1-s2.0-S0142941805001509-main
-
Upload
joel-e-valencia -
Category
Documents
-
view
213 -
download
0
description
Transcript of 1-s2.0-S0142941805001509-main
-
Mo
at
ith
*
Engi
acce
Polymer Testing 250142-9418/$ - see front matter q 2005 Elsevier Ltd. All rights reservKeywords: Functional analysis; Superposition; Bench-scale test; Heat release rate
1. Introduction
The heat release rate in a room fire has to be
understood [1,2] in hazard assessment. This will give
key information on the size of the fire; the rate of fire
growth and, consequently, the release of smoke and
toxic gases; the time available for escape or fire
suppression and the type of suppressive action that is
likely to be effective. Other attributes that define the fire
hazard, such as the possibility of having a flashover fire,
can be estimated.
Different combustibles, including both movable and
fixed fuel load [3], are stored in a building. The rate of heat
release in burning these materials together should be
estimated. Mostly likely, only the heat release rates of
individual materials or single items are available. How the
curves can be combined to estimate the resultant heat
release rate curve [4,5] should be understood.
The heat release rate per burning surface area of a
material can be measured by a cone calorimeter [4,6].
Models based on the cone calorimeter results have beenAbstract: In fire hazard assessment, the resultant heat release rate of burning different combustibles has to be known. The principle
of superposition is commonly applied to estimate the total heat release rate from the individual curves measured for single items.
Accuracy of such an approach will be studied with bench-scale tests in this paper.
The heat release rate curves of burning each sample cube of polymethylmethacrylate (PMMA), polyvinyl chloride (PVC),
polycarbonate (PC) and wood were first measured individually by a cone calorimeter. Radiative heat fluxes of 50 and 70 kW mK2
were applied. After that, a PMMA cube was burnt with a cube of another material under the same heat flux. The resultant heat
release rate curves of burning these two cubes were measured. Heat release rate curves of burning the single cube were used to
estimate the resultant curves. The technique of fundamental analysis will be applied for comparing the predicted curves with the
experiments. Importance of the parameter s for estimating the secant inner product cosine specifying the data points intervals will
also be discussed.
For the samples tested, it is observed that superposition gives good estimations of the total heat released curve if those for
individual items were measured under the same radiative heat fluxes. However, the results will not be so good where the curves
for each combustible were measured at different heat fluxes. This point is very important in estimating the possible heat release rate
for a design fire.
q 2005 Elsevier Ltd. All rights reserved.Property
Superposition of he
for combustibles w
W.K. Chow
Areas of Strength: Fire Safety Engineering, Research Centre for Fire
Received 29 June 2005;delling
release rate curves
bench-scale tests
, S.S. Han
neering, The Hong Kong Polytechnic University, Hong Kong, China
pted 2 September 2005
(2006) 7582
www.elsevier.com/locate/polytestdifferent applications such as for train compartments
[79].
ed.
doi:10.1016/j.polymertesting.2005.09.016
* Corresponding author. Tel.: C86 852 2765 7198.E-mail address: [email protected] (W.K. Chow).developed to predict the heat release rate for burning
those materials in bigger rooms [5], and applied for
-
THR Z
0
Q0ctdt (2)
Test A: Two sample cubes at two sides of the tray
with arrangements:
A1: PMMA and PC at 70 kW mK2, 25 mmunder the cone
A2: PMMA and PVC at 70 kW mK2, 25 mmunder the cone
A3: PMMA and PVC at 70 kW mK2, 50 mmunder the cone
A4: PMMA and PVC at 50 kW mK2, 50 mmunder the cone
A5: PMMA and wood at 50 kW mK2, 50 mmunder the cone
Test B: PMMA cube only at one side of the tray with
arrangements:
B1: PMMA at 70 kW mK2, 25 mm under thecone
B2: PMMA at 70 kW mK2, 50 mm under thecone
B3: PMMA at 50 kW mK2, 50 mm under thecone
Test C: PC cube only at one side of the tray with only
Schematic view of heat fluxes
Rfaff
Fig. 1. Cone calorimeter tests.
W.K. Chow, S.S. Han / Polymer Testing 25 (2006) 758276In this paper, how the resultant heat release rate
of two different polymeric materials can be
combined is explored. Polymethylmethacrylate
(PMMA), unplasticized polyvinyl chloride (PVC),
polycarbonate (PC) and oak wood widely used in
the market as consumer products and construction
materials are taken as examples. Samples of those
materials were selected and cut into small cubes of
size 20 mm. The samples were exposed to the same
conditions in a cone calorimeter for measuring the
heat release rates under heat fluxes of 50 and
70 kW mK2. The samples were tested individually
by themselves first. A sample PMMA cube was
then burnt with another sample for comparing with
the calculated heat release rate using Eq. (1).
2. Samples tested
Experimental measurements on one or two sample
cubes of PMMA, PVC, PC and wood were conducted
in a cone calorimeter. The samples were placed at the
side of the cone tray as shown in Fig. 1. The radiative
heat flux of the cone was set at 70 or 50 kW mK2. In
following the procedures in the standard tests [13],
samples were placed at 25 mm below the cone. In this
paper, some samples were also tested by moving
down to 50 mm below the cone [14]. This will give
different ventilation conditions as in real fire
scenarios. Different heat release rate curves can then
be achieved.
The testing arrangements as shown in Table 1 areThe combined heat release rate Q0T for burning twosamples A and B with heat release rates Q0A and Q0B issuggested to be [10]:
Q0T Z Q0A CQ
0B (1)
This was tested before with a cone calorimeter
[11,12].
The heat release rate per unit area Q0ct curves ofdifferent materials measured with bench-scale tests in a
cone calorimeter, time to ignition (TTI, in s), peak heat
release rate per unit area (pkRHR, in kW mK2) and
total heat released per unit area (THR, in MJ mK2) are
estimated. Note that THR is given by:
Nsummarized in the following:Test A
Tests B, C, D, E
100 mm20 mm cube
100 mm
Cone tray
Thermal radiation
R
Rfc
(a)
(b)
(c)one test:
-
Table 1
Functional analysis on the superposition results
Curves
tested
Para-
meters
A1: PMMACPC A2: PMMACPVC A3: PMMACPVC A4: PMMACPVC A5: PMMACwood
Same
heat flux
Under different
heat fluxes
Same
heat flux
Under different
heat fluxes
Different
heat flux
Same
heat flux
Different
heat flux
Under different
heat fluxes
Same
heat flux
Under different
heat fluxes
Same
heat flux
B1CC1 B2CC1 B3CC1 B1CD1 B2CD1 B3CD1 B1CD2 B2CD2 B3CD2 B1CD3 B2CD3 B3CD3 B1CE1 B2CE1 B3CE1
Q0ct Norm 0.13 0.21 0.46 0.17 0.31 0.55 0.19 0.23 0.51 0.70 0.5 0.22 0.82 0.52 0.15Cosine
(sZ1)0.86 0.83 0.56 0.83 0.53 0.16 0.44 0.72 0.14 K0.07 K0.02 0.16 0.11 0.16 0.60
Cosine
(sZ2)0.90 0.88 0.61 0.89 0.59 0.18 0.49 0.78 0.16 K0.07 K0.01 0.18 0.12 0.19 0.65
Cosine
(sZ3)0.91 0.91 0.63 0.91 0.62 0.20 0.54 0.80 0.17 K0.07 K0.01 0.20 0.12 0.21 0.70
Cosine
(sZ4)0.92 0.93 0.65 0.93 0.65 0.21 0.59 0.82 0.19 K0.07 0.01 0.22 0.13 0.23 0.75
Cosine
(sZ5)0.93 0.93 0.66 0.94 0.68 0.23 0.63 0.83 0.20 K0.06 0.02 0.25 0.15 0.25 0.80
THR Norm 0.08 0.16 0.30 0.16 0.25 0.39 0.06 0.14 0.31 0.05 0.51 0.04 0.61 0.41 0.11
Cosine
(sZ1)0.99 0.99 0.90 0.99 0.97 0.84 0.98 0.97 0.86 0.06 0.07 0.97 0.77 0.89 0.99
W.K
.C
ho
w,
S.S
.H
an
/P
olym
erT
esting
25
(20
06
)7
5
82
77
-
C1: PC at 70 kW mK2, 25 mm under the coneTest D: PVC cube only at one side of the tray with
arrangements:
D1: PVC at 70 kW mK2, 25 mm under thecone
D2: PVC at 70 kW mK2, 50 mm under thecone
D3: PVC at 50 kW mK2, 50 mm under thecone
Test E: Wood cube only at one side of the tray with
only one test:
E1: Wood at 50 kW mK2, 50 mm under thecone.
Each testing arrangement was tested several times to
check the repeatability [15]. Only one typical set of
results was used to study the superposition. Results of
the heat release rate per unit area Q0ct measured in thecone and the total heat released per unit area THR for
each test are shown in Figs. 26.
In a real fire, combustibles placed together are
exposed to different radiative heat fluxes. Therefore,
different external radiative heat fluxes and separation
distances among them should be assessed. For the two
samples as tested in this paper, there was a constant heat
flux emitted from the cone Rfc, a heat flux from the
adjacent burning sample Rfa and a heat flux feedback
from the flames Rff acting on the burning surface of the
sample, as shown in Fig. 1c. The distances between the
two samples might become shorter than 6 cm (even
2 cm for PVC) due to melting and swelling upon
burning. There might be stronger interaction between
the two combustibles due to the shorter distance.
Although Rfa might be higher than Rfc, both heat fluxes
are likely to be less than Rff . Except at very high values,
external heat fluxes such as Rfc would only be important
in ignition. Effects of these couplings should be further
studied quantitatively but are not included in this paper.
PVC samples were difficult to ignite under lower
1000
1500
2000
2500 A1 PMMA+PCB1 PMMA at 70 kWm2C1 PC at 70 kWm2S Calculated
B1
C1
S
ase
rate
per
uni
t are
a Q'
c / k
Wm
2
A1
(a)
0 100 200 300 4000
100
200
300To
tal h
eat r
elea
sed
per u
nit
Time / s
D1
Total heat released per unit area
Fig. 3. Test A2.
W.K. Chow, S.S. Han / Polymer Testing 25 (2006) 7582780 100 200 300 4000
500
Hea
t rel
e
Time / sHeat release rate per unit area
0 100 200 300 4000
100
200
300
400
500A1
B1
C1
S
Tota
l hea
t rel
ease
d pe
r uni
t are
a TH
R /
MJm
2
Time / sTotal heat released per unit area
(b)Fig. 2. Test A1.0 100 200 300 4000
500
1000
1500
2000
2500 A2 PMMA+PVCB1 PMMA at 70 kWm2D1 PVC at 70 kWm2S Calculated
Hea
t rel
ease
rate
per
uni
t are
a Q c
' / k
Wm
2
Time / s
D1
B1
S
A2
Heat release rate per unit area
400
500
are
a TH
R /
MJm
2
B1
S
A2
(a)
(b)heat fluxes. Therefore, higher heat fluxes of 50 and
-
W.K. Chow, S.S. Han / Polymer Testing 25 (2006) 7582 790 100 200 300 4000
500
1000
1500
2000 A3 PMMA+PVCB2 PMMA at 70 kWm2D2 PVC at 70 kWm2S Calculated
B2
A3
S
Hea
t rel
ease
rate
per
uni
t are
a Q'
c / k
Wm
2
Time / s
D2
Heat release rate per unit area
400
500
TH
R /
MJm
2
B2
A3
(a)
(b)70 kW mK2 were used. As observed in the tests, PVC
samples melted quickly and evaporated into fuel
vapour. A large quantity of smoke with irritating
smell was liberated upon exposure to the heat fluxes.
Among the four samples tested, PVC was the most
difficult to burn with the longest ignition time. Further,
PVC cubes did not burn steadily with charring. Taking
test A4 as an example, the heat release rate oscillated
with several peaks.
There was smouldering at first in burning the wood
samples. Char was formed later at the burning stage.
PMMA was ignited easily and burnt completely with a
steady rate. The PC samples were also difficult to burn.
However, once ignited, they burnt vigorously with
smoke liberated. Except for PMMA, some residues
were left after burning.
Rate of heat transfer inside the sample from the
external heat flux depends on the effective exposure
area and the distance away from the conical heater.
0 100 200 300 4000
100
200
300
Tota
l hea
t rel
ease
d pe
r uni
t are
a
Time / s
S
D2
Total heat released per unit area
Fig. 4. Test A3.0 200 400 6000
500
1000
1500
2000B3
S
A4 PMMA+PVCB3 PMMA at 50 kWm2D3 PVC at 50 kWm2S Calculated
D3
A4
Hea
t rel
ease
rate
per
uni
t are
a Q'
c / k
Wm
2
Time / sHeat release rate per unit area
300
400
500
nit a
rea T
HR
/ M
Jm2
B3
S
A4
(b)
(a)The heat flux might be reduced by 515 kW mK2 when
the distance of the sample from the heater was moved
from 25 to 50 mm when set at 50 and 70 kW mK2.
There were differences in the exposure areas for the
different samples upon burning. The melted PVC is an
obvious example. Results of heat release rate per unit
area deduced from the cone would be affected. The
exposure areas for all sample cubes were taken to be the
same upper surface area of 4 cm2. The accuracy of the
heat release rate would be affected by the above factors.
However, those effects should be the same to all
samples, giving very little deviations in judging the
superposition principle.
3. Superposition of heat release rate curves
Whether the individual heat release rate curves of
two different materials can be added together (i.e.
superposition) to give the resultant heat release rate
while burning both of them will be assessed by the
measured results [2,1012,16,17].
0 200 400 6000
100
200
Tota
l hea
t rel
ease
d pe
r u
Time / s
D3
Total heat released per unit area
Fig. 5. Test A4.
-
W.K. Chow, S.S. Han / Polymer Testing 25 (2006) 7582800 200 400 6000
500
1000
1500
2000 A5 PMMA+WoodB3 PMMA at 50 kWm2E1 Wood at 50 kWm2S Calculated
B3
S
E1
A5
Hea
t rel
ease
rate
Q' c /
kW
m2
Time / sHeat release rate per unit area
400
500
area
TH
R /
MJm
2
B3
(a)
(b)From the heat release rate per unit area curves Q0CAand Q0CB of two samples A and B, the transient heatrelease rate per unit area estimated Q0CTE is:
Q0CTEt Z 12
Q0CAt CQ0CBt
(3)
Experimental curve on the heat release rate per unit
area for burning the samples A and B Q0CTt under thesame heat flux and the calculated curve Q0CTEt fromEq. (3) are compared in Figs. 26.
Adding the heat release rate curves of two
combustibles by superposition is useful in predicting
real fire scenarios when the combustibles are not placed
too close to each other. The results can at least be taken
as a minimum estimation.
There might be some other effects which are more
obvious for bigger fires. A correction factor might be
required in using superposition. Assuming these effects
can be neglected under a specified standard external
heat flux higher than normal heat fluxes, the net heat
calculated:
0 200 400 6000
100
200
300
Tota
l hea
t rel
ease
d pe
r uni
t
Time / s
S
E1
A5
Total heat released per unit area
Fig. 6. Test A5. The parameter norm is a measure of the relativedifference in magnitude of the two curves.
The parameter inner product or cosine describes theangular difference between the resultant vectors to
provide a quantitative measure on the similarity of
the curve shape.
For good agreement between the experimental and
predicted curves, the value of the norm is expected to be
close to zero, and the value of the cosine is expected to
be close to one.
Following the recommendation by Peacock et al.
[18], the Euclidean norm is calculated by the ith
experimental and model values Ei and mi at the ith timerelease rate for one sample by burning it alone will be
the same as that from burning it together with other
combustible under the same conditions. Therefore, the
upper limits of predicted results can be determined by
applying the results tested under the same standard
external heat fluxes. Test results of each sample
exposed to the same conditions could be added, though
more tests should be carried out to confirm this.
Another method is to calculate the increase in heat
flux by the adjacent burning item. The geometries of the
two combustibles and the relevant flames, the variable
heat flux and other potential factors should be
considered. These aspects will be further reported
separately later.
4. Functional analysis
Instead of comparing the estimated results from
superposition with the experiments in qualitative terms
such as good, satisfactory or bad, functional
analysis proposed for evaluating fire models by
Peacock et al. [18] is used. Fire model predictions
have been compared with test data by Friday et al. [19]
with such approach.
As both experimental and predicted data can be
described by transient curves, functional analysis
would quantify the difference between two curves in
terms of magnitude and shape. The data points within
each curve are described by vectors, summing them up
would give a resultant single vector for each curve. The
distance between the resultant vectors for the predicted
and measured curves is the error. This error can be
normalized to provide a relative difference, or norm,
between the curves. The following parameters will beincrement ti with s data points to be considered at each
-
Norms and inner product cosines were calculated for
the curves of Q0 t and THR for each case under the
indicating very good predictions on curve magnitude.
The shapes of the curves are in fact very close, as shown
in the figures.
For s equal to 1, the computed values of cosine at
higher heat fluxes are higher than 0.72. However, the
values of cosine for Q0ct are 0.16 for test A4 and 0.60
experiment.
7. Conclusions
Samples of PMMA, PVC, PC and wood in different
From the above study, the heat release rate of
burning two material samples together can be estimated
tiK1miKs2=s2tiKtiK1
W.K. Chow, S.S. Han / Polymer Testing 25 (2006) 7582 81(with wood at 50 kW mK2) for test A5. A possible
reason might be because wood and PVC samples did
not burn steadily under the lower heat flux of
50 kW mK2.
Values of cosine would be higher for higher values
of s. For example, the values of cosine for tests A4 and
A5 would be changed to 0.25 and 0.80, respectively, by
taking s as 5.
Results on comparing the curves with functionalc
same radiative heat fluxes. The values were computed
over the burning duration period of 400 and 600 s for
radiative heat fluxes of 70 and 50 kW mK2,
respectively.
Functional analysis results of the point-to-point
comparison are presented in Table 1. It is observed
that the values of the norm are lower than 0.23,increment inside as:
jEKmjjEj Z
PniZ1
EiKmi2s
PniZ1
Ei2s (4)
The secant inner product cosine is:
The parameter s R1 would smoothe the results togive better estimates of large-scale differences. Higher
value of s might not overcome the effects of small-scale
noise between dense data, depending on the shapes of
the curves. Values of s will be varied as 1, 2, 3, 4 and 5
in this paper to investigate its effect on the secant inner
product cosine.
5. Superposition of curves under the same radiative
heat fluxes
E;mh ijEj,jmj Z
PniZsC1
EiKEiKsmi KmiKs=s2ti KPniZsC1
Ei KEiKs2=s2tiKtiK1,Pn
iZsC1mi K
sanalysis suggested that superposition is better for testsby simple addition, i.e. by superposition of the curves
measured for each sample under the same heat flux.arrangements were tested with a cone calorimeter under
different heat fluxes and distances from the conical
heater. Several tests were repeated for each testing
arrangement to ensure its repeatability. One typical set
of results was used to study the superposition.with the distance and exposure area. The result of one
sample tested in other conditions can be taken as a
reference curve, which might be varied under the same
initial conditions. Deviation of the calculated results by
superposition can be estimated by functional analysis.
If the curves under different heat fluxes are added
together, say B3 (under 50 kW mK2) with C1 (under
70 kW mK2) instead of B1 with C1, both the norm and
cosine compared with test A1 deviated from the
matching value of 0 and 1.0. The values of norm and
cosine are 0.46 and 0.56 respectively for B3 with C1
when s is 1. The value of cosine only increased to 0.66
when s is 5.
For curves under the same heat flux but at different
distances below the cone, say combining B2 of
70 kW mK2 for 50 mm and C1 for 25 mm, the values
of norm and cosine are 0.21 and 0.83, respectively. The
value of cosine increased up to 0.93 when s is 5.
Therefore, combining the curves measured under the
same heat flux but at different distances below the cone
would not give results deviating so much from theunder higher heat fluxes, under which the combustion
was more complete.
6. Curves under different radiative heat fluxes
For real fire scenarios, the heat release rate of burning a
combustible will be affected by the total heat feedback
and the total external heat fluxes, which might be varied
(5)Values of norm and cosine gave better agreement for
-
exposed to higher external heat fluxes, such as a
W.K. Chow, S.S. Han / Polymer Testing 25 (2006) 758282external thermal radiation might give more complete
combustion. The results can be taken as a minimum
estimation. The coupling effects between the combus-
tibles, external heat and ambient conditions should also
be considered.
Many more tests, especially full-scale burning
tests [16,20,21] should be carried out on those
samples to support the application of the super-
position principle.
Acknowledgements
This paper is supported by the RGC project
Determination of the concentration needed for extin-
guishing fires with clean agent heptafluoropropane
(FM200) under Grant No. B-Q669.
References
[1] C. Huggett, Estimation of rate of heat release by means
of oxygen-consumption measurements, Fire Mater. 4 (1980)
6165.
[2] R.D. Peacock, R.W. Bukowski, W.W. Jones, P.A. Reneke, V.
Babrauskas, J.E. Brown, Fire safety of passenger trains: a review
of current approaches and of new concepts, NIST Technical
Note 1406, National Institute of Standards and Technology,
Maryland, USA, 1994.
[3] W.K. Chow, C. Cheung, Aspect of fires for factories in Hong
Kong, J. Appl. Fire Sci. 5 (1) (1996) 1732.
[4] V. Babrauskas, S.J. Grayson, Heat Release in Fires, Elsevier,flashover fire with relatively less interaction, or when
they are placed not so closely together with relatively
independent burning.
However, the results of superposition might be
underestimated for real fires when the combustibles are
placed close to each other and with lower external heat
fluxes from the ceiling, walls and smoke layer. Highthe higher heat flux of 70 kW mK2. Examples of
burning PMMA with PVC, PC or wood demonstrated
this. Superposition can further be applied to burning
multiple combustibles. The ignition time, burning time
and peak heat release rate are key points to be
considered for superposition. The resultant curve can
be put into a computer model for simulating the fire
environment in hazard assessment.
Functional analysis suggested that the predicted
curves agreed better with the measured curves for the
tests under higher heat fluxes. Results of superposition
would be better when different combustibles areLondon, 1992.[5] U. Goransson Model, based on cone calorimeter results, for
explaining the heat release rate growth of tests in a very large
room, Interflam93Proceedings of Sixth International Inter-
flam Conference, Interscience, London, UK, 1993, pp. 3947
[6] ISO 5660-1: 2002(E), Reaction-to-Fire TestsHeat Release
Rate, Smoke Production and Mass Loss RatePart 1: Heat
Release Rate (Cone Calorimeter Method), second ed.,
International Organization for Standardization, Switzerland,
2002.
[7] G.J. Duggan, Usage of ISO 5660 data in UK railway standards
and fire safety cases, Paper 3, Fire Hazards, Testing, Materials
and Products, Proceedings of a One Day Conference, 13 March
1997, Rapra Technology Ltd, Shawburry, Shrewsbury, Shrop-
shire, UK, 1997.
[8] W.K. Chow, Fire safety in train vehicle: design based on
accidental fire or arson fire? The Green Cross March/April
(2004) 7.
[9] V.P. Dowling, N. White, Fire sizes in railway passenger saloons,
in: E.S. Kim et al. (Ed.), Proceedings of the Sixth AsiaOceania
Symposium on Fire Science and Technology, 1720 March
2004, Daegu, Korea, Korean Institute of Fire Science and
Engineering, 2004, pp. 602611.
[10] F.W. Mowrer, B. Williamson, Methods to characterize heat
release rate data, Fire Safety J. 16 (1990) 367387.
[11] W.K. Chow, H.W. Au Yeung, On the superposition of heat
release rate for polymeric materials, Arch. Sci. Rev. 46 (2)
(2003) 145150.
[12] W.K. Chow, Assessment on heat release rate of furniture foam
arrangement by a cone calorimeter, J. Fire Sci. 20 (4) (2002)
319328.
[13] ASTM E 135404a, Standard Test Method for Heat and
Visible Smoke Release Rates for Materials and Products Using
an Oxygen Consumption Calorimeter, ASTM International,
USA, 2004.
[14] R. Vanspeybroeck, P. Van Hees, P. Vandevelde, Combustion
behaviour of polyurethane flexible foams under cone calori-
meter test conditions, Fire Mater. 17 (1993) 155166.
[15] ISO 3534-1: 1993(E/F), StatisticsVocabulary and Symbols
Part 1: Probability and General Statistical Terms, first ed.,
International Organization for Standardization, Switzerland,
1993.
[16] ISO 9705: 1993(E), Fire TestsFull-scale Room Test for
Surface Products, International Standards for Organization,
Geneva, Switzerland, 1993.
[17] D.A. Smith, K. Shaw, The single burning item (SBI) test, the
Euro classes and transitional arrangement, Proceedings of
Interflam99, 29 June1 July, 1999, Edinburgh, UK,
Interscience Communications, London, UK, 1999, pp. 19.
[18] R.D. Peacock, P.A. Reneke, W.D. Davis, W. Jones, Quantifying
fire model evaluation using functional analysis, Fire Safety J. 33
(1999) 167184.
[19] P.A. Friday, F.W. Mowrer, Comparison of FDS Model
Predictions with FM/SNL Fire Test Data, NIST GCR 01-810,
National Institute of Standards and Technology, US Department
of Commerce, USA, 2001.
[20] N. White, V.P. Dowling, Conducting a full-scale experiment on
a railway passenger car, in: E.S. Kim et al. (Ed.), Proceedings of
the Sixth AsiaOceania Symposium on Fire Science and
Technology, 1720 March 2004, Daegu, Korea, Korean Institute
of Fire Science and Engineering, 2004, pp. 591601.
[21] W.K. Chow (Ed.), Special issue on full-scale burning tests,, Int.J. Eng. Performance-Based Fire Codes 6 (3) (2004).
Superposition of heat release rate curves for combustibles with bench-scale testsIntroductionSamples testedSuperposition of heat release rate curvesFunctional analysisSuperposition of curves under the same radiative heat fluxesCurves under different radiative heat fluxesConclusionsAcknowledgementsReferences