Basic studies of the mechanism of ignition of cellulosic materials

Tenth Symposium (International) on Combustion,

pp. 897-910,

T h e Combustion Institute, 1965

BASIC STUDIES OF THE MECHANISM OF IGNITION OF CELLULOSIC MATERIALS W. D. WEATHERFORD, JR. AND D. M. SHEPPARD Southwest Research Institute, 8500 Culebra Road, San Antonio, Texas

Mathematical and experimental studies are being conducted on the thermal processes involved in the ignition of slabs of woodlike substances. The results of extensive finite-difference machine computations suggest that the specified fuel-generation-rate criterion for sustained ignition, proposed by Bamford, Crank, and Malan, is incorrect. These results, however, also suggest that the experimental data of BaInford, Crank, and Malan reflect a thermal criterion of sustained ignition which has not been recognized previously. In order to adequately describe this critical thermal condition for symmetrical, two-sided heating of plane infinite-width slabs, a concept of a "thermal feedback wave" being propagated from the surface of symmetry to the heated surface is introduced, and the time required for this wave to reach the heated surface has been derived. Expressed in terms of dimensionless time (Fourier Number), this critical heating time appears to be constant for inert slabs of constant thermal properties. Also, it is approximately constant for noninert slabs of variable thermal properties, and it may decrease somewhat with increasing slab thickness when significant heat-generation effects are present. Experimental measurements of piloted-ignition thresholds have been conducted in an apparatus designed to simulate convective-source symmetrical heating of plane slabs. These experimental results and published data of prior investigators have been analyzed in terms of various ignition criteria. For such purposes, a generalized correlating concept is described which relegates each of the various ignition criteria to its proper position of relative importance for a particular set of conditions. As an aid for this generalized correlation technique, improved transient-heat-conduction data have been machine computed with the analytical solution for inert slabs, and the results are presented in graphical form. perimental data, to propose still another criterion for sustained ignition, and to examine over-all interrelations among the various suggested ignition criteria with the viewpoint of correlating these various criteria within a generalized concept, relegating each to its proper position of relative importance for a particular set of conditions. In order to facilitate this presentation, discussion of the prior investigations is deferred to a later section of the paper. Thereby, the concepts and data of the present work are included directly in this discussion.

Introduction The ignition and combustion of cellulosic materials involve complex combinations of transient physical and chemical processes. These are difficult to simulate mathematically, and, as a result, interpretation of experimental ignition d a t a often involves numerous simplifying assumptions. M a n y investigators have proposed certain criteria which must be satisfied for either transient or sustained ignition to occur in the evolved gases at the surface of the solid, and they have presented valid experimental data which appear to strengthen their propositions. However, collective consideration of the various criteria leads to apparent inconsistencies, and even contradictions, among some investigators. I t is apparent t h a t several different criteria related to surface temperature, fuel-vapor-generation rate, slab permeability, and flame stability must be satisfied before such ignition can be achieved or sustained. Therefore, it is the purpose of this paper to present additional ex-

Suggested Thermal Criterion for Sustained Ignition When a plane slab is heated symmetrically from both sides, the surface-temperature history is not perceptibly different from that exhibited b y an infinitely thick slab (semi-infinite case) during the early stages of the heating process. Eventually, however, the surface temperature

897

898

FIRE

RESEARCII

history of a finite-thickness slab begins to depart more and more rapidly from that which would be exhibited by an infinitely thick slab. It was noted during an early stage of the present program 1 that the experimental times to sustained piloted ignition reported by Banfford el al., 2 for symmetrical heating, appeared to correlate with such departures of the calculated surface temperature from the infinite-thickness case. It was also noted that the surface-temperature-history curves, computed in this laboratory for one-sided heating, indicated a critical slab thickness above which the surface temperature never exceeded that corresponding to an infinitely thick slab. This critical thickness was in approximate agreement with the experimental observation of Bamford et al., that slabs greater than 0.3 cm thick could not sustain piloted ignition by one-sided heating. The foregoing results suggested that a qualitative criterion for sustained ignition could be that the surface temperature must increase perceptibly more rapidly than would that of an infinitely thick slab. This is analogous to stating that the surface must receive sufficient feedback heat from within the slab to perceptibly alter its temperature history relative to that of an infinitely thick slab. Consequently, methods for establishing the occurrence of such critical thermal-feedback conditions have been considered, and a concept somewhat different from those normally considered in transient conduction studies has evolved. The following derivation and discussions pertain to this concept, and, therefore, certain new terms and definitions are introduced in the interest of clarifying the phenomena being described. Upon exposure of a plane slab to symmetrical heating, the surface of symmetry instantly experiences a heat flux. As heating continues, the initial thermal energy received instantaneously at the surface of symmetry may be visualized as moving back through the slab to the heated surface (counter-current to the net heat flux) by a random self-diffusion process. For the purpose of this derivation, it is assumed that the time required for this thermal feedback wave to reach the heated surface is specified by the Einstein diffusion relation: ( Ax2} = 2Dt~ where, in this case, l~2 = < Ax2>, and D signifies the thermal diffusivity. Expressing this defined time, t,, in terms of dimensionless time (Fourier Number) T', the previous relation becomes :1

"

If the slab were not inert, the numerical value of the thermal diffusivity could increase during passage of the thermal-feedback wave through the slab because of heat-generation effects, and, therefore, as indicated in Fig. 1, (r'c) (noninert slab) ~ 89 It is recognized that this approach represents a simplification; however, it provides a convenient basis for visualizing and classifying the early stages of transient-heat-conduction processes. In order to better visualize the possible significance of the thermal-feedback time, an alternate concept may be considered as follows: Upon exposure of a plane slab to symmetrical heating, a differential increment (of slab thickness) adjacent to the surface of symmetry instantly experiences a net heat flux through its surface (which is differentially displaced from the surface of symmetry). As heating continues, the mean temperature of this differential element increases, and the leading surface of this element may be defined as that hypothetical moving surface which experiences the same rate of temperature rise as does the over-all element (which extends from this moving surface to the surface of symmetry). As heating progresses, the leading boundary surface, thus defined, will move from the surface of symmetry through the slab toward the heated surface, in successive time increments as illustrated in Fig. 1. According to the original definition of the

SURFACE OF SYMMETRY

HEATED SURFACE

I

-

Ii

I--,

1

~&WAVEFRONT \~t~

INERT CASE

Vr

,."I, 0 Z hi

H

r

t

TC--2.

1

Fie. 1. Illustration of propagation of thermalfeedback wavefront from surface of symmetry to heated surface.

IGNITION

OF CELLULOSIC

leading surface of this element, the rate of temperature increase experienced by this moving surface of the element is identical to the rate of mean (relaxed) temperature increase of the entire element. Therefore, once time is specified, the mean temperature of the total element and the temperature and position of the leading surface are also specified, for a given set of process parameters. It can be shown that the time required for this hypothetical surface to move from the surface of symmetry back to the heated surface is identical to the above-defined threshold of diffusional thermal feedback. At the instant the defined hypothetical moving surface arrives at the heated surface, the thermal condition originally defined for the element behind the moving surface applies to the entire slab. In other words, prior to this instant, the rate of increase of the mean (relaxed) temperature of the total slab is less than the rate of surface-temperature rise. However, after this hypothetical moving surface reaches the heated surface, the rate of increase of the mean temperature of the slab becomes greater than that of the surface temperature. Hence, the thermal state of the slab could be described as becoming selfstabilizing, (relative to its behavior upon heatsource removal) for the first time at this critical heating time. For the case of one-sided heating, the previous definition of thermal-feedback time must be modified to account for the heat loss from the unheated face of the slab. On this basis, it can be shown that, for one-sided heating, values of Ir may occur which will require infinite time for the moving hypothetical surface to reach the heated surface. This result is in qualitative agreement with previously discussed experimental observations of a maximum thicknea~ for sustained ignition by one-sided heating.

Finite-Difference Computations for Heating of Noninert Slabs Analysis Method Description of Mathema2ical Model. The mathematical model is visualized as a flat slab having no edge effects, so that heat and vapor flow, normal to the surface, may be considered onedimensional. The material is considered to comprise volatilizable fuel in an inert matrix, with the physical and thermal properties of the matrix being independent of the fuel content. It is assumed that fuel vapor is generated by a firstorder reaction and that the generated fuel vapor escapes from the slab with negligible flow resistance. Heat transfer at heated and cooled

899

MATERIALS

surfaces is assumed to occur solely by uniform thermal convection with constant film coefficient. It is recognized that this model involves numerous over-simplifications; however, it provides a reasonable basis for exploring the influences of material and process parameters. The c()mt)lications which would be introduced by more sophisticated models are hardly justifiable at this stage of the study.

Summary of Basic Equations. The following relations summarize the equations employed in this study: Convection heat transfer at external surfaces:

h( To~ -- T,)

energy/area/time;

Conduction within slab:

K(OT/Ox)

energy/area/time;

Heat of vapor generation: -

-

q(Ow/Ot) energ):/volume/time;

Thermal accumulation :

cp(OT/Ol)

energy/volume/time;

Vapor-generation rate:

Ow//Ol = --kw exp (-- E / R T ) weight/volume/time; External-surface heat balance:

h ( T o : - T,) = --K(OT/Ox),; Internal heat balance:

o[g(OT/Ox) J/Ox = cp(OT/Ot) + q(Ow/Ot). Discussion of Mathematical Procedures. In order to solve the foregoing equations, the partial derivatives are replaced with equivalent finite differences, 3 using somewhat the same techniques as those employed by Bamford, Crank, and Malan. ~ Dimensionless variables are substituted for the quantities shown, and a fixed relationship between the time increment and the thickness increment is specified, in order to simplify the resulting equations. By means of these manipulations, the partial-differential equations may be solved with a digital computer in a manner analogous to the graphical method devised by SchmidO For these calculations, the values of the wood properties reported by Bamford, Crank, and Malan 2 have been employed in conjunction with the surface film coefficient recommended by

900

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FIRE RESEARCH

ld 6 :

0~"

=

( / X X = 0 . 5 CM }

SOL,O L,.ES: I(~?

"

M= O-

(Z~X =0.125 C M ) 667eK / ~k,

/ i I0 0

,,

SYMMETRICAL HEATING

T~o i

i

5 CM S L A B r iiiiii

I01

HEATING

~ I02

TIME.

i

i qt,i IO 3

MINUTES

Fro. 2. Effect of increment thickness on computed vapor-generation rate. Akita. 5 These values are wi p c q K h

= = = = = = E/R = k=

0.375 gm/em ~ 0.60 gm/cm 3 0.55 cal/gm ~ 86 eal/gm 2.7 X 10-4 cal/cm 2 see (~ 4.4 X 10-4 cal/cm 2 sec ~ 16,670~ 5 . 3 X l0 ssec -1.

Calculations were performed with a high-speed digital computer for three source temperatures (667 ~ 717 ~ and 767~ and four slab thicknesses (0.1, 0.5, 1.0, and 5.0 em), for both onesided heating and symmetrical, two-sided heating.

D~scussion of Computed Results Effect of Finite-Difference I n c r ~ t

Size. The first calculations performed for the 5 cm, symmetrical-heating case produced results represented by the dashed curves in Fig. 2. These calculations were repeated using one-fourth as large increments, and, as illustrated in ]?ig. 2, the curves were altered drastically. These results establish that 0.5-cm increments are much too thick for the finite-difference approximations. On the other hand, the successful superposition of the curves for the 0.1, 0.5, 1.0, and 5.0-cm slabs in Fig. 3 (to be discussed later), indicates that sufficiently small increments were employed for these cases. These increment thicknesses were 0.01, 0.05, 0.1, and 0.125 cm, respectively. The foregoing results indicate that, in computations for low-thermal-conductivity materials, excessive increment thicknesses may generate the illustrated undulations, regardless of incrementto-slab thickness ratio. In such cases, each

successive increment may undergo computed fuel depletion before significant vapor generation is indicated in the next increment. Accordingly, for the parameters used in these calculations, it appears that the maximum allowable increment thickness lies between 0.125 and 0.25 cm. In view of the foregoing observations, it appears that the computations reported by Bumford et al? did not accurately represent the mathematical model upon which they were based. Their computations, which involved the same wood properties as the present calculations, employed slab-thickness increments ranging from about 0.125 to 0.5 cm; and a maximum, followed by a minimum, was observed in the vapor-generation rate for each case, except for the 0.125-cm increments. Consequently, their conclusion, that a specified vapor-generation rate of 2.5 X 10-4 g m / c m 2 sec is required for wood to sustain ignition, does not appear to be valid, because this conclusion was based upon the probably erroneous undulating vapor-generation-rate curve.

Similitude Parameters. When the computed vapor-generation rates of the present work were plotted vs heating time, it became apparent that the influence of the source temperature T= could be accounted for by using the similitude factor, exp (E/RT=). The vapor-evolution-rate curves, when multiplied by this similitude parameter, are accurately superposed for the various temperatures, except for later heating stages exhibiting computed loss of greater than about half of the vo]atilizable matter at the surface. As would be expected from inert-slab heatconduction theory, ~b,, the ratio of the surface temperature rise to the difference between the ~.

',e,~7o' . . . . . . "% m

o'J . . . . . . . . . . . . . . . .

(e) ' ~ 7 /

//

i0I

I

02

I~

SLAB THICKNESS CM

I

a5

Lo

,x,o,/-..Z / ,x,o'/-.~/ 9 ///

I

I xlo~.-Z / IXI02.-Z /

" ~ i0o

/

/ /

/

/

.~

Z/"

~.o

INFINITE--

TH,CK,ESS SLAB

Ti = 300 ~ Ws ~ 0 . 5

I0-I

I0 ~ I01 HEATING TIME, MINUTES

Fro. 3. Generalized correlation for symmetrical heating.

IO t

IGNITION

OF

CELLULOSIC

heat source and surface temperatures, proved to be useful for normalizing computed surfacetemperature histories for the various source temperatures investigated. Here again, however, this similitude parameter loses accuracy when the computed fuel content at the surface falls below about half of its initial value.

Correlated Results. The results of the finitedifference computations for symmetrical, twosided heating are summarized in Fig. 3. This correlation indicates t h a t for a constant source temperature, a constant fuel-escape rate corresponds approximately to a constant surface temperature, except for very thin slabs (i.e., small values of Bi). The computed temperature data for the one-sided heating cases are presented in Fig. 4.

Analytical Computations for Transient Conduction in Inert Slabs During this program, published data on transient heat conduction in inert slabs4,~-~ were examined for the purpose of providing comparisons with the results of finite-difference computations for noninert slabs. I t was noted that, in a range of variables of interest to this program, the published data consistently indicated the possible occurrence of an anomaly in surface temperature histories. This anomaly suggested

2

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2

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4 5a

810"

2

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901

MATERIALS

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,

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,,,,,,

,

,

,,,,,

go

0.5~

I0 i(~l

I0 o I01 HEATING I'~IME, MINUTES

I0 ~

FIO. 4. One-sided heating of wood slabs. that the surface temperature of very-thin slabs could initially increase at slower rates than would that of very-thick slabs of the same material exposed to the same source conditions. I t was important for the objectives of this research program to determine whether such anomalous behavior could occur or whether such indications stemmed from inaccuracies in the presentation or interpretation of the published correlations. A digital computer was used to obtain an analytical solution of the differential equation l~ for the surface-temperature history of inert finite-thickness slabs, heated identically on both sides by a convective heat source. The assumptions made in this solution were: constant and

810"

Z

3

4 D5

810"

"L)B~= ( t h : / p c K

Fro. 5. Analytical results for transient heat conduction.

Z

3

4

56

810-

Z

902

FIRE RESEARCH

homogeneous slab properties; constant heattransfer coefficient; constant source temperature; and one-dimensional heat flow. The computed results reveal that the anomalies interpreted from published correlations were spurious, evidently resulting from series-convergence problems or loss of accuracy in graphical reproduction of the computed data. Therefore, the newly computed data are presented in Fig. 5, in sufficient detail to serve as an alternate source of published data on transient-heat conduction in inert slabs. Comparison of the analytical results for inert slabs, presented in Fig. 5, with the finite-difference computation results for noninert slabs, presented in Fig. 3, yields the following observation: The computed surface-temperature histories of noninert slabs are essentially the same as those calculated for inert slabs (within less than 10% deviation) for values of r t Bi2 and ~b~ less than about 5 and 10, respectively. This result suggests that, for this range of parameters, the inert-slab data of Fig. 5 may be employed without serious error for correlating experimental data obtained with various cellulosic specimens, provided that the specimen properties are not drastically different from those assumed in the noninert case illustrated in Fig. 3. Moreover, for this stated range of conditions, and specimen properties, the calculations for noninert slabs reveal that significant fuel depletion should not be experienced prior to ignition, either at the surface or within the slab.

Experimental Measurement of Piloted Ignition Thresholds for Convective-Source Heating An experimental slab-ignition apparatus has been developed as part of this research program, in order to provide additional convective-source, piloted ignition data for comparison with existing data. The operating principles of this device, and experimental observations, are briefly described in the following paragraphs.

(4), and then flows "sheetwise" through the spaces on each side of the specimen (6) [-between the gold-plated slabs (5)~. In this region, thermal energy is transferred to the specimen from the air and gold-plated slabs. The air and any ignition products are then exhausted to the atmosphere (8) or may be collected for analysis. Radiative transfer to the specimen is held to a minimum by gold plating the surfaces (5) which are viewed by the specimen, thus reducing their emissivity to as low as 0.02. The distance between the gold-plated slabs (5) and the specimen (6) is 0.635 cm, and the air velocities are such that the primary heat-transfer mechanism is gaseous conduction. Under these conditions, the film coefficient h is very nearly a function of the thermal conductivity of air only and, therefore, is approximately constant for constant air temperature. It was noted at the end of the reported series of experiments that some base metal had diffused through the gold plating (5). The surface, however, still remained glossy. The ignition specimen (6) and a dummy specimen (10) are mounted in an adjustable holder (7), in a manner similar to that of lantern slides. The dummy end of this holder is inserted into the ignition furnace during the start-up and

?

tol oo

o [-Ao

o

Apparatus The experimental apparatus, shown in Fig. 6, was designed to physically simulate convectivesource heating of plane slabs. Both symmetrical two-sided heating and nonsymmetrical one-sided heating studies may be conducted with this device. The operating principles of the furnace are discussed in the following paragraphs. The numbers in parentheses refer to identification numbers shown in Fig. 6. Air enters each side of the apparatus through equally spaced holes in the inlet manifold. It passes through heating sections (2), (3), and

SECTION

A-A

Fro. 6. Experimental slab-ignition apparatus.

IGNITION OF CELLULOSIC MATERIALS equilibration period. When the desired experimental conditions are achieved, the holder (7) is slipped rapidly through the furnace to its opposite position. Thus, the specimen surface is suddenly exposed to the convective-source conditions, and experimental time measurements are commenced at this point. Time-to-ignition data are measured by noting the time at which the surface temperature begins to rise sharply, indieating that flame (flashed back from the downstream ignitor) has stabilized on the specimen surface. The surface temperature is monitored by an array of quick-response thermocouples mounted on both surfaces of the specimen. Both thermocouple readings and scorch patterns indicate that ignition stabilization always occurs at the center of the specimen surface as expected. Other thermocouples are located throughout the furnace to determine air temperature, goldplated slab (5) temperatures, etc. A platinum glow-wire ignitor is located at the downstream edge of the specimen on each side of the specimen holder. These ignitors, which have proved adequate for igniting the evolved gases, do not TABLE

903

appear to contribute appreciable energy to the specimen. The ignition-test specimens are 15 cm square, with the area exposed to the convective source being 14 cm X 12 cm. Untempered hardboard specimens, smooth on both faces, and pure acellulose specimens, relatively smooth on both faces, were employed in this study.

Experimental Results Ignition-threshold measurements were made on untempered hardboard and pure a-cellulose specimens for three nominal slab thicknesses, ranging from about 0.3 to 2 cm, and for several initial source temperatures, ranging from 680 ~ to 830~ The results of these experiments are summarized in Table I and correlated in Fig. 7. No appreciable change in time to ignition was apparent for changes in air-flow velocities from about 10 to 70 cm/sec relative to the specimen surface. Hence, for this range of conditions, the Biot Number was not influenced by Reynolds Number. It was noted t h a t the temperature of the convective heat source (gold-plated slab) I

Summary of experimental ignition data obtained in this laboratory

K,* l~, cm

c,**

p, gm/cm 8 cal/cm sec ~

cal/gm ~

D,*** cm2/sec

T~, ~

tit, sec

ri~

Bi

0.096

Hardboard Specimens 0.174

0.174 0.490 0.490 0.162 0.169 0.99 0.479 0.479 0.482

1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06

4 X 1 0 -4 4 X 10-4 4 X 10-4 4 X 10-4 4 X 10-4 4 X 10-4 4 X 10-4 4 X 10-4 4 X 10-4 4 X 10-4 4 X 10-4 4 X 1 0 -4

0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24

16 X 1 0 -4 16 X 10-4 1 6 X 1 0 -4 1 6 X 10-4 16X 10-4 1 6 X 10-4 16 X 10-4 1 6 X 10-4 1 6 X 1 0 -4 1 6 X 1 0 -4 16 X 10-4 1 6 X 10-4

770 770 760 680 765 775 760 700 790 780 765 830

142 138 139 238 400 357 125 207 439 307 305 176

7.50 7.30 7.35 12.6 2.66 2.38 7.54 11.58 0.78 2.14 2.02 1.21

0.096 0.270 0.270 0.089 0.093 0.545 0.264 0.270 0.265

770 791 780 740 770

134 96 104 162 111

0.71 0.51 0.57 0.87 4.34

0.885 0.885 0.885 0.885 0.135

a-Cellulose Specimens 0.462

0.462 0.160

0.24 0.24 0.24 0.24 0.80

1.15 1.15 1.15 1.15 2.6

X X X X X

10-4 10-4 10-4 10-~ 10-~

* Obtained from Ref. 11. ** Calculated from D, p, and K. *** Obtained from Refs. 11 and 12.

0.42 0.42 0.42 0.42 0.32

11.4 11.4 11.4 11.4 10

X X X X X

10-4 10-4 10-4 10-4 10-4

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FIRE RESEARCH

.......

/

'/' 0.6

/

I0 t

with a nonradiant source, this characteristic is readily approached. However, in the case of radiant heating, the value of the effective heattransfer coefficient changes with time (as the surface temperature rises) because of reradiation effects and convective heat loss to the nonradiant ambient medium. In the radiant-ignition correlations presented by most workers, the irradiance is expressed as that measured with a radiometer. Hence, such irradiance values represent initial values only:

'1I '

h-~

10c

Hi = hr(Too -- T~). .

161 SYMBOL

6

680 700 765-780 n 790 n 830 c~ CELLULOSE 740 770-790 HARDBOARD

d (p

Q

I

t

H = h r ( T ~ - - T,) -t- he( Ta - - Ts),

n

o

iO-2

In practice, the actual heat flux at the slab surface may be expressed as

SOURCE TEMR~~

MATERIAL

[

I

I

~

9

I

I

I I I

i0-I "~'Bi z =

I

I

I

i0 ~

t

I

where h,. = H ~ ( T ~ 2 -t- T~2)(T,~ -~ T ~ ) / ( T ~ 4 - - T~4).

II

I0 I

th 2

KPC

Fro. 7. Piloted ignition data of this laboratory, correlated on basis of constant surface temperature, using inert-slab surface-temperature data. decreased perceptibly during each experiment (up to about 30~ However, since no provision had been made to record the temperature history of this heat source accurately, initial source temperatures have been used in subsequent correlations of the experimental data. The presented experimental data represent preliminary results of a continuing research program. Because of the exploratory nature of these experiments, no attempt was made to monitor or control the moisture content of the specimen slabs other than to package the asreceived specimens in plastic containers. Analysis of Ignition Criteria The following discussion reviews and reinterprets the experimental results of various investigators, in order to place the various approaches in common perspective. First, however, the following paragraph is offered for purposes of clarification. The calculations and correlating procedures developed in this paper are based upon all independent variables, such as the heat-transfer film coefficient, remaining constant throughout the heating process. In the case of convective heating

Obviously, h~increases as the surface temperature increases, so the use of constant initial irradiance values in graphical correlations does not represent the actual case. Martin and coworkers 12-15and Sauer 11have extensively studied the spontaneous ignition of blackened a-cellulose by intense thermal radiation. The experimental data usually have been correlated by plotting the radiant exposure (based on the initial irradiance and total exposure time) versus the product of this radiant exposure and the irradiance level (also initial value) for each specimen thickness. Figure 8 has been developed from the foregoing experimental results in terms of the parameters used in the present work, and shows the resulting normalized curves. It is apparent from these data that, although a fixed ignition temperature criterion is in agreement with the vertical and left-hand SUSTAINED IGNITION REGION

,, i o 3

~

NO

iO =

I

IO s

,

I

~

i

i

i i 4

IOr

i

Fie. 8. Correlation of spontaneous-ignition threshold data for ~-cellulose sheets (radiant heating with a 5500~ source).

I G N I T I O N OF C E L L U L O S I C M A T E R I A L S

portion of this ignition threshold correlation, it cannot explain the right-hand branch. However, as will be discussed subsequently, this latter branch is in qualitative agreement with the thermal-feedback criterion of sustained ignition which is developed in this paper. Because of the high source temperature, employed by Martin et al., ( T ~ -- T,) is essentially constant; hence, for all practical purposes, the coordinates of Fig. 8 are analogous to the normalized parameters of this work assuming radiant absorbtivies of unity, with the values of Bi being multiplied by the constant (T~ -- Ti). Using a value of 5500 ~ 14 for T~, and 300 ~ for Ti, a value of r I Bi2 of about 0.03 is derived from the vertical portion of the transient flaming-threshold correlation in Fig. 8. Considering this value of r ' Bi2 to apply in the limiting case as Bi approaches infinity, the data of Fig. 5 indicate a surface temperature function ~b8of 0.2. Using the value of 5500~ for the source temperature, and this derived value for ~bs, a spontaneous ignition temperature 900~ is derived. This result is in substantial agreement with the experimental spontaneous ignition-temperature measurement of 600~ to 900~ reported by Martin and coworkers. TM A comprehensive investigation of piloted ignition of wood was conducted by Bamford et al? Piloted convective heating was accomplished by direct contact with a gas flame for both symmetrical two-sided heating and unsymmetrical one-sided heating experiments. Ignition thresholds were measured by observing the time at which flaming would continue upon removal of the heat and pilot source. Consequently, this experimental technique precluded the detection of any threshold of transient flaming prior to the onset of sustained ignition. Based upon comparison of experimental data with finite-difference computations, these workers concluded that a fixed fuel-vapor-escape rate of 2.5 X 10-~ gm/cm 2 sec was required to sustain ignition for all slab thicknesses studied. As described elsewhere in this paper, the results of the present work appear to invalidate this particular fuelgeneration-rate criterion. Moreover, the computed fuel-generation rates of the present work at the sustained ignition threshold of Bamford et al., vary by orders of magnitude among the various specimens studied by them. On the other hand, as will be discussed subsequently, their experimental sustained ignition-threshold data, for both symmetrical and unsymmetrical heating, are in substantial agreement with the thermal feedback criterion of sustained ignition which is developed in this paper. Extensive experimental and theoretical studies of ignition of cellulosic materials by thermal

905

radiation have been reported by Simms and coworkers. 16-19 With the aid of indirect theoretical correlation techniques, Simms proposes a fixed surface temperature of about 525~ as the criterion which must be satisfied for spontaneous radiation ignition of cellulosic materials. He also interprets the piloted thermal-radiation ignition data of Bamford et al. 2 as suggesting a constant surface-temperature-ignition criterion. He derives a value of about 650~ as the surface spontaneous-ignition temperature suggested by the thermal radiation data of Sauer. 11 In his most recent publication, Simms presents data for piloted radiant ignition which indicate that the constant ignition temperature varies from about 300~ to 410~ as the position of the pilot flame is varied from about 0.6 to 2 cm from the irradiated specimen surface. Based upon considerations of the inflammability of fuel-air mixtures, Akita5 suggested that the criterion for piloted ignition should be the first attainment of a flammable fuel-air mixture. For a given combination of ambient conditions, this criterion would be analogous to a fixed minimum fuel-generation rate at the heated surface, and the computed data of Fig. 3 indicate that this is approximately analogous to a constant surface temperature. For convective-source spontaneous ignition and for intense thermal radiation spontaneous ignition, Akita5 found that a constant surface temperature was required. However, his derived value of 500~ for this temperature is based upon the use of semi-infmite slab theory for computing temperature profiles. The results, presented in Fig. 5 of this paper, reveal that for small Blot Numbers, this simplifying assumption could result in the deriving of spuriously low surface temperatures. Consequently, the 500~ spontaneous-ignition temperature, reported by Akita, is possibly too low. For extremely high irradiance levels, Akita's computed spontaneous-ignition temperatures 5 appear to be spuriously high, approaching 2000~ By referring to the thermal-radiation ignition data summarized in Fig. 8, it becomes apparent that Akita's experiments, which yielded the extremely high computed surface temperatures, probably represent points on the sustained ignition-threshold curve (right-hand branch in Fig. 8) rather than on the spontaneous transient-ignition-threshold curve. Experiments on the piloted ignition of cellulosic materials have been conducted by Buschman and eoworkers 2~ using a relatively lowtemperature radiation source (943~ Because of the substantial variation in effective heattransfer coefficient during the heating process using this low-temperature radiation source,

906

FIRE RESEARCH

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16 z

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i0 z

th 2

"E'Bi2 = KPC

Fro. 9. Alternate correlation of analytical results for transient heat conduction in symmetrically heated plane slabs with constant convective-source temperature. his data cannot be interpreted directly on the basis of tile constant Blot-Number results presented in this paper. However, an estimate of the surface temperature required for piloted ignition under these conditions has been obtained from Buschman's data by superposing his data on Fig. 5 and employing a short-path extrapolation to infinite Blot Number. The previously mentioned variation in Blot Number during the heating process should vanish under these conditions. This extrapolation procedure yields a value of about 350~ for the piloted ignition temperature, which is in substantial agreement with the previously discussed values reported by Simms. Generalized Correlation of Ignition-Threshold Data The foregoing analysis of ignition criteria leads to the following generalized concept for the systematic correlation of various ignition criteria: The normalized theoretical correlations for transient heat conduction in inert slabs, such as those presented in Figs. 5 and 9, may be considered as working graphs for correlation purposes. Superposition of experimental ignition threshold data upon a selected inert-slab, theoretical correlation should reveal clues regarding the nature of the criteria controlling the ignition. Consider the use of the theoretical inert-slab data presented in Fig. 9, for example, for correlating experimental spontaneous-ignition data. A threshold curve, such as one of the illustrated constant ~b~ parameters, would be anticipa~d for the spontaneous-ignition threshold if a fixed

surface temperature controls ignition. However, for large values of Bi which intersect this threshold curve at values of r ' less than about 89(below the r ' = 89line in Fig. 9), the resulting ignition would not be sustained. Consequently, in such cases, the heating process could continue along a constant Bi line until the thermal-feedback threshold of sustained ignition is achieved. However, once the transient ignition threshold occurs, tile boundary conditions are altered by the transient flames, and possible ablation effects, so that theoretical prediction of the critical heating time for sustained ignition is not feasible. In the event that the value of Bi is greater than the critical value for one-sided heating, continuing the heating process along a constant Bi line beyond the transient flaming threshold could eventually achieve the condition commonly referred to as thermal explosion. Considering tile use of Fig. 9 for correlating piloted-ignition data involves an additional assumption, namely, that the normalized fuelescape rate from the heated surface of the slab is constant for a constant value of ~b,. (Such a relationship is approximated by the finite-difference computations summarized in Fig. 3.) On this basis, superposition of experimental pilotedignition data on Fig. 9 should result in a threshold curve similar to that shown in Fig. 8, in which a line of constant ~b, represenLs the constant fuelrate criterion. However, as in the case of spontaneous ignition, for high values of Bi which intersect this piloted-ignition-threshold curve at values of r ' of less than about 89 transient flaming should occur. Continuing the heating process beyond this latter threshold should lead to sus-

IGNITION

OF

CELLULOSIC

tained ignition when the previously discussed thermal-feedback condition is achieved. For spontaneous ignition, the position of the fixed surface-temperature ignition-threshold curve should be expected to vary with the magnitude of the source temperature because ~b8 changes with source temperature for a constant surface temperature. Similarly, the position of the ignition threshold curve (represented by a line of constant ~b~in Fig. 9) for piloted ignition would be expected to vary with the source temperature for the same reason, and with the nature and location of the pilot relative to the slab because of the resulting changes in the fuel-generation-rate required for ignition. On the basis of these described correlating techniques, the experimental piloted-ignition data of the present program (Table I) were correlated satisfactorily using Fig. 5 as a working graph. On this basis, a constant surface-temperature criterion is indicated (apparently reflecting a constant fuel-generation-rate criterion) as illustrated by the horizontal lines in Fig. 7. Within experimental uncertainties, the data for hardboard and ~-cellulose appear to obey the same criteria. In order to compare these results with the experimental piloted-ignition data of Bamford el al. 2 (in which the source temperature was estimated to be about 800~ a constant surface-temperature threshold for a source temperature of 800~ has been interpolated from the experimental correlation in Fig. 7. Plotting this threshold and the experimental sustained-ignition-threshold data of Bamford et al., on the I01 PILOTED iSUSTAINED FLAME AFTER HEAT SOURCE REMOVAL

SUSTAINED FLAME AFTER HEAT SOURCE AND PILOT REMOVAL DATA OF REFERENCE

'= 0 . 3

907

MATERIALS

same basis as Fig. 9, yields the result shown in Fig. 10. The data of Bamford et al. fall on a line of constant r', in agreement with the proposed thermal-feedback criterion for sustained ignition. The various interpretations of the thresholds shown in Fig. 10 are based upon the discussions of ignition criteria presented earlier in this paper. The similarity between this correlation of convection-ignition data and that of radiationignition data shown in Fig. 8 is striking. Moreover, the correlation in Fig. 10 demonstrates that different ignition criteria, indicated by the data of various investigators, may be reconciled within the scope of the generalized concept discussed in this paper.

Notation D i m e n s i o n a l Variables

c D E

Specific heat of solid, cal/gm ~ Thermal diffusivity, em2/sec Activation energy of fuel volatilization, cal/mole h Heat-transfer coefficient, cal/cm ~ see ~ H Irradiance, cal/cm 2 sec k Reaction rate constant, sec-1 K Thermal conductivity of solid, cal/cm see ~ 1 Thickness of thermal feedback wave, cm lr Slab reference thickness for symmetrical heating case (equals half the symmetrically heated thickness), cm L Slab thickness, cm q Heat liberated by fuel volatilization, cal/gm Q Cumulative radiation exposure, cal/cm ~ Fuel-vapor-escape rate, gm/cm 2 see R Gas constant, eal/mole ~ t Time, minutes T Absolute temperature, ~ w Volatilizable content of solid, gm/em 3 x Distance from heated surface normal to slab surface, cm p Density of solid, gm/cm a

A/A~

=1

Dimensionless Variables T R A N S I E N T PILOTED ~FLAME AFTER HEAT SOURCE REMOVAL STAINED PILOTED FLAME IN PRESENCE OF HEAT SOURCE ( CORRELATED DATA OF THIS WORK ) I

16 =

I

i0 ~

i~ ~

iO I

th z --g'Bi~ = _ _

KPC

Fig. 10. Correlation of piloted-ignition threshold data for wood and a-cellulose slabs (symmetrical convective heating with 800~ source).

Bi = h l r / K ; Blot Number (for symmetrical heating case) M = 1/(AT) 112 = 1 / ( ~ X ) ; number of thickness increments ~- i'lrpc/wiK; fuel-vapor evolution rate W = w / w i ; fuel content X ~ x/Ir; thickness r ' -- K t / p c l ~ ; Fourier Number for symmetrical heating of slab of thickness, 21r ~b = ( T - T i ) / T = - T ) ; temperature-difference ratio

908

FIRE RESEARCH

Subscripts a c i 1 r s oo c ig

Proc. Cambridge Phil. Soc. (Part I) ~2, 166

ambient convective initial leading surface (or front) of thermal-feedback wave radiant slab surface heat source threshold of thermal feedback to heated surface observed ignition threshold ACKNOWLEDGMENTS

Grateful acknowledgment is given to Dr. R. A. Burton, Mr. D. Gross, Mr. P. M. Ku, and Dr. A. F. Robertson for their encouragement and suggestions, and to Mr. T. R. Jackson for conducting computer programming and supervising computer operations. Appreciation is expressed to the Fire Research Section of the National Bureau of Standards for furnishing the a-cellulose specimens used in this work, and to the Research Department of the Masonite Corporation for furnishing the hardboard specimens used in the program. Appreciation is expressed also to the General Electric Computer Department for providing computer time prior to installing a computer at Southwest Research Institute, and especially to Mr. E. A. Jacoby for checking the finite-difference program and conducting many of the computations. This work was supported in part bY the Office of Civil Defense, Department of Defense, through contract with the National Bureau of Standards. It is in the public domain and not subject to copyright. REFERENCES 1. WEATHERFORD,W. D., JR. : Mathematical Study of Wood-Burning Mechanisms, presented at 55th Annual AIChE Meeting, New York, Dec. 1962. 2. BAMFORD,C. H., CRANK,J., ANDMALAN,D. H.:

(1945). 3. SQUIRE, W. AND FOSTER, C. : A Mathematical Study of the Mechanism of Wood Burning, Southwest Research InstituteTechnicalProgress Report, February 1961; Fire Research Abstracts Revs. 3, 78 (1961). 4. McADAMS,W. H.: Heat Transmission, 3rd ed., McGraw-Hill, 1954. 5. AKITA,K.: Rept. Fire Research Inst. Japan 9, 1, 51, 77, 99 (1959); Fire Research Abstracts Revs. ~, 109 (1962). 6. GROBER, H.: Z. Ver. Deutsch. Ing. 69, 705 (1925). 7. Joco~, M.: Heat Transfer, Vol. 1, Wiley, 1949. 8. NEWMAN,A. B. : Ind. Eng. Chem. 28, 545 (1936). 9. SCHACK,A., GOLDSCHMIDT,H., AND PARTRIDGE, E. P. : Industrial Heat Transfer, Wiley, 1933. 10. CARSLAW,H. S. ANDJAEGER, J. C.: Conduction of Heat in Solids, p. 93, 2nd ed., Oxford University Press, London, 1948. 11. SAVER, F. IV[.: Ignition of Black a-Cellulose Papers by Thermal Radiation, U. S. Dept. of Agriculture Forest Service Interim Technical Report AFSWP-869, Sept. 1956. 12. MARTIN, S. B.: J. Appl. Phys. 31, 1101 (1960). 13. MARTIN,S. B. AND RAMSTAD,R. W.: TemperaSure Profiles in Thermally Irradiated Cellulose Accompanying Its Spontaneous Ignition, U. S. Naval Radiological Defense Laboratory Technical Report USNRDL TR-353, May 1959; Fire Research Abstracts Revs. 3, 29 (1961). 14. BROIDO, A. AND MARTIN, S. B.: Fire Research Abstracts Revs. 3, 193 (1961). 15. MARTIN, S. B.: Ignition of Cellulose Kindling Fuels by Very Brief Radiant Pulses, U. S. Naval Radiological Defense Laboratory Technical Report USNRDL-TR-660, July 15, 1963. 16. LAWSON,D. I. AND SIMMS, D. L.: Brit. J. Appl. Phys. 3, 288 (1952). 17. SIMMS,D. L.: Combust. Flame $, 293 (1960). 18. SIMM , D. L.: Combust. Flame 6, 303 (1962). 19. SIMMS,D. L.: Combust. Flame 7, 253 (1963). 20. BUSCHMAN,A. J., JR.: Private communication.

COMMENTS Dr. D. L. Simms (Fire Research Station, Boreham Wood): The results presented by Martin and by Weatherford and Sheppard confirm, in large part, the work already published by the Fire Research Station., 1-5 We have obtained the heat balance of an irradiated solid losing heat from both surfaces, assumed to be inert and totally absorbing. In dimensional form ~/pcl~ = Fl[~v/1, HI/K, kt/l ~, t/tp],

(1)

where ~ is the total energy in the pulse of duration

t and whose maximum occurs at time t~, p is the density, c the specific heat, k the diffusivity (k = K/pc), l the thickness of the material, 0 the temperature at distance x within the material, and H the Newtonian cooling constant. Two useful approximations are the semi-infinite solid (the thermally thick material) for which kt/l 2 < 1, and for the state with the linear temperature gradient (the thermally thin material) for which kt/l ~ > 1. (The actual value~ depends on the value of H1/K.) For the semi-infinite solid, Eq. (1),

IGNITION OF CELLULOSIC MATERIALS for constant intensities of ratiation, I, reduces to

Ydpc(kt)89 -~ F~[Ht/pc(kt)J],

(2)

where 0r is the surface temperature. For values of [Ht/pc(kt)lJ < 0.14, surface heat losses may be neglected, e and Eq. (2) reduces to

I (tt) = eonst.

(4)

where 0N is the mean temperature, and if Ht/pcl < 0.2, heat losses from both surfaces may be neglected, and Eq. (4) reduces to

Z = It = constant.

8. LAWREMCE, E. K.: Analytical study o] flame initiation, Sc.M. thesis, Dept. of Chem. Eng., Massachusetts Institute of Technology, Cambridge, Mass., 1952. 9. SIMMS, D. L. : The ignition of maierials by radiation, Ph.D. thesis (unpublished), London, Jan. 1964.

(3)

For the slab, Eq. (1) reduces to

Y,/pclO,~ -- FdHt/pcl),

909

(5)

Over a wide range of rates of heating (1-12 cal cm -2 sec-l), both for constant and varying impulses of radiation, this approach enables the time taken to ignite, both spontaneously and by pilot ignition, to be predicted from the thermal properties of the irradiated cellulosic materials, assuming that ignition occurs at a fixed surface temperature for thermally thick materials and that sustained ignition occurs at a fixed mean temperature for thermally thin materials (and not the surface temperature as quoted by Weatherford). However, we have pubfished a value of about 500~ for spontaneous ignition 0r, a value in agreement with that given by Akita ~and Lawrence, s and not the value of 600~ given by Martin. We have shown~ this difference to be due to the small size of the area used by Martin (~--3 cm~). The ignition time depends on the irradiated area; the correction factor for this region is about 20%, and this would explain the difference between our results. The value for sustained ignition given by us is 0~ -~ 525~ The value for pilot ignition increases with the distance of the pilot flame in the volatile stream, being nearly 300~ near the surface and 400~ at the edge of the volatile stream. The limitations of the purely thermal balance approach are discussed in some detail elsewhere1-5.0; the discussion also includes notes on the effects that the experimental apparatus may have on the ignition process. 1. LAWSON, D. J. AND SIMMS, D. L. : Brit. J. Appl. Phys. 3, 288, 394 (1952). 2. SIMMS, D. L.: Combust. Flame $, 293 (1960). 3. Ibid. 5, 369, 375 (1961). 4. Ibid. 6, 303 (1962). 5. Ibid. 7, 253 (1963). 6. L~.wsoN, D. J. ET AL.: The heating of panels by flue pipes, London, Fire Research Special Report No. 1, H. M. Stationary Office, 1952. 7. A~ITA, K.: Rept. Fire Res. Inst. Japan 7, 99 (1959).

Dr. S. Martin: I should like to say something about our own experiences with what we call "the effect of area of exposure." First of all, we have never observed any differences in threshold radiant exposures for transient flaming ignition (the phenomenon on which we have concentrated our attention and for which the 600~ surface-temperature measurements apply) for areas of exposure ranging from 0.375 in. diam up to a 3 in. X 3 in. square. Recent measurements at the Naval Applied Science Laboratory (NASL) with a 6-in. X 6-in. source, show a similar lack of "effect of area of exposure" for highirradiance responses, as compared to smaller exposure areas, until they are reduced down to a diameter of the order of several millimeters. We also share with our NASL colleagues the common experience that, at low irradiances of exposure (and it is difficult to assign a value, because it ls a function of the specimen thickness), flaming ignitions occur for the larger areas of exposure, at radiant exposures which would have caused glowing ignition in smaller, apertured area exposures. The second point I want to make is that the internal temperature measurements (and the resulting profile) described in my paper were made using an exposure area of twice the diameter (and, hence, four times the area) of the "spot" used with the radiometric measurements of surface temperature. Any reasonable extrapolation of the profile to the surface gives values of temperature rise above ambient at the instant of ignition,which are at least 600% I might add that the dark-adapted eye can perceive the incandescence of the exposed surface, just prior to the appearance of flame, when the specimen is exposed to a large-area, high~ intensity infrared source. Third, I am suspicious of temperature values which are deduced from heat-transfer considerations alone. For an inert material with invariant properties, such a procedure could be used with high reliability. For cellulose, though, until direct measurements show that lower surface temperatures accompany ignition when larger areas of exposure are used, I favor the higher values which we have determined experimentally. I t has been our custom for many years to aperture the radiant-energy "spot," so that only that portion which is quite uniform (say, within • is allowed to fall on the specimen. Now, we find that, at rela-

910

FIRE RESEARCH

tively low irradia~ce levels, we cause a sample to flame for an exposure which previously would have caused it to glow, by simply removing the aperture. This could be an area effect or it could be an effect of nonuniform irradiation. In an attempt to discriminate between these two possibilities, we repeated the apertured exposure, but additionally we east the penumbra of an opaque object over part of the exposed area. On a large number of exposures, without fail, the specimen flamed. I believe that what we have been calling an area effect may well be an effect of the nonuniformity of irradiation, which is common to large area sources. Dr. W. D. Weatherford, Jr.: The correlation procedures, employed in the paper, interrelate the various net energy-input (gain minus loss) parameters. On the other hand, the procedures employed by Simms et al. correlate the energy-input parameters with the energy-loss parameters. Consequently, the correlations of this work cannot be compared directly with those of Simms.

The important point of agreement between our work and that of Simms is the clear demonstration that a constant (r r Bi2)-type parameter defines the transient flaming threshold for thermally thick slabs; whereas, a (z'Bi)-type parameter identifies the sustained flaming threshold for thermally thin slabs. As illustrated in Fig. 9, a constant temperature criterion yields the simple relationships for these limiting cases given by Eqs. (4) and (5) in Simms' discussion. On the other hand, these calculated results of this work also provide information on intermediate cases. As noted by Simms, our discussion of his fixed temperature criterion did not specifically point out that, although his correlations involve the surface temperaturefor thermally thick slabs, they utilize the mean slab temperature for thermally thin slabs. Because the internal temperature gradient is approximately linear for thermally thin slabs, a constant mean temperature criterion in this case should also reflect a constant, but somewhat higher, surfacetemperature criterion.