SEP 2 0 T985

NBSIR 85-3163

Development of A Model for the

Heat Release Rate of Wood - A Status Report

William J. Parker

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

May 1 985

OC

I in part by:

‘ f* Emergency Management Agency

/?05

c.

NBSIR 85-3163

DEVELOPMENT OF A MODEL FOR THE

HEAT RELEASE RATE OF WOOD - A STATUS REPORT

William J. Parker

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

May 1 985

Sponsored in part by:

Federal Emergency Management Agency

U.S. DEPARTMENT OF COMMERCE. Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

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REPORT DOCUMENTATION PAGE

report number 2. GOVT ACCESSION NO. 3

READ INSTRUCTIONS

BEFORE COMPLETING FORM

RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtitle) DEVELOPMENT OF A MODEL

RELEASE RATE OF WOOD -

7. author^;

William J. Parker

5. TYPE OF REPORT 4 PERIOD COVERED

FOR THE HEAT

A STATUS REPORT

j Final

| S. PERFORMING ORG» REPORT NUMBER

NBSIR o 5- 3l£

3

9 _ C0nTRACT or granT num8ER(. s> EMW-E-12 39

9. PERFORMING ORGANIZATION NAME AND ADORESS

Center for Fire Research

U.S. National Bureau of Standards

Cai thersburg , MD 20899

11. CONTROLLING OFFICE NAME ANO ADDRESS

Federal Emergency Management Agency

Washington, D.C. 20^72

10. PROGRAM ELEMENT. PROJECT, TASK

AREA 4 WORK UNIT NUMBERS

2531 G

12. REPORT DATE

May 1985

13. NUMBER OF PAGES

106

1*. MONITORING AGENCY NAME 4 ADOR£SS(7/ different from Controlling Office) >5. SECURITY CLASS, (of chle report) Unclassified

15a. OECLASSIFICATION DOWNGRADING

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16. DISTRIBUTION STATEMENT (ot this Report)

Approved for public release: Distribution Unlimited

17. DISTRIBUTION STATEMENT (of the abatract entered in Block 20, ft different from Report)

Approved for public release: Distribution Unlimited

18. SUPPLEMENTARY NOTES

19. KEY WOROS (Continue on reverae aide If necessary and Identify by block number)

heat release rate, -wood, pyrolysis, heat of combustion,

thermal conductivity, computer models

ABSTRACT fContfaue on rtmM ft n eco emeiy mad. identify by block number)

This report describes the status of the development of a method f:

predicting the heat release rate of wood for different thickness® -

. moisture contents, and exposure conditions. A computer program

been set up on a microcomputer. Experimental techniques have deer,

devised to obtain the input data required by the model. These ha - elude (l) the thermal conductivity as a function of temperature a.-, percent loss, (2) the kinetic constants needed to describe the mas

W) » 1473 EDITION OF » MOV 65 IS OBSOLETE

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loss rate, (3) the heat of combustion of the volatile pyrolysis

products, and (U) the contraction factors due to charring. Sufficient data on these parameters -were taken to exercise the model.

Heat release rates and effective heats of combustion were measured

as a function of external radiant flux on 12.5 mm thick dry vertical specimens of Douglas fir particle board. The calculated and

measured peak heat release rate curves are similar in shape and

amplitude but differ significantly in time scale. This may be due

to the lack of thermal conductivity data on the char In the high

temperature range,

culat ed

There is very good agreement between the c aland measured effective heats of combustion. The initial

results with the model are promising.

UN UT.AfIFTFTED

SECURITY CLASSIFICATION OF THIS PAGEfWTian Data Entarad)
TABLE OF CONTENTS

Page

LIST OF FIGURES v

LIST OF TABLES viii

NOMENCLATURE ix

Abstract 1

1. INTRODUCTION 1

2. HEAT RELEASE RATE MODEL 5

3. THERMOCHEMICAL PROPERTIES 15

3.1 Pyrolyzer 15

3.2 Heat of Combustion of Pyrolysis Vapor 17

3.3 Calculation of Kinetic Constants from Mass Loss Data at

Constant Temperature 18

3.4 Contraction Factors 20

3.5 Heat of Pyrolysis

3.6 Parameters Dealing with Moisture 21

4. THERMOPHYSICAL PROPERTIES 21

4.1 Heat Capacity 21

4.2 Thermal Conductivity Data from Literature 22

4.3 Thermal Conductivity Measurements 24

5. CALCULATIONS OF HEAT RELEASE RATE USING THE MODEL 28

6. HEAT RELEASE RATE MEASUREMENTS IN THE CONE CALORIMETER 30

7. DISCUSSION 32

8. SUMMARY 40

9. FUTURE PLANS 41

10. ACKNOWLEDGEMENTS 42

11. REFERENCES 4 3

APPENDIX A. CALCULATION OF THE DENSITY OF THE GAS IN THE EXHAUST DUCT .. 52

APPENDIX B. CALCULATION OF THE FLCW OF NITROGEN THROUGH THE EXHAUST

DUCT 5 5

APPENDIX C. CALCULATION OF THE CARBON, HYDROGEN, AND OXYGEN RELEASE

RATES FROM BURNING WOOD 5 7

iii
LIST OF FIGURES

Page

Figure 1. Boundary Conditions and Subdivision of Burning Vertical Slab 65

Figure 2. Flow Chart for Computer Program 66

Figure 3. Pyrolyzer 67

Figure 4. Closure Slide 68

Figure 5. Heat of Combustion of Pyrolysis Vapor for Douglas Fir

Particle Board 69

Figure 6. Arrhenius Plot for Douglas Fir Particle Board 70.

Figure 7. Contraction Factors for Southern Pine 71

Figure 8. Contraction Factors for Douglas Fir Particle Board 72

Figure 9. Experimental Setup for Determining Thermal Conductivity 73

Figure 10. Thermal Conductivity as a Function of Temperature for

Charred and Uncharred Specimens of Southern Pine 74

Figure 11. Thermal Conductivity as a Function of Temperature for

Charred and Uncharred Specimens of Douglas Fir Particle Board 75

Figure 12. Calculated Front and Rear Surface Temperatures for Dry 12.7 mm

Specimen of Douglas Fir Particle Board Exposed at an External

Radiant Flux of 50 kW/m2 76

Figure 13. Calculated Char Depth for Dry 12.7 mm Specimen of Douglas Fir

Particle Board Exposed at an External Radiant Flux

of 50 kW/m2 77

Figure 14. Calculated Mass Loss Rate for Dry 12.7 mm Specimen of Douglas

Fir Particle Board Exposed at an External Radiant Flux

of 50 kW/m2 78

Figure 15 Calculated Heat Release Rate for Dry 12.7 mm Specimen of

Douglas Fir Particle Board Exposed at an External Radiant

Flux of 50 kW/m2 79

Figure 16. Calculated Effective Heat of Combustion for Dry 12.7 mm

Specimen of Douglas Fir Particle Board Exposed at an External

Radiant Flux of 50 kW/m2 80

Figure 17. Calculated Heat Release Rate for Dry 12.7 mm Specimen of Douglas

Fir Particle Board with an Assumed Heat of Pyrolysis of 400 kJ/kg

Exposed at an External Radiant Flux of 50 kW/m2 81

iv
List of Figures (continued)

Page

Figure 18. Calculated Heat Release Rate for 7% Moisture Content 12.7 mm

Specimen of Douglas Fir Particle Board Exposed at an External

Radiant Flux of 50 kW/m2 82

Figure 19. Calculated Heat Release Rate for Dry 6 mm Specimen of Douglas

Fir Particle Board Exposed at an External Radiant Flux

of 50 kW/m2 83

Figure 20. Calculated Heat Release Rate for Dry 12.7 mm Specimen of Douglas

Fir Particle Board Exposed at an External Radiant Flux

of 25 kW/m2 84

Figure 21. Calculated Heat Release Rate for Dry 12.7 mm Specimen of Douglas

Fir Particle Board Exposed at an External Radiant Flux of

75 kW/m2 85

Figure 22. Calculated Heat Release Rate for Dry 12.7 mm Specimen of Douglas

Fir Particle Board Exposed at an External Radiant Flux of

100 kW/m2 86

Figure 23. Measured Heat Release Rate for Dry 12.7 mm Specimen of Douglas

Fir Particle Board Exposed at an External Radiant Flux

of 25 kW/m2 87

Figure 24. Measured Heat Release Rate for Dry 12.7 mm Specimen of Douglas

Fir Particle Board Exposed at an External Radiant Flux

of 50 kW/m2 88

Figure 25. Measured Heat Release Rate for Dry 12.7 mm Specimen of Douglas

Fir Particle Board Exposed at an External Radiant Flux

of 75 kW/m2 89

Figure 26. Measured Heat Release Rate for Dry 12.7 mm Specimen of Douglas

Fir Particle Board Exposed at an External Radiant Flux

of 100 kW/m2 90

Figure 27. Measured Effective Heat of Combustion for Dry 12.7 mm Specimen

of Douglas Fir Particle Board Exposed at an External Radiant

Flux of 25 kW/m2 91

Figure 28. Measured Effective Heat of Combustion for Dry 12.7 mm Specimen

of Douglas Fir Particle Board Exposed at an External Radiant

Flux of 50 kW/m2 92

Figure 29. Measured Effective Heat of Combustion for Dry 12.7 mm Specimen

of Douglas Fir Particle Board Exposed at an External Radiant

Flux of 75 kW/m2 93

v
List of Figures (continued)

Page

Figure 30. Measured Effective Heat of Combustion for Dry 12.7 mm Specimen

of Douglas Fir Particle Board Exposed at External Radiant

Flux of 100 kW/2 94

Figure 31.

Measured Heat Release Rate Determined by the Three Analyzer

Method for Dry 12.7 mm Specimen of Douglas Fir Particle

Board Exposed at an External Radiant Flux of 50 kW/m2 95

Figure 32. Measured Effective Heat of Combustion Determined by the Three

Analyzer Method for Dry 12.7 mm Specimen of Douglas Fir

Particle Board Exposed at an External Radiant Flux

of 50 kW/m2 96

vi
LIST OF TABLES

Page

1. Thermal Conductivity Data on Fiberboard and Particle Board

from the Literature 45

2. Thermal Conductivity of Oven Dry Southern Pine as a Function

of Temperature 46

3. Thermal Conductivity of Charred Southern Pine as a Function

of Temperature 47

4. Thermal Conductivity of Oven Dry Douglas Fir Particle Board as

a Function of Temperature 48

5. Thermal Conductivity of Charred Douglas Fir Particle Board as

a Function of Temperature... 49

6. Input Data for Running the Model for Douglas Fir Particle

Board 50

vii
NOMENCLATURE

A

B

C

E

F

h

"p

K

l

L

Lv

m

M

n

N

n

P

q

R

t

T

x

frequency factor (s -

^)

mass transfer number

heat capacity (kJ/kgK)

activation energy (kJ/mol)

heat of combustion of volatiles (kJ/kg) (positive when heat is

evolved)

convective heat transfer coefficient (kW/nrK)

heat of pyrolysis (kJ/kg) (positive when heat is absorbed)

thermal conductivity (kW/m • K)

contraction factor

effective heat of gasification (kJ/kg) (positive)

latent heat of vaporization of water (kJ/kg) (positive)

mass (kg)

% moisture content

number of components

number of subdivisions of the specimen

molar flow (mol/s)

grouping defined by equation (2-14)

heat (kJ) (positive)

external radiant flux (kW/m )

rate of heat release (kW)

gas constant (8.314 kJ/mol • K)

time (s)

temperature (°C)

volume flow (m^/s)

distance up from bottom of specimen (m)

viii
X volume fraction

Z mass retention fraction

a radiative absorptivity and emissivity

AH heat of combustion (kJ/kg) (positive when heat is evolved)

Ap pressure drop across orifice plate (P a )

At time step (s)

AX thickness of each slice (m)

a) defined by equation (2-20)

p density (kg/m^)

a Stef an-Boltzmann constant (5.67 x 10”^ kW/m^ • K^)

Subscripts

c convection

C carbon

D thickness of specimen (m)

e external or exhaust

f f lame

g gas

H hydrogen

i designates a particular slice

k designates a particular wood component

N designates the slice bounded by the rear surface

o ambient or original

0 oxygen

R radiation

rel release

S front surface of specimen

vol volatiles

ix
w water

x normal to surface

y parallel to surface normal to grain

z parallel to surface along grain

Superscripts

A analyzer

A' analyzer with CO2 trapped out of it

S exhaust duct

• per unit time

per unit area

x
DEVELOPMENT OF A MODEL FOR THE HEAT RELEASE RATE OF WOOD - A STATUS REPORT

William J. Parker

Abstract

This report describes the status of the development of a method for

predicting the heat release rate of wood for different thicknesses, moisture

contents, and exposure conditions. A computer model has been set up on a

microcomputer. Experimental techniques have been devised to obtain the input

data required by the model. These include (1) the thermal conductivity as a

function of temperature and percent mass loss, (2) the kinetic constants

needed to describe the mass loss rate, (3) the heat of combustion of the

volatile pyrolysis products, and (4) the contraction factors due to charring.

Sufficient data on these parameters were taken to exercise the model. Heat

release rates and effective heats of combustion were calculated and measured

as a function of external radiant flux on 12.5 mm thick dry vertical specimens

of Douglas fir particle board. The initial results with the model are

promising.

Key words: heat release rate, wood, pyrolysis, heat of combustion,

thermal conductivity.

1. INTRODUCTION

The heat release rate is one of the most important fire properties of a

material. Whether a room fire will attain flashover depends on the total heat

release rate of all the materials in the room as well as its ventilation and

surface heat losses [1,2]. The rate of flame spread in the direction of air

1
flow is strongly dependent on the rate of heat release. In order to model the

fire growth in a room it is essential to have data on the heat release rate of

all of the materials involved as a function of the net heat transfer through

their front surface.

A number of calorimeters have been developed to measure the heat release

rate per unit area as a function of the external radiant flux [3,7]. The

corresponding net heat transfer through the flaming surface as required by

room fire growth models is not measured in any of these calorimeters. The

heat release rate curves as a function of time at a particular external

radiant flux are in general different for different calorimeters because of

the different conditions under which the data are obtained. The variables

include orientation, specimen size, heat transfer conditions at the rear face,

piloting arrangements, etc.

An approach which has been used with apparent success for determining the

heat release rate of polymethylmethacrylate (PMMA) is to define an effective

heat of gasification as

L =

q net

/m" (1-D

where is the net heat transfer through the surface and m" is the outward

mass flux. The mass loss rate used in equation (1-1) is measured under nonflaming conditions thus avoiding the uncertainties in measuring the flame heat

transfer. The net heat transfer to the specimen is equal to the absorbed

external radiant flux minus the reradiation and convective heat losses from

the front face. Tewarson [8] has cataloged values of L and the effective heat

of combustion, (AH)^^, for many materials.

2
A room fire growth model can calculate the net heat transfer rate through

the surface and use equation (1-1) along with the experimentally measured

value of L to determine the mass loss rate. The calculated heat release rate

is simply equal to

*rel

" (iH) eff a‘2)

Unfortunately both and L vary throughout the burning period for char

forming materials.

When L reaches a steady value it is an order of magnitude greater than

the heat of pyrolysis of cellulose [9], which is the major component of wood.

This suggests that L in this case is dominated by heat transfer and thus

depends on density, thickness, etc. Therefore, the effective heat of gasification is not a useful concept for wood.

A better approach for char forming materials is to develop a model which

predicts the mass loss rate as a function of time based on their thermochemical and thermophysical properties. Two general types of mass loss rate

models have been developed. Kanury [10] and others have used a pyrolysis

temperature model which can be solved analytically. It is assumed that a thin

pyrolysis front moves through the material. Virgin wood exists at all temperatures below the pyrolysis temperature and the final char exists above it.

This is satisfactory for high heat fluxes and long times.

However, for fire buildup in rooms we have to deal with the whole range

of fluxes and are particularly interested in early times. This requires the

3
use of kinetic models such as that originated by Kung [11] and improved upon

by Tamanini [12] and Atreya [13]. The kinetic models allow for pyrolysis to

occur at any temperature at a rate determined by an appropriate Arrhenius

expression. Again there are a number of other models but it is the one

refined by Atreya which will be built upon in this report.

It is also important to allow for moisture evaporation. The temperature

at any point in the solid is determined by solving the energy equation numerically.

Even the kinetic mass loss rate models are not without problems. Wood

decomposes along two principal pathways. In one case all of the gasified

material escapes; it will generally decompose into a variety of products

before it passes through the surface. It will have an overall heat of combustion similar to that determined with an oxygen bomb calorimeter. Along the

other pathway, char is formed with the release of water and other volatiles

having low heats of combustion. The effective heat of combustion,

will be determined by the ratio of the quantities following these two routes.

This ratio changes during the course of the test. The mass loss rate model

cannot accurately predict the heat release rate unless the change in effective

heat of combustion during the burning period is known.

In this report a model is presented which calculates the heat release

rate directly. Methods of providing the thermo chemical and thermophysical

properties required as input data for the model are described. Some of these

data are presented for Douglas fir particle board and the calculated and

measured heat release rates are compared. Douglas fir particle board was

A
chosen because of its use in a number of other fire research projects. The

material used was supplied by the Weyerhaeuser Company. It has an oven dry

density of 709 kg/m^. It is 12.7 mm thick and uses urea formaldehyde ( 6 % of

the mass of the original wood) as the adhesive. In addition there is 1/4

%

add-on each of urea and a paraffin-type wax. While the binder may have some

effect on the chemical and physical properties of the particle board, these

resultant properties are measured on the project.

2. HEAT RELEASE RATE MODEL

The heat release rate model described in this report (1) breaks the

specimen down into thin slices of equal thickness parallel to the surface as

seen in figure 1, (2) calculates the temperature of each slice using the

energy equation, (3) calculates the mass loss rate for each wood component

(cellulose, lignin, and hemi cellulose) in each slice using the rate equations,

(4) multiplies these rates by the local heat of combustion of the volatiles

generated by each component, and (5) sums these contributions over the depth

of the specimen to obtain the total heat release rate assuming complete

combustion of the volatiles leaving the front surface. The flow chart for the

computer program written to implement these calculations is shown in figure

2. The boundaries of each slice move as the specimen shrinks during the

burning period so that no solid material crosses a boundary. All of the

volatiles pass through the front surface. The transit time of the volatiles

from their generation site to the surface is neglected. However, the internal

surface convective heat transfer coefficient is assumed to be so large that

the volatiles are maintained in thermal equilibrium with the char through

which they pass. Secondary chemical reactions with the char layer are

5
neglected. The rate of mass generation for each component is expressed as a

function of the temperature and the mass retention fraction of that component

for each slice using an Arrhenius type expression. The mass retention

fraction is the ratio of the mass at any time to the original mass. It is

assumed that the instantaneous heat of combustion of the volatiles generated

by each component depends only on the mass retention fraction for that

component. This implies that the chemical composition of each component is a

unique function of its mass. The temperature profile as a function of time is

calculated from the energy equation using finite differences. The rate of

change of enthalpy, heat conduction, internal heat generation or absorption

and convective cooling by the flow of volatiles is taken into account. The

thermal properties are assumed to be a function of the temperature and the

total mass retention fraction for each slice. Then the instantaneous mass

retention fraction profile is determined by accounting for the cumulative loss

of volatiles. An adiabatic boundary condition is assumed at the rear surface

while the front face is exposed to a constant external radiant flux. Both of

these conditions can be made more general later if desired. The front surface

also loses heat by reradiation. Up to the time of ignition it also loses heat

by laminar free convection. This is justified for small surfaces such as

those in the heat release rate calorimeters. For wall fires it will be necessary to take turbulence into account. After ignition the convective heat

transfer from the flame to the surface is taken into account along with flame

radiation. The convective heat transfer coefficient is multiplied by a

blowing factor to account for the effect of the volatiles leaving the surface.

Ignition is assumed to occur when the calculated total heat release rate

reaches 30 kW/m^ which is the minimum heat release rate required to maintain, a

flame on the surface. The use of this ignition criterion will be discussed in

6
section 7. The flame is extinguished when the calculated heat release rate

again drops below 30 kW/m^ at the end of the flaming phase. Only the heat

release rate during the flaming phase is treated by this model.

The mass retention fraction for slice i is defined by

Z

i

, — m.

1

/ m?

i — III p x y z o

(2-1)

where m^ is the mass of slice i on an oven dry basis, p is its density, and

1,1, and l are the contraction factors (i.e. the ratios of the thickness,

x y z width and height of the slice to their original values). The superscript and

subscript o refer to the initial values.

The contributions of the individual wood components (e.g. cellulose,

hemicellulose and lignin) are additive so that

Z.

l

n

Zk=l

( 2 -2 )

where Z^ ^

is the mass of the k th component of slice i divided by the

original mass of the whole slice. It is necessary to know the reaction rate

and heat of combustion of the volatiles for each component as a function of

the temperature, T^, and the component mass retention fraction, Z^/Z°.

Here z£ is original mass fraction of the k th component.

The moisture is taken into account by assigning a moisture retention

fraction

7
( 2 - Z = m /m"? 3 ) w

i wi

1

where is the mass of adsorbed water located in slice i at any time. The

water produced by chemical decomposition is accounted for in the Z term.

The mass loss rate on a dry basis and heat release rate per unit area of

the original specimen are calculated by the following formulas:

m = AX N

z

t + it

i )

( 2 -4 )

where Z

C = Z(t) and AX

q is the original thickness of each slice (assumed to be

identical)

and

AX N . q" = P TT Z F

? ( Z “ 2

At

n rel ) o At . , i

v i i1 i=l

( 2 -5 )

where the heat of combustion of the volatiles is given by

F*r = z Fj z.

c

, /zj

k=l 1 , , i,k i,k i

( 2 -6 )

since z\ = Z

± (t) and Z i}

L k

= z i,k (t) then F i = F

i( t > t _ t _

The energy equation is first solved for the temperature. Then the rate

equations are used to update the mass retention fraction for each component in

each slice. The total mass retention fraction, Z^, for each slice is then

determined, the property values are updated and the energy equation is solved

for the temperature at the next time step.

8
The increase in enthalpy of an interior slice is equal to the heat

conducted in minus the heat conducted out minus the heat absorbed by the

pyrolysis gases passing through on their way to the front surface minus or

plus the heat absorbed or generated by pyrolysis and evaporation. The energy

equation for an interior slice can be written as

p AX (z5

+At

C. + Z t+AtC ) T

t+At

- (Z

C C. + ZC C ) TC oo^i i w. w.' i ^ 1 1 w.w.^i

= K.

1

t+At t+At

i-1 i

AX

t

c+4c

- T

c

. i i+i:f

AX

At Vz

fC m" ,+ C 5T 1 Si 1+1 w

i w

i+l

t+At t+At

i+1 i

2 At

m" + C

• •• > m ) w . w . ; i i

T

t+At + T

t+At

i-1

2 At

- h p AX [Zt - Z^ +At

) - L p AX (ZC - Z t+At p^oo^i ) i

J voo^w^ w

±

J ( 2 - 7 )

where m'\

Pp ^O

At

N

Sj=i

Z t+At

J )•

14

Assuming instantaneous mass transfer.

p AX

o o At

N

Zj=i

Z t+At

w.

J

)

( 2 -8 )

( 2 -9 )

9
( 2 - and h 10 ) P

i

n Z

i» k . z —r~ * k«l z\ P

k.

Here m” refers to the mass flow per unit original area of the specimen, not

the contracted area. The heat of pyrolysis of the slice, hp , is equal to the

weighted averages of the heat of pyrolysis of each component.

Since Z

t+At is not known ahead of the calculation of the temperature the

time step must be small enough to ensure that the approximations

7

t „ t+At 7 t-At „t

z . - z . » z . — z

.

11 11

and

z

t _ Z t+At

W

i

W

i

Z t_At _ z

c w

,

w

.

i

( 2 - 11 )

( 2 - 12 )

are valid. In the storage term (l.h. s. of equation (2-7)) it is easier to

consider the heat-up of all of the mass present in the slice at the beginning

of the time step including that lost by pyrolysis and evaporation during the

time step. This mass loss then must not be added to the pyrolysis gases

flowing through the slice as far as transpiration cooling of that layer is

concerned. Thus the mass flow rate through each slice is uniform, and equal

When the energy equation is modified to take the two approximations in

equations (2-11) and (2-12) into account and is divided through by p Q

AX

q

C^ it

can be rewritten as

10
( z

t

i

( T r- ^

-

K At l i i y z

»o

C

i

( “o)2tx

/_t+At

(

T i-1 + T

t+At

i+1 - 2 Cc )

+

N

Zj=i+l

t-At +

Cw

i

N

2C~ J-i+1

i

J

( Z t-At.

wj

r t+At t+At^

^ i+1 i-1 J

( z

i

t-At

L

t-At w

.

1 (2-13)

It is noted that AX = £ AX • x o

Let

K. I l At

p H

* y z

o 1

pM c.(ax ) i o i o x

(2-14)

and rewrite the energy equation in matrix format for solution of a set of

algebraic equations for T?+^ t using an implicit method:

'g. N 'w . N

- P. + Z fZ t_At - + -r-i- Z fZ

t "At - Z

C

) 1 2 r 4.4^1 ^ j 4^X1 ^ W 4 'C. j-i+1

i

J C. j-i+1

i

J

-pt+A t i-1

+ (2P.+Z

t + ZC 7r^)T

C+At+

^ l l w, C . > l

i i

'g< N

"P i~ 2

C. j-i+1

w N

°i *’ t-At „t-, i t-A t _ t . 2r 4.44., ^ i

2

C

5=1 + 1 V

w , rz

c + Z

c T*- rP- (Z*“At - Z

c

) - ~~ r

Z

t “At - z11 .) ^ i w

i

; l C

t

^ i C

i

^ w

i wi (2-15)

t+At

i+1

11
There is no mass flow of volatiles through the rear face which forms the

rear boundary of slice N. Hence equation (2-15) for i=N reduces to

C

w,

• t+At

N

(2-16)

Radiative and convective heat transfer must be taken into account at the

front surface which forms the front boundary of slice 1. Absorption and

emission of radiation within the depth of the specimen is assumed to be negligible. Prior to ignition the surface is cooled by laminar free convection.

After ignition it is heated by the flame. The front surface temperature, Tg

,

for these calculations is obtained by linear extrapolation from the center

points of the two slices nearest the surface,

The reradiation from the surface is given by

(2-18)

The energy flow across the front surface is given by

Vt = ^

+ - « ( T

s ' T

o) + hf

( T

f ' T

.) B/(ex»< B) - 15 (2 '19)

where

12
0) - eta (Tg + T*) (T

g + To

) + hB/(exp(B) - 1) ( 2 -20 )

and

B = m" (h + h

f )/C

where h is the convective heat transfer coefficient from the surface to the

ambient air which drops to zero after ignition, hf is the convective heat

transfer coefficient for the flame to the surface which is equal to zero prior

to ignition, Tf is the flame temperature, m” is the mass flux through the

front face, C„ is the heat capacity of the gas, and B is the mass transfer

o number introduced by Spalding [14], which is proportional to the mass loss

rate and thus accounts for blowing. Prior to ignition the radiant heat flux

from the flame, q" , is zero. rR

The energy equation for the first slice is given by a slight extention of

equation (2-7)

T

t+At

_ T

t+At

B/ (exp (B )-l ) - K l l

1 z y

At

13
+ (c. ij +

„t+At , t+4t

T

2 + Ti

*rz _wrv 2

. .... . . 3 t+At 1 _t+At

At - (C

g

^m

1 + C^m^) 2 T

1 2

T

2 At

h p AX f Z^“ Z t+At

) - L p AX (Zc - ZTM) pjO o

v 1

J V O

°^ W

1 W

1

,t _ „t+At-

( 2 -21 )

In final form this becomes

~w ~ Jl AX 'g, N Z

5 + < CT + P

1

1 + T KiT

2 “ + h

f B/(.xp(B)-l) + c“ z ( Z

5

^

Z

j)

1 1 • y z 1 j=2

g, N

Z

j'

w N + — y ( 7 t-^t TMt -> „t +

C

E l zw

Zw j T

1

1 j s2 j j

t+At

1 ^

+ "P

1 1 +2 Ktt V + hfB/(axp(B)-l)

y z

'g, N “ E (zfAt - zj)

1 j-2 J :

w N

L _ 7 t-At t Tt+At

C

E Zw

' Zw

X 2

1 j-2 j j

T 7^" + 7^ -JL) T^” 4= P

w, C, J 1 1 Ki £

M

e

' x

f

' ”*0 ' “f"f

J 11 y z

AX l o x 0" + k + U)T + h,T-B/(exp(B)-l)

P

1 r 7 t-At 7

t n _v r-t-At 7

t > Cj_ ^ Z

1 Zl^ C, '-w, w, 1 ( 2 -22 ) 1 W

1 W1

The change in mass retention fraction for each component of slice i during the

time step is given by

z iT - z

i >k= - (*u - z

f, k ) \ “p c- v«re

) At (2-23)

14
where Z

f k is the residual mass fraction of component k when pyrolysis is

completed in an inert atmosphere, and A

k and Ek

are the frequency factor and

activation energy for component k. The total mass retention fraction for

slice i is then given by

7 t+At

Ljl

n

Zk=l

The mass retention fraction for water is given by

Z t+At

= z

t M - A exp f- E /RT*+At

) At)

i 1

(2-24)

(2-25)

The parameters - K, p, C, C^, C

g

, a, Ak , Aw , Ek , E^ Fk , hp , l t l , and

- are needed as inputs to the model. While some of these data can be

obtained within the accuracy needed by consulting the literature, the thermophysical properties K, p, C, a, l , l , and l and the thermochemical

x y

z and hp must be determined experimentally for the

material of concern. Most of these parameters vary with temperature and the

mass retention fraction.

properties A

k

, Ek , Fk ,

3. THERMOCHEMICAL PROPERTIES

3.1 Pyrolyzer

The pyrolyzer shown in figure 3 was constructed to obtain the kinetic

constants Ak and Ek and the heat of combustion Fk required by the model. A

small cavity is created in the center of the aluminum block by bolting three

sections together. The block is heated to a constant and uniform temperature

15
by a hot plate and is insulated by 50 mm thick fiberglass batts. After a

constant temperature is reached, a 50 mm diameter 1 mm thick specimen is

inserted by placing it in the circular cutout in the sliding aluminum plate

shown in figure 4. When the plate is slid into position it effectively seals

off the insertion channel except for a small groove through which a 10 mil

chromel alumel thermocouple passes. There are also notches in the circular

portion of the plate to allow easy flow of nitrogen into the specimen chamber.

The thermocouple is attached to the specimen by threading it through a series

of holes and pulling the junction tight against the surface. A nitrogen

stream sweeps the volatile pyrolysis products up into a lean methane/oxygen

flame. The increase in CO 2 and H2 O and the drop in O 2 measured by the

analyzers are used to calculate the carbon, hydrogen, and oxygen content of

the volatiles according to the procedures outlined in Appendix C. The mass

loss rate necessary to calculate the kinetic constants A^ and is then given

by

m = m

c+ m

Q (3-1)

The heat release rate is calculated by determining the external oxygen

requirement for complete combustion to water and carbon dioxide and multiplying by 13100 kJ/kg. It takes 8 grams of oxygen to convert 1 gram of hydrogen

to water and 8/3 grams of oxygen to convert 1 gram of carbon to carbon

dioxide. The mass of oxygen present in the volatiles mist be subtracted from

the total required to completely oxidize the hydrogen and carbon in order to

determine the external oxygen requirement. It is assumed that 13100 kJ of

heat is released for each kilogram of oxygen consumed [15]. This approximation is good to within ± 5% for most organic compounds. Thus

16
(3-2)

*rel

’ 13100 < 8

“h + f

b

C ‘ V

The heat of combustion is simply

AH q^^/m. C 3 —3

)

At the time of this status report the gas analysis system is not

completely operative and thus alternate methods have been used to obtain these

data. Specimens were pyrolyzed for prescribed periods of time, removed from

the pyrolyzer, and weighed to obtain the mass loss rate data. The dimensional

changes were measured to obtain the contraction factors and j as a

function of the mass retention fraction.

3.2 Heat of Combustion of Pyrolysis Vapor

The gross heat of combustion of charred and uncharred specimens of

Douglas fir particle board were determined with the oxygen bomb calorimeter.

These data are plotted as open circles in figure 5. The data point on the

vertical axis is pure carbon which might be considered to be the ideal end

point in the charring process. However, in a fire situation it is the net

heat of combustion, which refers to the case where the water remains as a

vapor in the final state, that is important. From the overall chemical composition of the wood the amount of water produced during complete combustion can

be determined. Thus the heat of evaporation of the water can be taken into

account in order to obtain the net heat of combustion of the virgin wood. The

upper dashed curve is the net heat of combustion assuming a linear drop in the

correction factor for water as the final char is approached.

17
The heat of combustion of the volatiles is equal to the total heat

released during combustion of the wood minus the total heat released during

combustion of the char divided by the difference in mass between the wood and

the char. The instantaneous heat of combustion of the volatiles is given by

F = d(maH) _ 4H +

,m , d&H

_ (3-4)

dm^

0 df—

)

o

The derived values appear as closed circles in figure 5.

Using a linear approximation to the points between Z = 0. 4 and 1.0 the

heat of combustion of the volatiles can be represented over the range of

concern by

F - 20 [1.24 - Z] MJ/kg Z > 0.26

- 33.6 Z < 0.26

(3-5)

which is expressed by the lower dashed curve. Although the calculated points

demonstrate some curvature, the uncertainty in the assumed correction factor

for water does not justify the inclusion of additional terms in eq. (3-5).

3.3 Calculation of Kinetic Constants from Mass

Loss Data at Constant Temperature

Although there are several wood components present, each with different

kinetic constants, it was decided to try to fit the decomposition of particle

board to a single first-order reaction. This is the normal assumption for the

mass loss rate models. In that case for specimens at a constant temperature

18
dm

dt

= - (m - m^) A exp (- E/RT) (3-6)

so that

(m - m ) ln

f„ - m

1 ;) = “ c A exp E/RT)

^ o f

'

and

The final char fraction m^/niQ was found to be 0.225 after heating a

specimen wrapped in aluminum foil in an oven for 5 minutes at 560°C. The

intercept and slope of the plot of the l.h. s.of equation (3-5) against 1/T

yields a frequency factor A of 5.9 x 10^ s“* and an activation energy E

a of

121 kJ/mol for the Douglas fir particle board, as seen in figure 6. The

constancy of the l.h.s. of equation (3-7) for a given value of T depends on

the assumption of a single first order reaction. Since this assumption is not

completely valid, the expression in the brackets will vary for different

combinations of m and t even at a fixed temperature and thus could be responsible for some of the scatter in figure 6. While the data need to be analyzed

in terms of more than one reaction the constants determined in figure 6 are

used in the initial checkout of the computer model for heat release rate.

19
3.4 Contraction Factors

The contraction factors measured along the surface (i.e. , l and l ) for

y z southern pine are plotted in figure 7. The contraction is seen to be much

greater across the grain than it is along the grain. In addition, the thickness of each specimen was measured with a micrometer. There was considerably

more scatter in the latter data but they tended to center around the lower

curve. The contraction factors for Douglas fir particle board are displayed

in figure 8. The contraction is independent of direction and is midway

between the contraction factors for southern pine. The data fo,r Douglas fir

particle board can be represented by the expressions,

l = l =1=1 for 0.65 < Z < 1.0

x y z ~

lx

= V

" l

z = 1 “ (0,65 " 2)2 for z < °' 65

3.5 Heat of Pyrolysis

While differential scanning calorimeter (DSC) data has been taken on both

southern pine and particle board to determine the heat of pyrolysis, these

data have not been fully analyzed yet. The heat of pyrolysis is suspected to

be small and has been therefore set equal to zero in the model. Atreya [13]

has found that the results of his mass loss model for wood were relatively

insensitive to the heat of pyrolysis. That sensitivity was also checked on

this project by making a run with the model assuming a heat of pyrolysis of

400 kJ/kg which is approximately the value for alpha cellulose. The peak heat

release rate was reduced by 20%.

(3-8)

(3-9)

20
3.6 Parameters Dealing with Moisture

Atreya found his mass loss rate model to be very sensitive to the

moisture content [13]. He determined the frequency factor and activation

energy for the desorption of water experimentally to be 4.5 x 10-* s -

*- and

43.9 kJ/mole. The heat of vaporization of water is 2.4 MJ/kg. These values

were used in the present model.

4. THERMOPHYSICAL PROPERTIES

4. 1 Heat Capacity

The specific heat of wood does not depend on density or even

significantly on the species. However, it does depend rather strongly on

temperature. In 1912 Dunlap [16] described this temperature dependence up to

106°C for 20 different species of wood as

C = 1. 11 + 0.00486 T (4. 1)

In 1969 Koch [17] found that

C - 1. 11 + .0042 T (4-2)

for spruce pine between 60°C and 140°C where T is in °C and C is in kJ/kg°K.

The present model simply extends the linear relationship in equation (4-2) to

the highest temperature at which the wood retains its chemical structure. For

moist specimens the heat capacity of the wood and the heat capacity of the

21
moisture are linearly combined. The heat capacity of charcoal is reported to

be 0.67 kJ/kg «K [16]. For the purposes of the initial running of the model

the heat capacity has been assumed to vary linearly between wood and final

char and to have the same temperature dependence as for wood. Thus

C = (1.11 + 0.0042 T) (0.43 + 0.57 Z) (4-3)

for oven-dry wood and char.

4.2 Thermal Conductivity Data from the Literature

A universal formula for the thermal conductivity of wood (normal to the

grain) and plywood (across the thickness) as a function of density and moisture content was established experimentally by MacLean [18]. This is given by

K = [237 + 2.00 p (1 - .020 M)] x 10~7 kW/m-K. (4-4)

The density, p, is expressed in kg/m^ over a range of 300-800 kg/m^ and the

moisture content, m, in percent by weight over a range of 0-40%. This formula

was also found to hold for charred wood up to a 37% mass loss. It is noted

that when p goes to zero, k is equal to the thermal conductivity of air.

Hie ratio of the thermal conductivity along the grain to that across the

grain will depend on the fibril angle. A typical ratio is 2.5. The more

nearly aligned the fibers are along the length of the cell wall the higher the

thermal conductivity in grain direction.

22
Thermal conductivity data on oven dry fiberboard and particle board at

24 °C was obtained by Lewis [19] and is presented in Table 1.

Using these data and assuming that the contributions of the water and air

were the same in the fiberboard and particle board as they were in the wood,

equations of the same form as equation (4-3) were obtained for these

materials. For fiberboard

K = [237 + 1.11 p (1 - .036 M)j x

10~7 kW/m.K (4-5)

and for particle board

K = [237 + 1.37 p (1 - .029 M)] x 10

_7

kW/m.K. (4-6)

Lewis also reported average increases in thermal conductivity of 1.37 x 10“ 7

and 2.41 x 10 7 per deg C, respectively, for fiberboard and particle board.

The temperature dependence of the thermal conductivity of wood was given by

Kollmann [20] as

K = K

q

[1 + (1.1 - 9.8 x 10"4

p) (T - T

q )/ 100] kW/m-K (4-7)

The upper limit for this formula is 100 °C.

23
4.3 Thermal Conductivity Measurements

The thermal conductivity was measured on this project as a function of

temperature up to 250°C by exposing vertical specimens of thicknesses between

1 and 2 mm, which are at least 40 mm wide and high, to a radiant panel.

Thermocouples were attached to the front and rear surfaces. At equilibrium

the heat flowing through the specimen is lost from the rear face. Thus

where T^ and T2 are the front and rear surface temperatures, respectively.

The only unknown on the r.h.s. (i.e., could be calculated assuming laminar

free convection. Thus according to Schlichting [21],

where x is the distance from the bottom of the specimen to the thermocouple.

It can also be calculated from the energy balance:

K (Tj - T

2 )/D = 00 (T2 - T*)' + h2 (T

2 - Tq )

or

K = acr (T* - T*) + h

2 (T2 - Tj D/O^ - T

2

) (4-8)

(4-9)

c$" = no

e (T^ + T* - 2T*) + (Tj - TJ + h

2

(T

2 - T

o

) (4-10)

Thus

24
ctq" - aa (T^ + T^ - 2T^)

e W 2 o' (4-11)

If the temperature difference, T£ - T]_, is small enough that X and v are the

same at both faces and the thermocouple junctions are at the same height, the

ratio h^/h2 is found from equation(4-9) to be

As seen in figure 9 the 5 mil (0. 127 mm) diameter thermocouples attached

to the front and rear surface provide support for the specimen. The junctions

are held firmly against the surface by threading them through small diameter

holes and pulling tight. Improved thermal contact as well as a high and known

absorptivity is achieved by coating both surfaces of the specimen with a spray

coat of Krylon 1602* which has an absorptivity of 0.94 [22]. The effect of

the extra thickness provided by the paint has not been investigated yet. The

wires then go to a digital thermocouple readout with a built-in electronic

cold junction.

The external radiant flux incident on the front face is controlled by

varying the distance from the panel. Equilibrium is established in less than

one minute thereby allowing the specimen to go to relatively high temperatures

without significant decomposition as opposed to the standard guarded hot plate

method which takes many hours to establish thermal equilibrium. At each

distance the external heat flux and surface temperatures are recorded. A

*The product name is given for identification purposes only and does not

constitute an endorsement.

1/4

(4-12)

25
small computer program was written to calculate the thermal conductivity from

the above input data. The convective heat transfer coefficient is also calculated by the program as a check on the system.

Table 2 shows the results for a 1.27 mm thick oven dry specimen of

southern pine while table 3 shows similar data for a charred specimen. These

data are plotted in figure 10. The lines represent a least squares fit. The

extrapolated value of the thermal conductivity at 20°C is 1.22 x 10“^

kW/m »K compared to 1.23 x 10

-4 kW/m »K predicted by MacLean's formula (4-4)

using the measured density of southern pine which is 498 kg/m^. The

calculated values from eq. (4-4) for both charred and uncharred pine are

included in the figure.

The measured density of the char is 207 kg/m . However, the calculated

temperature coefficient using Kollman's formula (4-7) is an order of magnitude

higher than the measured one. The thermal conductivity data plotted in figure

10 can be expressed by the formula

K - 1.20 (1 + 0«0026 (1.35 - Z) T) (0.71 Z + 0.29) x 10~4 kW/m.K (4-13)

where the temperature is in °C.

The experimentally determined thermal conductivity of uncharred and

charred Douglas fir particle board is listed in tables 4 and 5 and plotted in

figure 11. The value of the thermal conductivity of uncharred particle board

at 20°C in figure 11 was determined with a guarded hot plate. The upper line

was obtained by a least squares fit. Because of the larger scatter and the

limited temperature range of the data the use of a least squares fit for the

26
lower line led to an unreasonably high value of the thermal conductivity of

the char at ambient temperature. Thus the lower line was passed through the

center of gravity of the data points and the calculated value of the thermal

conductivity using eq. (4-6) with the measured char density. The thermal

conductivity represented by the lines in figure 11 can be expressed as

K = 1.16 (1 + 0.0058 (1.6 - Z) T) (0.84 Z + 0.16) x

10~4

kW/m.K (4-14)

Equation (4-14) was used in the computer model. This equation was determined

for the temperature range over which wood could be expected to exist in its

original form and is simply extrapolated into the high temperature region.

High temperature data on charred specimens are needed to accurately predict

the thermal conductivity over the full temperature range required. The

measured value of the thermal conductivity at 20 °C using eq. (4-14) for

extrapolation is 1.24 x 10

_<^ kW/mK compared to 1.21 x 10”^ kW/m «K calculated

from equation (4-6) using a density of 709 kg/m^ for Douglas fir particle

board. The calculated and measured temperature coefficients were within 20%

for the particle board.

The rear surface convective heat transfer coefficient was calculated for

comparison with the measured values reported in table 2. At the highest heat

flux the rear surface temperature for uncharred southern pine was 234°C. In

this case the average film temperature in the boundary layer was 127 °C. The

thermal conductivity and kinematic viscosity at this temperature are

3.37 x 10 ^ kW/mK and 25.9 x 10~^m^/s [21], respectively. The thermocouple

junction was 0.02 m above the lower edge and the ambient temperature was

30 C. When these data were substituted into equation (4—9) the heat transfer

27
than the measured value. In addition to experimental errors, the flow may not

correspond to the ideal condition required by equation (4-8). On the other

hand the height of the particle board specimens was twice that of the pine

yielding a calculated coefficient at 230°C of 0.0079 which is 30% higher than

the measured value in table 4. These 30% differences only lead to a 10% error

in the thermal conductivity at 230 °C.

5. CALCULATIONS OF HEAT RELEASE RATE USING THE MODEL

The computer program requires input data for a number of parameters.

Some of these have been experimentally determined on the project, some have

been taken from the literature and some are simply assumed at this stage.

These parameters along with their assigned values and sources are listed in

Table 6. The front and rear surface temperature, the mass loss rate (equation

(2-4)), the heat release rate (equation (2-5)), the char depth, and the effective heat of combustion are all calculated as a function of time during the

test. The effective heat of combustion is simply equal to the ratio of the

heat release rate and the mass loss rate. The char depth is equal to AX

q

multiplied by the number of slices for which Z is less than 0.95. Some of

these outputs are plotted in figures 12 to 19 for different external radiant

heat fluxes, specimen thicknesses, and moisture contents. The baseline case

is for an oven dry 12.7 mm thick specimen of Douglas fir particle board

exposed to an external radiant heat flux of 50 kW/m^. In all cases the rear

surface is assumed to be insulated and impervious to the flow of volatile

pyrolysis products and water vapor.

28
The program has been set up on a Tektronix 4052 terminal using BASIC.

The total number of slices is limited to 60 by the capacity of the microcomputer. The longest acceptable time step is one second at an incident flux

of 25 kW/m2

, and 0.1 second at an incident flux of 100 kW/m2 . This can be

increased later on in the run. These critical times were determined by using

successively smaller time steps until there were no further changes in the

output data curves. The calculations require about 30 seconds per time step.

A typical run takes about 4 hours.

Thie calculated front and rear surface temperatures for a dry 12.7 mm

specimen of Douglas fir particle board exposed at an external radiant flux of

50 kW/m are shown in figure 12. The front surface temperature shows a cusp

at 45 seconds, when ignition occurred. It approaches 700°C by the time the

flame goes out. Figure 13 shows the predicted progression of the char front

into the material. The char front here is taken to be located at the center

point of the slice whose mass retention fraction has just dropped to 0.95.

After an initial rapid penetration the charring rate becomes nearly constant

until the rear surface temperature starts to rise. Then it increases

abruptly. The apparently constant rate may depend on specimen thickness.

Figure 14 shows the predicted mass flow through the front surface. The second

large peak occurs when the thermal wave is reflected from the insulated rear

face. This second peak would be missing altogether if the rear surface were

maintained at some low temperature. Figure 15 shows the calculated heat

release rate curve. Its features are similar to the mass loss rate curve

except that it rises abruptly from zero to 30 kW/m2 at ignition and the ratio

of the second and first peak is higher for the heat release rate curve. The

first peak is about 240 kW/m . The effective heat of combustion is plotted in

29
figure 16. It is relatively constant over the first part of the curve decaying only slightly to a minimum and then rising abruptly when the rear surface

begins to char. The magnitude during the early part of the curve is 12 MJ/kg

versus 20 MJ/kg for the gross heat of combustion of the uncharred particle

board determined by the oxygen bomb calorimeter. The bump in the curve around

400 s is an artifact caused by a change in the time step size at that point.

Throughout the above calculations, the heat of pyrolysis has been set

equal to zero. The effect of the heat of pyrolysis on the heat release rate

curve is displayed in figure 17 where it has been set equal to 400 kJ/kg which

is approximately the value for alpha cellulose. This resulted in a 20% drop

in the peak heat release rate and a substantially larger drop in the second

peak. Figure 18 shows the effect of a 7% moisture content. This is the

equilibrium value for Douglas fir conditioned at 50% RH at 23 °C. This results

in a drop in the peak heat release rate of about 10%. The value of the first

peak is relatively unaffected by decreasing the thickness of the slab but the

second peak is much higher and earlier in time as seen in figure 19. Lowering

the irradiance to 25 kW/m^ lowers the first peak and extends the time scale as

seen in figure 20. The calculated heat release rate curves for 75 and 100 kW

are presented in figures 21 and 22.

6. HEAT RELEASE RATE MEASUREMENTS IN THE CONE CALORIMETER

Heat release rate measurements were made on oven dry specimens of Douglas

fir particle board at external radiant flux levels of 25, 50, 75, and

100 kW/m^. The specimens were all 12.7 mm thick. The measurements were made

in the vertical orientation in the NBS cone calorimeter [7] and are shown in

figures 23 through 26.

30
The heat release rates are determined using the standard method for this

calorimeter which is based only on the oxygen concentration and the volume

flow measured in the exhaust duct. A standard estimated correction is made to

account for the difference between the molar flow of air into the system and

the molar flow of gas in the exhaust duct due to chemical reaction. The mass

loss rate is determined from the load cell.

The first peaks of the measured heat release rate curves increase with

the incident radiant flux but are about 20% lower than the calculated ones.

The second peaks are lower than the first peaks for the measured curves. This

is probably due to the absorption of some heat by the insulation material in

contact with the rear surface. The first peaks fall off faster and the second

peaks occur later for the calculated curves. This discrepancy could be due to

inadequate data on the thermal properties of the char at high temperature or

unrealistic kinetics defined by the assumption of a single first order

reaction. The calculated heat of combustion is close to the measured values

and is independent of the incident radiant flux. See for example figures 16

and 27-30. The early segments of these experimental curves to the left of the

dashed lines are due to instrumental problems and should be ignored.

The three analyzer method of calculating the heat release rate and effective heat of combustion in the cone calorimeter relies on the concentrations

measured in the carbon dioxide and water vapor analyzers as well as the oxygen

analyzer.

The density of the exhaust gases is determined from the concentrations of

oxygen, carbon dioxide and water vapor in the analyzers according to Appendix

31
A. This density along with the exhaust temperature and pressure drop across

the orifice plate in the duct determine the nitrogen flow through the system

according to Appendix B. The nitrogen flow along with the above concentrations were used in the calculation of the mass flows of carbon, hydrogen and

oxygen from the specimen using Appendix C. The latter quantities were used to

determine the mass loss rate and heat release rate and hence the effective

heat of combustion using the methods of section 3.2. The calculation of heat

release rate using all three analyzers is based on the assumption that the

fuel vapors generated by the burning specimen are composed only of carbon,

hydrogen, and oxygen and that combustion is complete. It is not recommended

for the determination of heat release rates in general. The heat release rate

and the effective heat of combustion determined by the three analyzer method

are shown in figures 31 and 32 for the 50 kW/m^ external radiant flux. These

curves depart from those determined by the standard method early in the

exposure because of as yet unresolved problems with the time response of the

water vapor measurement system.

7. DISCUSSION

The prediction of the heat release rate of wood involves (1) the development of a suitable computer program which includes all of the important

physics with acceptable assumptions and approximations and which converge to

the exact solution of the formulated equations and (2) the gathering of the

required input data on the properties of the particular wood specimen over a

large temperature and decomposition range.

32
The computer model includes a description of the heat transfer at the

surfaces, an ignition criterion, the formulation of an energy equation in the

interior along with rate equations for the various chemical species which make

up the solid wood, a means of accounting for the shrinkage of the char, and a

way of dealing with the fissures formed by the shrinkage. This model only

applies during the flaming phase. It is assumed that during this period the

oxygen is completely excluded from the surface so that there is no oxidation

of the char and the pyrolysis takes place in an inert atmosphere.

The heat transfer to the surface includes a specified external radiant

flux, radiation from the surface and convective heat losses assuming laminar

free convection. Laminar flow seems reasonable for the 100 mm high specimens

in the cone calorimeter which is used to check out the model. Turbulence will

have to be included in dealing with the heat release rate from a burning

wall. After ignition the convective loss term is replaced by flame radiation

and convective heat transfer to the surface. The radiation to the surface was

assumed to be 10 kW/nr based on measurements by Tewarson [8]. This would only

be expected to apply to small surfaces. The convective heat transfer coefficient was obtained by measuring the total flux to a 3 mm diameter water cooled

heat flux gage embedded in the surface. The 10 kW/m^ flame radiation was

subtracted from the 30 kW/m measured by the gauge. This difference was

divided by the difference between the flame temperature, which was measured by

a 2 mil thermocouple to be 1200°C, and the water temperature of 20°C. This

yielded a convective heat transfer coefficient of 0.017 kW/m «K. Any temperature dependence was neglected. However, the coefficients both before and

after ignition are modified by a blowing factor. This depends on the B number

which is equal to the product of the mass loss rate times the heat capacity of

33
the volatiles divided by the appropriate heat transfer coefficient. The heat

capacity of the volatiles was assumed to be the same as that of air. Emission

and absorption of radiation at the surface of the specimen depends on the

surface emissivity. This was determined to be 0.80 from the ratio of the

derivatives of the surface temperature with respect to the square root of the

time at the beginning of the exposure for unblackened and blackened specimens

exposed to a gas-fired radiant panel. Any change in spectral emissivity with

wave length was neglected. A state of the art flame heat transfer model needs

to be incorporated into the heat release rate model.

The piloted ignition criterion adopted here was the attainment of a

calculated heat release rate which would be sufficient to maintain a flame

over the entire surface of the specimen. For lower heat release rates the

shortening of the flame will lead to extinction. In the analysis of the

Steiner tunnel [23] it was found that this critical value was approximately

50 kW/m . However, prior to ignition when the test calculation is made there

is no flame heat transfer. Hence the calculated heat release rate would be

less than 50 kW/m at the time just prior to piloted ignition. It was reduced

to 30 kW/m so that ignition could be achieved in the model at an external

radiant heat flux of 25 kW/m which is sufficient to cause ignition of this

material in the cone calorimeter. This choice could have considerable impact

on the time to ignition but probably a minor effect on the heat release rate

beyond the very early part of the curve. In any event this is another part of

the model which needs to be improved.

It was necessary to use a difference formulation for the energy equation

because the dimensions of the slices and the material properties change during

34
che burning period and are, in general, different for each slice. A grid of

60 slices was necessary to prevent oscillations in the calculated heat release

rate versus time curve for the 12.7 mm Douglas fir specimens. This grid size

required a time step no greater than 1 second at an external radiant flux of

25 kW/m^ and 0.1 second for 100 kW/rn^. However, after the minimum in the heat

release rate curve the time step could be increased. The maximum permissible

time step was found by reducing it until there was no perceptible difference

in the generated heat release rate curve. The time step determined this way

did not satisfy the usual convergence criterion,

• KAt - < 1/2, (7-1)

Pc(Axr

"

in the case of the larger time steps. If the oscillations referred to above

were due to the violation of the convergence criterion, the effect of reducing

the grid spacing would be to aggrevate the problem. They are more likely to

be due to intolerably large changes in z or in the material properties over

the distance Ax.

An important element of this model is the ability to consider the rate

equation, heat of pyrolysis, heat of combustion of the volatiles generated

during pyrolysis, and heat capacity separately for each chemical component

present in the solid wood. However, as a practical consideration it is necessary to lump in so far as possible all of the species with similar properties

and ignore those that are present in very small quantities. Thus wood might

be considered to consist of three components - cellulose, lignin and heraicellulose — although hemi cellulose consists of a number of different carbohydrates and there is a small quantity of miscellaneous extractives present.

35
To make use of the additional detail it is necessary to measure the properties

of the individual components. Since this has not been done as yet, it has

been necessary to consider wood as a single chemical species in this report.

Assigning a single first order reaction to wood has not been very satisfactory

as can be seen in figure 6 where different combinations of m and t at a fixed

temperature do not lead to the same value for the ordinate as they would if

the rate were given by equation (3-6).

The char shrinkage normal to the surface is easily handled by the energy

equation by taking the change in slice dimensions into account. The reduction

in spacing results in higher temperature gradients which increase heat conduction. Shrinkage parallel to the surface, while the specimen width is maintained by the rigidity of the remaining virgin wood, sets up stresses which

relieve themselves by the formation of fissures. These are visible as deep

cracks in the surface. The reduction in the area of the region of the surface

between the fissures represents a reduction in the area through which heat is

conducted and also in the area normal to the external heat flux and the heat

flux from the flame. This results in a reduction in heat transfer. However,

the radiant flux can now penetrate deep within the specimen in the area of the

fissures. This is counteracted by the easy outflow of volatiles through the

fibers parallel to the surface. They flow into the fissures and carry the

excess heat with them as they exhaust through the cracks. Up until the time

of the fissure formation the volatiles cool the char layer as they pass

through it. Then the cooling is shut off as the layer is by-passed. The

depth of the fissures is taken to be the middle of the slice whose mass retention factor has just dropped to Zf + 0.05 (1 - Z f

)» This is where 95% of the

mass that can be lost is lost.

36
The bulk properties required as input to the model include the thermal

conductivity, heat capacity, char contraction factors, kinetic constants, and

the heat of combustion and heat capacity of the volatiles generated during

pyrolysis. Sensitivity tests with the model indicated that the shape of Che

heat release rate versus time curve was strongly dependent on the thermal

conductivity. Thermal conductivity data on this project were limited to

temperatures below 250 °C which is the temperature at which the lower molecular

weight species in wood start to decompose. It will be necessary to extend

these data up to 700°C on char. The measurements must be done in an inert

atmosphere to avoid glowing combustion of the char. The general formula for

the thermal conductivity of wood, equation (4-3), as a function of its density

and moisture content is probably adequate at room temperature. However, the

temperature dependence given by equation (4-6) does not appear to be adequate

particularly beyond its reported range of validity which is only up to 100°C.

At the present time it will be necessary to measure the temperature dependence

for each species of wood at its applicable density. It does appear, however,

that it may be possible to construct a temperature dependent heat conduction

model in which there is solid phase heat conduction through the fiber walls

and gas phase heat conduction and radiation through the pore spaces.

The general formula for the heat capacity of wood, equation (4-1), does

appear to apply to all woods over the temperature range for which they are

stable. However, data on the heat capacity of char at high temperatures is

needed. The heat capacity of the volatiles can be deduced from the measurements of the heat capacity of the char.

37
Figures 15 and 17 show the calculated heat release rates at an external

flux of 50 kW/m^ for assumed heats of pyrolysis of 0 and 400 kJ/kg, respectively. The effect on the shape and amplitude of the curve is significant.

Therefore, the heat of pyrolysis must be measured.

Comparison of figures 15 and 20 with figures 24 and 23 show that the

calculated ignition times are nearly twice as long as the measured ones. It

should be noted that the model assumes a constant absorptivity of 0.8 for the

incoming radiation. As the surface layer begins to char the absorptivity

should approach unity for the real specimen in the cone calorimeter and thus a

shorter measured time to ignition would be expected. The calculated char

depth (see figure 13) shows that the calculated time at which the surface

layer loses 5% of its mass is close to the time that the actual specimen

ignites. The calculated ignition temperature, indicated by the cusp in figure

12, was 420°C which is somewhat higher than the 380°C reported by Quintiere

and Harkleroad [24] for Douglas fir particle board. Choosing a critical

calculated heat release rate of less than 30 kW/m^ would have lowered the

calculated ignition temperature and shortened the calculated time to ignition.

As indicated earlier, the ignition criterion in the model must be improved.

It should also be noted that the effect of diathermacy is neglected in the

model. It is difficult to judge its impact on the time to ignition.

One of the motivating factors for the introduction of a heat release rate

model over that of a mass loss rate model was the variation in the effective

heat of combustion during the burning period. However, the calculated effective heat of combustion for dry Douglas fir particle board can be represented

by 12 MJ/kg to within ± 10% over the first three quarters of the burning

38
period for all fluxes between 25 and 100 kW/m . The constancy of the effective heat of combustion is also demonstrated by the similarity of the calculated heat and mass loss rate curves in figures 14 and 15. This is so in

spite of a large variation in the heat of combustion of the vapors over the

full range of decomposition for a single layer within the specimen. This

finding is in agreement with the measurements in the cone calorimeter. Thus a

constant effective heat of combustion might be used in the flame spread models

after all, at least for Douglas fir particle board. However, it is necessary

to measure the effective heat of combustion for the material rather than use

the gross heat of combustion measured in the oxygen bomb calorimeter. The

calculations demonstrate that the low values of the measured effective heat of

combustion of wood are not due to incomplete combustion but rather to the

difference in the carbon: hydrogen: oxygen ratio in the vapors from that of the

virgin wood.

The formulas developed in Appendices A, B, and C are included here

primarily because they will be used to determine the kinetic constants and the

heat of combustion of the vapors on this project in the future. The three

analyzer method used to obtain the heat release rate and the effective heat of

combustion of the specimen in the cone calorimeter, as shown in figure 31 and

32, serves as a partial demonstration of their use. It is unfortunate that

the water vapor analysis system was not functioning properly during the

initial phase of the project. The three analyzer method also provides a means

of determining the effective overall chemical composition of the volatiles in

the cone calorimeter using the formulas of Appendix C.

39
8. SUMMARY

This is a status report on the prediction of the heat release rate of

wood. While much remains to be done in order to obtain a completely satisfactory model, a first cut on the overall problem has been completed. A computer

program has been written, laboratory test methods have been devised to obtain

the critical input data, calculations have been made using the model and

comparisons have been made with experimentally determined heat release rates

from- the cone calorimeter. For the limited comparisons made, the predicted

and measured effective heats of combustion over most of the burning period are

within 25% and the peak heat release rates are within 20%. The shape of the

calculated and measured heat release rate curves are similar but the time

scales are substantially different. This may be due to inadequate data on the

thermal properties of char at high temperatures. The second peak of the

measured heat release rate curve is considerably smaller than the measured

one. This may be due to heat conduction into the marinite backing board.

The computer model is unique in that it (1) accounts for the change in

the heat of combustion of the volatiles generated during the pyrolysis period,

(2) accounts for char shrinkage, and (3) provides for different reaction rates

for the different components of wood. However this last capability was not

exercised during this first test of the model where a single first order

reaction was assumed. This is the standard assumption used in the kinetic

mass loss rate models.

New experimental techniques have been devised to measure the heat of

combustion of the volatile pyrolysis products and the thermal conductivity of

40
wood and wood char at higher temperatures than can be attained for pyrolyzing

materials using the standard methods. During the next stage of the project

the thermal conductivity measurements on the char must be carried to higher

temperatures still. Also high temperature data on the heat capacity of char

must be obtained. The experimental data obtained on the above properties were

determined from a limited number of tests and have not been subjected to a

rigorous error analysis. Therefore they must be regarded as preliminary data

at this point.

9. FUTURE PLANS

As this work continues improvements will be made in the model and in the

experimental methods employed to obtain the input data. Furthermore a much

broader data base will be obtained on the thermophysical and thermochemical

properties of wood and wood char, particularly at high temperature. In order

to reliably describe the kinetic constants for the thermal decomposition of

wood and the effective heat of combustion of its volatile pyrolysis products

as a function of time, it will be necessary to make these determinations on

the individual wood components (i.e. , cellulose, hemicellulose , and lignin).

The prediction techniques will also need to be extended to include other wood

products such as fiber board, hardboard, and plywood. The effect of fire

retardants will also be included.

Improvements to be made to the computer model will include (1) the reduction in grid size and in the time of calculation by transferring the program

to a larger computer, (2) a state of the art model for the flame heat transfer

to the front surface, (3) an improved ignition criterion, (4) modification of

41
the boundary condition at the rear surface to simulate the marinite block

typically used to back the specimen in the heat release rate calorimeter or

the simulation of the wall cavity during a room fire, and (5) a model for

calculating the impact of the fissures.

In the verification tests with the calorimeter some restraint system will

have to be used to hold the specimen in place as long as possible in order to

extend the period over which the calculated and measured heat release rates

can be compared. At present the warping of the specimen near the end of the

test allows flames to move around to the rear surface; or the specimen may

fall out of the holder altogether. For selected tests the specimen will be

instrumented with thermocouples to check the calculated temperature profiles.

Some effort will be devoted to measuring the heat flux from the flame to the

surface in the calorimeter.

Improvements in the pyrolyzer will be aimed at better heat transfer to

the specimen to reduce the amount of decomposition that it undergoes by the

time it reaches a constant pyrolysis temperature. Other problems with the

present pyrolyzer will only become apparent when it is finally used in the gas

analysis mode; those tests should begin soon. It will be beneficial to have

determined the critical thermo chemical properties by two entirely different

methods.

10. ACKNOWLEDGMENTS

This work was supported in part by FEMA. Henry Tovey served as the

technical monitor. In addition I am grateful to Bill Twilley who constructed

the pyrolyzer and helped on many of the other facets of the project.

42
11.

REFERENCES

1. Babrauskas, V. , "Estimating Room Flashover Potential," Fire Technology,

Vol. 16, No. 2, May 1980, pp 94-103.

2. McCaffrey, B.J., Quintiere, J. G. and Harkleroad, M.F. , "Estimating Room

Temperatures and the Likelihood of Flashover Using Fire Data

Correlations," Fire Technology, Vol. 17, No. 2, May 1981, pp 98-119.

3. Smith, E.E., "Heat Release Rate of Building Materials," ASTM Special

Technical Publication 502, June 1972.

4. Parker, W.J. and Long, M.E., "Development of a Heat Release Rate

Calorimeter at NBS," ASTM Special Technical Publication 502, June 1972.

5. Tewarson, A., "Heat Release Rate from Burning Plastics," J. Fire and

Flammability, _8_, 115 r 1977.

6. Tordella, J.P. and Twilley, W.H. , "Development of a Calorimeter for

Simultaneously Measuring Heat and Mass Loss," NBSIR 83-2708, Nat. Bur.

Stand. (U. S.), June 1983.

7. Babrauskas, V., "Development of the Cone Calorimeter — A Bench-Scale

Heat Release Rate Apparatus Based on Oxygen Consumption," NBSIR 82-2611,

Nat. Bur. Stand. (U.S.), Nov. 1982.

8. Tewarson, A. , "Physico-Chemical and Combustion, Pyrolysis Properties of

Polymeric Materials, " NBS-GCR-80-295, Nat. Bur. Stand. (U. S.).

9. Tang, W.K. and Neil, W.K. , "Effect of Flame Retardants on Pyrolysis and

Combustion of a-Cellulose, " J. of Polymer Sci. : C, 65 (1964).

10. Kanury, A.M. , "Rate of Burning of Wood (A Simple Thermal Model),"

Combustion Science and Technology, Vol. 5, 1972.

11. Rung. H.C., "A Mathematical Model of Wood Pyrolysis," Combustion and

Flame, Vol. 18, pp 185-195 (1972).

12. Tamanini, F. , "A Study of the Extinguishment of Wood Fires," Ph.D.

Thesis, Harvard University, May 1974.

13. Atreya, A. , "Pyrolysis, Ignition, and Fire Spread on Horizontal Surfaces

of Wood, Ph.D. Thesis, Harvard University, May 1983.

14. Spalding, D.B., Intern. J. Heat Mass Transfer, Vol. 1, pp. 192-207, 1960.

15. Huggett, C. , "Estimation of Rate of Heat Release by Oxygen Consumption

Measurements", Fire and Materials, Vol. 4, pp. 61-65 (1980).

16. Dunlap, F. , "The Specific Heat of Wood”, U.S. Dep. Agr. Bull. No. 110,

Washington, DC, 1912.

43
17. Koch, P. , "Specific Heat of Oven-Dry Spruce Pine Wood and Bark,” Wood

Sci. 1:203-214, 1969.

18. MacLean, J. D. , "Thermal Conductivity of Wood,” Heating, Piping and Air

Conditioning 13:380-391, 1941.

19. Lewis, W. C. , "Thermal Conductivity of Wood-Base Fiber and Particle Panel

Materials,” USDA Forest Serv. Res. Pap. FPL-77, 12 pp, Forest Prod. Lab.,

Madison Wisconsin 1967.

20. Kollmann, F.F.P. and Cote, W.A. , "Principles of Wood Science and

Technology, Volume I: Solid Wood”, Spinger-Verlag, New York, 1984,

p. 250.

21. Schlichting, H. , "Boundary Layer Theory," 4th Edition, McGraw Hill, 1960,

pp 332-334.

22. Brown, R. J. and Young, B.G. , "Spectral Emission at Ambient Temperatures",

Applied Optics, Vol. 14, No. 12, Dec. 1975, p. 2927.

23. Parker, W. J. , "An Assessment of Correlations Between Laboratory and Full

Scale Experiments for the FAA Aircraft Fire Safety Program, Part 3:

ASTM E84" , NBSIR 82-2564, Nat. Bur. Stand. (U.S.), Aug. 1982.

24. Quintiere, J.Q. and Harkleroad, M. , "New Concepts for Measuring Flame

Spread Properties", NBSIR 84-2943.

44
Table 1

Thermal Conductivity of Fiberboard and Particle Board

Density

(kg/m3

) Thermal Conductivity

Fiberboard

x 104 (kW/m .K)

Particle Board

200 0.50 0.52

400 0.66 0.75

600 0.82 1.04

800 1.05 1.35

1000 1.40 1.70

45
Table 2

Thermal Conductivity of Oven Dry

Southern Pine as a Function of Temperature*

External

Heat

Flux

(kW/m2

)

Front

Surface

Temp.

(°C)

Rear

Surface

Temp.

(°C)

Average

Temp.

<°C)

Thermal

Conductivity

x 104 (kW/m .K)

Rear Surface

Convective Heat

Transfer Coefficient

(kW/m2 »K)

3.6 122 107 114 1.28 .010

4.6 139 121 130 1.35 .011

5.6 158 137 148 1.41 .011

6.8 181 155 168 1.36 .011

9.1 213 180 . 197 1.42 .012

12.4 255 211 233 1.41 .013

15.7 287 234 261 1.46 0.014

*Specimen is 1*27 mm thick and has a density of 498 kg/m^.

46
Table 3

Thermal Conductivity of a Charred Specimen of

Southern Pine as a Function of Temperature*

External

Heat

Flux

( kW/ m2

)

Front

Surface

Temp.

(°C)

Rear

Surface

Temp.

(°C)

Average

Temp.

(°C)

Thermal

Conductivity

x 10^

(kW/m .K)

Rear Surface

Convective Heat

Transfer Coefficient

(kW/

m

2 • K)

3.6 124 101 113 0.75 0.010

4.6 148 120 134 0.78 0.010

5. 6

• 165 131 148 0.77 0.011

6.8 187 148 168 0.81 0.011

9.1 222 172 197 0.82 0.012

12.4 265 204 235 0.91 0.012

15.7 303 233 268 0.99 0.013

* Specimen is 1 . 22 mm thick and has a density of 207 kg/m

3

.

47
Table 4

Thermal Conductivity of Oven Dry Douglas Fir Particle

Board as a Function of Temperature*

External

Heat

Flux

(kW/m2

)

Front

Surface

Temp.

(°C)

Rear

Surface

Temp.

(°C)

Average

Temp.

rc)

Thermal

Conductivity

x 104

(kW/m/ .K)

Rear Surface

Convective Heat

Transfer Coefficient

(kW/m2 *K)

1.8 83 74 79 1.50 0.007

2.7 109 96 103 1.64 0.007

3.6 133 116 125 1.64 0.007

5.4 170 148 159 1.77 .006

7.2 205 177 191 1.98 .007

7.6 209 178 194 1.85 .008

8.9 233 199 216 1.95 .007

11.0 267 230 249 2.24 .006

12.0 288 249 269 2.28 .005

Specimen is 1.96 mm thick and has a density of 709 kg/nr

48
Table 5

Thermal Conductivity of a Charred Specimen of Douglas Fir

Particle Board as a Function of Temperature*

External

Heat

Flux

(kW/m2

)

Front

Surface

Temp.

(°C)

Rear

Surface

Temp.

(°C)

Average

Temp.

(°C)

Thermal

Conductivity

x 10 4 (kW/m/ .K)

Rear Surface

Convective Heat

Transfer Coefficient

(kW/m2 • K)

5.2 155 140 147 1.44 .010

6.2 168 151 159 1.53 .011

7.2 187 166 177 1.44 .011

9.7 221 195 208 1.60 .012

10.5 234 206 220 1.53 .011

11.4 251 222 236 1.60 .010

12.7 270 237 253 1.56 .010

*Thickness is 0.99 mm

Mass retention factor is 0.513.

49
Table 6

Input Data for

Property

Wood

Activation Energy

Pre-Exponential Factor

Heat of Pyrolysis

Original Density

Heat Capacity

Thermal Conductivity

Absorptivity

Contraction Factors

Final Char Yield

Volatile Pyrolysis

Products

Heat Capacity

Heat of Combustion

Water

Activation Energy

Pre-Exponential Factor

Heat of Vaporization

Heat Capacity

Flame

Temperature

Radiation

Total Heat Flux to

Cold Surface

Running the Model for Douglas Fir Particle Board

Value

121 kJ/mol

5.94 x 10 7 s"1

0

709 kg/m3

1.11 (1 + 0.0067 T) x (0.54 + 0.46Z) kJ/kg /.K

1.24 x 10~4 (0.35 + 0.65Z) x

(1 + (T-T0

) 6.8 x 10"4

) kW/m/ -K

0.8 Z > 0.75; 1.0 Z < 0.75

lyi - ly - lz ~ 1 f° r o. 65 < Z < 1 = 1 - (0.65 - Z) 2 for Z < 0.65

0.225

1.05 + 1.80 x 1 0

4 ( T-T

Q

) kJ/kg/ «K

20000 [1.24 - Z] kJ/kg

44 kJ/mol

4.5 x 10 3 s”1 2400 kJ/kg

4.19 kJ/kg/ .K, T < 100 °C

4.19 + 3.1 x 10~3 x (T-100) kJ/kg/ .K, T > 100°C

1200°C

10 kW/m2

30 kW/m2

Source

1

1

2

1

3

1

1

1

1

4

1

4

4

4

5

1

7

1

50
1. Experimentally determined on project.

2. Assumed.

3. Temperature Dependence - Koch [17]; dependence on charring assumed based

on published value for charcoal.

4. Atreya [13].

5. Handbook, of Chemistry and Physics.

6. Calculated.

7. Tewarson [8]

* Used in basic computer program

51
APPENDIX A

CALCULATION OF THE DENSITY OF THE GAS IN THE EXHAUST DUCT

In order to determine the volume and mass flows in the exhaust duct using

an orifice plate or a pitot static tube it is necessary to know the density of

the gas. The total mass flow through the duct is given by

m

N„ N, pco„

v

co.

jH

2

0 H2°

(A-l)

assuming complete combustion. Here nitrogen is taken to include all of the

gases in the atmosphere except oxygen, carbon dioxide, and water. For

simplicity its molecular weight will still be taken to be 28.

Hence the density is given by.

P C0 X

C0, P H 0

2

(A-2 )

Since

equation (A-2) can be written

( A-3 )

P = PN,

(P, ) xn +

CO., N.

) x;CO. (pH 2° N. ) X

,h

2o

( A-4)

The density of each species is equal to its molecular weight divided by the

molar volume at the reference temperature. At 0°C equation (A-4) becomes

52
p = (28 +

4 ^

+ 16 4, - 10 xj^/22.4 (A-5)

Use will now be made of the relationships between the volume fractions

measured in the analyzers and those existing in the exhaust duct. These are

derived in Appendix C. Since water vapor is trapped out of the CC>2 analyzer,

x co„ t 1 ~ Vo) 4. * (C-20)

If water vapor is trapped but CO2 is not trapped out. of the oxygen analyzer,

4, - 0 - 4,o) 4, • (C-23)

In the cone calorimeter both water vapor and CO 2 are trapped out of the oxygen

analyzer so that

v ^ ~ Vo) ^ " 4 ) 4 (C-25)

Combining equations (A-5), (C-20) and (C-25), one finds that the density of

the exhaust gases expressed in terms of the volume factions measured in the

analyzers is given by

P

_

4 - 5 + 0 -4jo) (4 4

2

u /5. 6 (A-6)

in the case of the cone calorimeter.

If the CO2 is not trapped then equations (A-5), (C-20) and (C-23) are

combined instead to yield

53
p - [4.5 + (1 - 4

2o

) ( 2 ’ 5 + + 4 42 )] /5 ' 6 (A-7)

54
APPENDIX B

CALCULATION OF THE FLOW OF NITROGEN THROUGH THE EXHAUST DUCT

The formulas for the calculation of carbon, hydrogen and oxygen release

rates, to be derived in Appendix C, require input data on the nitrogen flow in

the exhaust duct. The formulas for the nitrogen flow will be derived in this

section.

The mass flow of gas through the exhaust duct of the cone calorimeter is

measured with an orifice plate using the equation

(B — 1

)

If the orifice plate conforms to ASTM specifications, the pipe is straight for a -1 1/2 - 1/2 sufficient length on each side and the gas is air, C = 0.031 kg»s »K .Pa

Here Ap is the pressure drop across the orifice plate in Pascals and T

g is the

absolute temperature of the exhaust in K. The orifice plate was calibrated

(not on this project) with a known flow rate of CO

2 and C was found to be

0.028. Since C is proportional to the square root of the density of the gas

we can define a new calibration factor,

C* = /p/p . C (B-2

)

air

and use it in place of C in eq. (B— 1 ) . All densities and volume flows in

these appendices are referred to standard conditions (760 mm Hg and 0°C).

Nitrogen is taken to include all of the gases in the atmosphere other than

oxygen, carbon dioxide and water. The mass flow of nitrogen is given by

55
V

s

p N X

N

p 2 2

C* /Ap/T

e

(B-3)

Using equations (C-20) and (C-23) of Appendix C for the case where CO2 is not

trapped, we find that this can be written in terms of the analyzer concentrations as

/p p . air

c 1 - x

o - x

'CO, ; 4

2

o)

N„

/p P 0 0

- 4, air

(B-4)

Using equations (C-20) and (C-25) of Appendix C for the cone calorimeter where

CO2 is trapped out of the oxygen analyzer, we find

v - 7= 0 - 4,0)0 - 4o )o - 4) c (B-5) 2/pp„ 2 2 2 J e air

The density of the exhaust gas is given by either equation (A-6) or (A-7) from

2 Appendix A while the densities and P a^ r are 1.25 and 1.29 kg/m

respective ly.

56
APPENDIX C

CALCULATION OF CARBON, HYDROGEN, AND OXYGEN RELEASE RATES FROM BURNING WOOD

We wish to calculate the carbon, hydrogen and oxygen content of the

volatile pyrolysis products of wood from the volume fractions of oxygen,

carbon dioxide and water vapor in the combustion products along with the mass

flow of nitrogen through the system. It is assumed that

1. Wood is composed only of carbon, hydrogen, and oxygen.

2. All of the volatiles undergo complete combustion to water vapor and

carbon dioxide.

There are two situations of concern. The first is the pyrolyzer where

the pyrolysis takes place in the nitrogen stream and then is swept into a

methane flame where complete combustion takes place. The second situation is

the cone calorimeter where there is no supply of methane and the volatiles

simply burn in their own flame. The calculational procedures are identical.

The flow rate of methane is simply set equal to zero for the cone calorimeter

but is measured for the pyrolyzer or simply calculated from the volume

fractions of C^, CC^ and ^0 in the exhaust when the wood is absent.

The water vapor volume fraction, Xu ., is the same in the analyzer as it

0

is in the exhaust duct. However, the O

2 and CO2 volume fractions,

X^q and X^ , in the analyzers differ from their values in the exhaust

2

S

2

S duct, Xq and X^ , due to trapping of water vapor from the analyzers.

2 A2

. Furthermore X„ will depend on whether CO2 is also trapped out of the oxvgen

2

57
analyzer as it currently is in the cone calorimeter. Since both cases arise,

the following calculations will consider Case I where CC^ is not trapped and

Case II where it is trapped. It will be assumed that the molar flow ratios

are the same in the analyzers as they are in the exhaust duct for those

species which are present in both.

The mass flow rates will first be calculated in terms of the volume

fractions in the stack or exhaust duct. Then they will be transformed for

each of the two cases to be expressed in terms of the volume fractions in the

analyzers. The stack volume fractions are given in terms of the molar flows

by

n,0

2 (C— 1

)

O • 1 • . • I * 2 \

n

o

2 nco2 V

«n,nn

( C—2

)

and ( C—3 ) n T + n^ + n„„ + n T . N

2 °2 C0

2 " 2°

n.

•N (C-4)

Furthermore

(C-5)

58
Here nitrogen is taken to include all of the gases in the atmosphere other

than oxygen, carbon dioxide, and water. For simplicity its molecular weight

will still be taken to be 28.

The molar flows of the combustion products in the duct are related to the

carbon, hydrogen, and oxygen content of the volatile pyrolysis products, the

species present in the incoming air and the methane by the expressions,

nC0 9 n

C + nC0 9 + n

CH,

2 2 4

(C-6)

1 . nH

2 0 2 Ni

+

^i

2 0 + 2 nCH4

( G—7

)

. 1 • * • O /• . • O If O \ n

0 o 2 n

0 n

0 o

( nC0„

" nC0j 2 (°H o 0" “iLo' (C-8)

Combining equations ( C— 1 ) to (C-8) the molar flow ratios of atomic carbon,

hydrogen, and oxygen in the volatile pyrolysis products to the molecular

nitrogen flowing through the system are given by

_C_ V

CO,

X

CO, CH,

n„ 1 - X§„ - X

S 2 “C0

2 " X

H

2 0

1 ~ X

°

2 " Xc02 Xr2°

^2

(C-9)

%

2

*H,

2 ^o CH,

n„ 1 - X? - xL - X? „ 1 - X? - x!L - Xjj Q

-4

o

2 co2

h

2 o °2 C°2 “2

V

( C — 1 0 )

and

59
(C-ll)

2 X_ + 2 X

co

2 + ^0 2 X° + 2 X® + X.° o2 co2 h2 o

1 - Xrt - X

CO, V

- X

CO, - XV

"CO,

The ambient volume fractions X„ , X^„ » and X^

Q are determined from the

2 2 2

analyzers prior to the test with the traps bypassed.

Noting that

TMC 3 n

C

( C — 1 2

)

c“H 1 °H

28 .nXT

( C—1 3

)

% 4 “0

and

4

7

(C-14)

(C-15)

we find that

(C-16)

60
“H

H2° V

1—

o

a co

2

h

2 o ^2°

1 . m

N

" 4 m

CH.

2 4

(C-17)

and

4

. 2 V2 *°2+ ^2° 2 X

°2+ 2 X“2

nu = -=r

+ V 1 _ x

s - xs - xs °2 C°2 V

i _ v° — x° — x°

o

2 co

2

h

2 o

"n.

C C— IS)

Equations (C-16), (C-17) and (C— 1 8 ) are in terms of the volume fractions in

the exhaust ducts. It is necessary to establish the relationships between the

volume fractions in the analyzer and in the exhaust duct.

The concentration in the CO2 analyzer is given by

n

CO,

nN

2 + n

°2 + nC0

2

(C-19)

where the molar ratios are taken to be the same in the analyzer as they are in

the exhaust duct for N2 , O2 , and C02« Combining equations (C-2) and (C-19)

yields

x

co

2 " V 4C02

(C-20)

If CO2 is not trapped out of the oxygen analyzer (Case I) then

X* = °2 nN

2 + n

0

2 + nC0

2

(C-2 1

)

61
If CC>2 is trapped (Case II) then

0

,

°2 V"°2

(C-22)

Combining equations (1) and (21) yields

x

0

2 - 0 - 4,0 ) *5 (C-23)

for Case I. Combining equations (C-l) and (C-22) yields

X

0 o

f 1 “ X

C0„ ~ ^O^ ^ (C-24)

for Case II. Combining equations (C-20) and (C-24) expresses the volume

fraction of O

2 in the exhaust duct in terms of the volume fractions in the

analyzers,

4 - o - 4.o)

c

1 4>j 4 (C-25)

2 w

2

It can be seen from equations (C-20) and (C-23) that for Case I

1 - x

o - xL- 4o - 0 - 4oKi - xj - 4 ) (C-26)

'2 2

Substituting (C-20), (C-23) and (C-26) into (C-16), (C-17) and (C-18) yields

for Case I with no trapping

4>. CO, m

C 7 -xt "XA

m,. o o o l“N 4 CH,

°2 ~

C°2 °2 C°2 ^2°'

(C-27)

62
1 “H

= 14

H2° h

2 °

1 . m*, T m ^-4 0^4 '4o ) 'X

2o < 0/ 2 4

(C-28)

2 2 2 2 2

and

h

2o m

0

=

7

2 (<+4) ) 2x

o,

+2x

So 2

+x

S

2

o' + t 7———~ — 1 (C-29)

^<2 0 ^<

2

<

0z

) 1 -x

o

2

-x

co

2

-x

h

2 o )

2

It can be seen from equation (C-20) and (C-25) that

1 X

0

2 X

C0

2 ^0 f 1 ^O^ 1 ' X

0

2 ^ 1 X

C0

2

'* (C-30

)

Substituting equations (C-20), (C-25) and (C-23) into equations (C-16), (C-17)

and (C-18) yields for Case II (with trapping)

3 m0 = t

A

C0, CO,

. 3 . m

N0 ~ 4 m

C M CH, fl-X4 ' )(1-X* } 1-X° - X° - x° ) N

2

4 CH

4

\

^ 0„ A COJ 0„ C0„ H„0 ; /

(C-3 1

)

2 2

i

| *Y

XV i

i (C-32

)

m~ = t

'1($2 * 4>

2

) J

+ o-^LoK^jc1 -^) 1 - x

S

- x

2o„ - 4 ol'*2 4

2 °

2 X

S

2 + 2 X®2

+ *£ 0

(C-33)

63
Now we drop the superscripts S, A and A' and assume that the volume fractions

S are those measured in the analyzers, (X^ is the volume fraction in the

water vapor analyzer). We are assuming Case II where the CO2 is trapped.

Then

3 m = —

c

CO, CO,

7

\( 1 -x

o

2

)( 1 -x

Co

2

) 1'xo

2

'x

co 2

'xh

2 o V 4 m

CH

,

(C-34)

“H 14

^0 ^2 °

( 1 -xh

2 o )( '"V

(

L

"V 1 "X

o

2

’X

co

2

'}?2 o I

"

2 "

4 m

CH, (C-35)

4

, 2 (V x

co

2

^ "0 =

7

' +

.0 „0

h

2 °

2

^ X

0

2 +XC02

^ +X

H

2 0

^V^co,) x -x

o

2

-x

co

2

^

2 o /

"

2 m

N,

(C-36)

64
BURNING

SLAB

65

Boundaries

move

as

char

shrinks
66
PYROLYZER

67

Fiberglass

insulation
TOP

VIEW

OF

CLOSURE

SLIDE

(0

<0 O

68

Closure

Slide
HEAT

OF

COMBUSTION

(MJ/

kg)

0 0.2 0.4 0.6 0.8 1.0

MASS RETENTION FRACTION (z)

5. Heat of Combustion of Pyrolysis Vapor for Douglas Fir

Particle Board

69
ACTIVATION ENERGY AND FREQUENCY FACTOI

FOR DOUGLAS FIR PARTICLE BOARD

6. Arrhenius Plot for Douglas Fir Particle Board

70
CONTRACTION

FACTORS

FOR

SOUTHERN

PINE

UOlOVd NOIJ.OVU.LNOO

71

MASS

RETENTION

FRACTION

Contraction

Factors

for

Southern

Pine
CONTRACTION

FACTOR

FOR

PARTICLE

BOARD

CM

o

CO

a O

o

in

s O

<0

O

o

CO

I O

0) o

00

aoiovd NOiiovaiNoa

72

MASS

RETENTION

FRACTION

Contraction

Factors

for

Douglas

Fir

Particle

Board
9. Experimental Setup for Determining Thermal Conductivity

73
THERMAL

CONDUCTIVITY

(kW/m-K)

1.6

0.4 -

0.2 -

•o Method of section 4.3

A Calculated from Eq. (4-4)

50 100 150 200 250 300

TEMPERATURE (°C)

10. Thermal Conductivity as a Function of Temperature for

Charred and Uncharred Specimens of Southern Pine

74
THERMAL

CONDUCTIVITY

(kW/m-K)

11. Thermal Conductivity as a Function of Temperature for

Charred and Uncharred Specimens of Douglas Fir Particle Boar:

75
800

76

Calculated

Front

and

Rear

Surface

Temperatures

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

50

kW/m^
77

Calculated

Char

Depth

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

50

kW/m^
( S/3VW9 ) ILVa S$01 sswt

78

Calculated

Hass

Loss

Rate

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

50

kW/m

2
350

( 3VWMM ) 3!V« 3SVJT3b 1V3H

Calculated

Heat

Release

Rate

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant
s

g

QJ

OO

o

( 3WVMM ) NOUSne^OO JO 1V3H

80

Calculated

Effective

Heat

of

Combustion

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

50

kW/m

2
200

( 3VWMM ) 3!V« 3SVTQa 1V3H

Calculated

Heat

Release

Rate

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

with

an

Assumed

Heat

of

Pyrolysis

of

400

kJ/kg

Exposed

at

an

External

Radiant

Flux

of

50

kW/m

2
350

8

O

o

in

o

o

o

m

o

o

CXJ

8

o

CO

00

( 3VHVAIW ) 3iva 3SV3T3H 1V3H

82

Calculated

Heat

Release

Rate

for

1

%

Moisture

Content

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

50

kW/m

2
600

Calculated

Heat

Release

Rate

for

Dry 6

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

50

kW/m 2
300

( 3VWMX ) 31Vil 3SV3T3U 1V3N

20.

Calculated

Heat

Release

Rate

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

25

kW/m

2
400

( 2VW/MH ) 3IVd 3SVTT3d 1V3H

h2<2

UJio

85

21.

Calculated

Heat

Release

Rate

for

Dry

12.7

inm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

75

kW/m

2
500

86

22.

Calculated

Heat

Release

Rate

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

100

kW/m 2
300

C\J CVJ t- i-

( 2 W/M>Q 3iva 3SV3“I3d 1V3H

87

TIME

(s)

23.

Measured

Heat

Release

Rate

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

23

kW/m^
350

o

I) 3iva 3SV3H3d 1V3H

LU

ICD

<0b03

OQ

cm X O 3

1—

I

C fa

a> e u

•H C

O 3

a> *h a T3

cn 3

oS S

S iH3

r>« C

• M

CM 3 H J_> X

>s fa M

a e M

O M

<M CO

CU T3 M 3

CO CD fa oa

3 X

CD W

3

a; -a ^ M

3 3

fa o

ea M

3 3

a; i—i cm 3= O S

•H T3 M 3

CD Jj fa

CO 3^0 cd cn 3 *-i 3 *H cm 2 fa O

<•

CM

88
400

CO

co

so3

ul X o 3 c rAt

a)£—i c

o CT3 D —

-

“** •T3 cc£

£ —

CT3 r^«* c

• J- CNI u

X

ss a

Li

iu X V -o

-j x

!T3 CO as o

3> X

CO CzJ

CTJ aj -o

—i L

cu x

as O x a; V —• CM

3) U v

Li X

co r>.

a> —i vu,

in

CNI

( s UJ/AA>0 3iva 3SV313d 1V3H

89
450

( 2w/m>i) Hiva gsvaiaa ±V3H

90

26.

Measured

Heat

Release

Rate

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

100

kW/m^
o

(6>i/m) Nousnawoo jo iv3H

91

TIME

(s)

Measured

Effective

Heat

of

Combustion

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of2

5

kW/in^
(6>i/riAi) NousnaiAioo jo iv3H

92

TIME(s)

28.

Measured

Effective

Heat

of

Combustion

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

50

kW/m

2
(6>i/m) Nonsnawoo jo ivhh

93

29.

Measured

Effective

Heat

of

Combustion

for

Dry

12.7

mm

Specimen

of

Douglas

Kir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

75

kW/m

2
o

o

10

o

o

o

o

CO

o

o

C\J

o

o

10 o

CO CO

mom

CM CM

"

( 6>i/ph) Noiisnawoo do ivbh

c

<uso

V xj a. c

CO CO

1-1 f

73 £ co 0£

• F—

f

CM CO — C

u

>1 4J U xj Q X

Ed

S-i 0 xj CM CO c -o o <u •H CO M o • co a. 3 X

J3 Ed £

O X

U M

CO cm O

o oa M 0)

co —

i

0) u X -M

XJ

4) M

> co •H flj CM

CJ4) CM Ed•H -X

Ed o

O

-o

4) M

3

COco

4) cut s o

60 cm 3 O

O

a

Ed oon

94
350

O

09 C\J C\J 1- r3iva 3SV3“iaa 1V3H

95

Measured

Heat

Release

Rate

Determined

by

the

Three

Analyzer

Method

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

50

kW/m

2
(6>i/m) Nonsnawoo jo ivjh

Measured

Effective

Heat

of

Combustion

Determined

by

the

Three

Analyzer

Method

for

Dry

12.7

mm

Specimen

of

Douglas

Fir

Particle

Board

Exposed

at

an

External

Radiant

Flux

of

50

kW/m

2
HBS-H4A 'Wtv. 2-«C)

VJ.S. OIPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See i nstruction s)

1. PUBLICATION OR

REPORT NO.

NBSIR 85-3163

2. Performing Organ. Report No. 3. Publication Date

JULY 1985

4. TITLE ANO SUBTITLE

Development of a Model For The Heat Release of

Wood - A Status Report

5. AUTHOR(S)

William J. Parker

6. PERFORMING ORGANIZATION (If joint or other thanN&S, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

Gaithersburg, MD 20899

7. Contract/Grant No.

S. Type of Report Si Period Coverea

9.

SPONSORING ORGANIZATION NAME ANO COMPLETE ADORESS (Street. City, State, ZIP)

10.

SUPPLEMENTARY notes

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant in formation. If document includes a significant

bibliography or literature survey, mention it here)

This report describes the status of the development of a method for predicting

the heat release rate of wood for different thicknesses, moisture contents, and

exposure conditions. A computer model has been set up on a microcomputer. Experimental techniques have been devised to obtain the input data required by the model.

These include (1) the thermal conductivity as a function of temperature and percent

loss, (2) the kinetic constants needed to describe the mass loss rate, (3) the heat

of combustion of the volatile pyrolysis products, and (4) the contraction factors

due to charring. Sufficient data on these parameters were taken to exercise the

model. Heat release rates and effective heats of combustion were measured as a function of external radiant flux on 12.5 mm thick dry vertical specimens of Douglas

fir particle board. The calculated and measured, peak heat release rate curves are similar in shape and amplitude but differ significantly in time scale. This may be

due to the lack of thermal conductivity data on the char in the high temperature

range. There is very good agreement between the calculated and measured effective

heats of combustion. The initial results with the model are promising.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate <ey words oy :r~icz z-

:

heat release rate, wood, pyrolysis, heat of combustion, thermal conductivity,

computer models

13. availability

I X | Unlimited

I i For Official Distribution. Oo Not Release to NTIS

[HI Order From Superintendent of Documents, U.S. Government Printing Office, Washington, n r

20402.

I XI Order From National Technical Information Service (NTIS). Springfield, VA. 22161

14. NO. OF

PRINTED P A GES

15. P'

5 1 3 . 00
.. I ' si\. .