M E RESOURCE CENTfiE WR BUILDING EXCEUENCE
REPRINT
A Room-Corner Fire Model
including Fire Growth on Linings
and Enclosure Smoke-Filling
Colleen Wade, Jonathan Barnett
From: Journal of Fire Protection Engineering,
Building Research Assn
of New Zealand
Llbrary
Private Bag 50908
Porirua, New Pealand
Funding for the work presented here was provided by the Building Research Levy
and the Foundation for Research, Science and Technology.
ISSN: 0111 7459
J. of Fire Prot. Engr., 8 (4), 1997, pp 183-193
A ROOM-CORNER FIRE MODEL INCLUDING FIRE GROWTH
ON LININGS AND ENCLOSURE SMOKE-FILLING
COLLEEN WADE
Building Research Association o f New Zealand
Private Bag 50908 Porirua, New Zealand
JONATHAN BARNETT
Center for Firesafety Studies
Worcester Polytechnic Institute Worcester, MA USA
SUMMARY
This paper' describes the development of a computer fire model BRANZFIRE intended for
evaluating the performance and hazards associated with combustible room lining materials. It
comprises a single-room zone model fully integrated or coupled with a concurrent flow flame
spread and fire growth model applicable to a room-corner fire scenario. The fire growth model
uses fire property data obtained from a cone calorimeter as input.
The computer model is compared with some available experimental data, with reasonable
agreement. It is concluded that the model has the potential to differentiate the fire hazards
associated with different combustible walls and ceilings in enclosures using a sound scientific
approach.
The purpose of t h i s paper is to describe a
model for predicting t h e fire environment
i n a n enclosure resulting from a roomcorner fire involving combustible wall a n d
ceiling linings. The model combines a fire
growth model for a room-corner fire scenario with a conventional zone model based
on m a s s a n d energy conservation for a
room. A complete description of t h e model
physics i s described by Wade.'
Most existing fire zone model^^,^^^ generally do not account for t h e ignition a n d
burning of wall andlor ceiling lining mat e r i a l s a n d t h u s may underestimate t h e
a c t u a l r a t e of fire development a n d h a z a r d
i n cases where combustible room linings
a r e present. Furthermore, unlike m a n y
computer models t h a t have been developed, emphasis h a s been placed h e r e on
developing a user-friendly interface for
t h i s model, based on t h e Microsoft Win-
dows environment, t h u s making i t more
accessible to fire designers and fire protection engineers, a s well as other researchers.
T h e model described h e r e couples a flame
s p r e a d and fire growth model with a zone
model. The advantage of t h i s i s t h a t t h e
effect of t h e developing h o t layer on t h e
lining flame spread r a t e can be considered. As a hot layer develops, t h e room
surfaces a r e heated and therefore the energy
required to raise t h e t e m p e r a t u r e of t h e
wall a n d ceiling lining m a t e r i a l s to ignition i s lower. This means t h e lining i s
more easily ignited and the flame will spread
more readily across t h e surface, r e s u l t i n g
i n a higher h e a t release r a t e . Ventilation
t o t h e room will also have a n influence a s
t h e t o t a l h e a t release r a t e allowable i n t h e
room will be restricted by t h e available
oxygen supply. The interaction between
t h e fire growth a n d zone models is illust r a t e d i n Figure 1.
Wade, C.. and Barnett, J.. A Room-Corner Fire Model Including Fire Growth on
Linings and Enclosure Smoke-Filling
Flee G r a t h Model
(RoomCornsr Fire)
Height.
O u l p ~ t .Layer
l
Gar Tamps. Spedsr
Conrentrstion3,
U r i b i l 4 , F B ) elc
Figure 1. Structure of BRANZFIRE Model,
T h e only required i n p u t to t h e fire growth
model is t h e h e a t r e l e a s e r a t e p e r u n i t
T h e fire growth model described h e r e i s
a r e a c u r v e from t h e cone c a l o r i m e t e r
t a k e n from t h e work of K a r l ~ s o n . T~h~i s~ . ~ (Karlsson used d a t a a t a n i r r a d i a n c e of 50
model considers concurrent flow flame spread
kWlm2), t h e r m a l i n e r t i a k r c a n d s u r f a c e
for a combustible lining m a t e r i a l p r e s e n t
i g n i t i o n t e m p e r a t u r e Ti, for t h e l i n i n g
i n both t h e walls a n d ceiling. T h e a c t u a l
m a t e r i a l a l s o d e r i v e d f r o m cone c a l o r i m time-dependent h e a t release r a t e measured
e t e r a o r Liftg t e s t s . T h e relevance of e a c h
in t h e cone calorimeter i s used i n a n u of t h e sub-models is discussed h e r e .
merical solution of t h e velocity s p r e a d r a t e .
Lateral or downward spread i s not accounted
Ignition of the Wall Lining
for since t h e t o t a l h e a t r e l e a s e r a t e i s
dominated by concurrent flow flame s p r e a d
T h e t i m e t o ignition of t h e wall l i n i n g i s
i n t h i s configuration.
d e r i v e d from t h e g e n e r a l e q u a t i o n for
t r a n s i e n t h e a t conduction for a semi-infiThere are four sub-models to calculate different
n i t e solid exposed t o a c o n s t a n t n e t s u r p a r a m e t e r s which need t o be d e t e r m i n e d ,
face h e a t fluxlo a n d is given a s follows:
to e n a b l e t h e t o t a l h e a t r e l e a s e curve t o be
d e t e r m i n e d . They a r e :
1. Ignition of t h e wall l i n i n g
2. T e m p e r a t u r e of t h e h o t g a s l a y e r a n d
room surfaces
3. Ignition of t h e ceiling l i n i n g a n d s u b s e q u e n t flame s p r e a d
4. Calculation of t h e t o t a l h e a t r e l e a s e
rate.
4: i s t h e n e t h e a t flux from t h e b u r n e r
flame. Karlsson used 45 kW/m2 for t h e I S 0
9705 test.5 To i s t h e i n i t i a l t e m p e r a t u r e of
t h e wall.
J. of Fire Prot. Engr., 8 (4), 1997, pp 183-193
Temperature of the Hot Gas Layer
and Room Surfaces
Calculation of the Total Heat Release
Rate
I n Karlsson's Model A, correlations by
McCaffrey, Q u i n t i e r e a n d H a r k l e r o a d l 1
w e r e used to determine t h e gas temperat u r e i n a compartment fire. However, t h i s
will not be necessary here since t h i s fire
growth model will be coupled to a zone
model based on energy a n d mass conservation for t h e compartment fire. The zone
model calculates t h e time-dependent upper layer g a s t e m p e r a t u r e . The surface
t e m p e r a t u r e s of t h e wall and ceiling a r e
also obtained from t h e zone model, which
considers t h e h e a t t r a n s f e r processes between t h e hot upper g a s layer and t h e
surfaces i n t h e compartment.
Prior to ignition of t h e wall lining by t h e
g a s b u r n e r , t h e total h e a t release is Q,
After t h e wall ignites, b u t before t h e ceili n g ignites ( i . e . , t, < t < t), t h e total h e a t
release i s given by:
where ~ c" ( t )r e p r e s e n t s t h e h e a t release
r a t e per u n i t a r e a measured i n a cone
calorimeter t e s t a t a n irradiance of 50 kW/
m2. Following ignition of t h e ceiling lining
(t > t, + t), t h e t o t a l h e a t release r a t e is
given by:
Ignition of the Ceiling Lining and
Subsequent Flame Spread
S i m i l a r to t h e ignition of t h e wall lining,
t i m e to ignition of t h e ceiling lining is
given by:
q; i s t h e n e t h e a t flux from t h e flame.
Karlsson used 35 kW/m2 for t h e I S 0 9705
t e s t . 5 T8i s t h e surface t e m p e r a t u r e of t h e
wall a s obtained from t h e zone model solution a n d t a k e s into account pre-heating
of t h e ceiling lining.
The velocity of t h e pyrolysis front (expressed i n a r e a t e r m s ) is given by Karlsson5
as:
The flame a r e a c o n s t a n t K may be t a k e n
a s 0.01 m2/kW.5
where Va(t ) is t h e spread r a t e in a r e a
P
t e r m s a n d is calculated numerically from
Equation 3. The i n i t i a l pyrolysis a r e a i n
t h e ceiling i s given by:
The wall a r e a behind t h e b u r n e r i s represented by A, a n d i s t a k e n a s 0.65 m2 i n t h e
room corner t e s t . T h e h e a t o u t p u t from t h e
b u r n e r , Q ~is, specified a s 100 kW for t h e
f i r s t 300 seconds.
I n addition to t h e description of t h i s model
by Karlsson, a n upper limit h a s been placed
on t h e total h e a t release r a t e from t h e
ceiling m a t e r i a l d u e to t h e finite size of
t h e ceiling. This maximum h e a t release
r a t e i s given by multiplying t h e ceiling
a r e a by t h e peak r a t e of h e a t release per
u n i t a r e a for t h e ceiling m a t e r i a l (meas u r e d i n t h e cone calorimeter).
Wade, C..and Barnett, J., A Room-Comer Fire Model Including Fire Growth on Linings and Enclosure Smoke-Filling
Plume Entrainment
Conservation Terms
T h e zone model solves for t h e u p p e r a n d
lower layer t e m p e r a t u r e s , position of t h e
layer interface a n d species concentrations.
T h e p r e s s u r e equation is n o t solved. T h e
ordinary differential equations for the position
of t h e smoke layer interface above t h e base
of t h e fire, Z, a n d for t h e u p p e r l a y e r
t e m p e r a t u r e , T,, based on conservation of
m a s s a n d energy for t h e upper l a y e r a r e
given by:
T h e o r d i n a r y differential equation for t h e
lower layer t e m p e r a t u r e , T1, based on cons e r v a t i o n of m a s s a n d e n e r g y applied t o
t h e lower layer i s given by:
T h e m a s s flux e n t r a i n e d into t h e plume for
t h e continuous flaming, i n t e r m i t t e n t , a n d
buoyant plume regions respectively is
g i v e n by McCaffrey,13 with modifications
for t h e room-corner environment a s suggested by Mowrer a n d Williamson.14
F o r t h e corner fire, e n t r a i n m e n t r a t e is
t a k e n a s 0.59 sr! t h e e n t r a i n m e n t r a t e for
t h e s a m e fire in t h e c e n t e r of t h e room.I4
T h e e n t r a i n m e n t model used h e r e i s a s i m plification of t h e a c t u a l s i t u a t i o n . T h i s
model a s s u m e s t h a t t h e t o t a l h e a t release.
including t h e burnerlsource, wall lining,
a n d ceiling lining, can be r e p r e s e n t e d by
a single fire located a t t h e position a n d
h e i g h t of t h e burner. I n r e a l i t y only t h e
b u r n e r a n d p a r t of t h e wall l i n i n g e n t r a i n s
a i r from t h e lower layer t o t h e u p p e r layer.
T h e r e s t of t h e wall a n d t h e ceiling lining
a r e a l r e a d y in contact with t h e u p p e r g a s
l a y e r , so t h e y will e n t r a i n a i r a n d oxygen
from the upper (not the lower) layer. Therefore,
for t h e purpose of d e t e r m i n i n g t h e m a s s
flux e n t r a i n e d i n t o t h e corner-plume, only
t h e h e a t released by t h e burnerlsource i s
used i n t h e e n t r a i n m e n t correlation. T h i s
p a r t of t h e model could be improved i n t h e
future.
Vent Flows
T h e o r d i n a r y differential equation for t h e
u p p e r layer species, Yi,, (0,' soot, CO,, CO
a n d H20)concentration, based on conservation of energy applied t o t h e u p p e r l a y e r
i s given by:
These e q u a t i o n s a r e solved u s i n g a f o u r t h
o r d e r R u n g e - K u t t a technique. T h e r o u t i n e
comprises a n a d a p t i v e d r i v e r which e s t i mates the error and adapts the step size
t o achieve t h e specified accuracy.
T h e m a s s flow of a i r a n d h o t g a s e s t h r o u g h
a wall vent is driven by buoyancy. Bernoulli's
equation can be used to calculate t h e flows.
F o r two-way flow, t h e expressions given
by Rockett15 a r e used. T h e model p e r m i t s
m u l t i p l e v e n t s t o be specified, a n d d e t e r m i n e s t h e t o t a l v e n t flow by a d d i n g t h e
two-way v e n t flow for each. Therefore, t h e
calculation is acceptable w h e r e t h e v e n t s
a r e approximately a t t h e s a m e elevation
i n t h e walls, b u t will not correctly model
t h e c a s e w h e r e t h e r e i s predominantly i n flow through one v e n t a n d out-flow through
another.
J. of Fire Prot. Engr., 8 (4), 1997, pp 183-193
The m a s s flow of hot gases flowing out of,
a n d cooler gases flowing i n t h r o u g h , a
rectangular vent i s given by t h e following
equations.15
2
mi =-CdWo
3
112
Text
(12)
A m a s s balance for t h e compartment gives
m, = mi +mf . If we a s s u m e t h a t ?itf << mi,
t h e n t h e position of t h e n e u t r a l plane can
be found by e q u a t i n g Equations 11 a n d 12.
This i s done by a process of i t e r a t i o n a t
each timestep a f t e r a s s u m i n g a n initial
value for t h e location of t h e n e u t r a l press u r e plane. A discharge coefficient of 0.68
i s assumed a s recommended by P r a h l a n d
Emmons.16
Heat Transfer
T h e model i n c o r p o r a t e s a f o u r - w a l l r a d i a t i o n exchange a l g o r i t h m following t h e
m e t h o d described by Forney.17 This algor i t h m allows t h e ceiling, upper wall, lower
wall, a n d floor to t r a n s f e r r a d i a t i o n independently among each other. Radiant heating
of t h e s e surfaces by t h e f l a m e s is also
considered by t r e a t i n g t h e fire as a point
source. The emission of radiation by soot
particles in t h e upper layer and absorption
by carbon dioxide and water vapor is also
considered for both layers. The radiation
exchange submodel i s required t o determine t h e n e t r a d i a n t h e a t flux emitted or
absorbed by each room surface ( i . e . , upper
and lower walls, ceiling a n d floor). These
r a d i a n t fluxes a r e combined w i t h t h e convective h e a t flux a n d used a s t h e boundary
condition for t h e h e a t conduction calculations, while t h e g a s layer absorption d u e
to carbon dioxide a n d w a t e r vapor a n d
emission d u e to soot particles a r e required
for t h e energy source t e r m s i n t h e ordinary differential equations of the zone model.
An implicit one-dimensional, 20-node finite-difference scheme w a s used t o calcul a t e h e a t conduction t h r o u g h t h e ceiling,
upper walls, lower walls, a n d floor. This
allows t h e t e m p e r a t u r e a t a n y node to be
calculated, by solving a s e t of s i m u l t a neous equations for t h e unknown nodal
t e m p e r a t u r e s a t each t i m e step.18 The detailed calculations for all t h e h e a t t r a n s fer processes a r e n o t given h e r e , b u t can
be found i n Reference 1.
Description of Experiment
A full-scale room-corner fire t e s t w a s carried out i n a n experimental house facility
i n order to g a t h e r experimental d a t a for
comparison with the predicted results obtained
from BRANZFZRE. T h e t e s t w a s carried
o u t i n a single room m e a s u r i n g 3.16 m long
by 2.73 m wide by 2.37 m high, a n d includi n g a vent opening i n one wall which was
1.0 m high by 0.405 m wide. T h e sill w a s
located 0.825 m above t h e floor. T h e room
was lined with 25 mm of paper-faced gyps u m plasterboard on t h e walls a n d ceiling,
a n d t h e floor consisted of 20 mm thick
flooring grade particleboard.
The ceiling was f u r t h e r lined w i t h 3 mm
thick medium d e n s i t y fiberboard spaced
off t h e existing ceiling with timber b a t tens. Two s t r i p s of medium d e n s i t y fiberboard, 600 mm wide, were also fixed to t h e
walls each side of one of t h e corners i n t h e
room. An ignition source comprising a square
p a n (250 mm x 250 mm) of i n d u s t r i a l g r a d e
hexane (Pegasol 1516) w a s placed i n t h e
room corner, and t h i s was i n t e n d e d to provide a n approximate h e a t o u t p u t of 85 kW.
The effective h e a t of combustion for t h i s
p a r t i c u l a r fuel w a s determined i n a cone
calorimeter to be 42.9 MJ/kg.
The room was i n s t r u m e n t e d w i t h two t h e r mocouple trees, which s p a n n e d floor to
ceiling, a n d measured t h e g a s tempera-
Wade, C.. and Barnett. J., A Room-Comer Fire Model Including Fire Growth on Linings and Enclosure Smoke-Filling
t u r e s in t h e room a t discrete locations a n d
h e i g h t s above t h e floor. Each t r e e included
e i g h t thermocouples. A weigh-bridge based
on a cantilevered beam w a s used to record
t h e m a s s loss r a t e of fuel from t h e p a n
d u r i n g t h e experiment. T h e deflection of
t h e beam w a s m e a s u r e d by s t r a i n gauges
a n d calibration done u s i n g known weights
placed i n t h e suspended t r a y . T h e m a s s
loss d a t a recorded d u r i n g t h e experiment
w a s used, t o g e t h e r w i t h t h e effective h e a t
of combustion of t h e fuel (previously det e r m i n e d ) , to prescribe t h e time-depend e n t r a t e of h e a t r e l e a s e of t h e ignition
source ( i . e . , b u r n e r ) used a s i n p u t t o t h e
computer simulations.
were considered (25 a n d 30 kW/m2) a s the
ignition source was not in contact with t h e
comer wall surfaces (offset by about 10 mm).
T h e s i m u l a t i o n used h e a t r e l e a s e r a t e per
u n i t a r e a d a t a from t h e cone calorimeter
m e a s u r e d a t a n i r r a d i a n c e 35 kWIm2,
while t h e i g n i t i o n t e m p e r a t u r e ( 2 8 5 " C )
a n d t h e r m a l i n e r t i a ( 1 . 1 2 1 kW2s/m4K2)
for t h e m e d i u m d e n s i t y fiberboard m a t e r i a l w e r e e s t i m a t e d u s i n g t h e method of
QuintiereZObased on a s e r i e s of cone calorimeter experiments a t irradiances in the
r a n g e 10-75 kW/m2.
T h e predicted r a t e of h e a t r e l e a s e i s shown
i n F i g u r e 2 . T h e h e a t r e l e a s e r a t e from t h e
room w a s not m e a s u r e d experimentally.
T h e predicted a v e r a g e u p p e r l a y e r t e m p e r a t u r e compared t o t h e e x p e r i m e n t i s
shown in F i g u r e 3. T h e s e n s i t i v i t y of t h e
model t o t h e n e t h e a t flux from t h e f l a m e
t o t h e wall c a n be s e e n w i t h t h e two v a l u e s
used b r a c k e t i n g t h e e x p e r i m e n t a l r e s u l t s
reasonably well. I t i s noted t h a t t h e comp u t e r s i m u l a t i o n predicted a t r a n s i t i o n t o
oxygen-limited b u r n i n g a t a r o u n d 120-140
seconds. Following t h i s time, t h e h e a t rel e a s e r a t e w a s predicted t o fall a n d be
controlled by t h e available oxygen entrained
i n t o t h e corner plume. Although t h e model
Results and Computer Simulations
T h e g a s t e m p e r a t u r e m e a s u r e m e n t s from
t h e thermocouple t r e e s were used t o calc u l a t e t h e h e i g h t of t h e l a y e r interface,
average u p p e r layer, a n d average lower
l a y e r g a s t e m p e r a t u r e s , u s i n g t h e method
developed by Cooper e t a1. l9
T h e model BRANZFZRE w a s used t o s i m u l a t e t h e room-corner e x p e r i m e n t . T h e n e t
h e a t flux t o t h e ceiling a h e a d of t h e pyrolysis f r o n t w a s a s s u m e d t o be 30 kW/m2,
while two v a l u e s for t h e wall h e a t flux
0
100
200
300
4W
5W
600
Time leecondd
[
- -
- Calculated using wag FIUX of 25 WVW
Figure 2. Rate of Heat Release - 3 mrn MDF Linings
-Calculated using w a l ~
I
~ ofu 30
xW ~ Y
J. of Fire Prot. Engr., 8 (4), 1997, pp 183-193
I
-
Exoeriment
Time (seconds)
-Calculated usina Wall Flux of 30 kWlnF I
-. - . - Calculated usina Wall Flux of 25 kWhn'
Figure 3. Upper Layer Temperature - 3 rnrn MDF Linings
predicted a brief period a t which temperat u r e s exceeded 600 "C, a general t r a n s i tion to a fully-developed fire was not predicted. This was consistent with observations i n t h a t t h e r e was no distinct flashover of t h e room. The t e s t observations
also showed a period of intense b u r n i n g
a n d h e a t release which corresponds q u i t e
well with t h e time of rapid increase i n
predicted h e a t release. T h i s level of i n tense burning t h e n reduced slightly, which
is also consistent with the transition to
a v e n t i l a t i o n - c o n t r o l l e d fire. I t c a n a l s o
be s e e n t h a t a g r e e m e n t r e d u c e s over t h e
l a t t e r s t a g e of F i g u r e 3 . T h i s m a y be a
r e s u l t of n o t modelling b u r n o u t of t h e
lining material.
A comparison with a single t e s t r e s u l t h a s
been described. Many more comparisons
a r e required before t h e accuracy of t h e
model can be evaluated.
T h e model described i n t h i s paper w a s
programmed using Microsoft Visual Basic
Version 3.0. The software is designed to
r u n u n d e r t h e Microsoft Windows environm e n t , a n d a s a r e s u l t t h e usual graphical
user interface exists, a s illustrated in
F i g u r e 4, for t h e opening screen. D a t a i s
i n p u t by t h e user through a series of menus,
forms, and drop-down lists. Following completion of a model r u n , t h e r e s u l t s a r e immediately available to view in t h e form of
g r a p h s (see Figure 41, spreadsheet o u t p u t ,
or a complete printed summary of i n p u t
d a t a a n d results. Context-sensitive on-line
help i s also available, although t h i s h a s
not y e t been fully implemented for all p a r t s
of t h e software.
The model described is under continuing
development a t t h e Building Research
Association of New Zealand, in collaboration with Worcester Polytechnic Institute.
I t i s intended to improve and expand on
various parts of the model and i t s user interface, including t h e addition of improved
flame spread and fire growth routines.
The combined fire zone a n d fire growth
model described h e r e could be used to diff e r e n t i a t e t h e fire performance and likely
189 -
Wade. C.. and Barnen. J.. A Room-Comer Fire Model lncludina Fire Growth on Lininas and Enclosure Smoke-Fillina
I
I
I
Figure 4. Main Menu and Screen.
Figure 5. Graphical Output Available.
fire h a z a r d s associated with different room
l i n i n g m a t e r i a l s in a m a n n e r c o n s i s t e n t
with sound scientific a n d engineering principles. It provides a good basis for f u r t h e r
development a n d enhancement because i t
h a s a very good user interface a n d h a s been
well documented, making i t more a t t r a c tive t o fire designers a n d fire protection
engineers. F u r t h e r comparisons w i t h exp e r i m e n t s a r e required.
T h e a u t h o r s wish t o t h a n k Professor N.
Dembsey of Worcester Polytechnic I n s t i t u t e for valuable discussions r e g a r d i n g t h i s
work which contributed t o w a r d s t h e f i r s t
a u t h o r ' s M a s t e r of Science degree. T h a n k s
a r e also extended t o G r a h a m Cowles a n d
P e t e r Collier of t h e B u i l d i n g R e s e a r c h
Association of New Zealand for t h e i r h e l p
J. of Fire Prot. Engr., 8 (4), 1997, pp 183-193
with t h e experiments. The work reported
was jointly funded by t h e Building Research Levy a n d t h e Foundation for Research, Science and Technology (New Zealand).
T
= temperature (K)
Text
= exterior a m b i e n t t e m p e r a t u r e
(K)
T.
'g
= surface t e m p e r a t u r e for ignition
(K)
Af
AW
Ao
= floor a r e a of t h e room (m2)
T,
= t e m p e r a t u r e of t h e lower g a s
layer (K)
Tu
= t e m p e r a t u r e of t h e upper g a s
layer (K)
T.
= reference t e m p e r a t u r e of
= wall a r e a behind b u r n e r (m2)
= i n i t i a l pyrolysing a r e a i n
ceiling (m2)
C~
= specific h e a t of a i r ( J l k g K)
Cd
= discharge coefficient
g
= gravitational constant
H
= height of t h e ceiling above t h e
base of t h e fire ( m )
krc
K
= flame a r e a c o n s t a n t (m2/kW)
= m a s s flow r a t e of hot gases o u t
t h r o u g h t h e v e n t (kg/s)
mP
91
9,
= m a s s flow r a t e of a i r e n t r a i n e d
into t h e plume (kgls)
= n e t h e a t t r a n s f e r to t h e lower
gas layer (kW)
= n e t h e a t t r a n s f e r to t h e upper
g a s layer (kW)
g/
W
0
Y1.1.
= total h e a t release from t h e fire
(kW)
t
= time ( s )
tP
= dummy variable of integration
= width of v e n t opening ( m )
= m a s s fraction of species i i n t h e
lower layer
YI., U
= mass fraction of species i i n t h e
upper layer
Z
= height of t h e smoke layer from
t h e base of t h e fire ( m )
= mass flow r a t e of cool gases i n
through t h e vent (kg/s)
mo
Va(t) = velocity of t h e pyrolysis front
(m2/s)
= t h e r m a l i n e r t i a (W2s/m4K2)
= mass loss r a t e of t h e fuel (kgls)
mi
ambient a i r (K)
ziv
= height of t h e n e u t r a l plane ( m )
r
= density (kgIm3)
AT
= radiative fraction of energy loss
by radiation from t h e flame1
plume
2,
= time to ignition of t h e ceiling
lining (s)
5',
= time to ignition of t h e wall
lining (s)
Vi
= yield of species i from t h e
pyrolysing fuel ( k g species ilkg
fuel)
- 191 -
Wade, C.. and Barnett. J.. A Room-Corner Fire Model Including Fire Growth on Linings and Enclosure Smoke-Filling
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9. ASTM E 1321-90,Standard Test Method
for Determining Material Ignition and
Flame Spread Properties, American Society for Testing and Materials, Philadelphia, PA, 1990.
10. Saito, K., Quintiere, J.G., and W i l l i a m s ,
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First International Symposium, Hemisphere Publishing Corporation, 1985.
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Harkleroad, M.F., "Estimating Room Temperatures and t h e Likelihood o f Flashover using Fire T e s t Data Correlations,"
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Combustible Lining Materials i n Enclosures, Report T V B B 1009,Lund Univers i t y , Department o f Fire S a f e t y Engineering, Lund, Sweden, 1992.
14. Mowrer, F.W., and Williamson, R.B., "Estimating Room Temperatures from Fires
along W a l l s and i n Corners," Fire Technology, V o l . 23, No. 2, p p . 133-145,
1987.
Karlsson, B., "Models for Calculating
Flame Spread on Wall Lining Materials
and t h e Resulting Heat Release Rate i n
a Room," Fire Safety Journal, p p . 365386. 1994.
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a n Enclosure," Combustion Science and
Technology, V o l . 12, p p . 165-175,1976.
Karlsson, B., "Mathematical Models for
Calculating Heat Release i n t h e Room
Corner Test," Fire and Flammability o f
Furnishing and Contents o f Buildings
ASTM STP 1233, p p . 216-236, American Society for Testing and Materials,
Philadelphia, PA, 1994.
ASTM E 1354-92,Standard Test Method
for Heat and Visible Smoke Release Rates
for Materials and Products Using a n
Oxygen Consumption Calorimeter,American
Society for Testing and Materials, Philadelphia, PA, 1992.
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Flow through a n Opening," Combustion
and Flame, V o l . 25, p p . 369-385,1975.
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T r a n s f e r Occurring i n a Zone Model,"
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1994.
18. Incropera, F.P. and De W i t t , D.P., Fundamentals of Heat and Mass Transfer,
J o h n W i l e y and Sons, 1990.
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Harkleroad, M., Quintiere,
J . and R i n k i n e n , W . , " A n Experimental
S t u d y of Upper Layer Stratification i n
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Full-Scale Multiroom F i r e Scenarios,"
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741-749, 1982.
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and Harkleroad, M., New
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