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United States Department of Agriculture Review of Forest Service Forest Information Products Laboratory Related to the Research Note FPL-0145 Issued 1966 Charring Rate of Wood

Slightly Revised 1980 SUMMARY

Buildings constructed with heavy timber for posts, beak, girders, and flooring have often proven themselves fire resistant because of the slow rate of charring and loss of strength of wood under fire exposure. However, much of the information relating to fire endurance of such construction is empirical in nature. To remain competitive with other construction materials more precise data should be obtained upon which to design and predict fire endur­ ance of wood assemblies. A long-range program to obtain these data is proposed as part of the fire research studies at the U.S. Forest Products Laboratory.

A research program was established in cooperation with the National Forest Products Association to determine the charring rates for wood and the effect of temperature, species, density, moisture content, and grain direction on these rates. The literature review presented here was made as an initial part of that study. Information is summarized on the mechanism of thermal degrada­ tion of wood, properties affecting rate of , models and measured rates of char development, and heat liberation during of wood. Related studies on the mechanism of thermal degradation of plastic polymers and analytical degradation models are also summarized. Contents

Page

Nomenclature ...... ii

Subscripts ...... iv

Introduction ...... 1

Studies on Degradation of Wood to Char . . . . 2 Mechanism of Degradation to Char ...... 2 Comparative Char Resistance of Wood Species ...... 6 Models of Char Development ...... 6 Measured Rates of Char Development . . . . 14 Properties Affecting Rate of Degradation to Char ...... 21 Heat Liberation and Absorption During the Combustion of Wood ...... 29

Studies on Degradation of Other Polymers to Char ...... 32 Mechanisms of Degradation to Char . . . . . 32 Degradation Models ...... 36

Summary of Findings ...... 45

Literature Cited ...... 46

Appendix ...... 54

FPL-0145 Nomenclature

Symbol Description Dimensions

A frequency factor, a material constant 1/sec.

a,b proportionality constants ------3 C molar concentration g.-mole/cm.

Cp specific heat at constant pressure cal./g. C.

E cal./g.-mole

F latent heat of fusion cal./g.-mole

f numerical coefficient ------

H cal./mole 2 h heat transfer coefficient cal./cm sec. °C.

J Joule's mechanical equivalent of heat ergs/cal.

K Arrhenius rate constant 1/sec.

k thermal conductivity cal./sec. cm. °K. 2 m mass g. sec. /cm ¶m m rate of mass change g. sec./cm. ¶t n unit outer normal to closed volumetric surface ------2 q heat flux cal./cm. sec.

R gas constant cal./deg. g.-mole

S surface ------

s char or melt layer thickness cm.

FPL-0145 ii Symbol Description Dimensions • s charring rate (¶s/¶t) cm. /sec.

T temperature °C.

t time sec. 3 V volume cm.

v rate of char formation ------

mass average velocity cm./sec.

absolute velocity cm./sec.

W mass weight g.

W net rate of material depletion or production g./sec.

X material coordinate ------2 a thermal diffusivity cm. /sec.

D change in enthalpy, heat of combustion cal./g.-mole

D time period ------

e emissivity ------3 r density or specific gravity g./cm. 2 4 s Stefan-Boltzmann constant cal./sec./cm/ /°K

f fraction of material ------

FPL-0145 iii Subscripts

Symbol

c char

D dry

d decomposed material

dp depolymerization f fusion

g gas

i initial condition

n index integer

o initial condition (t = o)

P plastic or polymer

r residue

u unreacted

W wet

w surface

FPL-0145 iv REVIEW OF INFORMATION

RELATED TO THE CHARRING RATE OF WOOD

By

E. L. SCHAFFER, Research Engineer

1 Forest Products Laboratory, Forest Service U.S. Department of Agriculture

Introduction

Wood is known to have low mass density and relatively low heat conduction properties. The char layer that is formed when wood is exposed to fire further lowers the effective heat transfer properties. Therefore, when massive wood sections, posts, beams, girders, and flooring are exposed to fire, these prop­ erties control the rate of char penetration or, equivalently, the temperature rise resulting in degradation of the wood at interior points.

When a single massive section of wood is exposed to fire until sustained flaming exists on the surface, the combustible volatiles just below the wood sur­ face provide the . However, as the surface acquires a thicker layer of char, the amount of heat transferred by surface flaming decreases as the liberation of volatiles decreases. In proportion to char depth and decreasing heat transfer, the amount of volatiles liberated from the uncharred wood then decreases until flaming stops. Hence, for the continuous degradation to char of a massive wood section, another source of impinging fire is required. This phenomenon is evi­ dent in the difficulty of burning large logs in a fireplace without sufficient kindling material.

The depth of char on a massive wood section under continuous exposure to fire increases until the char layer itself begins to degrade at the surface. The thickness of the char layer is not of prime interest, but it influences the dimen­ sional rate at which the solid wood underneath is converted to char.

1 -Maintained at Madison, Wis., in cooperation with the University of Wisconsin.

FPL-0145 The rate at which the cross-sectional dimensions of a wood structural mem­ ber decrease is of paramount interest in determining its load-carrying capacity. Of further interest, of course, is the effect of the transferred heat and moisture on the strength properties in the noncharred section.

The rate at which polymers degrade to char is an important consideration in the space program. Nose cones of rockets are covered with a low thermally con­ ductive, but degradable material which acts as an insulative barrier for protec­ tion of instruments housed within the cone during leaving and reentering the earth's atmosphere. In order to provide enough insulation under this high- temperature exposure, the rate at which a material degrades to char must be known, and much has been accomplished in characterizing polymeric materials for this application. Much of the theory and information developed concerning the thermal degradation of polymers can also be applied in the study of the ther­ mal degradation of wood.

This report summarizes what has been published in the literature about the combustion of wood and the rate of char development in both wood and other polymeric materials. A related report2 discusses experimental results and analysis of charring rates of wood investigated at the U.S. Forest Products Laboratory in cooperation with the National Forest Products Association. Studies on Degradation of Wood to Char

Mechanism of Degradation to Char 3 Hawley (23) and others present a simplified description of the mechanism of the combustion of wood. The combustion of wood is usually initiated by destruc­ tive distillation of the wood, which produces both combustible and incombustible volatiles, and nonvolatile combustible . The actual combustion of the wood becomes the combustion of the products of this initial distillation. If com­ bustion on the surface of the wood continues, four degradation zones within the wood and parallel to the exposed surface may be described (13).

Zone A, initial temperature to 200° C. (392° F.).--Wood begins to lose the water of constitution at about 105° C. (221° F.) (57). Weight loss proceeds slowly as nonignitible gases are liberated (19). The wood lignins and hemicellu­ loses undergo glassy transitions at temperatures ranging from 130° to 190° C. depending upon the moisture available, as water uptake lowers this transition temperature (20).

2 Schaffer, E. L. 1967. Charring rate of selected woods--transverse to grain. USDA FS Res. Pap. FPL 69. Forest Prod. Lab., Madison, Wis. 3 Underlined numbers in parentheses refer to Literature Cited at the end of this report. -2- FPL-0145 Zone B, 200° to 280° C. (392° to 536° F.).--Decomposition of hemicellulose begins at 200° C.4 Hydrolysis of cellulose and of lignin and cellulose follow in order. These reactions may be exothermic or endothermic depending upon the amount of oxygen present; a trace of oxygen may convert endothermic processes to exothermic ones. Figure 1 shows the nature of the combustion process in wood within this range in both an oxygen and a nitrogen atmosphere. 3 Wood cellulose softens at temperatures between 200° to 240° C. and this point is not markedly affected by the presence of moisture. Cellulose and hemicellulose darken simultaneously with the onset of cellulose softening, and weight losses of between 26 and 39 percent (average 35 percent) indicate that pyrolysis occurs here (20).

Zone C, 280° to 500° C. (536° to 932° F.).--Tang 4 further indicates that a small wood specimen will rapidly begin to lose weight above 280° C., and if oxygen is present in the wood, the process will be highly exothermic; the peak of the exo­ therm being reached at about 315° C. (600° F.) (fig. 1). Hawley (23) generally describes the range from 280° to 320° C. as the area where wood undergoes destructive distillation. Gases pour forth from this zone toward the surface. If liberation is rapid enough, these gases will blanket the wood surface, thereby excluding oxygen and protecting the charcoal from burning oxidation; charcoal is therefore left to accumulate. The accumulating char will delay attainment of the exothermal point in the wood beneath, due to its lower thermal conductivity as compared to wood (13, 24).

Zone D, above 500° C. (932° F.).--At 500° C. (incipient red heat) the charcoal glows and is consumed (13). When surface temperatures rise somewhat beyond 1,000° C. (yellowish-red heat), is consumed at the surface as rapidly as the reaction zones penetrate into the piece (13, 40).

Surface ignition and charring of the surface have been observed to occur simultaneously, and hence ignition temperature and charring temperature can be used synonymously.

Bamford, Crank, and Malan (5), in a series of experiments on slabs of wood, exposed the surfaces to high irradiance levels and applied a pilot flame to the surface until the flames began to spread. They observed that ignition occurred at a nearly fixed temperature. Prince (45) exposed 1-1/4- by l-1/4-inch wood blocks to constant furnace temperatures between 180° C. (356° F.) and 430° C. (806° F.). He observed a variation in the time required for a pilot flame to

4 Tang, W. K. The effect of inorganic salts on pyrolysis, ignition, and combustion of wood, cellulose, and lignin. 1964. Ph.D. thesis, Department of Chemical Engineering, University of Wisconsin, Madison. FPL-0145 -3- M 113 163 Figure I.--The combustion of wood and charcoal as determined by differential thermal analysis, according to Tang (footnote 4).

Heating rate: 12° C. per minute by conduction and convection

Atmosphere : Oxygen and nitrogen at atmospheric pressure ignite gases liberated from the blocks. At 430° C. (806° F.) less than 1/2 minute was necessary, but at 180° C. (356° F.) 15 to 40 minutes were required for ignition. No observation was made of the surface temperature upon ignition, however. Tang (footnote 4, p. 3) used a thermogravimetric balance to determine the ignition temperature of small samples (0.20 - 0.40 grams) of ponderosa pine. Oxygen was supplied at 90 milliliters per minute, atmospheric pressure was maintained, and samples were subjected to different heating rates (from 6" C. to 30° C. per minute). Ignition temperatures obtained were nearly constant (287° to 294° C.) and are shown in table 1. One notes that, according to the previously described temperature zones in the combustion of wood, the wood begins to be destructively distilled to char at this temperature level.

Table 1.--Ignition characteristics of ponderosa pine1 .

FPL-045 -5- Comparative Char Resistance of Wood Species

Bryan and Doman (l4) compared the char resistance of about 70 species. Specimens were 1/2 inch thick and exposed to a gas flame until burnthrough occurred, the time to burnthrough being the criterion of resistance rating. They found that, of the common American species, the order of decreasing resistance is as shown in table 2.

A measure of rate of char development was also obtained by Baker (4, pp. 26-29) by exposing small simply supported beams (1/2 by 1/2 by 6 inches) of mainly Australian species to an enveloping flame while the beam was subjected to a con­ stant knife edge load of 448.84 grams (15.71 ounces) at center span; the end of the test was the time at which the load fell. By this method he was therefore including the effect of fire on strengthin addition to wood degradation. His results, in minutes, are tabulated in descending order of resistance in table 2, also. A definite difference exists between the results of Baker and those of Bryan and Doman because of the different experimental methods.

Work at the U.S. Forest Products Laboratory on 10 American species of 1-inch-thick vertical boards, exposed to ASTM E-119 fire conditions (3) (fig. 2), was done in 1936. One side of the board was exposed to these open-gas-flame temperatures until flaming appeared on the unexposed side. The average rate of burnthrough by this method for the 10 species is given in order of descending resistance in table 2 as well.

Models of Char Development

The first comprehensive treatment in attempting to describe the combustion of wood was given by Bamford, Crank, and Malan (5) in 1946. They proposed that the temperature distribution within a thermally decomposing body could be obtained by solving the heat conduction equation with an added term for heat evolution in the material. This equation is:

(1)

where

(2)

FPL-0145 -6- Table 2.--Char resistance of selected species

FPL-0145 -7- Figure 2.--ASTME-119 time-temperature curve (3).

M 28856 F and k =thermal conductivity Cp =specific heat at constant pressure W =weight of volatile products per cubic centimeter of wood q =heat evolved at constant pressure per gram of volatile products formed E = R =gas constant T = absolute temperature t =time A =frequency factor

Equation (2) is a first-order Arrhenius reaction equation (16) to tie the rate of combustion to the volatile concentration W at time t and absolute temperature T (see Appendix). They (5) further investigated the solution of the modified heat conduction equation (1) for a plate of thickness 2L subjected to flames at both faces. For the heat transferred from the flames to the surface, they suggest that the total heat transferred is a sum of three terms:

A forced convection term of form h(T - T ), where h is a heat transfer (a) f o coefficient, T is the flame temperature, and T is the surface temperature. f o

4 (b) Radiation from flames of form se T , where e is the emissivity of the f flame and s is Stefan-Boltzmann constant. 4 Radiation loss from surface of form s T , assuming the wood to radiate (c) o as a black body.

Combining the three, the total heat transferred to the surface H(T ) is: o

(3)

Equation (3) can be utilized in prescribing a boundary condition at the surface for the solution of the heat conduction equation (1) of:

(4)

FPL-0145 -9- In substituting the Arrhenius reaction equation (2) into (1), they assumed the following values for the constants.

E = 33,160 (calories per mole) 8 k = 5.3 x 10 (per second) q = 86 (calories) Wo =0.375 (grams per cubic centimeter) R = 1.987 (calories per gram-mole per °K)

No consideration is included in equation (1) for the effect of moisture diffusion in the exposed wood, and hence a solution to this equation for temperature distri­ bution could possibly only apply to ovendry wood.

Squire and Foster (55) recognized that the main physical problem in the development of a theory to describe the burning of wood is the boundary condi­ tion at the burning surface. Rather than utilizing equation (4) to describe this boundary condition, they proposed a relationship of the form:

(5) where DH =heat of combustion f =numerical coefficient

This was preferable to equation (4) because it takes into account that the flame is, in fact, supported by flammable gases liberated by the wood decomposition and that heat input from the flame affects the rate of decomposition. The coeffi­ cient f represents the proportion of heat liberated in the flame that is returned to the wood. In this work and subsequent work by Squire (56) and Weatherford (66, 67) analytical analyses of the heat-conduction equation (1) are applied to the ignition and sustained flaming of wood.

It is important to recognize that the first-order Arrhenius reaction of equa­ tion (2) assumes that reactant concentration W affects the rate of decomposition. Adler and Enig (1) state that in exothermic reactions in which the heat of reaction is relatively small, such as occurs in the burning of wood and similar cellulosic materials, the assumption of constant reactant concentration cannot be made.

Stamm (58) analyzed data that MacLean (36) obtained in heating southern pine, white pine, Douglas-fir, and Sitka spruce for different periods of time. Speci­ mens were 6 inches along the grain and 1 by 1 inch in cross section. He plotted

FPL-0145 -10- logarithms of residual weight against heating time and found a linear relation­ ship. This indicated that weight loss followed a first-order reaction. The activa­ tion computed were about 16,000 calories per mole. This is almost one-half the values (29,500 calories per mole) obtained on very thin specimens (1/16 inch thick). Stamm described the reaction as taking place at the surface of the solid, and because so many different reactions take place simultaneously, the effective reaction is heterogeneous.

Tang (footnote 3, p. 3) utilized a two-stage general equation, suggested by Martin (39) to describe the weight loss of thin veneers under differing tempera­ tures:

(6) and where W = residue weight of sample at time t r W =weight loss at completion of reaction d W =weight loss at time t K = Arrhenius rate constant

He termed the kinetic reaction as pseudo-first-order homogeneous because of the possible complexity of the reactions that occur. The two rate constants K 1 and K are distinctly shown by the differing slopes in figure 3 with inflection 2 occurring at 325° C. (616°F.). 7 The first stage is in the range 280° C. < T < 325° C. with A = 1.93 x 10 1- 1 (per minute)-- E = 23 (kilocalories per mole), and the second stage is in the range 325° C. 1 8 < T < 350° C. with A = 3.92 x 10 (per minute)-- 2 2 E = 54 (kilocalories per mole). 2 The samples used in all of the preceding theories are assumed to be small so that (a) they decompose uniformly and (b) the solid- to-gas reactions are localized without steep gradients for diffusion of heat or mass transfer into them. In the case where samples are not small, such as those used by MacLean (36),

FPL-0145 -11- Figure 3.-- for pseudo-first-order kinetics of pyrolysis of wood, a-cellulose, and lignin (from thermogravimetric analysis and rate of weight loss data; Tang. footnote 3, p. 3). differences in the application of kinetic theory to the same material may be observed in experimental results. Generally, in solid-state reactions the con­ cepts of concentration and order of reaction have no significance. The reaction velocity is here defined as the change with time of the layer thickness of prod­ uct formed, or of the weight of this layer, or of the number of gram equivalents of product formed. Consequently, a rate constant K cannot be defined in the same way as for reactions in gases and solutions. If one accepts the same conditions as for gas reactions, K must be independent of time, have the factor per second in its dimensional formula, and increase exponentially with temperature. An activation energy for the reaction can thus be derived (18), and the K is of the Arrhenius form:

(7)

Blackshear (10) states that the rate constants K and activation energies E in equations (6) and (7) can be affected by changes in the structure of the combus­ tion region, the thickness of the various zones, and the temperature profile. Hence, he continues, it is reasonable to assume that given a long slab of mate­ rial with fixed boundary conditions (i.e., (a) final combustion temperature and combustion product composition and (b) initial temperature and composition), there must exist a characteristic solution to the problem. Although the charac­ teristics of the combustion zone change with time during the transient period after ignition if the boundary conditions are held constant, the system must ultimately come to steady state in which none of the properties change with time in a coordinate system which is stationary with respect to the wave of heat. When this situation is established, constants in the Arrhenius expression describe the physical situation. These constants are empirical and have to be experimen­ tally averaged to describe the combustion process. Blackshear indicates finally that it would be possible to represent the burning rate per unit area by a single equation of the form

where T is some characteristic temperature of the system, such as the surface temperature, and A is a material parameter. Both E and A are suggested to be time dependent.

FPL-0145 -13- Vorreiter (65) and Lawson, et al. (34) indicate that the char depth, s, can be described by

(8) where t is the duration of fire exposure. Vorreiter further links the material constant a to the specific gravity, r, of the wood by

where r is the char specific gravity and approximately equal to 65 percent of c the inital specific gravity of the wood.

If equation (8) is differentiated with respect to time t, the rate of char forma­ tion is time dependent as well and is given by:

(9)

Measured Rates of Char Development

Lawson, et al. (34), found that spruce timber beams 1-1/2 to 2 inches in breadth under fire exposure initially charred rapidly, having an average rate of 1/30 inch per minute during the first 5 minutes. As the char built up, however, the rate was reduced to 1/50 inch per minute after 30 minutes' exposure.

The moisture content of the sections was 12 percent, and the results of the tests indicated that the rate, v, could be adequately described by the equation

in the range 5 < t < 30 minutes, where t is the exposure time. At the inter­ mediate times the rate can be seen to be .025 inch per minute (1/40 inch per minute) and would represent the slope of a straight line through the char depth- time graph of their experimentally obtained data.

FPL-0145 -14- In addition, it has been reported (22) that the rate of burning, which is assumed to be the rate of char development, of wood slabs heated on one face at three 2 different intensities of radiation (0.5, 0.7, and 1.0 calories per centimeters per second) appears to be uniform for a period after initial degradation.

Jean (28) attributes the increased rate of degradation to char at initial expo­ sure to the violent .thermal shock. In experiments, he observed that the first few millimeters are destroyed within 2 to 3 minutes after ignition, and it is only after 4 millimeters (5/32 inch) char depththatthe rate of carbonization becomes regular. Fire exposure was applied according to the equation:

(10)

where t =minutes T =temperature (°C.) To =initial temperature (°C.)

It was concluded in experiments on 1-inch-thick southern pine boards at the U.S. Forest Products Laboratory in 1936 that, with the exception of the first 5 minutes of fire exposure [ASTM E-119] (3), the rate of char development appears to be constant. This behavior can be seen in figure 4 in which the aver­ age depth of char is plotted against exposure time. An important additional result, indicated in the curves of figure 4 for both the accumulated weight loss and weight of charcoal produced, is that their rate of change is apparently con­ stant after the initial 10 minutes of exposure. This indicates the possible exist­ ence of a direct tie between dimensional char development and mass loss of wood under fire exposure. Rates of char development in other 1-inch-thick species exposed in the same way are included in table 2.

In another experiment conducted at the U.S. Forest Products Laboratory (60) on laminated 2- by 8-inch nominal Douglas-fir planks, a uniform rate of carboni­ zation (or char development) was also observed, after an initially higher rate, during fire exposure applied according to the ASTM E-119 (3) time-temperature curve (fig. 2). This uniform rate was on the order of 1.54 inch per hour (.0652 centimeter per minute). Figure 5 illustrates the temperature distributions within this laminated section for various times; charring temperature is assumed to be about 550° F. It can be shown that the exposure temperatures described by Jean in equation (10) are not very different from those of the ASTM curve, and hence the uniform rates of Char development under the two fire condi­ tions are realistic.

FPL-0145 -15- M 130 380 Figure 4.--Maximum char depth, accumulative weight loss, and weight of charcoal produced under fire exposure (ASTM E-119) of one surface of I-inch-thick southern pine boards.

Average dry specific gravity » 0.585 Average moisture content » percent Figure 5.--Temperature distribution within 7-1/2-inch-thick laminated Douglas-fir slab versus fire exposure time (60).

M 95832 F Horizontal and vertical wood plates of 1 centimeter thickness and area of 100 centimeters2 were exposed to vertical flames by Vorreiter (65). He found that the char depth development on a horizontal plate exposed from below was greater than that of the vertical plates. One would expect this to be the case from observations of horizontal and vertical structural components after fires.

From experiments on spruce and beech, he developed the following formula for depth of char s on a vertically fire-exposed plate:

where a,b =species constants r = specific gravity of wood r = specific gravity of char c t =duration of flaming (minutes) and for spruce: ρ =0.43 a = 0.345 b = 1.3 for beech ρ = 0.71 a = 0.142 b = 1.8

The above equation indicates the specific gravity of the char was assumed to be 65 percent that of the undegraded wood. Also, there evidently is an error in the interpretation of the above depth of char equation; for example, the depth of 3 char in vertically flame-exposed spruce (r = 0.43 gram per centimeter ) after about 3 minutes is predicted to be 1 centimeter (0.4 inch). This, then, would indicate complete burnthrough of their 1-centimeter-thick plate in 3 minutes, which is quite unlikely.

Dorn and Egner (15) conducted load tests of fire-exposed beams that had cross sections from 3 by 8 inches to 5 by 16 inches. The fire temperatures were con­ trolled in accordance with German Industrial Standard DIN 4102 which prescribes temperatures slightly higher than the ASTM E-119-61 (3) fire conditions. The species for each beam were a combination of spruce and fir initially at moisture content values between 12.5 and 19.0 percent and having specific gravities between 0.445 and 0.475. The average depth of char, measured in the direction of width, after 30 minutes offireexposurewas approximately 0.67 inch (1.7 centi­ meters) with averages for each section ranging from 0.65 to 0.67 inch (1.65 ­ 1.70 centimeters), and approximately 1.58 inch (4 centimeters) after 60 minutes of fire exposure.

FPL-0145 -18- The 1.58-inch depth of char in 60 minutes closely parallels the 1-1/2-inch­ per-hour char development rate cited by others for large sections. However, the depth at 30 minutes would indicate a rate of char of 1.34 inch per hour if only one surface had been exposed to fire.

The average depth of char measured in the height direction was somewhat greater, being between 0.65 and 0.74 inch (1.65 - 1.90 centimeters) after a 30-minute exposure and about 2.5 inches (6.25 centimeters) after 60 minutes of exposure.

Imaizumi (25) subjected loaded laminated beams of Yezo spruce (Ajau Fichte. Picea jezoensis Carr.) to fire exposure temperatures prescribed by Japan Industrial Standard JIS-1301 which develops temperatures slightly below that of ASTM E-119-61 (3) conditions at any given time. The beam dimensions were about 7.1 by 17.1 inch (18.0 by 45 centimeters) with an average dry specific gravity of .408 and average moisture content of 12.8 percent. After a 30-minute exposure, average reduction in the dimensions of the cross-section was recorded. These reductions corresponded to rates of char development of 1.42 inch per hour (3.6 centimeters per hour) in the width dimension and 1.89 inch per hour (4.8 centimeters per hour) in the height dimension.

The depth of char on timber beams (1-1/4 to 2 inches thick) was plotted versus exposure time in a British Standard fire-resistance test from data given by Lawson, Webster, and Ashton (34). The mean line corresponded to a rate of char development of about 1/40 inch per minute and was proportional to the rate of weight loss. Webster and Ashton (68) found during fire-resistance tests of different species and thicknesses (1/2 to 2 inches) that the probable char develop­ ment rate was 1/40 inch per minute.

Short-time exposures to fire (ASTM E-119) of 1.87- by 3.62-inch Douglas-fir sections by Schaffer4 indicated a rate of 1/30 inch per minute (fig. 6). The fact that this rate is greater than in the preceding investigations (34, 68) may be attributed to two-dimensional exposure of a relatively small section.

In experiments to determine the variation inthermal conductivity and diffusiv­ ity of wood near burning temperatures, Midgeley (42) observed that the char layer thickness essentially reached a constant value after 19 minutes of expo­ sure to a heater at 600° C. (1112° F.), table 3. This was observed for specimens of air-dried ash (Fraxinus excelsior) and larch (Larix spp.). When the thickness of charcoal consumed was added to the char layer thickness for the duration of

4 Schaffer, E. L. The effects of fire on selected structural timber joints. 1961. M.S. thesis, Department of Civil Engineering, University of Wisconsin, Madison.

FPL-0145 -19- Figure 6.--Char depth versus fire exposure time for a 1.87- by 3.62-inch Douglas-fir sec­ tion (Schaffer, footnote 4, p. ). Fire exposure was in accordance with ASTM E-119 (3). the 1,068-minute exposure test, it was apparent that the total amount of wood degradation had increased very slowly in the 38- to 360-minute period. Of par­ ticular note during this same period was the fact that the char layer increased slightly in thickness while the amount of charcoal consumed remained constant. Hence, she concluded that after 38 minutes of exposure, a well-developed heat flow barrier was created and it was only after this was degraded that char development could continue.

In all of the tests described, no attempt was made to correlate char resistance to any other wood properties excepttheorientationof the rings and wood density, which appeared to have some significance.

Table 3.--Depths of burnt material in ash-wood cylinders (42)

Properties Affecting Rate of Degradation to Char

As indicated by the studies of Vorreiter (65) in the preceding section, the density (specific gravity) of wood seems to have a pronounced effect on the depth of char produced for a given duration of fire exposure.

FPL-0145 -21- Four possible parameters may control the rate of burning of cellulosic materials (22). These parameters are:

(a) Density (b) Permeability along the grain (c) Moisture content (d) Thickness

Thermal conductivity was also expected to be important, but it is largely deter­ mined by the density.

Permeability along the grain may be over 10,000 times that across it, so that in a one-dimensional test in order to prevent the escape of vapor anywhere but through the heated face itself, the thickness must be somewhat greater than one- thousandth the width or length of an exposed specimen. In boards of fir or pine, and Parana pine of different thicknesses and moisture content levels exposed to different intensities of radiant heat, the rates of burning (as measured by weight loss) were proportional to density and less dependent on moisture content in the 0-30 percent range than might be expected. The lateral dimensions of the speci­ men were not given, and the effect of thickness appeared to be small over the range of 0.6 to 5.0 centimeters (0.25 to 2 inches).

The rate of the weight loss-to-density ratio increased with increasing perme­ ability along the grain. Specimens (2.5 centimeters thick) of a highly permeable wood, Abura, and a highly impermeable wood, Makore, which have very different charring rates but approximately the same densities, were sealed on all surfaces except the heated one and exposed to intensities of radiation of 0.5 and 1.0 2 calories per centimeter per second. The rates of charring of both woods were reduced and the difference between them was reduced, but not eliminated (21, 22).

The preliminary result that the effect of thicknesson char rate over the range of 0.6 to 5.0 centimeters (0.25 to 2 inches) appears small is quantitatively supported by Akita (2). By recording the temperature distribution in wood boards, he found that the char layer is not dependent upon the board thickness if the board is thick enough. Coupling this with other findings (22), one can assume that the effect of thickness of the specimen is negligible for thicknesses greater than 1/4 inch.

Recognition of the effect of wood density and mass on resistance to char has been utilized in heavy-timber construction for many decades (62). An example of such construction for fire resistance is shown in figure 7.

FPL-0145 -22- Figure 7.--Heavy timber or mill-type construction is commonly used when fire resistance is desired (62).

M 93575 F Work at the U.S. Forest Products Laboratory in 1936 on 1-inch-thick speci­ mens of southern pine subjected to ASTM E-119 fire exposure conditions indi­ cated that density or annual rings per inch have little or no effect upon rate of char development. From rate data on white oak (table 2), a marked influence of ring orientation was observed. A higher rate of char development was observed when the rings were oriented parallel to the exposed face (1.62 inches per hour) than when they were oriented normal (1.39 inches per hour). An orientation at 45° to the exposed face showed a rate (1.50 inches per hour), midway between the two orientations.

According to Hawley (23), moisture content values on the order of 50 to 100 percent are effective in retarding the rate of combustion because of the large amount of heat required to evaporate the water. At low concentrations moisture still retards combustion; a fire burns noticeably faster in wood at 10 than at 20 percent moisture content. He further states that low specific gravity will speed combustion partly because of more rapid heat penetration and partly because it gives a greater surface area per unit weight.

The influence of moisture can be observed even in initially dry material freely burning in air. This phenomenon was noted by Blackshear and Murty (9) during the burning of dry-pressed cellulose cylinders up to 2.5 inches in diam­ eter. Because water and other condensable vapors are produced by the pyrol ­ ysis process in cellulose, some of thevapordiffuses into the solid and condenses while the rest leaves through the surface. The migration, condensation, and subsequent regasification as the material degrades had a pronounced effect on the temperature-time histories on the interior of the cylinder. For example, in figure 8 the temperature-time history for one cellulose cylinder indicates a “dwell” in temperature at 100° C. after 6 minutes of burning at depths below the degrading surface of 0.535 inch. This dwell can be attributed to the regasifica­ tion and forced diffusion of moisture existing at these points. Blackshear and Murty term this a “thermostatic effect.”

A second observation from their work (9) was that the burning rate, as meas­ ured by rate of mass loss, depended upon the diameter of the cylinders. A log- log plot of their data is shown in figure 9 and indicates a relatively linear rela­ tionship. A slight effect of cylinder orientation can be noted in the assumed functional relationship, but this requires more data for verification. Of particu­ lar interest was the observation that in almost every specimen studied, the burning rate remained nearly constant after ignition for approximately one-third the total burning time. The initial (maximum) mass loss rate was proportional to the initial diameter d of the cylinder as well: i

FPL-0145 -24- Figure 8.--Temperature-time histories of various locations in a burning 2.5-inch-diameter cylinder, according to Blackshear and Murty (9). Figure 9.--Dependency of mass-free burning rate on diameter of dry cellulose cylinders, according to Blackshear and Murty (9). where m is the initial mass of the cylinder. i Another observation from their work (9) was that the rate at which temperature Ti (the temperature at which cellulose gasifies) propagates into the cylinder under constant flame temperature can be expressed proportionally as:

where ri is the initial radius and D is the distance from the cylinder surface at which the flame effectively burns. This distance, D, would be similar to the thickness of the gaseous boundary layer around the cylinder.

Shorter (53) attributes load supporting failure of prestressed concrete beams under fire exposure to spallation of the concrete. The base material would then be inadequately protected by the surface material. In similar fashion, if char is spalled from a fire-exposure surface due to thermal stress rupture, then the insulative value of the char layer is reduced. This leads to an increased rate of char development.

Truax (60) reports that in a 7-1/2-inch-thick laminated Douglas-fir section exposed to fire, temperature characterizing the base of the amorphous char layer was 550° F. (288° C.) after 20 minutes' exposure (fig. 5). An estimate of temper­ ature at the base of the char layer before 20 minutes of exposure varied from 615° to 550° F. This was termed the charring temperature. Therefore, the more rapidly this point is raised to this temperature the more rapid will be the rate of char development. Hence, exposure temperature will be of importance if char thermal properties are relatively constant.

Simms (54) points out several experimental studies which conclude that char­ ring occurs at a point in a solid when the temperature at that point reaches a certain fixed value. Work by Williams (70) substantiates this; he assumed that charring occurs at a fixed temperature and found an adequate correlation between his measured and predicted depths of char for short exposure times. 5 E.K. Lawrence also concluded that this fixed charring temperature criterion was sufficient in ignition prediction and that the rate of production of volatiles is not a critical factor here.

5 Lawrence, E. K. Analytical study of flame initiation. 1952. M.S. thesis, Department of Engineering, Massachusetts Institute of Technology, Cambridge.

FPL-0145 -27- The char formed during the combustion of wood is fissured, contains zones in various states of decomposition, and hence is a heterogeneous material. The fissures that occur govern both volatile release and heat transfer, thereby affecting the rate of degradation of woodtochar. Earlier work at the U.S. Forest Products Laboratory on 1-inch-thick boards, however, showed the char base to be quite uniform in location in denser woods (such as red oak and maple) but with woods (such as the pines and basswood) the char depth was slightly deeper at the base of fissures in the char.

Wolgast (71), in a discussion of the surface flammability of wood, recognized that decreasing thermal conductivity coefficients in wood are directly due to increasing void volume. Increased void volume speeds flame spread because of localized overheating and simultaneous heat accumulation at the solid lattice. If the term ‘thermal degradation” is analogous to “flame spread” then one should be able to assume that the volumetric rate of degradation will increase with increasing void volume as well. Stamm (59) shows that the percent voids in wood are related to the dry specific gravity and mass of the wood solids by the equation:

where ρ =dry specific gravity (moist volume basis) 1.46 = specific gravity of extractive-free wood solids

The heat capacity of the wood solids can be assumed constant for any wood, which means that the more mass available to absorb heat energy, the slower will be the degradation. Mass, of course, is directly proportional to the specific gravity of the wood.

In a kinetic study of the thermal decomposition of wood, Wright and Hayward (72) found that the decomposition rate for disks cut across the grain was approximately twice that for disks cut along the grain. Exposure temperature was 600° C. (1112° F.). The reaction rate was substantially the same for both cedar and hemlock, which suggested that the factor which controls the overall rate of the decomposition reaction is not the chemical composition of the wood, but rather a physical characteristic.

Combustible volatile content is linked to spread of flames on a material (23), and may therefore influence as well the rate of char development.

FPL-0145 -28- In summary, the following wood properties may influence the rate of char development under fire exposure and should be considered (a) density (specific gravity), (b) thermal conductivity, (c) moisture content, (d) permeability, (e) ring orientation, (f) thickness of specimen, (g) charring temperature, (h) com­ bustible volatile content, and (i) char layer characteristics (thickness, fissure depths and widths, permeability, and thermal conductivity). Also environmental conditions such as exposure temperature and type of heat source may influence the rate of char development.

Heat Liberation and Absorption During the Combustion of Wood

The heat of combustion of wood is determined by the complete pyrolysis in an oxygen atmosphere of small, dry wood specimens. Heats of combustion for various species determined in this way are given in table 4 (44,47,31). Except for differences in the amount of lignin and ash and in the amount of composition of extractives, little variation is to be expected in the fuel value of different species (23). Conifer softwood resins have been found to have heats of combustion as high as 17,500 B.t.u. per pound (11). Generally, one finds the range in heats of combustion of hardwoods from 8,300 to 8,700 B.t.u. per pound, and that of softwoods between 9.000 to 9,700 B.t.u. per pound. These heats are based upon ovendry wood (11).

Moisture in wood requires heat for evaporation and therefore decreases the total heat available to the wood. Heats of combustion of moist wood are, therefore, lower than. those of dry wood. A linear correction may be applied to heats of combustion of moist wood to determine dry heat of combustion values.

An approximation of the heat of combustion of moist wood knowing its dry heat of combustion is given by (43):

where ∆H =dry heat of combustion d M.C. = moisture content of wood (percent) ∆H = moist heat of combustion and is shown in figure 10 as the lower curve (23). The heat of combustion reduc­ tion on a moist wood weight basis is shown in the upper curve of figure 10.

FPL-0145 -29- M 130 370

Figure I0.--Relation between moisture content and heat of combustion of wood, according to Hawley (23). Table 4.--Heats of combustion of common wood species (44,47,31)

FPL-0145 -31- In the incomplete pyrolysis of wood only a portion of the heat indicated by heat of combustion is released. A clear example of this is the pyrolysis of wood to charcoal. Browne and Brenden (12) partially pyrolyzed small ponderosa pine specimens to specific weight loss (volatization) levels in a thermogravimetric balance. This degradation under temperatures between 240o and 822° C. was done in a nitrogen atmosphere. The residual specimens were then pyrolyzed in an oxygen bomb calorimeter to determine the heat of combustion. (The degrading temperature did not influence the results.) They utilized the equilibrium expression:

where ∆ H is the heat change of the individual reactions. C The heat of pyrolysis ∆H pyrolysis was found to be less than 5 percent the heat of combustion by Klason (31) and Tang (footnote 3, p.3). Roberts (46) reports this quantity as 60 calories per gram, hence, it was neglected. This left:

Utilizing this equation and the experimental data, Browne and Brenden deter­ mined the heat of combustion of released volatile products for many levels of volatization as shown in figure 11. From this experiment, the heat released in the pyrolysis of wood can be estimated.

Studies on Degradation of Other Polymers to Char

Mechanisms of Degradation to Char

The necessity of thermal insulation on the nose cones of rockets to protect delicate instruments during exit and reentry into the earth's atmosphere led to extensive work on the analysis of many polymers under this exposure. Israel (26) provides a comprehensive annotated bibliography on progress in this area to about May of 1964. He also suggests other earlier bibliographies that may be of help to individuals interested in investigating this area more completely.

The protection of structures in an environment of high thermal flux can be accomplished by blocking some of the thermal input (i.e., reducing the severity of the environment), radiating a large amount of thermal energy from the surface, storing thermal energy by a temperature rise of the body, moving thermal

FPL-0145 -32- M 127 604

Figure 11.--Heat of combustion of released volatile products (percent of total heat) as function of degree of pyrolysis (volatilization) for ponderosa pine (12). energy to other locations by a temperature rise of some transpiring fluid, or dissipating thermal energy by chemical or physical spalling of the surface. The most practical method, and the most applicable one for a wide variety of envi­ ronments, involves the use of a sacrificial covering (i.e., an "ablative" heat shield) to achieve thermal protection (26). It is this method and its analysis which are discussed in this section.

Plastics used as thermally protective materials fall into three basic categories: (a) unreinforced plastics that decompose into gases upon being heated, leaving practically no char; (b) unreinforced plastics that decompose into gases and partly into char, and (c) char-forming plastics incategory (b) that are reinforced with various organic and vitreous (glassy) fibers (52).

Under exit and reentry thermal exposure, an ablative material will have several characteristic physicochemical aspects (50). (A general model for clarification of terminology in this discussion is presented in fig. 12.) Initially, the material acts like a heat sink. Energy absorbed at the surface is conducted into the substrate and stored by the effective heat capacity of the material. Heat penetrates at a slow rate due to the low thermal diffusivity. Consequently, the surface temperature rises rapidly until thermal degradation begins. Organic components of the ablating material are depolymerized or pyrolyzed into various gaseous products, such as hydrogen, carbon monoxide, methane, ethylene, acetylene, water, and various hydrocarbon fragments. These species are injected by diffusion and convection into the adjacent boundary layer, and continually envelop the surface in a layer of "relatively cooler gases." Consequently, the initial temperature and velocity gradient in the boundary layer are altered beneficially. Lapple, et al., (33) state that this is the start of ablation and term the rate at which decomposition products enter the boundary layer as the "ablation rate."

Thermal degradation of the organic material may take place with the forma­ tion of a rigid, nonuniform, and porous carbonaceous material. Gases formed in the substrate pass through this surface char layer, absorb heat, and minimize further internal heat transfer.

As more polymer degrades, the char layer increases in thickness at the expense of the unreacted polymer below it. While the gases pass through the char residue, the char becomes hotter and the degradation vapors are exposed to higher temperatures. As a result, they may experience further degradation or pyrolysis. The char may also undergo additional degradation, either within itself or by interaction with the degradation vapors.

FPL-0145 -34- Figure 12.--Terminology for ablation process (50).

M 130 369

The char continues to grow in thickness until the surface of the char layer itself begins to ablate. Ultimately, the char layer may reach a quasi-steady state in which it assumes a fixed thickness. If such a state is reached, the rate of entry of decomposition products into the gaseous boundary layer is equal to the rate at which the unreacted polymer degrades. The rate of polymer degrada­ tion may be also called the rate of ablation under these conditions.

At very high temperatures, radiation transport becomes an important mechan­ ism of heat transfer between materials and within semitransparent and trans­ parent solids (63, 29). This phenomenon supplements ordinary thermal conduction in transporting energy from hotter to colder regions and must be included when considering materials that melt or vaporize, rather than form a carbonaceous char, when exposed to high temperatures.

Pyrolysis experiments reported by Madorsky and Straus (37, 38) indicate that for many useful materials the thermal degradation of polymers occurs over a narrow temperature range. Hence, Kauzlarich (30) suggests that the primary parameter for typical ablating plastics is simply the effective heat of ablation. This is defined as the ratio of the heat transfer rate at the ablating surface to rate of mass loss.

FPL-0145 -35- Vojvodich and Pope (64) investigated the behavior of a charring material in high-velocity streams of arc-heated air, nitrogen, and argon. Their purpose was to determine (a) whether chemical reactions occur between the material and its environment, (b) whether the reactions are homogenous and/or hetero­ geneous, and (c) what the influence of the reactions is upon the heating rate to the material surface. The behavior of the material proved to be highly sensitive to the composition of the test gas. This problem arises in determining the chem­ ical interaction between an ablation system and boundary-layer flow (fig. 12). It was found, more specifically, that the surface temperature and total mass-loss rate were highly sensitive to composition of the test gas. Char mass-loss rates in argon and nitrogen were comparable, which suggested that the nitrogen is chemically inert and the mechanism of char removal for these gases is mechan­ ical or thermal erosion. The corresponding mass-loss rates were higher in air; hence it was concluded that chemical removal occurred under heterogenous com­ bustion. Surface temperatures were higher in air than in nitrogen for all heating rates.

Degradation Models

As in the combustion of wood, the thermal degradation of other polymers is generally a complex irreversible chemical process that occurs over a range of temperatures.

The most common way to approach the description of the rate of mass loss is to apply the equation of continuity to each phase of the process and then to either assume or determine the kinetics of the gross reactions. Following a notation used by Bird, Stewart, and Lightfoot (8), the principle of conservation of mass is applied to a stationary control volume. This simply is a material species balance equation which states that the rate at which mass is accumulated within the volume equals the rate at which mass is transported out by convection and diffusion plus the net rate of productiondue to . Mathematically stated this is:

(11) where subscript, i, denotes the mass species considered.

FPL-0145 -36- The surface integral can be transformed into a volume integral by the Gauss- Ostrogradskii Divergence Theoremif all functions are continuous and continuously differentiable and the volumetric region is simply connected:

Since the balance volume is stationary, the first volumetric integral can be differentiated by application of the Leibnitz formula yielding:

Combining the last two equations with equation (11) yields:

Because the volume selected was arbitrary, the integrand must be identically zero. Hence, the species equation of continuity is:

(12)

In a polymer being degraded to a gaseous product and char, in which the gases are then the only material diffusing, the rate of change of the polymer can be expressed as:

(13) where i is replaced by thenotationforthe polymer, p. Likewise the rate of mass change of the char (subscript c) is:

(14)

FPL-0145 -37- A number of investigators have employed chemical reaction rates (expressed th as one or more n - order reactions) with Arrhenius temperature dependent rate coefficients to describe the rate at which an active material decomposes. This approach is developed from thermogravimetric analysis experiments on, the particular polymer. When this information is combined with equation (13), two types of expressions are obtained. One type indicates a variable rate that depends upon such factors as the amount of material unreacted or the rate at which temperature rises in the material, and a quasi-steady rate which depends upon such factors as the surface temperature and thermal properties of the material.

Other expressions have been developed which adequately describe the rates of degradation without using Arrhenius temperature dependence coefficients. Con­ sideration of both the Arrhenius form and other form that describe the rate of degradation of polymers follows.

Among the variable rate expressions employing Arrhenius dependence is that of Wells (69). He employs a quite general equation for the rate of density change, as a function of the degrading material's density and temperature only. This equation is the sum of four similar terms, each of which is signifi­ cant in a given temperature range:

(15)

where ρ =density at time t ρo =initial density T =characteristic temperature E. = activation energy i N. = reaction order i A. =material frequency factor i Madorsky and Straus (38) studied the rate of degradation of many plastic materials and found this rate to be closely first order with respect to the chem­ ically active material fraction:

(16)

FPL-0145 -38- where =density fraction of unreacted material. φu This equation can be generated by one term of Wells’ (69) equation with i = 1, N. = 1.0, and i

Lapple (33) recognizes that vaporization at the base of the char layer involves other considerations than just reaction, but that it should be possible to include the vaporization in a first-order Arrhenius-type expression. In employing equa­ tions similar to Wells (69) and Madorsky and Straus (38), he recommends that two terms be included--one covering the reaction of the vapor and the other the vaporization of the solid phase. Hence, a single term equation, such as that of Madorsky and Straus (38), applied to char-forming polymers, utilizes activation energies, E, and frequency factors, A, which are therefore effective average values of the two phases. He further explains that activation energy would be a function of the vapor pressure of the degrading material and that the frequency factor would depend upon char properties. His equation including the effective average activation energy, E, and frequency factor, A, is similar to that of Madorsky and Straus (38):

(17)

Joule’s constant, J, is also included to consider the mechanical conversion of material to heat. Scala (48) assumes that the rate of depolymerization of plastic to char can be expressed by:

which differs from the other expressions shown thus far in that the rate is con­ sidered a function of the difference between the polymer density and char density. Equations of continuity for polymer, char, and gas phases were also used in combination with kinetics of pyrolysis for a variable rate of degradation (17). t The rate of polymer degradationcanbegivenby a single n h- order reaction with Arrhenius rate constant as follows:

(19)

FPL-0145 -39- Combining this with the fact that there is no overall production of mass, i.e.:

then the rate of change of both char and polymer mass can be written as:

(20)

Under certain conditions of heating, quasi-steady behavior in the degrading. polymer may be reached. Quasi-steady behavior is characterized by a constant rate of charring which is reached when heat input and heat dissipated or required for degradation are in balance. This heat required for degradation or dissipation is termed the quasi-steady effective heat of ablation, H , and is defined by eff Schmidt (51) in terms of the charring rate, s, as:

(21)

At the onset of heating, a plastic material responds solely as a heat sink, and a transient heating state will exist for a period

(22)

at which point surface recession is stabilized. Increasing the heating rate thus decreases the time required to reach steady-state ablation (49 ,51).

When the quasi-steady charring rate, s, is reached, this rate may be deter­ mined from expressions previously developed (17 ,32) if the mass loss is assumed to occur primarily in the char layer and the average char density is known. The solid mass loss is then equated to the gases liberated at the surface:

(23)

FPL-0145 -40- The total mass loss of the material can be approximated by (32):

(24)

hence the charring rate can be approximately expressed as:

(25)

Scala (48) substitutes equation (18) into equation (25) and further utilizes an approximate solution for the temperature distribution in the reacting plastic of:

(26) where

(27)

T = char-polymer interface temperature and c

Integration of the completely defined integrand of equation (25) produces an expression for the charring rate:

Equation (28) is good for small values of δ (32). If δ is neglected completely (heat of depolymerization is small, etc.), a simpler form is obtained as given by Steg (59):

(29)

FPL-0145 -41- If the properties of the degrading material are such that cracks occur in the char or it begins to flake, Barker et al. (6) state that the diffusion of heat or reactants is no longer controlled by the char layer thickness; the mechanism of heat transfer through the char layer is accomplished by convection and/or radiation. They propose the char depth can be estimated by the equation:

(30) and the rate constant, K, is given by an Arrhenius-type law:

When this is combined with equation (30) it yields:

(31)

The char depth of graphite, cloth-reinforced phenolic plastic, .5- and 1.0-inch thick were described by equation (31).

This concludes the review of typical investigations that utilized the equation of continuity and Arrhenius temperature dependence to obtain expressions for the rate of charring.

Other expressions for the rate of charring do not use the factor of Arrhenius temperature dependence. In the case where the char layer formed is relatively homogeneous, Barker and his associates (6) reasoned that the rate of polymer degradation is controlled by diffusion of heat through the char layer and by the temperature of the char surface, and that the rate of formation of the char is inversely proportional to the char layer thickness and directly proportional to the temperature driving force. The temperature driving force is the tempera­ ture difference between the char surface and the decomposition temperature of the material. This is expressed mathematically as:

(32) where or integrating

(33)

FPL-0145 -42- When the surface temperature is constant, the rate is proportional to the square root of time:

(34)

When the char layer is completely nonadherent, the rate of formation is inde­ pendent of the amount of material charred and can be expressed as:

(35)

This evidently assumes that the reactant is infinite or that the surface tempera­ ture is very high so that diffusion of heat into the material may be neglected.

Masters (41) discusses the unidirectional melting ablation of a large slab. A characteristic melting temperature T is assumed, and a temperature variation f with depth was expected as indicated in figure 13. Further rather ideal assump­ tions in the analysis are: (a) heat losses from face of the slab are negligible, (b) rate of heat absorption at the exposed face and all relevant physical properties of the material and exposure medium remain constant with time, and (c) the physical properties of the solid and liquid phase concerning conduction of heat are the same. Through writing an expression for total heat absorbed H t to o time t, Masters obtains:

(36)

where F is the latent heat of fusion.

Differentiating with respect to time, he obtains H as: o

FPL-0145 -43- which when solved for s• yields the transient rate:

(37)

This has an upper boundary for rate s• of:

(38)

It is supposed that by substituting a charring temperature Tc for the melting temperature T , the application to a charring material may not differ greatly in f results.

Figure 13.--Temperature versus depth diagram In a melting ablating solid, according to Masters (41).

M 130 363

FPL-0145 -44- Summary of Findings

This review indicates that information on the charring rate of wood has been limited to special experiments resulting in empirical relationships for predicting char depth or rate of char. However, experiments and proposed models of the rate of char in other polymers have been prolific during the last decade, thereby providing a good foundation for the analysis of the rate of char in wood.

A comparison of the limited models developed for the rate of char in wood with that of other polymers suggests that the principle of conservation of mass, coupled with Arrhenius-type temperature dependence, may be appropriate in the physical description of the charring rate of wood. For example, Vorreiter (65) and Lawson (34) found that the char depth in wood can be expressed as:

If K is the Arrhenius rate constant given by:

where T would be a characteristic temperature, equation (31) by Barker et al. (6) is generated.

Other models for defining the charring rate of polymers depend upon such parameters as the charring temperature, the temperature difference between the char surface and decomposition temperature of the material, thermal coeffi­ cients, mass, and applied heat flux These models exhibit promise of application to the charring rate of wood.

It appears that the significant wood properties that affect its rate of char will be mass density, moisture content, thermal properties k, α, Cp , annual ring orientation with respect to the heated surfaces, charring temperature, and com­ bustible volatile content.

Blackshear’s and Murty’s (9) observations of temperature-dwell at the boiling point of water, even in initially dry cellulose, indicate that moisture may delay the rise to the charring temperature of the wood. An excess of moisture, how­ ever, is shown by Shorter (53) to have a disastrous spallation effect on concrete under fire exposure. This phenomenon could have the same effect in the wood char layer, thereby decreasing the insulative thickness of the char. FPL-0145 -45- The charring temperature of wood appears to lie in the range of 540° to 600° F. (280° to 320° C.) as estimated by the degradation zones in wood (23, 27, and Tang, footnote 3, p. 3) and the temperature at the base of the char layer pointed out by Truax (60). Ignition temperatures of wood also appear to lie in this range (5, Tang, footnote 3, p. 3).

It also appears that the heat liberated in the combustion of wood species to various stages of char can be determined from the total heats of combustion for the species (31,44,47) and the percent of the total heat contained in the volatiles as a function of volatilization.

Literature Cited

( 1) Adler, J., and Enig, J. W. 1964. The critical conditions in thermal explosion theory with reactant consumption. Combustion and Flame 8: 97-103.

( 2) Akita, K. 1959. Studies on the mechanism of ignition of wood. Report of Fire Res. Inst. of Japan 9(1,2), 98 pp.

( 3) American Society for Testing and Materials 1961. Standard methods of fire tests of building construction and mate­ rials. ASTM Designation E 119-61.

( 4) Baker, R T. 1919. The hardwoods of Australia and their economics. State of New South Wales, Sydney, Australia.

( 5) Bamford, C. H., Crank, J., and Malan, D. H. 1946. Combustion of wood. Proc. Cambridge Phil. Soc. 42: 166-182.

( 6) Barker, D. H., Kordig, J. W., Belnap, R D., and Hall, H. F. 1964. A simplified method of predicting char formation in ablating rocket exit cones. Presented at the Seventh Nat. Heat Transfer Conf. Amer. Inst. Chem Eng.-Amer. Soc. Mech Eng., Cleveland.

( 7) Beck, J. V. 1962. Thermocouple temperature disturbances in low conductivity mate­ rials. Trans. Amer. Soc. Mech Eng., J. Heat Transfer 84(Ser. C): 124-132.

FPL-0145 -46- ( 8) Bird, R. B., Stewart, W. E., and Lightfoot, E. N. 1960. Transport phenomena. John Wiley and Sons, N.Y.

( 9) Blackshear, P. L., Jr., and Murty, K. A. 1964. Heat and mass transfer to, from, and within cellulosic solids burn­ ing in air. Tech. Rep. No. 2 (OCD-OS-62-89),Univ. of Minn. Inst. Technol., Minneapolis.

(10) 1962. The measurement of physico-chemically controlled ablation rates. Tech. Rep. No. 1 (AD 285 460). Univ. of Minn. Inst. Technol., Minneapolis.

(11) Brown, H. P., Panshin, A. J., and Forsaith, C. C. 1952. Textbook of wood technology. Vol. II, McGraw-Hill, N.Y.

(12) Browne, F. L., and Brenden, J. J. 1964. Heat of combustion of the volatile pyrolysis products of fire- retardant treated ponderosa pine. U.S. Forest Serv. Res. Pap. FPL 19. Forest Products Lab., Madison, Wis.

(13) Browne. P. L. 1958. Theories of combustion of wood and its control--A survey of the literature. U.S. Forest Serv., Forest Products Lab. Rep. No. 2136. Madison, Wis.

(14) Bryan, J., and Doman, L. S. 1940. Fire resistance--the comparative resistance to fire of various species of timber. Wood 5(1): 19-23.

(15) Dorn, H., and Egner, K. 1961. Fire tests of glue-laminated beams. Holz-Zentralblatt 28: 435-438, Stuttgart.

(16) Frost, A. A., and Pearson, R. G. 1961. Kinetics and mechanism. Ed. 2. John Wiley and Sons, N.Y.

(17) General Electric Reentry Systems Dep. 1964. Final report on analytical comparisons of ablative nozzle materials. Contract NAS 3-2566, Nat. Aeron. Space Admin., Lewis Research Center, Cleveland.

FPL-0145 -47- (18) Gomes, W. 1961. Definition of rate constant and activation energy in solid state reactions. Nature 192: 865-866.

(19) Goos, A. W. 1952. The thermal decomposition of wood. Chapter 20 in Wood , Vol. II, by Louis E. Wise and Edwin C. Jahn, 2nd edition, Reinhold Pub. Co., N.Y.

(20) Goring, D. A. I. 1963. Thermal softening of lignin, hemicellulose, and cellulose. Pulp and Pap. Mag. Can. 64: t517-527.

(21) Great Britain Ministry of Technology and Fire Offices’ Committee, Joint Fire Research Organization. 1965. Fire Research 1964; report of the Fire Research Boardwiththe report of the Director of Fire Research. London.

(22) 1964. Fire Research 1963; report of the Fire Research Board with the report of the Director of Fire Research. London.

(23) Hawley, Lee F. 1952. Combustion of wood. Chapter 19 in Wood Chemistry, Vol. II, by Louis E. Wise and Edwin C. Jahn, 2nd edition, Reinhold Pub. Co., N.Y.

(24) Hodgman, C. D. 1963. Handbook of chemistry and physics. Ed. 44, Chemical Rubber Pub. Co., Cleveland.

(25) Imaizumi, K. 1962. Stability in fire of protected and unprotected glued-laminated beams. Norsk-Skogindustri 4: 140-151.

(26) Israel, M. H., and Nardo, S. V. 1964. An annotated bibliography on ablation and related topics. Polytechnic Institute of Brooklyn.

(27) Jakob, M. 1959. Heat transfer. Vol. I, John Wiley and Sons, N.Y.

FPL-0145 -4a- (28) Jean, Marcel 1963. The behavior in fire of wood and wood-based materials. Presented at the IUFRO Fifth Conference on Wood Technology, held at the U.S. Forest Products Laboratory, Madison, Wis.

(29) Kadanof, L. P. 1958. Radiative transport within an ablating body. Avco Res. Lab. Rep. 37, Wilmington, Mass.

(30) Kauzlarich, J. J. 1965. Ablation of reinforced plastic for heat protection. Trans. Amer. Soc. Mech. Eng., J. Appl. Mech. 32(Ser. E): 177-182.

(31) Klason, P., Heidenstam V. G., and Norlin, E. 1907. Theoretical investigations into carbonization of wood (Sweden) II. Dry distillation of pine, spruce, birch, and beechwood. Ark Kemi, Mineral, Geology, 3(1).

(32) Lafazan, S., and Siegel, B. 1963. Ablative thrust chambers for space application. Chem Eng. Prog. Symp. Ser. 59(40): 39-50. Amer. Inst. Chem Eng., N.Y.

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FPL-0145 -53- APPENDIX

In the study of homogeneous chemical reactions, the rate of the reaction is generally determined by chemical kinetic (dynamic) theory. Mechanisms in reacting materials are analyzed by kinetic methods, thereby making individual steps in the reaction understandable without all of the details. Rate expressions are of the form of a product of powers of chemical concentrations (16)

and the order of the reaction is given by the sum of all the exponents of the concentrations:

When experimental conditions for a given reaction are such that one or more of the concentration factors are constant (or nearly constant) these factors may be included in the constant K. Further, in this case the reaction is said to be of ”pseudo-nth order” or “kinetically of the nth order” where n is defined by the previous equation. K is called the rate constant, or specific reaction rate.

th An n order reaction of a single component takes the form

In typical temperature-dependent reactions, the reaction rate increases with increasing temperature. This may be called an Arrhenius temperature depend­ ence. The rate constant K must include this temperature effect if present. It is usually found that plotting (log K) versus 1/T is nearly linear with negative slope and the graph may be therefore expressed as:

FPL-0145 -54- where E is the Arrhenius activation energy and R is the gas constant. a There are reactions where the rate constant will not simply increase without bound with increasing temperature, but approaches a constant value A asymptot­ ically (fig. 14). In this case, A is also a function of temperature and an equation describing this must be utilized as follows:

where i must be determined and E is not necessarily the same as E . The acti­ a vation energy E is related to E by: a

and may differ greatly.

Figure 14.--Variation of rate constant with temperature (16).

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