Effects of sample orientation on radiative ignition

COMBUSTION AND FLAME 44:223-245 (1982)

223

Effects of Sample Orientation on Radiative Ignition* TAKASHI KASHIWAGI Centerfor Fire Research, National Bureau of Standards, Washington, D.C. 20234

The effects of sample orientation on autoignition delay times and the minimum external radiant flux for autoignition were studied using a CO 2 laser and a gas fired radiant panel as external radiant sources with PMMA and red oak as samples. Ignition delay times were shorter with the horizontal sample than with the vertical one at the same external radiant flux. The minimum external radiant flux for ignition was also less with the horizontal sample. The absorption of external radiation by the boundary layer of decomposition products for the vertical orientation is significant, although its amount is less than the absorption through the plume for the horizontal orientation. Surface temperature at ignition is higher with vertical sample orientation than with horizontal at the same external radiant flux. A theoretical calculation of the surface temperature history with endothermic gasification significantly underestimates the experimental results; this raises a question of the applicability of regression rate expression derived from steady state experiments to the dynamic heating condition.

1. INTRODUCTION It has been observed that the absorption of external radiation by decomposition products in the gas phase is significant during the preignition period after an irradiated sample starts to decompose [1,2]. This absorption of energy by the decomposition products raises the gas phase temperature above that of sample surface. The increase in the gas phase temperature can be sufficient to initiate the exothermic gas phase chemical reactions in order for radiative autoignition to occur. In the previous two studies [1, 2], external radiation was directed normal to a horizontally mounted sample. Since the plume of decomposition products rises directly into the incoming external radiation, a horizontal orientation causes the strongest interaction between the external radiation and the decomposition products, However, it is not clear that other orientations, such as a vertically mounted sample irradiated by * Contribution from the National Bureau of Standards, not subject to copyright in the United States.

Copyright © 1982 by The Combustion Institute Published by Elsevier North Holland, Inc. 52 Vanderbilt Avenue, New York, NY 10017

horizontal external radiation, would ignite with the same gas phase mechanism. The vertically mounted sample forms a thinner buoyant boundary layer of decomposition products, and interaction of the plume with horizontal external radiation is much less than that of a horizontal sample. Then sample orientation with respect to the direction of the external radiation would affect ignition delay time and the minimum external radiant flux for ignition. Unfortunately, there has been little information available to examine this hypothesis under the same well-controlled experimental conditions. The objective of this study was to investigate experimentally the effect of the sample orientation on ignition mechanism. In order to observe and quantify the above-mentioned effects, the transmittance of the external radiation, surface temperature, and gas phase temperature were measured continuously during the ignition period with different sample orientations. The effect of the sample size on ignition was also studied by using a large sample with a large gas fired radiant panel as the external radiant source. The results were compared with those using a small sample with a CO, laser as the external radiant source.

0010-2180/82/010223+2352.75

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2. EXPERIMENTAL APPARATUS For most of the tests, a CO 2 laser (CW operation) was used as the external radiant source. Advantages and disadvantages of use of the CO2 laser as a radiant source for ignition studies have been discussed in previous studies [1, 2]. A schematic illustration of the experimental apparatus is provided in Fig. 1. A lens with a focal length of 6.2 cm was used to expand the Gaussian laser beam to obtain a nearly uniform flux distribution on the sample. The external radiant flux distribution at the sample surface position was measured prior to each ignition experiment by traverses with a water cooled flux meter having a 2.5-mm-diam sensing element. There are two differences in experimental details between this study and the previous studies: (1) the sample was exposed in an open room instead of the quiescent chamber used in the previous study, and (2) a slightly larger area of the sample (about 3.5 cm diam) was irradiated because of a larger laser beam diameter which resulted from a new output coupler lens on the laser. It was observed that air motion with the open room condition caused frequent irregular plume motion with the horizontal sample.The amplitude stability of the radiant flux was typically + 3%.

A rotating mirror "shutter" was used to provide a step-function irradiance and remained "open" through the ignition event. When the sample was mounted horizontally, the incident laser beam was directed downward normal to the sample surface. When the sample was mounted vertically, the incident laser beam was directed horizontally normal to the sample surface. Two materials were used in this study, polymethylmethacrylate (PMMA) and red oak. The dimensions of the sample were 7.5 cm square x 1.5 cm thickness for PM MA and 7.5 cm square × 1.7 cm thickness for red oak. Ignition was determined by the first light emission detected by a photomultiplier (response S-5). Surface and gas phase temperatures on the axis through the center of the irradiated sample were measured by 25-#m-diam chromel-alumel thermocouples during the ignition period. The effect of absorption of the external radiation by the thermocouple wire was determined by measuring the output of the thermocouple exposed to the external radiation in open air. The results are shown in Fig. 2. The increase in temperature of the wire above room temperature is plotted against various external radiant fluxes. The data show that the temperature of the wire increases between 10 and

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20°C above room temperature in the range of the radiant fluxes used in this study. The increase in temperature is limited by reradiation and convection from the heated wire to the surroundings. This range of temperature increase due to the absorption of external radiation is about the same as the uncertainty of the temperature measurement during ignition, and the effect on measured temperature is considered to be negligible. For the measurement of surface temperature, the thermocouple wire was electrically heated and melted onto the PMMA sample surface to make good contact with the sample and to minimize the heat conduction loss along the wire. For red oak samples, the wire was pressed onto the surface before a test by a ceramic pestle. In both cases, the wire was secured to the sides of the sample. Gas phase temperature was measured by an identical thermocouple suspended and kept under tension, thus avoiding any change in location by its expansion when heated. New thermocouple wire was used for each experiment, The transmittance of the external radiation through the decomposition products in the gas phase was continuously measured during the ignition period using a water cooled flux meter having a 2.5-mm-diam sensing area coated with camphor soot. The sample had a 4-mm-diam hole through

its center through which the flux meter measured the value of the incident radiant flux reaching the sample surface through the plume or the boundary layer of decomposition products. Since the thickness of a PM MA sample was 1.5 cm and a red oak sample 1.7 crn, and the duration of the experiment was at most 60 sec, heat conduction through either sample was negligible. Therefore, the flux meter measured only the external radiant flux from the laser before the decomposition of the sample and the decaying incident flux after gasification began (i.e., that portion of the external flux transmitted through the decomposition plume or boundary layer).Sinceinthecaseofthehorizontalsample, the flux meter did not completely seal the hole through the sample, natural convection produced a small upward air flow through the vertical hole. This flow prevented the back flow of decomposition gases into the hole. However, it is not clear that this was also true in the case of the vertically mounted sample with a horizontal hole, although there were no signs of deposition of condensed materials in the hole and no visible changes in the surface of the hole after the experiment. The boundary layer of decomposition products was not noticeably changed or irregular over the hole. To determine whether sample size has a bearing on the effect of sample orientation on ignition,

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3. RESULTS AND DISCUSSION 3.1. Ignition Delay Time Ignition delay times with the horizontal samples and the vertical samples were measured under various external radiant fluxes. Results are shown in Figs. 4 and 5 for PMMA and red oak, respectively. Both figures indicate that, for this test series,

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larger size samples were tested using a gas burner assembly. The experimental apparatus has been described in detail elsewhere [3] and its description is briefly discussed here. Gas heated radiant panels were used as an external radiant source in the gas burner assembly. The radiant panels formed a rectangular box of 60 cm width, 60 cm height, and 30 cm depth as shown in Fig. 3. The size of the array of gas burners is 60 x 60 cm for two larger sides and 30 x 60 cm for two smaller sides. For the horizontal samples, the burners on all four sides were used. For the vertical samples, as shown in Fig. 3, only half of the burners were operated. Various sizes of sample were used with this apparatus to find the effect of sample size on ignition, The sample was inserted by a carriage-elevator arrangement from below into the inside of the chamber. A forced air flow through the chamber of about 30 cm/sec from below was supplied. Ignition delay time was measured visually with the aid of a stop watch.

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ignition delay time with vertical radiation normal to the horizontally mounted sample is shorter than that with horizontal radiation normal to a vertical sample surface. Another important feature shown in the figures is the difference in ignition delay time between the previous data [1] and this study with the horizontal sample. As previously described, there are two differences between the experiments: the open room condition and a slightly larger irradiated area (previously a little less than 3 cm diam compared to about 3.5 cm diam in the present study). In the open room condition, it was observed that drafts in the room caused irregular motion of the plume of decomposition products instead of a stable plume near the sample surface. The motion in the surrounding atmosphere apparently enhances the mixing of decomposition products with air. A similar effect of the turbulence in the surrounding atmosphere on ignition was also reported by Simms [4].

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The relation between ignition and sustained flaming after the removal of the external radiation is shown schematically in Fig. 6. It shows that a flame is not sustained at high external radiant flux if the external radiation is removed shortly after

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ignition. However, flame is sustained after the removal of the external radiation if the external flux is continued a certain period after ignition. This required supplemental period is less with a decrease in external radiant flux. Below about 13 w/cm 2 for vertical PMMA and about 11 w/cm 2 for horizontal PMMA, flame is sustained even if the external radiation has ceased immediately after ignition. The sudden discontinuity between regions of sustained flame and nonsustained flame reported by Mutoh et al. [5] was not observed by this study. Flame was not sustained without a continuation of the external radiation for red oak in the range studied in this work. The ignition trends described above were studied using a rather small sample and the CO 2 laser as the external radiant source. To confirm the above trend for a more realistic fire condition a larger sample and an external radiant source with a broad emission spectra were used. Three different heights of 7.5, 15, and 22.5 cm with 7.5 cm width add 1.5 cm thickness of PMMA and 1.7 cm thickness of red oak were used for the vertical sample orientation in the large gas burner assembly described in the previous section. Also, 7.5 c m x 7.5 cm and 15 cm x 15 cm square samples of PMMA and red oak were used for the horizontal sample orientation. The external radiant flux at the sample surface was at 6 w/cm 2 for both sample orientations. Ignition delay time results are shown in Table 1. For the vertical sample orientation, no ignition was observed for PMMA with three different heights of samples, although vigorous decomposition and considerable weight loss of the sample were observed. For horizontal sample orientation, ignition was observed for both samples. No significant effect of the sample size on ignition delay time was observed for either sample. On the other hand, ignition delay time of red oak became shorter with taller samples for vertical sample orientation. Ignition delay time of red oak is shorter than that of PMMA for both orientations. Also, these results show that ignition delay time for the horizontal sample is shorter than that for the vertical sample. These two trends agree qualitatively with those observed in the experiments with the C O 2 laser. However, these results emphasize that ignition delay time and minimum external radiant flux for

228

TAKASHI KASHIWAGI TABLE 1

delay time and the minimum external radiant flux for ignition under the radiative autoignition mode are not unique, and they depend strongly on the experimental conditions. Additional detailed measurements were conducted to analyze the effects of the sample orientation on ignition. The results are

Ignition Delay Time with Large Samplesa Horizontal Sample Orientation Size Ignition Delay Time Width Height PMMA Red Oak 7.5 cm × 7.5 cm 15 cm x 15 cm

76 see 72 sec

21.5 sec 20.5 sec

described in the next sections.

Vertical Sample Orientation Size Ignition Delay Time Width Height PMMA Red Oak 7.5 cm x 7.5 cm 7.5 cm × 15 cm 7.5 cm x 23 cm

No ignition No ignition No ignition

3.2 Attenuation

The transmittance of the external radiation through the ,lume of decomposition products for the horizontal sample or the boundary layer for the vertical sample was measured with P M M A a n d r e d

50.5 sec 44.0 sec 41.5 sec

oak under various external radiant fluxes. Results are shown in Figs. 7 and 8 for P M M A and red oak, respectively. The ordinate is the transmittance, which is actual incident flux on the sample surface I, normalized by the external radiant flux I o. Therefore, the ratio I / I o stays at 1 until the start of the decomposition. The fluctuation of the curve with the horizontal sample was caused by the wandering motion and instability of the rising plume. However, the curve with the vertical sample is smooth because of the stable boundary layer flow of decomposition products.

a Comparison of ignition delay times of various sizes of PMMA and red oak between the horizontal and vertical sample orientations using the gas burner assembly. 10 = 6w/cm2"N°igniti°nmeansthatigniti°nwasn°t°bserved during 5-min period. ignition cannot be determinedquantitativelybythe specification of only the sample and the external radiant flux. The sample orientation, the sample size, and the surrounding condition of the atmosphere must be specified. Consequently, ignition 1.0

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Results for both samples and configurations show a strong dependence of the transmittance on the external radiant flux. At high external radiant flux, the transmittance quickly decays to rather low levels after thedecomposition starts. On decreasing the external radiant flux, one finds that the decrease in the transmittance after the decomposition starts is less. Although the transmittance through the boundary layer of decomposition products along the vertical sample is higher than that through the plume at the same external radiant flux, the amount of attenuation through the boundary layer is surprisingly high. Since the thickness of the boundary layer of decomposition products is much less than the height of the rising plume, the concentration of decomposition products in the boundary layer is apparently much greater than that in the plume due to a higher vaporization rate. Some additional data to support this will be discussed later where results regarding surface temperatures are described. Results with PMMA show that the transmittance decreases monotonically with time after the start of its decomposition at various external radiant fluxes. However, results with red oak show that the transmittance has a minimum in

time and then it increases gradually except at high external radiant flux. It was observed that the surface started charring vigorously and its color became glowing with time. The observed increase in the transmittance might be caused by the radiation from the charring surface through the observation hole to the flux meter. This possibility was examined by the installation in the hole of a thin aluminum cylinder cooled at one end with water. This prevented the radiation from the charred surface reaching the flux meter. Results showed the same trend in the above discussed transmittance curve with the cylinder and without it. Therefore, the observed trend of the transmittance is not caused by radiation from the charring surface to the flux meter. This indicates that the rate of decomposition products increased initially with time but later decreased. The decrease in the production rate of decomposition products is apparently caused by growth of the char layer, which acts as an insulating layer for heat conduction and mass transfer of decomposition products. This effect of the char has also been described in theoretical studies [6, 7-1.It is also possible that the nature of the decomposition products was changed

230 by further cracking upon passage through the hightemperature char layer from the pyrolysis zone. The results here clearly show the importance of attenuation of the external radiation by decomposition products for both sample orientations, However, the attenuation characteristics depend strongly on the spectrum of the external radiation. The wavelength of the CO 2 laser (10.6 ~m) is longer than those typical of emission from fires. In a previous study, an electric heater was used as a grey body radiant source to investigate the effects of emitter wavelength on attenuation [1]. The results with a horizontal sample showed that the quantitative characteristics of the attenuation might be different with the different radiant source but that the qualitative characteristics remain the same. This is because there are numerous strong absorption bands of organic compounds in the infrared wavelengths where the typical fire emits. Therefore, it is reasonable to postulate that the attenuation of the external radiation by decomposition products is important during the ignition period for both sample orientations in a real fire situation. At present, it appears probable that the decomposition gases of both samples absorb the external radiation. Also, the scattering characteristics of particulates produced from the decomposition fall in the Rayleigh regime for CO 2 laser radiation (2nrp/2 < 1, where rp is radius of particulates and 2 laser wavelength) [1]. Therefore, particulates also tend to absorb the external radiation rather than to scatter it. For this reason, the observed attenuation of the CO 2 laser is mainly absorption, but it is not clear whether it is by the gases or particulates, or both. For typical fires, because of the shorter wavelength of the emission spectrum, scattering by particulates might be as significant as absorption during the ignition period [8].

3.3 Gas Phase and Surface Temperatures The absorption shown in Figs. 7 and 8 implies an increase in gas phase temperature above the surface temperature (at which the gases are generated). The increase in gas phase temperature due to absorption of the external radiation can be roughly

TAKASHI KASHIWAGI estimated for the case of the boundary layer along the vertical sample by a simple calculation. It is assumed that there exists an average gas velocity and temperature in the buoyancy-driven boundary layer. This assumption is not highly accurate, but it is reasonable for an order of magnitude analysis. The control volume is assumed to be a rectangular box having the average boundary layer thickness d and a width and a height of D (beam diameter). Then, the increase in gas phase temperature above the surface temperature is roughly approximated by

A T " (I° - I)D pgCpVd' where pg is gas density, C p is specific heat, and V is the average upward gas velocity. With PMMA, D is 3.5 cm, d__l cm, ps__8xl0 -~ g/cm 3 (20~ monomer at 500°C), Cp is 1.5 J/g K, V - - x / ~ _ ~ 60 cm/sec, where g is the acceleration due to gravity (980 cm/sec2). With I o - I = 4 J/cm 2 sec from Fig. 7, AT~ 195K Therefore, it is to be expected that the increase in gas phase temperature will be significant and measurable during the ignition period. To confirm this increase in gas phase temperature near the surface due to absorption, gas phase temperature and surface temperature at the center of the irradiated area were simultaneously measured by using two fine thermocouples with the vertical sample orientation. The detailed technique was described in the discussion of the experimental apparatus. Results are shown in Fig. 9 for PMMA and Fig. 10 for red oak. Transmittance of the external radiation was also measured with separate experiments and is displayed in both figures. Both figures show that surface temperature becomes higher than the gas phase temperature shortly after the irradiation of the surface begins. During this initial period, the transmittance stayed at unity, indicating that the decomposition of the sample was negligible. Therefore, the process during this period is the growth of a buoyancy driven boundary layer near a heated vertical wall. Convection

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from the hot surface transfers energy to heat the gas phase. The temperature difference between the surface and the gas phase tends to increase with time at this early phase of the heating period. After about 2 sec of irradiation for PMMA and 1 sec for red oak, decomposition starts and transmittance decreases. With increasing surface temperature, the rate of decomposition increases and more decomposition products are released into the boundary layer. This increases the absorption of the external radiation in the gas phase and reduces the incident flux to the surface. In turn, this causes the rate of increase in the gas phase temperature to be much more rapid than that at the surface. At about 3.2 sec for PM MA and 1.2 sec for red oak, the gas phase temperature at 0.15 cm above the surface becomes higher than the surface temperature. For PMMA, the surface temperature became fairly constant at about 46(FC. The gas phase temperature continues to increase gradually up to a little over 560°C with a gradual decrease in transmittance. The difference between surface temperature and gas phase temperature at 0.15 cm above the surface becomes a little over 100°C. A similar trend

is also observed with red oak. Although gas phase temperature was measured only at 0.15 cm above the surface, and this would not necessarily be the highest temperature in the boundary layer, the results show clearly that gas phase temperature is higher than the surface temperature. The magnitude of the temperature difference is also in reasonable agreement with the previously calculated estimate. This tends to confirm the significance of an increase in gas phase temperature due to the absorption of external radiation. However, this does not exclude the possibility of a gas phase temperature increase due to exothermic reactions of decomposition products with oxygen. Further study with simultaneous measurement of gas phase and surface temperature in a nitrogen atmosphere is necessary to exclude the possibility of contributions from exothermic reactions. The significant amount of absorption of the external radiation shown in Figs. 7 and 8 causes a reduction in the incident flux. This implies a corresonding decrease in the rate of rise of surface temperature. To confirm this, surface temperatures during the preignition period were measured with

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horizontal and vertical samples under various external radiant fluxes. The comparison between them is shown in Fig. 11 for P M M A and in Fig. 12 for red oak. As implied by the transmittance results shown in Figs. 7 and 8, the surface temperature of the horizontal sample is irregular because of unstable motion of the rising plume of decomposition products. The curves of surface temperature for the vertical samples are stable because of the steadiness of the boundary layer. The figures show that surface temperatures with the vertical samples are higher than those with the horizontal samples at the external radiant fluxes studied in this work. Since transmittance of the external radiation with the vertical samples is higher than with the horizontal samples, a difference in surface temperature for different sample orientation would be caused by the difference in transmittance. To confirm this, the

surface temperature is calculated including the experimentally observed variation of absorption of the external radiation, endothermic pyrolysis for PM MA, convection loss, and reradiation loss from the surface. The effects of each term on surface temperature for both sample orientations are obtained and will be discussed. In the calculation, the thermal properties of the materials are assumed to be constant and the external radiation is absorbed at the surface. The latter approximation is adequate as long as

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where ~ is thermal diffusivity and a is the effective absorption coefficient of the material. Equation (1) means that the penetration distance of the conductive thermal wave below the solid surface far exceeds the in-depth distance of the absorption of the external radiation. This is true for P M M A with the C O 2 laser radiation (roughly am 100 cm -1 [9]) during the ignition period except during the first few seconds after the irradiation starts, but it may not be true for red oak due to its porosity [10]. Therefore, it is expected that the calculated surface temperature tends to be an overestimate for red oak and probably for PMMA at early times, but the accuracy of the calculation is adequate to discern the effects of the attenuation and of the other processes noted above on surface temperature history. The governing equation is OT ~2T Ot- = ~ OX z "

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Here ~ is thermal ditfusivity; K, thermal conductivity; r, surface reflectance; Io, external radiant flux; E, surface emissivity; tr, the Stefan-Boltzmann constant; h, convective film coefficient; p, density; Q~, latent heat of vaporization; k, linear surface regression rate; To, room temperature; and I, incident radiant flux. In Eqs. (3) and (4), to is the time when the decomposition starts. The convection term is based on cooling of the surface by the entrained air drawn in from the room temperature environment. However, after the gas phase is heated by the absorption of the external radiation, convection (or conduction) actually occurs from the hot gas phase to the cooler surface. In this calculation, the change in the sign of the convection, initially from the surface to the gas phase and later from the gas phase to the surface, was not

included. Only the early convection loss from the surface is considered. This tends to lower the surface temperature calculated after vaporization begins, but this is a small effect. The term makes little contribution to the energy balance, as will be described later. The expression for h is taken as an average film coefficient over the characteristic length of a heated plate [11]. The expression for the film coefficient due to laminar boundary layer driven by natural convection over the vertical sample is h=O.54(K/D)(GrPr)lm,

(7)

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and McAlevy et al.'s data [14]. Since weight loss expressions measured by a thermal gravimetric analysis (TGA) apply to low heating rates and require some kind of decomposition model to convert to a linear regression expression [15], they are not considered in this work. Chaiken et al.'s data were obtained by means of a technique that involved forcibly pressing a PM MA strand against a heated porous plate. Due to the intense surface heating rates so generated, linear pyrolysis rates in the range encountered in combustion applications were produced. Their best fit expression for the measured results is

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32

Fig. 12. Comparison of measured surface temperature with horizontal (---) and vertical ( - - ) sample of orientation for red oak. X, ignition,

Pr the Prandtl number; p ~, gas density; g, acceleration of gravity; t, expansion coefficient; AT, temperature difference between surface and environment; #, viscosity of the gas; and D, diameter of the irradiated area. Values of these parameters are based on air at 300°C for PMMA and at 400°C for red oak. In Eqs. (3) and (4), the value for r is 0.05 for PMMA and 0.09 for red oak; these are determined from reflectance measurements around the CO 2 laser wavelengths [2]. The value for • is 0.90 for PMMA and 0.85 for red oak; these are estimated from reflectance measurements averaged over wavelengths of 2.5-15 #m. Values of physical properties used to calculate surface temperature are p = 1.2 g/cm 3, K = 1.9 x 10-3 J/cm sec K, specific heat C = 1.5 J/gK for PMMA; and p =0.7 g/cm 3,

K=l.5xlO-3j/cmsecK, C=l.4J/gKforred oak [12]. Expressions for the linear regression rate of PMMA were taken from Chaiken et al.'s data [13]

(10)

where R is universal gas constant, 8.32 J/mole K, and T~ is the surface temperature in degrees Kelvin. McAlevy et al.'s data were measured by mechanically feeding the sample to maintain its surface position constant while its surface was subjected to intense convective heating by immersion in the exhaust jet of a laboratory rocket motor. The surface temperature was measured by an imbedded fine thermocouple and by an IR emission measurement using an optical pyrometer. They observed two "surface" temperatures; one was the temperature of transition from solid-like to liquid-like behavior, and the other was the temperature of transition between condensed phase and vapor phase behavior. The latter was higher than the former. The linear regression rate based on the former temperature was very close to that of Eq. (10). The expression based on the latter temperature was deduced from McAlevy et al.'s data and is k = 910 exp (-71,000/RT~) cm/sec.

(11)

It is important to note that both Eqs. (10) and (11) were derived from steady state data. Equation (10) applies to the range of surface temperature 300~600°C and Eq. (11) to 450~600°C. It is interesting to note that the measured surface temperature is much higher than that achieved in TGA experiments with much slower heating rates.

ORIENTATION EFFECTS ON RADIATIVE IGNITION The value of the latent heat Q v for PMMA is taken as 1610 J/g [16]. No expression for the linear surface regression rate of red oak was found in the literature; furthermore, there is some confusion about the endothermicity or exothermicity of the decomposition process. In view of the complex mechanism of char formation and its growth, a calculation including the decomposition of red oak is beyond the scope of this paper. The surface temperature was calculated without the decomposition process only to show the behavior and relative importance of the other energy terms at the surface, Incident radiant flux ! in Eq. (4) is derived as follows: Since I/Io decreases roughly exponentially with time after the decomposition starts, as shown in Fig. 7, it is expressed as

(I/Io) = exp {-fl(t-to) }.

(12)

235

combinations of terms in Eq. (4) switched on, such as with the absorption in the gas phase and without the decomposition, without the absorption and the decomposition, and with the absorption and the decompositon expressed by the results Chaiken et al. or McAlevy et al. The calculated results are compared with the experimentally measured surface temperature history as shown in Fig. 13 for PMMA with the horizontal orientation and in Fig. 14 with the vertical orientation at an external radiant flux of 11.3 W/cm 2. All calculations include losses due to convection and reradiation from the surface. Without absorption in the gas phase or the decomposition at the surface (top curve), the calculated surface temperature is much too high compared to the measured result. However, with the absorption and the decomposition expressed by either surface regression rate [(2R=pQvk and QRc by Chaiken et al. with Eq. (10) or QRM by

The decay constant of the transmittance fl and the time when the decomposition starts t o are functions of I o and were obtained by a curve fit to the experimental data over a wide range of the external radiant flux [2]. The expression for horizontal PMMA is fl=0.00461 exp (0.277•0);

(13)

m

,

,

,

Q= 0

I/1o=[1-rl: Const, Q! =O

-" ~

/

-"

""

i/lo =ll-rl,lltm

_ o

for vertical PMMA,

~ i, : c , , , t

~ / ~ . ~

3°°

-

I/1o = flt), QR = 0

i

/ /~=0.00713 exp (0.16110);

(14)

[/10 =tlt),t~m

/ ]

t/t0 = ~tl, ~Rc

i

and for horizontal red oak, I

/~=0.(X)0962 exp (0.354•0).

(15)

However, transmittance for vertical red oak changes with time in a more complicated way than the simple monotonic decrease for PMMA as shown in Fig. 8. Therefore, the experimental data itself for I/I o was used for vertical red oak. Equation (2) was solved numerically with Eq. (3) as the boundary condition before the decomposition starts and later with Eq. (4) after the decomposition starts. The change of the surface temperature with time was calculated with various

t [] iw 0T

0

I

4

[

s

I

12

I

ts

I

2o

24

rmt Istml

Fig. 13. Comparison of surface temperature change with time between experimental data (---) and calculated.resuits for ( - - ) for horizontally mounted PMMA: QR, endothermic flux for decomposition (QR - P Q v k ) ; Q R c using Chaiken et al.'s data by (10); and QRM using MeAlevy et al.'s data by Eq. (11). 10 = 11.3 W/cm2.

236

TAKASHI KASHIWAGI I

I I /!a,~l ~r~ ~ Const. / o ~ ~ / /J

l

I

!/lo= fit]

0.~ / /// [ 1 ~ " - ~ ~

g i

xa,=(1-,I.0~ .

~

---L/~ ~'t~n"

Vt

t/l, :~tja~

I/ I

/

P

to the better fit of transmission of external radiation expressed by Eq. (12) to experimentally measured results with the vertical sample orientation than with the horizontal sample orientation. The less accurate fit of transmittance for the latter case is caused by the unstable wandering motion of the plume affecting the change in transmittance as shown in Fig. 7. A typical example of surface temperature change with time affected by unstable plume is shown in Fig. 15 for •0=8.3 W/cm 2. At early times after the exposure to the external radiation, the calculated surface temperature is an overestimate probably due to the approximation that the absorption of the external radiation occurs at the surface instead of in depth. This overestimation is consistent at different external radiant fluxes and with both sample orientations. The large underestimation in the calculated surface tempera-

1W 0T

i

i

t !

i

t

[~Cl

f

Fig. 14. Comparisonof surface temperature change with time between experimentaldata (---) and calculated resuits ( - - ) for vertically mounted PMMA (Io = 11.3 W/cm%. McAlevyetal.withEq.(ll)],thecalculatedsurface temperature is too low compared to the measured result. This is true even without the absorption of the external radiation. The calculated surface temperature with the absorption and without t h e , decomposition agrees best with the experimental data for both sample orientations. Fairly good agreement of the calculated surface temperature with the experimental data is shown in Fig. 15 for the horizontal sampleorientationOrientatiOnforand in Fig. 16 for the vertical sample several fluxes with the absorption in the gas phase and without the decomposition. This indicates little contribution from the endothermic decomposition in the energy balance at the surface. In contrast, absorption by the decomposition products appears to indicate a substantial decomposition rate. This discrepancy will be discussed in detail later. Figures 15 and 16 show a better agreement of the calculated results with the vertical sample orientation than with the horizontal sample orientation. This is due

1t3

~ I-iu.-. ,p..-----ta~

/

i

i t ] /f i g'/ ;;/

^ .. ,~. . . . . . i

/

r

1,:u,/~, i i

/

"l-t'/,,7 ,,' II/~//,,~'"

-t J

~ I~ll~l// [I'// fl// [i[,

I-I [ ]

l,lt i,0

t

0T 0

J 4

I 8

J

I

I

[

12

is

2o

24

rmfml Fig. 15. Comparisonof surface temperature change with time between experimentaldata (---) and calculatedresults ( ; I/I 0 =/'(t), QI~ = 0) under various external radiantfluxes for horizontally mounted PMMA. e, ignition.

ORIENTATION EFFECTS ON RADIATIVE IGNITION

237

Io = 16.3 w/cm 2 11.3

J!l' I :

200

t

r

100 oT 0

I 4

I 8

I 12

I 16

I 20

I 24

{S~C} Fig. 16. Comparison of surface temperature change with time between experimental data ( - - - ) and calculated results ( - - ) under various external radiant fluxes for vertically mounted PMMA. e, ignition.

ture in cases with both the gas phase absorption and the endothermic heat of decomposition is also clear for other external radiant fluxes as shown in Fig. 17 with the horizontal sample orientation and in Fig. 18 with the vertical sample orientation, These indicate that the effect of endothermic decomposition on surface temperature is potentially very significant. This is also shown in Fig. 19 for the varying major contributions to the heat balance at the surface for PMMA. QcoN is the heat conduction flux into the material, QRc endothermic flux for decomposition, and 0AT flux absorbed in the gas phase. These three account for about 8090~o of the external radiation. The other terms for PMMA are convective heat loss (about 5~o), surface reflection (about 5~o), and reradiation loss (about 6~ of the external radiation) [17]. The conduction loss is the major one at early times after the exposure to irradiation, but it decreases rapidly with time because of the deeper penetration of the

thermal wave; the temperature gradient near the surface becomes more gentle. The conduction loss does not differ significantly between the two sample orientations. The absorption in the gas phase and the endothermic decomposition share most of the rest of the external energy and are inversely proportional to each other. They differ significantly between the two sample orientations. There are several discrepancies in Fig. 19 and in the above discussion. The first inconsistent result can be seen in the trends of the energy loss due to endothermic decomposition and the gas phase absorption in Fig. 19. After about 5 sec for the horizontal sample orientation and about 8 sec for the vertical sample, QRC decreases monotonically with time but QAT (from experiment) increases monotonically for the vertical sample orientation. For this orientation, it is expected that the amount of absorption should be roughly proportional to the rate of the production of decomposition prod-

238

TAKASHI KASHIWAGI 500[

I

I

f

I

I

I

I 16

I 20

I 24

ILl

40O

I

: 12--~.,-=

0

1 4

. . . . . . . .

I

1

IO0

OI

I 9

I 12

T!

28

[SECl

Fig. 17. Comparison of surface temperature change with time with (---, OR = (~RC) and without ( ) endothermic surface decomposition (I/I 0 = f ( t ) ) under various external radiant fluxes for horizontallymounted PMMA.

ucts. Therefore, the trend of 0R C with time should be qualitatively the same as that of ~AT"Also, for the horizontal sample orientation, (~AXis roughly proportional to the integral of QRc with respect to time. In Fig. 19, {~ATis much steeper in its increase with time compared to the integral of QRO A change in the decomposition products from PMMA is not believed to occur, so the explanation should not lie there, The second discrepancy is that the difference between the calculated surface temperature with endothermic decomposition and the experimental results is too large to be explained by uncertainties in the present experiments. However, the amount of the absorption in the gas phase, measured experimentally, indicates substantial decomposition. This indicates a significanteffect of theendothermicityof the decomposition on the energy balance at the surface. This is in conflict with the above discussion where inclusion of the endothermicity was found to

have an excessive limiting effect on the surface temperature change with time as shown in Figs. 13, 14, 17, and 18. The third discrepancy is the difference in the surface temperature between the two sample orientations. In the calculated surface temperature, the effect of the endothermic decomposition on the surface temperature is so significant that it overshadows the effect of the sample orientation and there is little difference in calculated surface temperature between the two sample orientations, at most 10-15°C. However, the difference in the experimentally measured surface temperature between them, as shown in Fig. 11, is as large as 50°C. A similar value for the difference in the surface temperature between the two sample orientations is estimated by the calculation without the endothermic decomposition. This is shown in Fig. 20. A resolution of the above discrepancies can be attempted by a further critical comparison between

ORIENTATION EFFECTS ON RADIATIVE IGNITION ~0

~ i

1

239

I Je = 16.3 w/cm2

I

f

I

I 16

I 20

I 24

i -//J

-/ 100

OT 0

I 4

I 8

I 12

26

mat is~c)

Fig. 18. Comparison of surface temperature change with time with (---) and without ( ) endothermic surface decomposition (I/I 0 = f ( t ) ) under various external radiant fluxes for vertically mounted PMMA.

the model and the experiment. There are two differences between them; one is the convective heating from the heated gas phase to the surface, and the other is the surface regression. Both ofthese effects are not included in the model. After absorption of the external radiation becomes significant, additional convective heating from the heated gas phase to the cooler surface would increase the surface temperature somewhat. If the additional convective heating to the surface is included in the calculation, the calculated surface temperatures would be a little higher. However, this increase would be small, comparable to the small effect of convective cooling, The moving boundary at the surface due to gasification adds a convection term consisting of the regression rate times the temperature gradient at the surface in the governing equation (2). With this term, the surface moves in the same direction as the thermal wave and the temperature gradient

near the surface tends to become steeper than without this term. This implies an increase in the heat loss into the material by thermal conduction, tending to decrease the surface temperature. Therefore, the neglect of surface regression in the model yields an overestimate of the surface temperature. For this reason, the overestimation of the endothermicity of decomposition is not caused by the absence of the convective term in the calculation. The discrepancies discussed above are apparently due to a different reason. In the model, the incident radiant flux at the surface was obtained empirically. This is related to the amount of the absorption of the external radiation and also to the rate of the decomposition via the concentration of absorbing gases (and particulates) in the gas phase. However, in the model, the rate of the decomposition was derived independently from the previously published data based on steady state

240

TAKASHI KASHIWAGI 1.0

I

I

[

I

I

I

1

i

0.9 0.8

....

rr~

0.7

,~

11t

~"

\ "~- 0.5

\

8AT

,,t

=

/

0.4

\ \~i

'

"

O.2

"----_.

0.1

"~

0

2

4

$

S

10

-

12

14

16

l|

Tim IStCl

Fig. 19. Energy balance terms at the PMMA surface with endothermic decomposition: QCON = -K(~T/~X);{~AT = I0 - I; and QRC = oQvke(I0 = 11.3 W/cm2).

conditions. The discrepancies appear to be caused by the determination of the incident radiant flux and the rate of the decomposition independently. It is possible that the linear regression rate obtained in steady state conditions might overestimate the gasification rate under the dynamic heating case used in this study (at equal surface temperatures). In the dynamic condition, the temperature distilbution inside the material is not unique as it is in the steady state case, but rather it is variable with heating rate and time. The temperature distribution can be steeper or more gentle than that of the steady state with the same surface temperature, It appears probable that the total gasification rate is related to the temperature distribution [15]: lower rate with steeper temperature distribution; greater rate with gentle ones at the same surface temperature. Then, the gasification rate may not be expressed only as a function of surface temperature under the dynamic heating condition. At present, it is not- well understood how the temperature gradient and the amount of heat in the material affect the gasification rate in the dynamic heating case.

If we assume that the calculated linear regression rate derived from the steady state condition overestimates the endothermicity under the dynamic condition, then the calculated surface temperature changes with time are similar to those shown in Figs. 13 and 17. Bamford et al. 1-18] proposed a critical mass flux of decomposition products for piloted ignition at approximately 2.5 x 10 -4 gm/cm 2 sec. Their value is about 20-40 times smaller than those calculated by Eqs. (10) and (11) and tends to support the above assumption, but it is not conclusive because the value was proposed for wood and also for piloted ignition. The calculation of surface temperature of PMMA indicates that the linear regression rate derived from the steady state condition is about 5 times larger than that required to fit this experimental data. It appears that the endothermic decomposition term of the energy balance at the surface is not significant during the ignition period of PMMA. The change in surface temperature with time for red oak was calculated numerically using the experimentaUy measured incident fluxes similar to those shown in Fig. 8. Comparison between the two

ORIENTATION EFFECTS ON RADIATIVE IGNITION r

, .

, ~

'

, -

,

-

• o

~ v , i " I

~'-'--"-~-] ~ ° u ,/m, .......... \

/

-

_~

am

IW

241

is obtained in the calculations for Io = 11.9 W/cm 2. A much weaker dip is also shown for Io=7.6 W/cm 2. A similar dip is also observed experimentally as shown in Fig. 12. This is caused by an increase of the incident radiant flux after its initial decrease as shown in Fig. 8. Although the calculated change in surface temperature with time agrees qualitatively with the experimental results; further refinements, including char formation and variable thermal properties with temperature, are necesary for better quantitative agreement. The varying surface energy balance terms for red oak are shown in Fig. 22. A significant difference from the energy balance of PMMA shown in Fig. 19 is the importance of reradiation from the surface. This is due to the high surface temperature, which can exceed 700°C as shown in Figs. 12 and 21, compared to a maximum surface temperature of about 450°C for PMMA shown in Figs. 11 and 20.

,-

0T 0

I

I

J

I

I

4

8

12

16

20

24

Tree( [StCJ

IlOO

r

r

I

I

1

Fig. 20. Comparison of calculated PMMA surface temperature change with time without endothermic decomposition under various external radiant fluxes for orien-

sample orientations is shown in Fig. 21 for various external radiant fluxes. They include reradiation and convection losses from the surface, conduction into the material and absorption of the external radiation in the gas phase. As described earlier, the effect ofendothermic or exothermic decomposition heat on surface temperature was not included in this calculation. The basic trend of higher surface temperature for the vertically mounted samples than those for the horizontally mounted samples agrees with the experimental observation shown in Fig. 12. With 10 = 7.6 W/cm z in Fig. 21, surface temperatures for both sample orientations overlap each other and do not follow clearly the above described trend. This is because of small attenuation of the external radiation for both sample orientations at low fluxes and also of the uncertainty in the incident flux through unstable plume with the horizontal sample. It is interesting to note that a dip in the rate of temperature increase

~6.s ~ I ~

i0 =7.sw/cm' .

[

/

.

.

/

.

.

/

.

.

.

~

.

/

-"""

3oo

,?o'f o

L 4

L 8

i ~ ~2 Ts 2o 24 11 I~l Fig. 21. Comparison of calculated red oak surface temperature change with time for the horizontal (---) and vertical( - - ) sample orientation. I / I 0 = f ( t ) , O R = O.

242

TAKASHI KASHIWAGI

u 1.0 I

0.9

I

I

;

I

I

I

I

I

L

U \

~

t"1/

o

~

N

0.3 0.3

/ / /

/

/

~

.

"~.~

~

}:

~

0.2

Q HAD

IIATN

'~"

•

0.1 •

-

f

0

O

I 4

2

I 6

I 8

I IO

I 12

I 14

1

16

18

TiUt (StC)

Fig. 22. Energy balance terms at the red oak surface: QCON 10 - I; and (~I~AI) = e=Ts4. QI~ = 0,10 = 11.9 W/cm 9.

Figures 19 and 22 show that the relative importance of the terms in the surface energy balance also depends to some extent on the characteristics of the material, As described in detailin the previous paper [1],if the surface temperature at ignition was unique for

500

f

i

]

-K(aT/aX); QATN

=

each sample, a simple model based only on the heat conduction in the sample might be good enough to characterize ignition delay time and the minimum external radiant flux required for ignition. For this reason, surface temperature at ignition was measured for vertical and horizontal sample orien-

r

t

I

I

w

I

I

• 450

•

• e • ee

400-

•

35O 1"

=

l

i

l

I

i

I

i

i

L

2

4

6

8

10

12

14

16

18

20

EXTERNALRADIANTFLUX (W/cm 2)

Fig. 23. Comparison of PMMA surface temperature at ignition between the horizontal (e = autoignition) and vertical (A = autoignition) sample orientation.

ORIENTATION EFFECTS ON RADIATIVE IGNITION No

. . . . . .

_ •, ss0

"

\~ , ~ "~,',

,

• m

!'~

2J

4J

~

~

.o 1~ 12J 14' ls~ is'

2o

tITtlIIOU,nmAHTI=LUXIW/m21

Fig. 24. Comparison of red oak surface temperature at ignition between the horizontal (s = autoignition) and vertical (-= atttoignition)sample orientation, tation over a wide range of the external radiant flux. Surface temperature at ignition was determined by measurements of surface temperature at the time of light emission caused by the onset of flaming as determined by the photomultiplier. Observed surface temperature at ignition is shown in Fig. 23 for P M M A and in Fig. 24 for red oak. There is some scatter in the data, but the trends are clearly shown in both figures. Surface temperature at ignition of P M M A is fairly constant around 400°C for the horizontal sample and around 450°C for the vertical sample. Surface temperature at ignition for red oak increases with a decrease in the external radiant flux for both sample orientations; it is described in Ref. [1] that, at high external radiant flux levels, the absorption of the external radiation by the decomposition products ignites red oak, but, at low flux levels, red oak is ignited by the high temperature surface as an induced pilot. As is the case with PMMA, surface temperature at ignition with the vertical sample orientation is significantly higher than that with the horizontal sample orientation. Therefore, for radiative autoignition, a specific critical surface temperature at ignition unique to a particular material does not exist, Here we examine further the differences in the ignition mechanism between the vertical and horizontal sample orientations to find why ignition occurs early and the minimum external radiant flux for ignition is lower for the horizontal sample than

243

the vertical one. In radiative autoignition, three necessary conditions must be satisfied simultaneously: (1) sufficient amounts of fuel and oxygen must be available in the gas phase so that the local mixture ratio is near or within the flammability limits; (2) the gas phase temperature must be sufficiently high to initiate and accelerate gas phase chemical reactions; (3) the size of the local hightemperature zone must be sufficient to overcome heat losses during the ignition period and must be sustained long enough to permit runaway chemical reactions and stable heat feedback from flame to fuel. On the other hand, only the first and third conditions must be satisfied for piloted ignition since the pilot temperature is high enough to initiate chemical reaction if its location is in the region where the mixture ratio satisfies the first condition. With a high-temperature pilot, ignition is determined by the first condition. In the previous study [1] for the horizontal sample orientation, piloted ignition delay time was much shorter and minimum external radiant flux for the piloted ignition mode was less than those for the autoignition mode. This indicates that condition (1) on the fuel-oxygen mixture ratio is satistifed at an early time in the autoignition situation. However, condition (2) on the high-temperature gas phase is not satisfied in the autoignition mode, and it takes a long time to attain this condition. This means that the fuel--oxygen mixture ratio, by the time when autoignition can occur, will be fuel rich due to continuing fuel production and higher sample temperatures. The ignition delay can then be controlled by the concentration of available oxygen; this is observed by Mutoh et al. [5]. Autoignition is generally controlled by the transport process of surrounding oxygen into the plume or the boundary layer needed to satisfy condition (1). It appears that the plume of decomposition products from the horizontal sample engulfs oxygen from the surroundings by virtue of its vortex ring formation and its stability. Drafts in the room affect the stability of the plume and increase the mixing of oxygen into the plume. This effect observed in this study is as described earlier; ignition delay time becomes shorter with an open air experiment than in a confined chamber. A similar conclusion was also reported by Simms I-4].

244 The vertical sample produces a stable boundary layer of decomposition products, and the relatively small size of the sample used in this study generate a laminar boundary layer, which does not mix with oxygen as efficiently as the unstable plume, However, if the height of the sample becomes tall enough, a turbulent boundary layer of the decomposition products will be formed and the mixing will be more efficient. This could be the reason why the ignition delay time becomes shorter with the taller red oak sample ignited by the radiation from the gas assembly burner, Several factors are related to satisfying the second and third conditions: (1) surface temperature at which the decomposition products are released into the gas phase; (2) the amount of the local absorption of the external radiation by the decomposition products that heats the gas phase further; (3) cooling by the entrainment of air at room temperature. For the vertical sample orientation, surface temperature becomes higher than that for the horizontal sample for type of samples as described in the previous section. Then, the concentration of the decomposition products in the gas phase for the vertical sample becomes higher than that for the horizontal sample, which makes more fuel rich in the boundary layer and more difficult to ignite. Since the amount of the local absorption is roughly proportional to the concentration of the decomposition products, the increase in local gas phase temperature via local absorption for the vertical sample would be higher than that for the horizontal sample. Therefore, gas phase temperature in the boundary layer over the vertical sample tends to be higher than that in the plume over the horizontal sample. However, with the horizontal sample, the plume of the decomposition products can be heated for a long time because the plume rises along the direction of the incoming external radiation. Temperature in the plume remains high. With the vertical sample, the boundary layer of the decomposition products is heated only a short time as it moves across the area over the sample, which interacts with the incoming external radiation, After the decomposition products flow past the sample or out of irradiated area by the incoming external radiation, the gas phase temperature cools off rapidly. This means that the ignition charac-

TAKASHI KASHIWAGI teristics of the vertical sample orientation depend on the sample size and the size of the area irradiated by the external radiation. These processes compete with each other, and it is not clear which process controls the effect of the sample orientation on ignition, although experimental results clearly indicate an early ignition and lower minimum external radiant flux for the horizontal sample orientation. Further detialed measurements of the distributions of temperature and species concentrations in the gas phase over the sample during the ignition period are necessary to clarify this question. Some data on these were reported recently [5]. 4. CONCLUSION The effects of the sample orientation on autoignition delay time and the minimum external radiant flux for autoignition were studied with PMMA and red oak. Vertical radiation normal to a horizontally mounted sample and horizontal radiation normal to a vertically mounted sample were studied using a CO 2 laser as the external radiant source. Results show shorter ignition delay times under the same external radiant flux and lower minimum external radiant flux for ignition with horizontal samples than with vertical samples. This trend was also confirmed by another experiment with larger samples and an array of gas fired burners as the external radiant source. Many factors, such as the sample size, the size of the irradiated area, surrounding atmospheric condition, and sample orientation, affect radiative ignition delay time and the minimum external radiant flux required for ignition. Therefore, specilying the sample material and external radiant flux cannot uniquely determine ignition delay time or the minimum external radiant flux for ignition; these depend highly on the experimental conditions. It is observed that the absorption of the external radiation by gaseous decomposition products is significant with both sample orientations, although the amount of the absorption for the vertical sample is less than for the horizontal one. For vertically mounted red oak, this is only true for the early phase of the ignition period. The absorption

ORIENTATION EFFECTS ON RADIATIVE IGNITION becomes less after the char layer becomes thick enough to reduce the amount of decomposition products released into the gas phase. Surface temperature is higher than gas phase temperature before decomposition starts, but the latter becomes higher than the former after decomposition starts. This trend confirms the gas phase heating by the absorption of the external radiation, but it cannot exclude the possibility of exothermic gas phase chemical reactions of decomposition products with oxygen in air. Surface temperature at ignition is fairly constant for P M M A under various external radiant fluxes, around 400°C for the horizontal sample and about 450°C for the vertical one. For red oak, surface temperature at ignition increases with a decrease in the external radiant flux for both orientations. As is the case with PMMA, surface temperature at ignition is higher for the vertical sample than for the horizontal one. The calculation of P M M A surface temperature indicates that calculated results, based on experimentally measured incident fluxes, reradiation, and convection losses from the surface and conduction into the material, agree reasonably well with experimental data for both sample orientations. However, the calculation including endothermic decomposition at the surface underestimates the surface temperature significantly and does not indicate the significant effects of the sample oftentation on surface temperature that were observed experimentally. These are some problems in the application of the linear regression rate derived from the steady state experiment to the dynamic heating conditions used in this work. This work is partially supported by the Air Force Office of Scientific Research under Contract AFOSR-ISSA-80-O0010. The author wouM like to thank Dr. Thomas J. Ohlemiller for his valuable discussions about the mechanism of radiative ignition and Mr. William Wooden for his assistance in conducting the experiments.

245

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Received 18 December 1980; revised 16 March 1981