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Mechanisms of ignition of thermally irradiated cellulose
MECHANISMS OF IGNITION OF THERMALLY IRRADIATED CELLULOSE N. J. ALVARES AND S. B. MARTIN
Stanford Research Institute, Menlo Park, California The experimentally determined dependence of spontaneous ignition of radiantly heated cellulose on atmospheric variables is presented and compared with calculated responses based on an idealized model of thermal autoignition in the gas phase. The atmospheric variables are: total pressure (subatmospheric to 4 atm), oxygen concentration (pure diluent to pure oxygen), and diluent replacement (helium and carbon dioxide substituted for nitrogen). As both total pressure and oxygen concentration are increased from their ignition-limiting values (e.g., air at 0.15 atm pressure and 16% oxygen in nitrogen-oxygen mixtures at 1 arm), the times required for ignition fall monotonically from large values (relative to ignition time in air) to values that are substantially less than ignition times in air. The effect of diluent changes is similarly profound. These data render untenable previously reported speculation regarding initiation by the sudden appearance of active species among the pyrolysis products. They are shown to be consistent with the classical processes of thermal autoignition. A simplified model incorporating these processes has been developed. Details of the model and results obtained with it are reported. Introduction
Ignition of solids b y remote heating has received much experimental and some theoretical attention. 1 I t is now possible to describe quantitatively the gross details of ignition behavior in air and to predict, with considerable confidence, ignition thresholds of untested materials. The exact mechanism responsible for ignition, however, is still uncertain. A notable case in point is the spontaneous ignition of thermally thick cellulosic slabs heated in air with intense thermal radiation, i.e., irradiances of the order of 4 cal cm-2 sec-1 or greater. I t is a remarkable experimental fact t h a t when such a solid is exposed to a constant flux H, it ignites after an exposure duration ti which is inversely proportional to the square of the flux absorbed. Moreover, when materials of differing physical properties are tested, the parameter group aH(t~)l/2/(kpc) 1/2 (where k is thermal conductivity, a is radiant absorptance, and pc is the volumetric heat capacity) remains constant over a wide range of exposure conditions. The solution of the heat-conduction equation for opaque, semiinfinite solids has the form
A T (x, t) = 2all (t/'ll'l'Cpc) 112 exp (-- x~/4at) -
-
89 erfcEx/2 (at)l/2J, 905
where AT(x, t) is the temperature rise a t any depth x as a function of the duration of heating t, and a is the thermal diffusivity. A t the irradiated surface (x -- 0), the expression simplifies to
AT (0, t) = 2all (t/~rkpc ) 1/~. Accordingly, the
observation
of
constant
aH (ti)l/2/(kpc) 1/2 suggests t h a t a criterion for spontaneous ignition is the attainment of a fixed surface temperature. This expectation has been confirmed experimentally by optical measurements of temperature of the exposed surface during irradiation in air. ~ These measurements reveal that a surface temperature of about 600~ is consistently achieved at the onset of ignition, regardless of the magnitude of the radiant flux over a considerable range of values. The constancy of s u r f a c e temperature at ignition is an intriguing discovery. Its generality suggests that it is of fundamental importance to an explanation of the ignition process, and y e t its simplicity belies the ease of its interpretation. I t does not in itself reveal the nature of the ignition process; in fact, the very constancy of surface temperature a t ignition has been difficult to explain mechanistically. The rate of cellulose decomposition becomes rapid above 300~ and the composition of
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COMBUSTION OF SOLID ORGANIC MATERIALS
volatile fuel produced does not appear to change drastically as the temperature rises3 The rate of volatile emission from an irradiated slab goes through its maximum value at about the time of ignition, but both the peak rate and the time-integrated amount of volatiles vary over wide ranges of values with varying heat loads. 4 It is noteworthy that none of these factors can explain a fixed 600~ criterion for ignition. One plausible mechanism consistent with the constant surface-temperature criterion is initiation of chemical chain reactions b y the sudden appearance in the pyrolysis products of chemically reactive species, e.g., free radicals, at the time when the heated surface reaches temperatures of about 600~ There is, in fact, some indirect evidence of this in the minor pyrolysis products which increase suddenly in amount or make their first detectable appearance at that time. This led to the hypothesis, advanced by M a r t i n 1 at the Tenth Symposium, that the process was "pyrolytically triggered." On the other hand, it must be recognized that the development of a simple "thermal autoignition" in the gas phase at the mixing interface, i.e., along the boundary streamline between the air and the effluent stream, could lead to a similar result if the temperature coefficients of the reactions were of sufficient magnitude. The work described here is an a t t e m p t to find evidence for the choice between these mechanistic interpretations of the spontaneous ignition phenomenon.
Experimental Procedure In order to explore the parameters of ignition of cellulose exposed to intense thermal flux, cellulosic samples were exposed in atmospheres where (1) the total air pressure was varied over a wide range, (2) the oxygen concentration was varied in a mixture of nitrogen and oxygen at a high and low total pressure, and (3) the oxygen concentration was varied with other diluents replacing the nitrogen of air. The time to ignition t, and the temperature of the cellulosic surface at the time to ignition T, were the recorded response variables in the different atmospheric environments. [-Similar experiments ~,6 have been contrived to explore mechanisms for ignition of solid propellants. Inasmuch as propellants contain oxidants, such results may, or may not, pertain to our problem.-I The source of thermal radiation is a Mitchell carbon arc 7 with refracting optics, providing a 1.5-in.-diameter spot of uniform intensity at
the sample-plane focus. The thermal radiation beam is directed through a Pyrex window into an 18-in.-diameter controlled-atmosphere chamber which contains an adjustable specimen holder located at the sample-plane focus. The square-wave exposure is regulated b y a twoblade, solenoid-activated shutter with a 10millisecond opening time. The specimens are sheets of blackened alpha-cellulose, 20 mils thick and 6 in. square (material 4095). s Flamedetector probes, with 900 V dc impressed across them, are located on the specimen holder in such a way that the conduction gap is directly above the thermally exposed area of the specimen. At the instant of ignition, the ions generated by the flame create a conduction path across the gap. The signal thus generated is photographically recorded with an oscilloscope. The relative flux-time history is concurrently recorded on the same photograph by use of the signal from a photocell that is exposed obliquely to the light reflected from the specimen. The absolute value of the radiant flux is determined by a black-body calorimeter. The temperature of the irradiated surface is measured by the optical system shown schematically in Fig. 1. The detector is a liquidnitrogen cooled lead sulfide cell with a 3.41micron, narrow-band-pass, interference filter. The arc radiation is restricted to the wavelength region below 2.5 microns by a 89 Plexiglass filter in the beam. The emittance of the black alpha-cellulose has been measured to be nearly unity at 3.41 microns; thus, the response of the detector, after calibration with a standard black body, is directly equatable with the surface temperature. 2 The output of the detector is recorded by an oscilloscope and camera. A mechanical vacuum pump and gas-inlet manifold are provided so that various atmospheric environments may be established within the chamber. The pressure of the various gases introduced into the chamber is measured by a mercury manometer, and a muffle fan is included to ensure proper mixing of the gases. All exposures were made at the irradiance level of 7.3 cal cm-2sec-I, and all measurements of the ignition time were referenced to the ignition time in 1 arm of dry air. Artificial air was produced by a mixture of 21% oxygen and 79% water-pumped nitrogen. Exposures of alphacellulose, in artificial air and in dried natural air, yield ignition times that vary 4 - 5 % about a mean value of 1.1 sec, and a surface temperature at the ignition time of ~ 6 2 0 ~ =t=20~ The =t=5% variation in the ignition time in air is dominantly the result of arc-output fluctuation. The ignition responses of alpha-cellulose
IGNITION OF THERMALLY IRRADIATED CELLULOSE
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REAR SURFACE 'PLANE MIRROR
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FIG. 1. Schematic of the ignition chamber showing the plan-view arrangement of the apparatus. specimens were measured under the following conditions: (1) varying total pressures from 0.1 to 4.0 atm of dry natural air, (2) varying oxygen concentrations at total pressures of 1.0 and 0.2 atm, in which the concentration of oxygen was varied from pure oxygen to the level where ignition is no longer possible regardless of the length of exposure, and (3) varying oxygen concentrations at 1-arm total pressure of "artificial air" (i.e., a mixture containing 21% oxygen) in which the diluent nitrogen was replaced by carbon dioxide in one case and helium in another. Particular attention was given to the moisture content of the specimen, as it was found that the ignition time is roughly 20% to 30% longer for specimens which have
not been outgassed. For this reason, every specimen was held at a pressure of about 5 torr for 1 hr before the measurement atmosphere was introduced into the chamber. Natural air, when used, was passed through a large volume of Drierite before introduction into the chamber. When a mixture of gases was used to make artificial air, the drying procedure was not necessary. Homogeneous atmospheres were ensured by mixing with the included muffle fan. Following the introduction of the desired atmosphere, the exposure was made and the resultant signals were photographically recorded. Most of the exposures resulted in a transient ignition of the specimen, i.e., the flaming ceased at the conclusion of the exposure. I t was con-
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COMBUSTION OF SOLID ORGANIC MATERIALS flaming, indicating that the back surface temperature rose significantly during exposure.
5.0
Experimental Results
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400
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PARTIAL PRESSURE
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Fie. 2. ~ h e effect on the time to ignition of varying the oxygen partial pressure in the diluents-nitrogen, helium, and carbon dioxide. These measurements were all made at 1 arm. sidered necessary that the samples be thick enough to approximate a semi-infinite slab configuration for the purpose of diagnostic comparison of data and to simplify the theoretical treatment; however, at total pressures less than 0.3 arm, the long exposures resulted in sustained 5.0
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Figure 2 is a composite of three sets of measurements that compare the ignition time with variab!e oxygen concentrations at 1 arm total pressure in "artificial airs" made up of nitrogen, helium, and carbon dioxide, respectively. Helium and carbon dioxide were chosen as diluents since they have heat conductivities that are, respectively, much higher and slightly lower than nitrogen, and also since they are inert (more precisely, nonoxidizing) and readily obtainable. It is to be noted that helium, which has a conductivity almost a factor of 10 larger than nitrogen, always exhibits a longer time to ignition than nitrogen, while carbon dioxide, which is approximately 10% lower in heat conductivity, exhibits the only values shorter than the nitrogen data. Carbon dioxide was perhaps not the best choice for a low-conductivity diluent, since its extinguishment properties are partially attributed to its chemical reactivity. This reactivity could be a major reason for the high oxygen concentration ignition limit observed in Fig. 2. Its relatively large heat capacity and its high radiant emittance are probably also involved. Figure 3 plots experimental data expressed as the ratio of the ignition: time t~ at various total pressures of dry air, to the ignition time to at 1 arm of dry air. [-The curves in this and in Figs. 4 and 5 are results of numerical calculations using the model to be described subsequently.] The low-pressure limit for ignition (under these experimental conditions) is just below 0.15 I
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ATMOSPHERES (TOTAL PRESSURE)
FIG. 3. The effect of total air pressure on ignition time; a comparison of the analytical results with experimental data.
IGNITION OF THERMALLY IRRADIATED CELLULOSE atm. The datum point at 0.15 atm indicates
a t~/to of 4.2. This datum point is the average of several determinations at this pressure. However, an equal number of exposures at 0.15 arm did not ignite, but did char the specimen. To confirm t h a t 0.15 a t m is very close to the limiting lower pressure for ignition of alphacellulose, exposures were made on thicker (30-mil) samples. With the thick specimens, it was not possible to obtain an ignition below 0.15 atm; however, tJto was roughly 50% higher. This difference in ignition time is undoubtedly due to the fact t h a t both the 20and 30-rail specimens were not thick enough to approximate a semi-infinito solid for the longest exposures. However, it is to be noted that, at 0.3 atm (the lowest pressure at which transient ignition occurs), the trend of the data is established sufficiently for our purposes. At high pressures, the ignition time decreases with increasing pressure, up to at least 4.0 arm. These data (within the pressure limitation of this experiment) indicate t h a t the ignition response time is a monotonically decreasing function of total pressure. Figure 4 is a composite graph where the data points show (1) the variation of ignition temperature with total pressure over the pressure range of 0.1 to 1.0 atm, and (2) the variation of the ignition temperature with oxygen concentration in a total pressure of 1 atm. I t can be seen t h a t the ignition temperature varies inversely with the total pressure and, consequently, with the total oxygen concentration.
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The trend of the temperature data is quite similar to the ignition-time data. These data show that the ignition temperature decreases monotonically with increasing oxygen concentration over this limited pressure range. We have observed t h a t the time to ignition decreases as the atmospheric pressure increases. Also, ignition will not occur (in this experimental environment) below 0.15 atm. Further, the ignition time in strictly inert diluents (nitrogen and helium) increases with the magnitude of the heat conductivity of the diluent gas, but there is an anomalous effect when carbon dixode is used. Along with this effect, we see t h a t the time to ignition varies inversely with the oxygen concentration when the total pressure is held constant; thus, the trend of the ignition time is the same in Figs. 2 and 3. The trend of the surface-temperature d a t a at the time of ignition is similar to the trend of the ignition d a t a when the total pressure or the oxygen concentration is varied. This fact can be seen by comparison of Figs. 2 and 3 with Fig. 4. Some unexpected phenomena have been observed during the course of the measurements. For example, a very definite and constant change in slope occurs in the surface-temperature rise at 500~ regardless of pressure or oxygen concentration. At 500~ the rate of temperature rise T decreases abruptly to a significantly lower ~', and continues until ignition occurs at about 600~ We also observed that T varies inversely with oxygen concentration in both the measurements where total pressure was either changed or held fixed. Note t h a t this effect was apparent both before and after the 500~ change in slope. Measurements of the ignition response versus oxygen concentration at a total pressure of 0.2 atm show the same characteristics as similar measurements at 1.0 atm. However, ignition will occur at far lower oxygen partial pressures as long as the ratio of oxygen to nitrogen remains about 1 to 5.
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I00 200:300 400 500 600 700 OXYGEN PARTIAL PRESSURE FxG. 4. The effect of total air pressure and oxygen concentration on the surface temperature at the time of ignition; a comparison of the analytical results with experimental data. (Note that the oxygen partial pressure for the total pressure data was computed by assuming the normal oxygen concentration of air to be 21 per cent.)
F r o m the experimental results, the concept t h a t ignition is triggered by the sudden appearance of chemically reactive species among the pyrolysis products is clearly untenable and, of the two postulated mechanisms, only the thermal autoignition mechanism is worthy of further consideration. Our purpose in what follows is not to describe a rigorous theory for the hypothesis of thermal autoignition, but merely to explore its feasibility using a relatively simple and much idealized
910
COMBUSTION OF SOLID ORGANIC MATERIALS
model of the complex system. We will describe how the model was developed, use it to calculate numerical values of the dependence of ignition times on total pressure, oxygen concentration, and the replacement of nitrogen with another inert gas of very different physical properties, and then look for qualitative (or at most, semiquantitative) agreement with our experimental data. If the simple model is successful, then the effort needed to derive a more sophisticated model will be in order. In developing the model, we have applied the basic concept of the Semenov thermal autoignition theory to an idealization of the gasphase interface between the pyrolytic effluent from the heated surface and the surrounding atmosphere. Considering some elemental volume of gas in the region where the stoiehiometric fuel/oxidant concentration ratio exists, we postulate t h a t ignition will occur when the heatrelease rate due to chemical reaction just exceeds the rate of heat losses from the element. The threshold condition is therefore given by the equation
L
=
If then, in the region of diffusive mixing, the function f represents the spatial distribution of pyrolysis products expressed as a mass fraction of the total mixture, the mass fraction of oxidant at any point is 9 E o [ - O ] / E ~ff~Fil = a (i -- f), i
while t h a t of fuel is ~FEF]I
E ~s
= ~f,
i
and, a t the stoichiometric point, ~o - m ~ o [ O ] . # E m ~ , [ / ] ~ , = ~ (i - f~,), i
~F -----~I~F[F].J E ~l%~[i].t = ~f.t, i
where
f~r =
~/(~ +
~=).
Therefore,
qw,
where L is the rate of heat loss (units of energy per unit volume per unit time), q the heat of the oxidation reaction (units of energy per unit mass reacted), and w the rate of the reaction (units of mass per unit volume per unit time). The rate of the oxidation reaction can be represented by an equation of the form w = # (#F/#O) m (ttoP/RT)", where ttF and t~o are the mass fractions of fuel and oxidant in the stoichiometric mixture, P is the total pressure, R the gas constant, and T the temperature. As given, the over-all order of the reaction is n, while m is the order in fuel only. If we assign values to the concentration of oxidant in the atmosphere and to fuel in the undiluted pyrolysis products, and assume that the mass diffusivities of all component gases of the system are of equal magnitude, then we can readily evaluate the concentrations of the reactants at positions in the mixing zone where they are in stoichiometric proportions. Let a = 9 ~ o [ O ] / ~ l ~ N [ N ] be the mass ratio of the oxidant to its diluent in the atmosphere, and let fl = ~ T ~ F [ F ] / ~ % M [ M ] be the mass ratio of fuel to its diluent in the pyrolytic effluent. With equal mass diffusivities, these quantities will apply generally throughout the gas-phase system. Further, let ~ = ~Y~F[F]st/D]lo[O]st be the stoichiometric mass ratio of fuel to oxidant.
,o = ~ / ( ~
+ ~)
and .F = ~ / ( ~
+
~).
Returning to the rate equation, the principal dependence of rate on temperature is contained in the expression ]c -- A exp ( - E/RT). If E is large, the rate of reaction will have a strong dependence on temperature; and, as the temperature is fncreased, there will come a point, the value of which depends upon the magnitude of E, at which the heat-generation rate will exceed the heat-loss rate, everything else being equal. The pertinent temperature is probably not the temperature of the irradiated surface a t the instant of ignition. Rather, it is less than the temperature of the effluent stream by an amount that depends on how much dilution occurs with the ambient atmosphere in providing a near-stoichiometric mixture. Furthermore, the gases evolved by the decomposing solid may or may not achieve thermal equilibrium with the hot surface during their brief passage through it. These are potentially important factors and should be treated analytically in a more sophisticated model; in' this preliminary mode] they have been neglected. We have, in fact, identified
IGNITION OF THERMALLY IRRADIATED CELLULOSE the temperature T with the temperature of the gas-solid interface, whose dependence on time and radiant flux we have approximated by the solution of the heat-conduction equation for the opaque semiinfinite solid, viz., T (t) = To + E2b/(Tr ~/2) ]" [ H (W ~)/(kpc)ll~J. The value of the "fitting constant" b was chosen to give a temperature rise of about 600~ for the incident flux-exposure times known from extensive experimentation to just result in ignition in air. Its value of about 0.5 is thought to represent a combination of three factors that act to make the sensible heat flux less than the incident: (1) the less-than-total absorptance by the surface, (2) the heat losses from the surface, and (3) endothermie chemical sinks. Heat losses from the gas-phase volume element can be treated as Newtonian and unidimensional, since the heating rate is high enough to ensure no convection effects? Again, sophistication could be added to the model by the analysis of heat flow across the nonsteady diffusional gradient. We chose, however, to relate the heat loss rate L to the over-all temperature drop ( T - To) without regard to the distances separating the reacting volume from the ambient. I-This choice is equivalent to assuming that the breadth of the diffusive mixing zone does not vary appreciably during the times of interest.] The two are thus related through the introduction of an artificial "heat-transfer coefficient" h, thus L--h(T--
To).
It is reasonable to expect that the magnitude of the heat-transfer coefficient is determined by the conductivities of the component gases. Accordingly, the heat-transfer coefficient can be given the form (ako + kN) + ~ (/3kF + kM)] h
=
'
where ko and kN are the conductivities of the oxidant and its diluent, respectively, kF and kN are the conductivities of the fuel and its diluent (i.e., the nonfuel components of the pyrolysis products), respectively. In this way, we arrive at a new constant K which is independent of composition and, therefore, can be evaluated for air (by requiring that the solution agree with the observed ignition time) and then be applied generally. The foregoing equations were solved numerically with a digital computer for wide
911
variations in atmospheric parameters. The sensitivity of the solutions to most of the parameters whose values were uncertain (i.e., the effect of varying ~, a, n, m, and i~F) was evaluated by repeating the solutions with selected values of these throughout their range of reasonable variation. The parameters K, q, and A were not varied because they can be lumped together in a fitting constant whose value is adjusted to fit the time of ignition in air to its experimentally determined value; and it was felt that varying the value of E would be meaningless inasmuch as it is associated with the temperature of the irradiated surface rather than with the actual (and unknown) temperature of the stoichiometric region of the gas-phase mixing region. The parameter /3 was taken to have values in the range 0.1 to 1. Inspection of the equation for rate of reaction reveals that the effect of total pressure on ignition is independent of ~, but that the value of /~ should affect the dependence of ignition time on oxidant concentration. The numerical solutions agree with this expectation and indicate that the sensitivity of the dependence on oxidant concentration is quite insignificant. Figure 3 compares the calculated values of ti/to (the curve) with the experimental data points taken in air at pressures ranging from less than 0.15 to 4 arm. The chosen constants that apply to the theoretical solution shown in the figure are as follows: n = 3,
m = 2,
~=0.5,
a=0.1.
The excellence of the agreement is obvious. Figure 4 depicts the change in surface temperature at ignition for both the cases where total pressure and where oxygen concentration are varied at 1 atm total pressure. The agreement between the experimental points and analytical curves is reasonably good over the central portion of the range, but becomes progressively worse at both higher and lower levels of 02 concentration. Figure 5 illustrates the change in time of ignition with oxygen concentration for atmospheres having both nitrogen and helium as diluents of the oxygen. The agreement is excellent, except, as before, at the extremes. The success of the thermal-autoignition model is remarkable, in view of its simplicity. Moreover, its failings are such as to encourage its further development. For example, its inability to properly represent the sharp increase in ignition time for oxygen concentrations less than those in air could be attributed to the neglect of radiative heat loss in the model. In fact, the very high surface temperatures, which correspond to the
912
COMBUSTION OF SOLID ORGANIC MATERIALS
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An alternative hypothesis, thermal autoignition, has been shown to be consistent with the dependence of ignition behavior on total pressure, oxidant concentration, and choice of inert diluent. A simple model of this process affords numerical solutions that fit the d a t a remarkably well, encouraging the development of a more sophisticated theoretical description.
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OXYGEN PARTIAL PRESSURE (ram Hg)
FIG. 5. Comparison of analytical results and experimental data for the dependence of ignition time on oxygen partial pressure in air made with nitrogen and helium diluents. calculated ignition times under such conditions, are never observed in irradiated cellulose, simply because it ablates away before such temperature can obtain, even at extremely high radiant-flux levels. The model is readily adaptable to account for such effects. On the other hand, at high oxygen concentrations, the model predicts ignition times whose temperatures are too low for appreciable pyrolysis to occur in the short times available. I t is entirely reasonable to expect that the limiting time at high oxygen concentrations is governed entirely by the onset of pyrolysis, a factor which is totally neglected in the model. The kinetics of the pyrolysis reactions of cellulose are resonably well established, and a logical extension to the model would include them.
Conclusions
In view of the experimental evidence, the earlier concept that spontaneous ignition is triggered by the sudden appearance of reactive species in the pyrolysis must be abandoned.
a A b c
radiant absorptance, dimensionless Arrhenius coefficient, mass units fitting constant, dimensionless specific heat capacity of cellulose, cal g-1 oc-1 E activation energy, cal mole-1 F refers to fuel f spatial distribution of the mass fraction of pyrolysis products, dimensionless fst value of f at the stoichiometric location, dimensionless h dummy heat-transfer coefficient cal cm -3 oC--1 H radiant flux per unit area (irradiance) cal cm-2 sec-~ Fi] molar concentration of ith component of gas mixture, mole cm -s k thermal conductivity of cellulose, cal cm cm-2 sec-lOC-1 ki thermal conductivity of i t h component of gas mixture, cal cm cm -2 sec-~ ~ ]~ rate constant, mass units L rate of heat loss, cal cm-a m order of the reaction in fuel, dimensionless M refers to nonfuel portion of pyrolysis products 9E~ molecular weight of ith component of gas mixture, g mole-~ n over-all order of the reaction, dimensionless N refers to atmospheric diluent O refers to oxidant P total pressure, arm q heat of reaction, cal g-l; based on total material reacted R gas constant, cal ~ mole-~ t time from beginning of exposure, sec t~ time to ignition, sec to specific value of time to ignition in air at 1 atm, sec AT(x, t) temperature rise with time as a function of depth, ~ T surface temperature at tl, ~ rate of temperature rise, ~ sec-~ w rate of reaction, g cm-3 sec-1 x depth of cellulosic material, cm
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IGNITION OF THERMALLY IRRADIATED CELLULOSE a
K
P (7
thermal diffusivity (cm 2 see-l); mass ratio of oxidant to atmospheric diluent, dimensionless mass ratio of fuel to nonfuel pyrolysis products, dimensionless fitting constant, sec cm-~ mass fraction of i t h component of stoichiometric mixture, dimensionless density of cellulose, g c m -3 stoichiometric mass ratio of fuel to oxidant, dimensionless
913
3. LIPSKA, A. E. AND WODLEY, R. A.: J. Appl. Polymer Sci. 18, 851 (1969). 4. MARTIN, S. B. AND RAMSTAD, R. W.: Stable Pyrolysis Products of Cellulose Exposed to Intense Thermal Radiation, USNRDL TR-810, Jan. 1965. 5. BEYER, R. B. AND FISHMAN, N.: "Solid Propellant Ignition Studies with High Flux Radiant Energy as a Thermal Source," Progress in Astronautics and Rocketry, Vol. 1, p. 673, Academic Press, 1960. 6. OHLEMILLER, T. J. AND SOMMERFIELD, M.:
Acknowledgment We are indebted to Professor F. A. Williams, University of California, San Diego, for suggesting the thermal-autoignition approach to the interpretation of our data--the approach that led to the model presented here. REFERENCES 1. MARTIN, S. B.: Tenth Symposium (International)
on Combustion, p. 877, The Combustion Institute, 1965. 2. ALVARES,U. Z.: Measurements of the Temperature of the Thermally Irradiated Surface of Alpha-Cellulose, USNRDL TR-735, March 1964.
AIAA J. 6, 878 (1968). 7. BROIDA, T. R.: The Production of Intense Beams of Thermal Radiation by Means of a High Current Arc and Relay-Condenser Optical System, USNRDL TR-417, Nov. 1953. 8. BUTLER, C. P., MARTIN, S. B., AND LAI, W.: Thermal Radiation Damage to Cellulosic Materials, Part II. Ignition of Alpha-Cellulose by Square Wave Exposure, USNRDL TR-135, Nov. 1956. 9. ALVARES, N. J., BLACKSHEAR, P. L., JR., KANURY, A. M. : "The Influence of Free Convection on the Ignition of Vertical Cellulosic Panels by Thermal Radiation," Combustion Sci. and Technol., 1,407 1970.
COMMENTS D. H. Fine, M.I.T. You have shown that your data fit some of the predictions of thermal explosion theory. However, a chain-thermal reaction or even an exothermic chain-branching reaction could equally well explain your data. Your conclusions, therefore, do not in themselves mean that the nature of the explosion is thermal. The fundamental postulate of thermal-explosion theory is concerned with the temperature of the system. If the temperature increases at an accelerating rate, the system has exploded because of a thermal mechanism; other experimental observations are incidental to this unique prerequisite. Authors' Reply. Reference 1 in the paper shows evidence that ignition may result when the surface temperature of the cellulose reaches a critical value (,~600~ where the pyrolytic breakup of the cellulosic molecule results in a surge of species that are easily ignitable. There was some speculation that these species included free radicals, which could possibly "pilot" the ignition mechanism in the gas phase. To investigate this speculation, ignition-delay and surface-temperature measurements were undertaken in selected atmospheric environments. I t soon became
evident that the surface temperature of the cellulose at the time of ignition was a monotonically decreasing function of the oxygen partial pressure, regardless of the total pressure. Thus, the previously proposed ignition mechanism was wholly untenable. Figure A illustrates the effect of oxygen concentration on the surface temperature. The indicating arrows in each record show an abrupt change in the rate of temperature rise, respectively: (1) the start of exposure, (2) a change in the temperature rise curve, which may indicate the start of pyrolysis, (3) the ignition point, and (4) the end of exposure to the thermal radiation source. The slope change in the surface temperature rise curve (indicated by 2) always starts at about 500~ This may indicate that, a t relatively high irradiances, the pyrolysis reaction does not commence significantly until the temperature of the cellulose reaches this level. Plates C and D suggest that there is an effect of oxygen concentration at the rate of surface temperature rise for the same heat flux and total pressure. The temperature record always exhibits a sudden jump (indicated by 3 in Plates C and D) at the time ignition occurs, resulting, apparently, from emission by the flames. The flames are optically thin,
914
COMBUSTION OF SOLID ORGANIC MATERIALS
/
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NO IGNITION 4 f
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PLATE D
COMPOSITE OF SURFACE TEMPERATURE RISE DATA EXPOSURES IN VARIOUS PRESSURES AND OXYGEN CONCENTRATIONS WHERE: PLATE A IS ~10 -4 ATMOSPHERES, 21% 02; PLATE B IS 0.2 ATMOSPHERES, 21% 02; PLATE C IS 1.0 ATMOSPHERE, 21% 02; PLATE D IS 1.0 ATMOSPHERES, 50% 02 . :FIG. A
thus the increase in temperature does not correspond to the actual flame temperature, and if irradiation is continued, the signal will continue to rise at a slightly greater rate, apparently due to the additional flux from the flames. Since the "appearance of species" mechanism for this ignition phenomenon did not appear to satisfy the data, we tried the simple thermal mechanism of ignition, as explained in the paper, to see if it would fit the data. Kere, the point of
major comparison was the ignition delay and the surface temperature at the time of ignition (indicated by 3 on the curves in Fig. A). The reaction is assumed to occur in a slab of gas so close to the surface that its temperature, up to the time of ignition, can be assumed to be the surface temperature. Upon ignition, the gas-phase reaction attains the flame temperature instantaneously so far as our experimental t i m e base is concerned.
Stanford Research Institute, Menlo Park, California The experimentally determined dependence of spontaneous ignition of radiantly heated cellulose on atmospheric variables is presented and compared with calculated responses based on an idealized model of thermal autoignition in the gas phase. The atmospheric variables are: total pressure (subatmospheric to 4 atm), oxygen concentration (pure diluent to pure oxygen), and diluent replacement (helium and carbon dioxide substituted for nitrogen). As both total pressure and oxygen concentration are increased from their ignition-limiting values (e.g., air at 0.15 atm pressure and 16% oxygen in nitrogen-oxygen mixtures at 1 arm), the times required for ignition fall monotonically from large values (relative to ignition time in air) to values that are substantially less than ignition times in air. The effect of diluent changes is similarly profound. These data render untenable previously reported speculation regarding initiation by the sudden appearance of active species among the pyrolysis products. They are shown to be consistent with the classical processes of thermal autoignition. A simplified model incorporating these processes has been developed. Details of the model and results obtained with it are reported. Introduction
Ignition of solids b y remote heating has received much experimental and some theoretical attention. 1 I t is now possible to describe quantitatively the gross details of ignition behavior in air and to predict, with considerable confidence, ignition thresholds of untested materials. The exact mechanism responsible for ignition, however, is still uncertain. A notable case in point is the spontaneous ignition of thermally thick cellulosic slabs heated in air with intense thermal radiation, i.e., irradiances of the order of 4 cal cm-2 sec-1 or greater. I t is a remarkable experimental fact t h a t when such a solid is exposed to a constant flux H, it ignites after an exposure duration ti which is inversely proportional to the square of the flux absorbed. Moreover, when materials of differing physical properties are tested, the parameter group aH(t~)l/2/(kpc) 1/2 (where k is thermal conductivity, a is radiant absorptance, and pc is the volumetric heat capacity) remains constant over a wide range of exposure conditions. The solution of the heat-conduction equation for opaque, semiinfinite solids has the form
A T (x, t) = 2all (t/'ll'l'Cpc) 112 exp (-- x~/4at) -
-
89 erfcEx/2 (at)l/2J, 905
where AT(x, t) is the temperature rise a t any depth x as a function of the duration of heating t, and a is the thermal diffusivity. A t the irradiated surface (x -- 0), the expression simplifies to
AT (0, t) = 2all (t/~rkpc ) 1/~. Accordingly, the
observation
of
constant
aH (ti)l/2/(kpc) 1/2 suggests t h a t a criterion for spontaneous ignition is the attainment of a fixed surface temperature. This expectation has been confirmed experimentally by optical measurements of temperature of the exposed surface during irradiation in air. ~ These measurements reveal that a surface temperature of about 600~ is consistently achieved at the onset of ignition, regardless of the magnitude of the radiant flux over a considerable range of values. The constancy of s u r f a c e temperature at ignition is an intriguing discovery. Its generality suggests that it is of fundamental importance to an explanation of the ignition process, and y e t its simplicity belies the ease of its interpretation. I t does not in itself reveal the nature of the ignition process; in fact, the very constancy of surface temperature a t ignition has been difficult to explain mechanistically. The rate of cellulose decomposition becomes rapid above 300~ and the composition of
906
COMBUSTION OF SOLID ORGANIC MATERIALS
volatile fuel produced does not appear to change drastically as the temperature rises3 The rate of volatile emission from an irradiated slab goes through its maximum value at about the time of ignition, but both the peak rate and the time-integrated amount of volatiles vary over wide ranges of values with varying heat loads. 4 It is noteworthy that none of these factors can explain a fixed 600~ criterion for ignition. One plausible mechanism consistent with the constant surface-temperature criterion is initiation of chemical chain reactions b y the sudden appearance in the pyrolysis products of chemically reactive species, e.g., free radicals, at the time when the heated surface reaches temperatures of about 600~ There is, in fact, some indirect evidence of this in the minor pyrolysis products which increase suddenly in amount or make their first detectable appearance at that time. This led to the hypothesis, advanced by M a r t i n 1 at the Tenth Symposium, that the process was "pyrolytically triggered." On the other hand, it must be recognized that the development of a simple "thermal autoignition" in the gas phase at the mixing interface, i.e., along the boundary streamline between the air and the effluent stream, could lead to a similar result if the temperature coefficients of the reactions were of sufficient magnitude. The work described here is an a t t e m p t to find evidence for the choice between these mechanistic interpretations of the spontaneous ignition phenomenon.
Experimental Procedure In order to explore the parameters of ignition of cellulose exposed to intense thermal flux, cellulosic samples were exposed in atmospheres where (1) the total air pressure was varied over a wide range, (2) the oxygen concentration was varied in a mixture of nitrogen and oxygen at a high and low total pressure, and (3) the oxygen concentration was varied with other diluents replacing the nitrogen of air. The time to ignition t, and the temperature of the cellulosic surface at the time to ignition T, were the recorded response variables in the different atmospheric environments. [-Similar experiments ~,6 have been contrived to explore mechanisms for ignition of solid propellants. Inasmuch as propellants contain oxidants, such results may, or may not, pertain to our problem.-I The source of thermal radiation is a Mitchell carbon arc 7 with refracting optics, providing a 1.5-in.-diameter spot of uniform intensity at
the sample-plane focus. The thermal radiation beam is directed through a Pyrex window into an 18-in.-diameter controlled-atmosphere chamber which contains an adjustable specimen holder located at the sample-plane focus. The square-wave exposure is regulated b y a twoblade, solenoid-activated shutter with a 10millisecond opening time. The specimens are sheets of blackened alpha-cellulose, 20 mils thick and 6 in. square (material 4095). s Flamedetector probes, with 900 V dc impressed across them, are located on the specimen holder in such a way that the conduction gap is directly above the thermally exposed area of the specimen. At the instant of ignition, the ions generated by the flame create a conduction path across the gap. The signal thus generated is photographically recorded with an oscilloscope. The relative flux-time history is concurrently recorded on the same photograph by use of the signal from a photocell that is exposed obliquely to the light reflected from the specimen. The absolute value of the radiant flux is determined by a black-body calorimeter. The temperature of the irradiated surface is measured by the optical system shown schematically in Fig. 1. The detector is a liquidnitrogen cooled lead sulfide cell with a 3.41micron, narrow-band-pass, interference filter. The arc radiation is restricted to the wavelength region below 2.5 microns by a 89 Plexiglass filter in the beam. The emittance of the black alpha-cellulose has been measured to be nearly unity at 3.41 microns; thus, the response of the detector, after calibration with a standard black body, is directly equatable with the surface temperature. 2 The output of the detector is recorded by an oscilloscope and camera. A mechanical vacuum pump and gas-inlet manifold are provided so that various atmospheric environments may be established within the chamber. The pressure of the various gases introduced into the chamber is measured by a mercury manometer, and a muffle fan is included to ensure proper mixing of the gases. All exposures were made at the irradiance level of 7.3 cal cm-2sec-I, and all measurements of the ignition time were referenced to the ignition time in 1 arm of dry air. Artificial air was produced by a mixture of 21% oxygen and 79% water-pumped nitrogen. Exposures of alphacellulose, in artificial air and in dried natural air, yield ignition times that vary 4 - 5 % about a mean value of 1.1 sec, and a surface temperature at the ignition time of ~ 6 2 0 ~ =t=20~ The =t=5% variation in the ignition time in air is dominantly the result of arc-output fluctuation. The ignition responses of alpha-cellulose
IGNITION OF THERMALLY IRRADIATED CELLULOSE
907
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:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
REAR SURFACE 'PLANE MIRROR
SAMPLE
L
ELECTRICAL FEED THROUGH
HOLDER
F r o MANOMETER
CIRCULATING FAN
FRONT SURFACE PLANE MIRROR
V~4CUUM "PUMP QUARTZ W NDOW
/
5.41 MICRON INTERFERENCE FILTER
FOCUSING MIRROR
LIQUID Nz COOLED PbS
FIG. 1. Schematic of the ignition chamber showing the plan-view arrangement of the apparatus. specimens were measured under the following conditions: (1) varying total pressures from 0.1 to 4.0 atm of dry natural air, (2) varying oxygen concentrations at total pressures of 1.0 and 0.2 atm, in which the concentration of oxygen was varied from pure oxygen to the level where ignition is no longer possible regardless of the length of exposure, and (3) varying oxygen concentrations at 1-arm total pressure of "artificial air" (i.e., a mixture containing 21% oxygen) in which the diluent nitrogen was replaced by carbon dioxide in one case and helium in another. Particular attention was given to the moisture content of the specimen, as it was found that the ignition time is roughly 20% to 30% longer for specimens which have
not been outgassed. For this reason, every specimen was held at a pressure of about 5 torr for 1 hr before the measurement atmosphere was introduced into the chamber. Natural air, when used, was passed through a large volume of Drierite before introduction into the chamber. When a mixture of gases was used to make artificial air, the drying procedure was not necessary. Homogeneous atmospheres were ensured by mixing with the included muffle fan. Following the introduction of the desired atmosphere, the exposure was made and the resultant signals were photographically recorded. Most of the exposures resulted in a transient ignition of the specimen, i.e., the flaming ceased at the conclusion of the exposure. I t was con-
908
COMBUSTION OF SOLID ORGANIC MATERIALS flaming, indicating that the back surface temperature rose significantly during exposure.
5.0
Experimental Results
4.0
3.0 CO 2-AHe ~
N I
2.0-
1.O-
0
1
0
I
I
L
200 OXYGEN
[
400
I
I
600
PARTIAL PRESSURE
800 (ram Hg)
Fie. 2. ~ h e effect on the time to ignition of varying the oxygen partial pressure in the diluents-nitrogen, helium, and carbon dioxide. These measurements were all made at 1 arm. sidered necessary that the samples be thick enough to approximate a semi-infinite slab configuration for the purpose of diagnostic comparison of data and to simplify the theoretical treatment; however, at total pressures less than 0.3 arm, the long exposures resulted in sustained 5.0
i
4.0
I
I
i
I
i
I
I
9 EXPERIMENTAL
9
r-
I
I
Figure 2 is a composite of three sets of measurements that compare the ignition time with variab!e oxygen concentrations at 1 arm total pressure in "artificial airs" made up of nitrogen, helium, and carbon dioxide, respectively. Helium and carbon dioxide were chosen as diluents since they have heat conductivities that are, respectively, much higher and slightly lower than nitrogen, and also since they are inert (more precisely, nonoxidizing) and readily obtainable. It is to be noted that helium, which has a conductivity almost a factor of 10 larger than nitrogen, always exhibits a longer time to ignition than nitrogen, while carbon dioxide, which is approximately 10% lower in heat conductivity, exhibits the only values shorter than the nitrogen data. Carbon dioxide was perhaps not the best choice for a low-conductivity diluent, since its extinguishment properties are partially attributed to its chemical reactivity. This reactivity could be a major reason for the high oxygen concentration ignition limit observed in Fig. 2. Its relatively large heat capacity and its high radiant emittance are probably also involved. Figure 3 plots experimental data expressed as the ratio of the ignition: time t~ at various total pressures of dry air, to the ignition time to at 1 arm of dry air. [-The curves in this and in Figs. 4 and 5 are results of numerical calculations using the model to be described subsequently.] The low-pressure limit for ignition (under these experimental conditions) is just below 0.15 I
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POINTS
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3.0 ~
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2.0
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9
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ATMOSPHERES (TOTAL PRESSURE)
FIG. 3. The effect of total air pressure on ignition time; a comparison of the analytical results with experimental data.
IGNITION OF THERMALLY IRRADIATED CELLULOSE atm. The datum point at 0.15 atm indicates
a t~/to of 4.2. This datum point is the average of several determinations at this pressure. However, an equal number of exposures at 0.15 arm did not ignite, but did char the specimen. To confirm t h a t 0.15 a t m is very close to the limiting lower pressure for ignition of alphacellulose, exposures were made on thicker (30-mil) samples. With the thick specimens, it was not possible to obtain an ignition below 0.15 atm; however, tJto was roughly 50% higher. This difference in ignition time is undoubtedly due to the fact t h a t both the 20and 30-rail specimens were not thick enough to approximate a semi-infinito solid for the longest exposures. However, it is to be noted that, at 0.3 atm (the lowest pressure at which transient ignition occurs), the trend of the data is established sufficiently for our purposes. At high pressures, the ignition time decreases with increasing pressure, up to at least 4.0 arm. These data (within the pressure limitation of this experiment) indicate t h a t the ignition response time is a monotonically decreasing function of total pressure. Figure 4 is a composite graph where the data points show (1) the variation of ignition temperature with total pressure over the pressure range of 0.1 to 1.0 atm, and (2) the variation of the ignition temperature with oxygen concentration in a total pressure of 1 atm. I t can be seen t h a t the ignition temperature varies inversely with the total pressure and, consequently, with the total oxygen concentration.
: IO00H''] I1(19
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EXP ANAL [ POINTS SOLN ,"V~,RYING[02] I I ! (AT P=I ATM) / D i ~ l
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909
The trend of the temperature data is quite similar to the ignition-time data. These data show that the ignition temperature decreases monotonically with increasing oxygen concentration over this limited pressure range. We have observed t h a t the time to ignition decreases as the atmospheric pressure increases. Also, ignition will not occur (in this experimental environment) below 0.15 atm. Further, the ignition time in strictly inert diluents (nitrogen and helium) increases with the magnitude of the heat conductivity of the diluent gas, but there is an anomalous effect when carbon dixode is used. Along with this effect, we see t h a t the time to ignition varies inversely with the oxygen concentration when the total pressure is held constant; thus, the trend of the ignition time is the same in Figs. 2 and 3. The trend of the surface-temperature d a t a at the time of ignition is similar to the trend of the ignition d a t a when the total pressure or the oxygen concentration is varied. This fact can be seen by comparison of Figs. 2 and 3 with Fig. 4. Some unexpected phenomena have been observed during the course of the measurements. For example, a very definite and constant change in slope occurs in the surface-temperature rise at 500~ regardless of pressure or oxygen concentration. At 500~ the rate of temperature rise T decreases abruptly to a significantly lower ~', and continues until ignition occurs at about 600~ We also observed that T varies inversely with oxygen concentration in both the measurements where total pressure was either changed or held fixed. Note t h a t this effect was apparent both before and after the 500~ change in slope. Measurements of the ignition response versus oxygen concentration at a total pressure of 0.2 atm show the same characteristics as similar measurements at 1.0 atm. However, ignition will occur at far lower oxygen partial pressures as long as the ratio of oxygen to nitrogen remains about 1 to 5.
# 6oo-
Theoretical Interpretation z o o -
450
-
I
I
I
I ~"'T
I
I00 200:300 400 500 600 700 OXYGEN PARTIAL PRESSURE FxG. 4. The effect of total air pressure and oxygen concentration on the surface temperature at the time of ignition; a comparison of the analytical results with experimental data. (Note that the oxygen partial pressure for the total pressure data was computed by assuming the normal oxygen concentration of air to be 21 per cent.)
F r o m the experimental results, the concept t h a t ignition is triggered by the sudden appearance of chemically reactive species among the pyrolysis products is clearly untenable and, of the two postulated mechanisms, only the thermal autoignition mechanism is worthy of further consideration. Our purpose in what follows is not to describe a rigorous theory for the hypothesis of thermal autoignition, but merely to explore its feasibility using a relatively simple and much idealized
910
COMBUSTION OF SOLID ORGANIC MATERIALS
model of the complex system. We will describe how the model was developed, use it to calculate numerical values of the dependence of ignition times on total pressure, oxygen concentration, and the replacement of nitrogen with another inert gas of very different physical properties, and then look for qualitative (or at most, semiquantitative) agreement with our experimental data. If the simple model is successful, then the effort needed to derive a more sophisticated model will be in order. In developing the model, we have applied the basic concept of the Semenov thermal autoignition theory to an idealization of the gasphase interface between the pyrolytic effluent from the heated surface and the surrounding atmosphere. Considering some elemental volume of gas in the region where the stoiehiometric fuel/oxidant concentration ratio exists, we postulate t h a t ignition will occur when the heatrelease rate due to chemical reaction just exceeds the rate of heat losses from the element. The threshold condition is therefore given by the equation
L
=
If then, in the region of diffusive mixing, the function f represents the spatial distribution of pyrolysis products expressed as a mass fraction of the total mixture, the mass fraction of oxidant at any point is 9 E o [ - O ] / E ~ff~Fil = a (i -- f), i
while t h a t of fuel is ~FEF]I
E ~s
= ~f,
i
and, a t the stoichiometric point, ~o - m ~ o [ O ] . # E m ~ , [ / ] ~ , = ~ (i - f~,), i
~F -----~I~F[F].J E ~l%~[i].t = ~f.t, i
where
f~r =
~/(~ +
~=).
Therefore,
qw,
where L is the rate of heat loss (units of energy per unit volume per unit time), q the heat of the oxidation reaction (units of energy per unit mass reacted), and w the rate of the reaction (units of mass per unit volume per unit time). The rate of the oxidation reaction can be represented by an equation of the form w = # (#F/#O) m (ttoP/RT)", where ttF and t~o are the mass fractions of fuel and oxidant in the stoichiometric mixture, P is the total pressure, R the gas constant, and T the temperature. As given, the over-all order of the reaction is n, while m is the order in fuel only. If we assign values to the concentration of oxidant in the atmosphere and to fuel in the undiluted pyrolysis products, and assume that the mass diffusivities of all component gases of the system are of equal magnitude, then we can readily evaluate the concentrations of the reactants at positions in the mixing zone where they are in stoichiometric proportions. Let a = 9 ~ o [ O ] / ~ l ~ N [ N ] be the mass ratio of the oxidant to its diluent in the atmosphere, and let fl = ~ T ~ F [ F ] / ~ % M [ M ] be the mass ratio of fuel to its diluent in the pyrolytic effluent. With equal mass diffusivities, these quantities will apply generally throughout the gas-phase system. Further, let ~ = ~Y~F[F]st/D]lo[O]st be the stoichiometric mass ratio of fuel to oxidant.
,o = ~ / ( ~
+ ~)
and .F = ~ / ( ~
+
~).
Returning to the rate equation, the principal dependence of rate on temperature is contained in the expression ]c -- A exp ( - E/RT). If E is large, the rate of reaction will have a strong dependence on temperature; and, as the temperature is fncreased, there will come a point, the value of which depends upon the magnitude of E, at which the heat-generation rate will exceed the heat-loss rate, everything else being equal. The pertinent temperature is probably not the temperature of the irradiated surface a t the instant of ignition. Rather, it is less than the temperature of the effluent stream by an amount that depends on how much dilution occurs with the ambient atmosphere in providing a near-stoichiometric mixture. Furthermore, the gases evolved by the decomposing solid may or may not achieve thermal equilibrium with the hot surface during their brief passage through it. These are potentially important factors and should be treated analytically in a more sophisticated model; in' this preliminary mode] they have been neglected. We have, in fact, identified
IGNITION OF THERMALLY IRRADIATED CELLULOSE the temperature T with the temperature of the gas-solid interface, whose dependence on time and radiant flux we have approximated by the solution of the heat-conduction equation for the opaque semiinfinite solid, viz., T (t) = To + E2b/(Tr ~/2) ]" [ H (W ~)/(kpc)ll~J. The value of the "fitting constant" b was chosen to give a temperature rise of about 600~ for the incident flux-exposure times known from extensive experimentation to just result in ignition in air. Its value of about 0.5 is thought to represent a combination of three factors that act to make the sensible heat flux less than the incident: (1) the less-than-total absorptance by the surface, (2) the heat losses from the surface, and (3) endothermie chemical sinks. Heat losses from the gas-phase volume element can be treated as Newtonian and unidimensional, since the heating rate is high enough to ensure no convection effects? Again, sophistication could be added to the model by the analysis of heat flow across the nonsteady diffusional gradient. We chose, however, to relate the heat loss rate L to the over-all temperature drop ( T - To) without regard to the distances separating the reacting volume from the ambient. I-This choice is equivalent to assuming that the breadth of the diffusive mixing zone does not vary appreciably during the times of interest.] The two are thus related through the introduction of an artificial "heat-transfer coefficient" h, thus L--h(T--
To).
It is reasonable to expect that the magnitude of the heat-transfer coefficient is determined by the conductivities of the component gases. Accordingly, the heat-transfer coefficient can be given the form (ako + kN) + ~ (/3kF + kM)] h
=
'
where ko and kN are the conductivities of the oxidant and its diluent, respectively, kF and kN are the conductivities of the fuel and its diluent (i.e., the nonfuel components of the pyrolysis products), respectively. In this way, we arrive at a new constant K which is independent of composition and, therefore, can be evaluated for air (by requiring that the solution agree with the observed ignition time) and then be applied generally. The foregoing equations were solved numerically with a digital computer for wide
911
variations in atmospheric parameters. The sensitivity of the solutions to most of the parameters whose values were uncertain (i.e., the effect of varying ~, a, n, m, and i~F) was evaluated by repeating the solutions with selected values of these throughout their range of reasonable variation. The parameters K, q, and A were not varied because they can be lumped together in a fitting constant whose value is adjusted to fit the time of ignition in air to its experimentally determined value; and it was felt that varying the value of E would be meaningless inasmuch as it is associated with the temperature of the irradiated surface rather than with the actual (and unknown) temperature of the stoichiometric region of the gas-phase mixing region. The parameter /3 was taken to have values in the range 0.1 to 1. Inspection of the equation for rate of reaction reveals that the effect of total pressure on ignition is independent of ~, but that the value of /~ should affect the dependence of ignition time on oxidant concentration. The numerical solutions agree with this expectation and indicate that the sensitivity of the dependence on oxidant concentration is quite insignificant. Figure 3 compares the calculated values of ti/to (the curve) with the experimental data points taken in air at pressures ranging from less than 0.15 to 4 arm. The chosen constants that apply to the theoretical solution shown in the figure are as follows: n = 3,
m = 2,
~=0.5,
a=0.1.
The excellence of the agreement is obvious. Figure 4 depicts the change in surface temperature at ignition for both the cases where total pressure and where oxygen concentration are varied at 1 atm total pressure. The agreement between the experimental points and analytical curves is reasonably good over the central portion of the range, but becomes progressively worse at both higher and lower levels of 02 concentration. Figure 5 illustrates the change in time of ignition with oxygen concentration for atmospheres having both nitrogen and helium as diluents of the oxygen. The agreement is excellent, except, as before, at the extremes. The success of the thermal-autoignition model is remarkable, in view of its simplicity. Moreover, its failings are such as to encourage its further development. For example, its inability to properly represent the sharp increase in ignition time for oxygen concentrations less than those in air could be attributed to the neglect of radiative heat loss in the model. In fact, the very high surface temperatures, which correspond to the
912
COMBUSTION OF SOLID ORGANIC MATERIALS
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An alternative hypothesis, thermal autoignition, has been shown to be consistent with the dependence of ignition behavior on total pressure, oxidant concentration, and choice of inert diluent. A simple model of this process affords numerical solutions that fit the d a t a remarkably well, encouraging the development of a more sophisticated theoretical description.
I
4.O EXPERIMENTALDATA 9
He
o N2 ANALYTICAL RESULTS SOLID LINE = He AS DILUENT DASHED LINE: N2 AS DILUENT
3.0
-
0
--
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2.0
1.0 --
o
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I 0
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600
Nomenclature
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[ 800
OXYGEN PARTIAL PRESSURE (ram Hg)
FIG. 5. Comparison of analytical results and experimental data for the dependence of ignition time on oxygen partial pressure in air made with nitrogen and helium diluents. calculated ignition times under such conditions, are never observed in irradiated cellulose, simply because it ablates away before such temperature can obtain, even at extremely high radiant-flux levels. The model is readily adaptable to account for such effects. On the other hand, at high oxygen concentrations, the model predicts ignition times whose temperatures are too low for appreciable pyrolysis to occur in the short times available. I t is entirely reasonable to expect that the limiting time at high oxygen concentrations is governed entirely by the onset of pyrolysis, a factor which is totally neglected in the model. The kinetics of the pyrolysis reactions of cellulose are resonably well established, and a logical extension to the model would include them.
Conclusions
In view of the experimental evidence, the earlier concept that spontaneous ignition is triggered by the sudden appearance of reactive species in the pyrolysis must be abandoned.
a A b c
radiant absorptance, dimensionless Arrhenius coefficient, mass units fitting constant, dimensionless specific heat capacity of cellulose, cal g-1 oc-1 E activation energy, cal mole-1 F refers to fuel f spatial distribution of the mass fraction of pyrolysis products, dimensionless fst value of f at the stoichiometric location, dimensionless h dummy heat-transfer coefficient cal cm -3 oC--1 H radiant flux per unit area (irradiance) cal cm-2 sec-~ Fi] molar concentration of ith component of gas mixture, mole cm -s k thermal conductivity of cellulose, cal cm cm-2 sec-lOC-1 ki thermal conductivity of i t h component of gas mixture, cal cm cm -2 sec-~ ~ ]~ rate constant, mass units L rate of heat loss, cal cm-a m order of the reaction in fuel, dimensionless M refers to nonfuel portion of pyrolysis products 9E~ molecular weight of ith component of gas mixture, g mole-~ n over-all order of the reaction, dimensionless N refers to atmospheric diluent O refers to oxidant P total pressure, arm q heat of reaction, cal g-l; based on total material reacted R gas constant, cal ~ mole-~ t time from beginning of exposure, sec t~ time to ignition, sec to specific value of time to ignition in air at 1 atm, sec AT(x, t) temperature rise with time as a function of depth, ~ T surface temperature at tl, ~ rate of temperature rise, ~ sec-~ w rate of reaction, g cm-3 sec-1 x depth of cellulosic material, cm
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IGNITION OF THERMALLY IRRADIATED CELLULOSE a
K
P (7
thermal diffusivity (cm 2 see-l); mass ratio of oxidant to atmospheric diluent, dimensionless mass ratio of fuel to nonfuel pyrolysis products, dimensionless fitting constant, sec cm-~ mass fraction of i t h component of stoichiometric mixture, dimensionless density of cellulose, g c m -3 stoichiometric mass ratio of fuel to oxidant, dimensionless
913
3. LIPSKA, A. E. AND WODLEY, R. A.: J. Appl. Polymer Sci. 18, 851 (1969). 4. MARTIN, S. B. AND RAMSTAD, R. W.: Stable Pyrolysis Products of Cellulose Exposed to Intense Thermal Radiation, USNRDL TR-810, Jan. 1965. 5. BEYER, R. B. AND FISHMAN, N.: "Solid Propellant Ignition Studies with High Flux Radiant Energy as a Thermal Source," Progress in Astronautics and Rocketry, Vol. 1, p. 673, Academic Press, 1960. 6. OHLEMILLER, T. J. AND SOMMERFIELD, M.:
Acknowledgment We are indebted to Professor F. A. Williams, University of California, San Diego, for suggesting the thermal-autoignition approach to the interpretation of our data--the approach that led to the model presented here. REFERENCES 1. MARTIN, S. B.: Tenth Symposium (International)
on Combustion, p. 877, The Combustion Institute, 1965. 2. ALVARES,U. Z.: Measurements of the Temperature of the Thermally Irradiated Surface of Alpha-Cellulose, USNRDL TR-735, March 1964.
AIAA J. 6, 878 (1968). 7. BROIDA, T. R.: The Production of Intense Beams of Thermal Radiation by Means of a High Current Arc and Relay-Condenser Optical System, USNRDL TR-417, Nov. 1953. 8. BUTLER, C. P., MARTIN, S. B., AND LAI, W.: Thermal Radiation Damage to Cellulosic Materials, Part II. Ignition of Alpha-Cellulose by Square Wave Exposure, USNRDL TR-135, Nov. 1956. 9. ALVARES, N. J., BLACKSHEAR, P. L., JR., KANURY, A. M. : "The Influence of Free Convection on the Ignition of Vertical Cellulosic Panels by Thermal Radiation," Combustion Sci. and Technol., 1,407 1970.
COMMENTS D. H. Fine, M.I.T. You have shown that your data fit some of the predictions of thermal explosion theory. However, a chain-thermal reaction or even an exothermic chain-branching reaction could equally well explain your data. Your conclusions, therefore, do not in themselves mean that the nature of the explosion is thermal. The fundamental postulate of thermal-explosion theory is concerned with the temperature of the system. If the temperature increases at an accelerating rate, the system has exploded because of a thermal mechanism; other experimental observations are incidental to this unique prerequisite. Authors' Reply. Reference 1 in the paper shows evidence that ignition may result when the surface temperature of the cellulose reaches a critical value (,~600~ where the pyrolytic breakup of the cellulosic molecule results in a surge of species that are easily ignitable. There was some speculation that these species included free radicals, which could possibly "pilot" the ignition mechanism in the gas phase. To investigate this speculation, ignition-delay and surface-temperature measurements were undertaken in selected atmospheric environments. I t soon became
evident that the surface temperature of the cellulose at the time of ignition was a monotonically decreasing function of the oxygen partial pressure, regardless of the total pressure. Thus, the previously proposed ignition mechanism was wholly untenable. Figure A illustrates the effect of oxygen concentration on the surface temperature. The indicating arrows in each record show an abrupt change in the rate of temperature rise, respectively: (1) the start of exposure, (2) a change in the temperature rise curve, which may indicate the start of pyrolysis, (3) the ignition point, and (4) the end of exposure to the thermal radiation source. The slope change in the surface temperature rise curve (indicated by 2) always starts at about 500~ This may indicate that, a t relatively high irradiances, the pyrolysis reaction does not commence significantly until the temperature of the cellulose reaches this level. Plates C and D suggest that there is an effect of oxygen concentration at the rate of surface temperature rise for the same heat flux and total pressure. The temperature record always exhibits a sudden jump (indicated by 3 in Plates C and D) at the time ignition occurs, resulting, apparently, from emission by the flames. The flames are optically thin,
914
COMBUSTION OF SOLID ORGANIC MATERIALS
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COMPOSITE OF SURFACE TEMPERATURE RISE DATA EXPOSURES IN VARIOUS PRESSURES AND OXYGEN CONCENTRATIONS WHERE: PLATE A IS ~10 -4 ATMOSPHERES, 21% 02; PLATE B IS 0.2 ATMOSPHERES, 21% 02; PLATE C IS 1.0 ATMOSPHERE, 21% 02; PLATE D IS 1.0 ATMOSPHERES, 50% 02 . :FIG. A
thus the increase in temperature does not correspond to the actual flame temperature, and if irradiation is continued, the signal will continue to rise at a slightly greater rate, apparently due to the additional flux from the flames. Since the "appearance of species" mechanism for this ignition phenomenon did not appear to satisfy the data, we tried the simple thermal mechanism of ignition, as explained in the paper, to see if it would fit the data. Kere, the point of
major comparison was the ignition delay and the surface temperature at the time of ignition (indicated by 3 on the curves in Fig. A). The reaction is assumed to occur in a slab of gas so close to the surface that its temperature, up to the time of ignition, can be assumed to be the surface temperature. Upon ignition, the gas-phase reaction attains the flame temperature instantaneously so far as our experimental t i m e base is concerned.