (4), i.e. m "1.146 kg/s. !*3 The other data used in the prediction are listed in Table 2. The results are shown in Figs 3—9. 3.1 The effect of fire ventilation The effects of ventilation on soot concentration within a flame and mean flame radiative temperature are shown in Figs 3 and 4, respectively. For wellventilated fires, the f and ¹ are almost independent of '. On the other 7 &
Fig. 3. Dependence of f on '. V
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Fig. 4. Dependence of ¹ on '. &
Fig. 5. Predicted ¹ for both scale fires. &
hand, for under-ventilated fires, the f increases and ¹ decreases steeply as 7 & ' increases, due to the incomplete combustion and heat loss from soot particles. It is suggested that fuels having sootier flames have lower flame temperatures. 3.2 The effect of the chemical structure of the polymers From Figs 1 and 2, and Table 1, it can be seen that the ! and ! have the A C same a, b and m values for all polymers in this study, therefore the ratios of s /s and s /s are expected to be independent of the chemical structures of A A0 C C0 the fuels. The ! , on the other hand, has different a, b and m values, and the S
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Fig. 6. s
R0
versus ¸ for well-ventilated fires. SP0
Fig. 7. Predicted ¹ and s for well-ventilated combustion. & R
ratios of g /g and s /s depend on the chemical structures of the polymers S S0 R R0 (see Table 2 and eqn (14)). 3.3 The effect of fire scale It was found that in large-scale fires the heat release rate and mass burning rate per unit surface area of fuel increase with fire size because of the increase in the flame radiative heat flux, and finally reach their asympotic values3,4. The prediction of ¹ for both scale fires in Fig. 5 shows that ¹ is almost & & independent of the fire size.
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Fig. 8. Comparison of predicted ¹ . &
Fig. 9. Comparison of predicted s with the experimental data. R
3.4 The effect of the fuel’s smoke-point It has been found that the flame radiant fraction for fuels burning in air is principally determined by the fuel’s smoke-point11. The flame radiant fractions of the polymers at well-ventilated conditions are shown in Fig. 6, as a function of the fuel’s smoke-point. For comparison, the experimental data of other fuels and eqn (1) are shown simultaneously. It can be seen that the relationship between the flame radiant fraction and smoke-point of the polymers is in good agreement with eqn (1).
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3.5 The GFR model and comparisons The Global Flame Radiation Model of de Ris and Orloff1 was also used to predict s and ¹ . The values predicted from the GFR Model for wellR & ventilated polymer fires are shown in Fig. 7, which are in excellent agreement with the prediction from the proposed model. With slight modification of the GFR Model1, s and ¹ can be predicted for under-ventilated combustion. R & The results from both models for wood crib fires are shown in Figs 8 and 9, compared with the experimental data reported in de Ris and Orloff1. In addition, the ¹ of PMMA suggested in Drysdale2 and Tien et al. 9 is 1573 and & 1538 K, respectively; the predicted value in this study is about 1480 K. This comparison indicates that the proposed approximate model is satisfactory for predicting s and ¹ for both well- and under-ventilated polymer fires. R & 4 SUMMARY Fire ventilation is an important factor affecting enclosure fire behaviour. For under-ventilated fires, the flame radiant fraction and temperature depend on the fire ventilation. On the other hand, for well-ventilated fires, they are almost independent of the ventilation. As discussed in this paper, flame radiation and its ventilation effects could be predicted by using the following two models: the slightly modified Global Flame Radiation (GFR) Model and the !- correlation based model proposed in this paper. In addition, flame radiation from well-ventilated polymer fires may, to a certain extent, simply be predicted from the correlation between the radiant fraction and the smoke point. The GFR Model as well as the correlation are based on the smoke point, which is sometimes quite difficult to measure for solid materials. However, the proposed approximate model is based on the combustion efficiencies, which can easily be measured, and is therefore expected to be used more extensively. REFERENCES 1. Tewarson, A., Jiang, F. H. & Morikawa, T., Combustion and Flame, 95 (1993) 151—69. 2. Drysdale, D., An Introduction to Fire Dynamics. Wiley-Interscience, New York, 1985. 3. Tewarson, A., Generation of heat and chemical compounds in fires. In SFPE Handbook of Fire Protection Engineering, Section 3, Chapter 4. National Fire Protection Association, Quincy, MA, USA, 1995, pp. 3-53—3-124. 4. Jiang, F. H., Proc. 1st Asian Conf. on Fire Science and ¹echnology. International Academic Publishers, 1992, pp. 404—409.
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5. Tewarson, A., Jiang, F. H. and Alpert, R., Non-thermal fire damage effect of ventilation. 12th Panel Meeting of the UJNR Panel on Fire Research and Safety, Tsukuba and Tokyo, Japan, 27 November—2 October 1992. 6. Tewarson, A., Proc. 20th Int. Symp. on Combustion. The Combustion Institute, Pittsburgh, PA, USA, 1984, pp. 1555—1566. 7. Kawagoe, K., Fire Behaviour in Rooms. Report No. 27, The Building Research Institute, Scuba, Japan, September 1958. 8. Newman, J. S. & Steciak, J., Combustion and Flame, 67 (1987) 55—64. 9. Tien, C. L., Lee, K. Y. and Stretton, A. J., SFPE Handbook of Fire Protection Engineering. National Fire Protection Association, Quincy, MA, USA, 1988, pp. 1-92—1-105. 10. Holman, J. P., Heat ¹ransfer. McGraw-Hill, Scarborough, CA, USA, 1976. 11. Markstein, G. H., 20th Int. Symp. on Combustion. The Combustion Institute, Pittsburgh, PA, USA, 1985, p. 1055.