Experimental and Theoretical Study of the Ignition and Smoldering of Wood Including Convective Effects

Experimental and Theoretical Study of the Ignition and Smoldering of Wood Including Convective Effects R. BILBAO,* J. F. MASTRAL, M. E. ALDEA, J. CEAMANOS and M. BETRÁN Department of Chemical and Environmental Engineering, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain and J. A. LANA Direction of Technology, Construction and Environment, Enagas-Gas Natural, Ctra Madrid, km. 306,4, 50080 Zaragoza, Spain Ignition, as one of the most important processes during the initiation and development of a fire, needs to be studied in different situations. In this work, an experimental and theoretical study of the ignition of wood, including convective effects, has been performed. The experimental study includes tests of both spontaneous and piloted ignition with air flows at different velocities over the sample. Depending on the conditions, smoldering was observed, followed either by ignition or extinction. In some cases, decomposition of the sample occurred without the appearance of a flame. A mathematical model has been used that includes the kinetics of thermal decomposition of wood, the latent heat of vaporization of water, and variable thermal properties. The model provided the temperature at each point in the solid, the local conversion of solid, the time to smoldering, and the time to ignition of the material. In general, reasonable agreement between experimental and theoretical results was obtained. 2001 by The Combustion Institute NOMENCLATURE A s maximum pyrolysable fraction of the sample C ps solid heat capacity (J/g K) F factor taking into account the variation of conversion with temperature (Eq. 6) h c coefficient of convective heat transfer (W/m 2 K) H dry basis fraction of moisture content in the sample I average radiant heat flux (kw/m 2 ) k rate constant (s 1 ) K s solid thermal conductivity (W/m K) L sample thickness (m) q e incident radiant heat flux (W/m 2 ) q r radiant heat losses (W/m 2 ) ( r A ) reaction rate of wood thermal decomposition (g/m 3 s) t time (s) T temperature (K) *Corresponding author. E-mail: ceamanos@posta.unizar.es T f T b x X s Greek letters temperature of the heat-flux meter without sample (K) water boiling temperature (K) spatial position from the sample surface (m) dry basis solid conversion heating rate of solid (K/s) i heating rate used for the determination of the kinetic constants (K/s) H r enthalpy of reaction (pyrolysis or combustion) (J/g) H v moisture vaporization enthalpy (J/g) s density (g/m 3 ) Subscripts c char m virgin wood 0 initial conditions (t 0) s solid gas phase COMBUSTION AND FLAME 126:1363 1372 (2001) 2001 by The Combustion Institute 0010-2180/01/$ see front matter Published by Elsevier Science Inc. PII 0010-2180(01)00251-6

1364 R. BILBAO ET AL. INTRODUCTION An accurate prediction of fire risk requires an adequate description of the initiation and development of a fire. In the case of wildland fires, ambient conditions such as wind velocity or material moisture should be taken into account. When air flows over a sample, it influences heat transfer at the surface, the pyrolysis rate is much slower and the condition of the combustible gas mixture changes [1]. Atreya and Abu-Zaid [2] studied this process by using Douglas Fir wood and included the effects of water content, oxygen concentration, and velocity of the air. Increasing the air velocity resulted in an increase in the time to ignition, although only velocities of 0.1 and 1 m/s were used. It was concluded that for either a lowered oxygen concentration or an increased air velocity, both ignition delay and ignition temperature were higher. Thermal decomposition of the solid occurred significantly before ignition, so that the solid cannot be considered to be inert. Thus, the thermal decomposition of the solid should be addressed carefully. Ignition can be attained at low air-flow rates, but under certain conditions, the emission of volatiles can be decreased or dilution of the combustible gas can occur, so that gas-phase combustion can no longer be sustained. A direct attack on the char s surface by oxygen, known as smoldering, then takes place. During this stage, the solid temperature increases and heat release can be observed, although flames do not appear. At the same time, toxic gas is produced; this can propagate unnoticed and be transformed into very rapid, flaming combustion capable of destroying the material completely. Different studies have been carried out addressing the conditions necessary for smoldering to occur, the factors influencing its spread rate and the conditions leading to flaming combustion [3 9]. The materials studied usually have been powdery or porous materials, such as cellular polymers or cellulosics. Materials with lower porosity, such as wood, have received less attention. In this case, the combustible for smoldering is the char generated in the first stage of thermal decomposition or oxidative pyrolysis [7]. In general, past studies indicate that the most important influence is that of the oxygen concentration in the atmosphere. The process of smoldering is controlled by the supply of O 2,so a minimum concentration exists, below which the materials do not experience smoldering. Ohlemiller [9] studied the influence of the airflow velocity on the smoldering process for U-shaped channels of solid wood. He observed that both the smolder propagation rate and peak temperature were highly dependent on air velocity in the range 9 to 22 cm/s. For higher air velocities, smoldering was increasingly likely to be transformed into flaming combustion. Both ignition and smoldering combustion are clearly influenced by air flow, but they have usually been studied separately. This work is focused on the smoldering and/or ignition of pinewood samples when they are exposed to different radiant heat fluxes and air-flow velocities. In both cases, serious deterioration of the material occurs. The experimental conditions have been chosen to approximately fit those observed in real scale experiments of natural gas explosions. The objective is the study and prediction of the behavior of a material to determine the conditions giving to deterioration, caused either by smoldering or ignition, for application to risk analysis. The times to smoldering and/or ignition have been obtained for both spontaneous and piloted ignition by using a range of wind velocities, close to real ambient conditions. A simple mathematical model has been formulated, which includes the kinetics of thermal decomposition for the material and the thermal effects of the solid drying (water evaporation). The values of times to smoldering or to ignition have been calculated and compared with the experimental values. EXPERIMENTAL SYSTEM AND PROCEDURE Figure 1 shows a general view of the experimental system and the different components. The combustion chamber was a (750 750 700 mm) refractory steel enclosure with walls insulated to minimize heat losses. Different openings in the base of the chamber allowed air to flow in from the outside. The heating element

IGNITION AND SMOLDERING OF WOOD 1365 Fig. 1. Schematics of the experimental system. was an electrical resistance wound in the shape of a truncated cone; this allowed for radiant heat fluxes of up to 100 kw/m 2 at the sample s surface. In the experiments without air flow, the ignition source was a propane-air flame, 10 mm in length, located 10 mm above the sample. In experiments with an air flow over the sample, the source was electrical sparks generated in the gap between two electrodes at a rate, which can be modified. To measure the radiant and total heat fluxes on the sample, two Gardon-type heat-flux meters (water-cooled and gas-purged) have been used. The air-flow velocity was measured at different points over the sample with an anemometer before the heating began. The temperature at different locations on the sample and in the gas phase were determined by K-type thermocouples (0.5-mm diameter). These measurements, as well as the radiant heat flux, were recorded by a computer at intervals of 1 s. The ignition experiments were carried out by using (110 110 19 mm) Pinus Pinaster wood samples with a water content of 9 wt.% on a dry basis. The sample s surface was covered with a slab of insulation material during the heating-up of the electrical resistance. Once a steady regime was reached, the insulation material was removed swiftly, leaving the sample exposed to the heat flux. The experimental conditions chosen in the ignition experiments were radiant heat fluxes ranging from 10 to 55 kw/m 2 and wind velocities ranging from 0 to 5 m/s. Smoldering and flaming combustion times were recorded visually. If ignition did not take place within 15 min, ignition was considered not to have occurred and no ignition was recorded. Before the ignition experiments, preliminary experiments were carried out with the heat-flux meters to determine the incident heat flux on the sample and the influence of air velocity on the heat flux. Tests with a given radiant heat flux and different air velocities were performed. Some differences were observed between the preliminary experiments and the ignition experiments. In the preliminary experiments, no sample was used, the heat-flux meters being located at the same distance from the radiant panel as for the sample in the ignition experiments. Because the temperature, T f, of the total heatflux meter was constant and lower than the gas temperature (T ), convective heating of the meter occurred. As the air velocity increased, the gas temperature decreased, as did the convective heating to the meter. The radiant heat flux in the preliminary experiments showed a maximum once the heat-flux meter was exposed, followed by a slight decrease until a constant value was reached. However, in the ignition experiments, the solid temperature, T s, increased, reaching higher values than the gas temperature. The sample suffered convective losses as the air velocity increased. This increase and the increase in the solid temperature during the experiments caused the convective heat flux to increase according to h c (T s T ). The average heat flux received by the sample until ignition was applied. MATHEMATICAL MODEL The simple mathematical model used describes the thermal decomposition of a material exposed to a constant radiant heat flux and an air flow over the sample s surface. It includes the basic physical and chemical phenomena taking place during the thermal decomposition of the solid material and does not use fitting parameters. The main assumptions of the model are: 1. The solid surface is exposed to a radiant heat flux. Heat losses due to re-radiation, convection and conduction towards the solid are taken into account. Steady-state convection is considered, and the effect of the evolved gases from the solid on convective heat transfer is considered negligible. 2. Heat transfer in the solid is one-dimensional,

1366 R. BILBAO ET AL. by conduction and with variable thermophysical properties. Because the thickness of the slabs used in the experiments is 19 mm, they are considered thermally thick [10, 11]. 3. There are no mass transfer limitations inside the solid. Gases are emitted immediately after they are formed due to degradation. 4. The kinetics of pyrolysis, obtained by thermogravimetric techniques, are considered for inside the solid, whereas combustion kinetics are considered on the surface. The oxygen concentration in the gas phase is assumed constant and is not affected by dilution by the evolved gases from the solid or by consumption due to combustion. 5. The latent heat of evaporation of water with a variable boiling point and heat of vaporization is considered. 6. The sample s volume remains constant. This transient system can be described by the time-dependent partial differential equation: [ s C ps T s ] t [ s H] t ( H v ) K s 2 T s x 2 ( H r )( r A ) (1) where ( H v ) is vaporization enthalpy, H is the water content, ( H r ) is the enthalpy of pyrolysis or combustion, and ( r A ) is the rate of thermal decomposition. During drying, the second term on the right-hand side is zero due to the low temperature. During thermal decomposition, the second term on the left-hand side is zero, because the solid has been completely dried (H 0). On the surface, the enthalpy and chemical kinetics obtained in air are considered. Inside the sample, the enthalpy and kinetics of pyrolysis are considered for temperatures below 623 K and of combustion for temperatures over 623 K, when the combustion of char starts [12]. The equation governing the rate of weight loss by thermal decomposition is: ( r A ) s t dx s 0 dt (2) X s being the dry basis conversion of solid. The boundary conditions used: t 0 T s T 0 X s 0 H H 0 q e 0 q r 0 (3) t 0 x L t 0 x 0 T s x 0 (4) T q e q r K s x h c (T s T ) 0 (5) Equation 5 shows the heat balance for the surface. In this equation, q e is the radiant heat flux, q r is the radiative heat loss, and the next terms are the heat conducted into the sample and the convective heat loss, respectively. The incident radiant heat flux was determined experimentally in the preliminary experiments, and the radiant heat losses were calculated by using an emissivity of 0.78 for the material [13] and the surface temperature calculated from the model. The influence of air velocity is included in the model through the convective heat transfer term, h c (T s T ). The values of h c were calculated by using the air velocity over the sample and the reported correlations [14 16] for free and forced convection over a horizontal plate. The parameters included to solve the equations in the mathematical model have been obtained either by using other experimental systems or from the literature. As stated previously, fitting parameters have not been used. The kinetic equations for the thermal decomposition of wood were obtained previously [12,17] and checked in different experimental systems [18]. The general kinetic equation is: dx s /dt) k (A s X s ) F ( i ) (6) where k is the rate constant obtained in thermogravimetric dynamic experiments carried out at a heating rate i, A s is the maximum pyrolysable weight fraction (the maximum conversion for each temperature), and F is a factor that takes into account the variation of conversion with temperature in experiments with a constant rate of temperature increase [17]. The sample surface, in contact with air, degrades with the rate constants for thermal decomposition in air. The values used had been

IGNITION AND SMOLDERING OF WOOD 1367 experimentally determined previously [12] and are: 192 T 292 C, 0 X s 0.20 k (s 1 ) 1.54 10 4 exp ( 9454/T) (7) 292 T 320 C, 0.20 X s 0.64 k (s 1 ) 6.16 10 14 exp ( 23212/T) (8) 320 T 370 C, 0.64 X s 0.75 k (s 1 ) 7.83 10 4 (9) 370 T 468 C, X s 0.75 k (s 1 ) 2.33 10 8 exp ( 17782/T) (10) In the interior of the sample, where there is no oxygen, the rate constants are those obtained under inert conditions [17] and are: T 290 C k (s 1 ) 2.83 10 4 (11) 290 T 325 C k (s 1 ) 6.01 10 2 exp ( 8266/T) (12) T 325 C k (s 1 ) 1.66 10 16 exp ( 26663/T) (13) Previously [19] the heat of reaction of Pinaster Pine had been measured experimentally using a DSC in an inert atmosphere. Two consecutive stages were observed: first, an endothermic stage with a heat of reaction H r 274 J/g, in which decomposition of the cellulose and part of the hemicellulose took place; second, an exothermic step with H r 353 J/g, in which decomposition of the lignin took place. These values were applied inside the sample for temperatures below 623 K. For temperatures over 623 K, the combustion of the char had been experimentally observed in thermogravimetric analysis [12]. On and inside the sample for temperatures over 623 K, the heat of reaction used was that of combustion. The values were also obtained by DSC and are a function of the solid s conversion: H r 0 for X S 0.30, H r 4950 J/g for 0.30 X S 0.76, and H r 17400 J/g for X S 0.76. The thermal conductivities of pinewood and char were obtained experimentally [19]. The heat capacity was taken from the literature [20]. The values of these properties are K m 0.103 W/mK,(C p ) m 1.67 J/g K for pine wood, and K c 0.0687 W/m K, (C p ) c 1.0 J/g K for char. As mentioned above, these properties are assumed to vary linearly with conversion. Of course, thermal properties depend on temperature but taking them to be independent of temperature, as here, has proved useful previously [19]. Besides the enthalpy change on thermal decomposition, the latent heat of evaporation of water was also included in the model. It has been assumed that evaporation does not take place at a constant temperature, but occurs over a temperature range, and that the necessary heat supply varies during the drying of the material. The reason is that both the boiling point of water and its latent heat of evaporation depend on the moisture remaining in the sample. Thus, as evaporation takes place, the boiling point and latent heat increase; their dependencies on moisture content were proposed by Kent et al. [21] and Siau [22], respectively. The model predicts the temperature and the solid s conversion at different points in the sample. From these values a global conversion can be calculated for the solid. DISCUSSION Experimental Results The experimental times to smoldering and to ignition obtained for different radiative heat fluxes and wind velocities are shown in Tables 1 and 2 for spontaneous and piloted conditions, respectively. The predicted results are also shown and will be commented on below. Be-

1368 R. BILBAO ET AL. TABLE 1 Values of the Experimental Times to Smoldering and to Ignition with a Comparison with Predicted Times to Deterioration, All for Spontaneous Ignition Ī (kw/m2) Air velocity (m/s) Experimental Predicted t smoldering (s) t ignition (s) t deterioration (s) 23.8 0 110 737 900 31.2 0 13 30 114 41.0 0 Not observed 15 33 44.2 0 Not observed 11 26 53.5 0 Not observed 16 17 25.0 1 176 285 130 29.9 1 82 900 a 79 30.0 1 57 156 86 40.0 1 Not observed 42 41 43.1 1 Not observed 9 36 36.1 1.5 50 636 59 28.0 2 140 900 a 140 37.2 2 52 597 63 42.2 2 26 178 48 43.0 2 72 700 47 55.2 3 22 45 39 26.0 5 900 900 a 900 a Experiments in which ignition was not observed in 900 s. cause smoldering is not a phenomenon with a defined starting point, it is necessary to note what time to smoldering is considered to be in the following discussion. After initial thermal decomposition, darkening of the sample surface was observed, when smoldering or combustion of the char layer starts. The time at which glowing was observed visually has been labeled as t smoldering, keeping in mind that this glowing is just part of the general process of smoldering. This process continued and eventually ignition and transition to flaming combustion occurred. In these cases, both t smoldering and t ignition were recorded. In some cases smoldering was not observed but there was ignition, so only times to ignition are shown in Tables 1 and 2. Ignition was considered not have occurred if the ignition delay was longer than 900 s. Some remarks should be made about the experimental results. In both spontaneous and piloted experiments, smoldering was not observed for some heat fluxes and air flows, e.g., in a quiescent environment and with a pilot flame. The results show that the velocity of the air had a major influence on the occurrence of smoldering. As the air flow increased and the heat flux decreased, smoldering was more likely to occur. In general, when comparing the results for different air velocities, larger differences in times to ignition were observed than in times to smoldering. This can be explained by taking into account that ignition, as a gas-phase process, is affected more than smoldering by convection. As has been mentioned, the air flow can affect the oxygen concentration on the sample s surface and, indirectly, the smoldering temperature. The effect on ignition is much more direct, because it affects the conditions of the combustible mixture. The radiative heat flux has a stronger influence than the air velocity on smoldering and ignition of the material. Small differences in the heat flux introduce relatively important differences in the times to ignition, which are especially important for low and medium heat fluxes. Obviously, for a given air velocity, the time to ignition decreases as the radiative heat flux increases. For similar heat fluxes, the time to ignition increased with the air velocity, as observed previously [2, 23], due to cooling of the surface and the dilution of the combustible gases generated in the thermal decomposition of wood. The relative influence of these two causes depends on the value of the heat flux. For high heat fluxes ( 55 kw/m 2 ), the ther-

IGNITION AND SMOLDERING OF WOOD 1369 TABLE 2 Experimental Times to Smoldering and to Ignition for Piloted Ignition, as well as Predicted Times to Deterioration Ī (kw/m 2 ) Air velocity (m/s) Experimental Predicted t smoldering (s) t ignition (s) t deterioration (s) 10.1 0 Not observed 900 a 900 14.3 0 Not observed 389 230 20.0 0 Not observed 180 83 25.8 0 Not observed 36 41 29.9 0 Not observed 29 29 44.1 0 Not observed 13 11 53.5 0 Not observed 10 10 13.8 1 900 900 a 900 20.0 1 317 423 302 25.0 1 128 170 130 30.0 1 95 110 78 43.0 1 Not observed 47 36 53.0 1 Not observed 22 29 20.0 2 510 900 a 786 24.9 2 275 365 221 29.8 2 125 169 114 43.0 2 48 77 47 53.0 2 Not observed 38 34 23.2 3 390 900 a 648 30.0 3 145 209 161 43.0 3 51 74 57 51.0 3 47 57 44 25.0 4 643 790 797 30.9 4 237 306 212 43.2 4 46 84 71 52.0 4 48 68 50 29.0 5 620 900 a 504 37.0 5 130 492 144 42.9 5 160 210 91 52.0 5 Not observed 129 60 a Experiments in which ignition was not observed in 900 s. mal decomposition of the solid is very rapid, and gas concentrations are high enough to remain unaffected by dilution by the air flow. In this case, only convective cooling significantly affects the time to ignition. However, for low radiative heat fluxes, the emission of volatiles is slow, so that they are entrained by the air flow while being generated. Moreover, the surface temperature increases more slowly, so that the rate of thermal decomposition is slower. This influence can be observed for a heat flux of 44 kw/m 2 and becomes very important for heat fluxes below 30 kw/m 2. It is also important to note that the critical heat flux for ignition increases as the wind velocity increases. Similar trends are observed for spontaneous ignition. Comparison of Theoretical and Experimental Results The above mathematical model predicts the thermal decomposition of a material. Also, the temperature at different locations in the solid can be predicted. In this work, the experimental results showed different behavior, depending on the heat flux and air-flow rate over the sample. Ignition can occur both with and without air flow, although with air flowing, smoldering initiation and deterioration of the sample can take place before ignition (if present). The main objective of this work was the prediction of the time at which the sample starts to deteriorate. These predictions can be applied to risk analysis

1370 R. BILBAO ET AL. models, in which the integrity of structures needs to be known and quantified. Thus, it is important to suggest valid criteria which, when coupled with this general model, allow the prediction of the time at which deterioration of the material starts, due either to smoldering or to ignition. When both phenomena smoldering and ignition can occur, and considering the safety-related objective, the criterion should be conservative and predict the first phenomenon appearing. The most commonly used criterion is that of a critical temperature on the material s surface. The value used in this work will be based on the experimentally observed phenomena. When smoldering is not observed and only ignition occurs, the critical temperatures are those corresponding to spontaneous or piloted ignition. Previously [24], the critical surface temperatures were found to be 558 K for piloted and 798 K for spontaneous ignition, when the air velocity was very low. The results showed that the time to ignition under different conditions (low and medium heat fluxes, constant or variable heating) could be predicted reasonably well by using a single value of the critical surface temperature. Atreya and Abu- Zaid [2] found an increase in the piloted ignition temperature as the air velocity was increased. For heat fluxes of 35 kw/m 2 and air velocity increasing from 0.1 m/s to 1 m/s, the ignition temperature increased by 15 K. In the present work, for piloted ignition, no smoldering was observed mainly in the experiments with a quiescent environment. Therefore, in these cases a value of 558 K was used as the critical surface temperature. The prediction of the onset of smoldering has been addressed similarly. It is suggested that for smoldering, the critical surface temperature changes with the radiative heat flux. This criterion is based on the fact that thermal decomposition depends on the heating rate (or the heat flux). When the heat flux is increased, and thus the heating rate of the sample, the yield of volatiles increases, but the yield of char decreases. A higher yield of volatiles can cause the oxygen concentration to be lower at the sample s surface. A lower yield of char implies less combustible material available for smoldering. Both facts mean that a higher surface temperature is needed for smoldering. To quantify this Fig. 2. Verification of the smoldering criterion, Eq. 14. criterion it has been considered that for very low heat fluxes, smoldering would start at the temperature of thermal decomposition of the material, i.e., the critical surface temperature for piloted ignition. Taking into account that the values correspond to experiments with air velocities higher than 1 m/s, a value of 573 K has been considered for low heat fluxes. For high heat fluxes and thus, higher surface temperatures, spontaneous ignition would occur first, so the critical temperature for spontaneous ignition can be considered to be the maximum smoldering temperature. In general, it has been experimentally observed that smoldering is not observed over 40 kw/m 2, so this can be considered to be the maximum heat flux for smoldering to occur. Taking this into account the following criterion is suggested: T smoldering 573 6 I (14) where T smoldering is in K and I in kw/m 2 ; Eq. [14] is valid for I 40 kw/m 2. For I 40 kw/m 2 spontaneous ignition is considered to occur, its critical temperature being 798 K. Figure 2 shows this relationship, together with surface temperatures obtained with the model for the smoldering times experimentally obtained. It can be observed that the trends are similar and the criterion can be appropriate. Tables 1 and 2 show the experimental times to ignition and times to smoldering for spontaneous and piloted ignition at different air-flow velocities, together with the theoretical results obtained by using the criteria described above.

IGNITION AND SMOLDERING OF WOOD 1371 Fig. 3. Comparison of experimental and theoretical times for material deterioration. In general, good agreement is observed between the experimental and theoretical results with spontaneous ignition, although the theoretical results are slightly higher than the experimental ones. The differences are more important for low heat fluxes and no air flow over the sample. It can be observed that the experimental results change sharply from 737 s for 23.8 kw/m 2 to 30 s for 31.2 kw/m 2. For higher heat fluxes the theoretical time is close to the experimental time to ignition. For piloted ignition and an air flow over the sample, the results of this model have been compared with those obtained with the model of Lawson and Simms [25]. Although the simple formula suggested by Lawson and Simms gives adequate results under conditions of a stagnant atmosphere and relatively high heat fluxes, better agreement is obtained with the model presented in this work when relatively low heat fluxes and/or an air flow over the sample surface exists. Figure 3 compare theoretical and experimental times to material deterioration for both piloted and spontaneous conditions. Although the data are plotted in log coordinates, the agreement is fair for a wide range of conditions. CONCLUSIONS The influence of convection on the ignition of wood has been studied both experimentally and theoretically for piloted and spontaneous ignition using different air flows over a sample. The results were compared with those obtained in quiescent conditions. In the presence of a pilot spark and with air flowing over the sample, smoldering was generally observed before ignition. In some cases, total conversion of the sample was observed without transition to a flame. The experimental times to ignition and times to smoldering increased with the velocity of the air. The ignition delay is due to cooling of the surface and, depending on the air velocity and radiative heat flux, to the dilution of the combustible gases. The prediction of the time of initiation of smoldering is important. The mathematical model used for the thermal decomposition of the material includes the kinetics of pyrolysis and combustion of wood, the latent heat of evaporation of water and variable thermal properties. A smoldering criterion has been suggested; it consists of a critical smoldering temperature, which depends only on the radiative heat flux. The theoretical and experimental times to ignition and times to smoldering show good agreement. The authors express their gratitude to Enagas- Gas Natural for providing financial support for this work and for a research grant awarded to M. Betrán. REFERENCES 1. Fernández Pello, A. C., in Combustion Fundamentals of Fire (G. Cox, Ed.), Academic Press, London, 1995, p. 31. 2. Atreya, A., and Abu Zaid, M., Proceedings of the Third International Symposium on Fire Safety Science, Elsevier Applied Science, London, 1991, p. 177. 3. Palmer, K. N., Combust. Flame 1:14 (1957). 4. Baker, R. R., Combust. Flame 30:21 (1977). 5. Moussa, N. A., Toong, T. Y., and Garris, C. A., Proceedings of the Sixteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, 1977, p. 1447. 6. Ohlemiller, T. J., Prog. Energy Combust. Sci. 11:277 (1985). 7. Ohlemiller, T. J., Combust. Flame 81:341 (1990). 8. Dosajnh, S., Peterson, J., Fernandez Pello, A. C., and Pagni, J., Acta Astronautica 13:689 (1986). 9. Ohlemiller, T. J., Proceedings of the Third International Symposium on Fire Safety Science, Elsevier Applied Science, London, 1991, p. 565. 10. Janssens, M., Proceedings of the Third International Symposium on Fire Safety Science, Elsevier Applied Science, London, 1991, p. 167. 11. Mikkola, E., and Wichman, I., J. Fire Materials 14:87 (1990).

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