Tunnelling and
Underground Space
Technology
incorporating Trenchless
Technology Research
Tunnelling and Underground Space Technology 20 (2005) 223–229
www.elsevier.com/locate/tust
Full-scale burning tests on studying smoke temperature
and velocity along a corridor
L.H. Hu a, R. Huo a, Y.Z. Li a, H.B. Wang a, W.K. Chow
a
b,*
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui, China
Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China
b
Received 25 February 2004; received in revised form 19 August 2004; accepted 29 August 2004
Available online 11 November 2004
Abstract
Full-scale burning tests were conducted in a long corridor to study the variations in smoke temperature and velocity. The results
were compared with the expressions proposed in the literature. It appeared that the reduction in temperature down the corridor can
be fitted by an exponential function on the distance. The power law equation by Bailey et al. [Bailey, J.L., Forney, G.P., Tatem,
P.A., Jones, W.W., 2002. Development and validation of corridor flow submodel for CFAST. J. Fire Prot. Engg. 22, 139–161] also
agreed fairly well with the measured data for dimensionless distance away from the fire source less than 0.4 or when the distance
from the fire source is less than 35 m. The distribution of velocity along the corridor can also be fairly well fitted by exponential
equations.
2004 Elsevier Ltd. All rights reserved.
Keywords: Smoke temperature; Velocity; Decay; Corridor; Tunnel; Fire
1. Introduction
Consequent to the arson fire in a long tunnel in Daegu Korea on February 18, 2003, killing 198 people, and
two more arson fires in Hong Kong and Russia, there
are concerns on tunnel or long corridor fires. Statistics
have shown that smoke was the most fatal factor in fires
(Babrauskas et al., 1998; Besserre and Delort, 1997),
especially in tunnel fires where large amount of toxic
gases were released due to incomplete combustion. In
order to provide appropriate fire safety, the physics of
smoke spreading should be well understood first
(Buchanan, 1994, 1999). Zone models have been developed to predict the smoke layer. The results are useful
in assessing the critical time of smoke descending to
the dangerous height. The basic assumption of these
zone models is that the temperature of the upper smoke
*
Corresponding author. Tel.: +852 2766 5843; fax: +852 2765 7198.
E-mail address: bewkchow@polyu.edu.hk (W.K. Chow).
0886-7798/$ - see front matter 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tust.2004.08.007
layer is the same everywhere, and the time taken to form
the ceiling jet is potentially ignored (Fu and
Hadjisophocleous, 2000; Jones et al., 2000; Jones,
2001). In tunnels or long corridors, there are at least
two steps in smoke spreading:
the ceiling jet forming phase;
the smoke layer descending phase.
The smoke temperature and velocity will be reduced
significantly at positions away from the fire source. It
might take a long time to form a smoke layer. In other
words, zone models might not be applicable for studying
smoke spreading in tunnels or long corridors (Bailey
et al., 2002; Chow, 1996; Forney, 1997; He, 1999; Jones
and Quintiere, 1984). There were proposals on dividing
the tunnel into smaller zones. However, entrainment in
the ceiling jet might be different in a tunnel.
There are some studies on reduction in smoke temperature and velocity along the tunnel as reported in
224
L.H. Hu et al. / Tunnelling and Underground Space Technology 20 (2005) 223–229
the literature. The spread of smoke under a beamed ceiling had been studied by Delichatsios (1981). An expression for the average distribution on DT average
temperature rise at distance x along the beamed channel
was derived as follows:
(
1=3
1=3 )
DT l
x l
¼ 0:49 exp 6:67 St
;
ð1Þ
DT 0 H
H H
where DT0 is the temperature rise near the ceiling over
the fire source, l is one half of the corridor width, H is
the ceiling height and St is the Stanton number.
The temperature decay along the corridor appears to
follow an exponential function. Some exponential
expressions were established by Evers and Waterhouse
(1978) empirically and verified by Kim et al. (1998) in
a corridor of length 11.83 m (He, 1999; Evers and
Waterhouse, 1978; Kim et al., 1998).
However, a power law distribution was also proposed
by Bailey et al. (2002) from their three-dimensional computational fluid dynamics model with large eddy simulation LES3D and tests in an 8.51 m long corridor as
follows:
x=16:7
1
DT ¼ DT 0
:
ð2Þ
2
Whether changes in smoke temperature distribution
will follow an exponential or power law decay along a
long corridor with length larger than 50 m is still unknown. This should be studied carefully before using
the results for designing smoke control systems in real
tunnels.
Information on smoke velocity should be well understood. An empirical exponential expression on the
smoke layer advance velocity u at position x was also
established by Hinkley (1970) for distribution of buoyancy-driven corridor flow
u
2kl
¼ exp ðx x0 Þ
;
ð3Þ
u0
3mcp
where u0 is the smoke velocity at a reference distance x0
and k is the heat transfer coefficient.
In this study, full-scale burning tests were conducted in an 88 m long corridor. Smoke temperature
under the ceiling was measured and the corridor flow
velocity was calculated. Whether the decay of smoke
temperature and velocity can still be described by
exponential distribution in such a long corridor will
be discussed. The results are also compared with BaileyÕs expression to see whether it can be used in such
long corridors.
2. Simplified theoretical analysis
The spread of the smoke front along the ceiling can
be seen as one-dimensional as shown in Fig. 1. Taking
into account the air entrainment, friction with the ceiling
_
(shear stress s) and heat loss to the ceiling (heat flux q),
the steady-state equations for the ceiling jet front were
obtained as follows (Kunsch, 1999):
d
ðqhuÞ ¼ qa we ;
dx
d
d 1
ðqhu2 Þ ge ðqa qÞh2
Momentum :
dx
dx 2
Continuity :
¼ qa we ua s;
1
s ¼ cf qu2 ;
2
Energy :
d
_
ðqhuT Þ ¼ qa we T a þ q:
dx
ð4Þ
ð5Þ
ð6Þ
ð7Þ
The entrainment velocity we can simply be taken as
proportional to the velocity of the ceiling jet
we ¼ bu:
ð8Þ
The heat loss to the ceiling mainly depends on the
heat transfer to the ceiling. The temperature of the contact surface far away from the fire is assumed to be equal
to the temperature of the air flow. With these assumptions, the heat loss of the ceiling jet front to the ceiling
material can be expressed as follows (Kunsch, 1999):
Fig. 1. Simplified model for infinitesimal analysis.
L.H. Hu et al. / Tunnelling and Underground Space Technology 20 (2005) 223–229
q_ ¼ aðT w T Þ ¼ aðT a T Þ:
ð9Þ
If the factor of the friction dominates the velocity decay, that is, ignoring the factor of density difference,
substituting Eq. (10) into (11) gives
Former studies showed that the entrainment is very
small with b = 0.00015, while the friction coefficient in
the tunnel falls within the range cf = 0.0055–0.0073
(Kunsch, 1999). The entrainment part on the right side
of the momentum equation can be ignored when compared with the friction part.
Thus, ignoring the total entrainment part in the continuity equation and momentum equation, the following
equations are obtained:
u
0
¼ eK 2 ðxx0 Þ ;
u0
qhu ¼ const:;
with
ð10Þ
d
d 1
1
qhu2 ¼
ge ðqa qÞh2 cf qu2 ;
dx
dx 2
2
d
ðqhuT Þ ¼ aðT a T Þ:
dx
ð11Þ
ð12Þ
225
du
1
¼ cf dx:
u
2h
ð20Þ
Integrating both sides of the above equation, and
putting in the initial condition, x = 0, u = u0, gives
K 02 ¼
cf
:
2h
ð21Þ
ð22Þ
So, it can be seen from Eqs. (18) and (21) that the distribution of the ceiling jet front velocity should also fall
into an exponential decay.
Substituting Eq. (10) into (12) gives
dT
a
dx:
¼
ðT a T Þ qhu
ð13Þ
Integrating both sides of Eq. (13), and substituting
the initial condition, x = 0, T = T0, gives
a
T Ta
¼ eqhuðxx0 Þ :
T0 Ta
ð14Þ
So, the decay of temperature of ceiling jet front along
a corridor can be simplified as follows:
DT
¼ eK 1 ðxx0 Þ ;
DT 0
ð15Þ
with
K1 ¼
a
;
qhu
ð16Þ
that indicates an exponential distribution.
From Eq. (11), it seems that there are two factors on
the right side that govern the velocity distribution in a
corridor.
If the factor of density difference between the ceiling
jet front and ambient gas dominates the velocity decay,
that is, ignoring the factor of friction, the following
equation was obtained by former researchers to describe
the velocity distribution (Jones et al., 2000; Bailey et al.,
2002)
rffiffiffiffiffiffiffiffiffiffiffiffi
DT
u 0:7 gh :
ð17Þ
T
So, substituting Eq. (15) into (17) gives
u
¼ eK 2 ðxx0 Þ ;
u0
ð18Þ
with
K 2 ¼ K 1 =2:
ð19Þ
3. Experimental procedure
Experiments were conducted in an underground corridor measuring 88 m long, 8 m wide and 2.65 m high.
The north end was closed while there was an opening
of size 4 m (width) · 2.65 m (height) at the south end.
The corridor is located in an underground shopping
mall under construction next to a railway station in
Southern China. The sidewalls were made of concrete
and the ceiling was made of gypsum. The ambient temperature was about 27 C. The schematic view of the
experimental layout and the corridor is shown in Fig.
2. Diesel pool fires were set up at floor level about 9 m
from the north end and in the middle of the two
sidewalls.
Two sets of thermocouples and one set of thermal
resistors were used to measure the smoke temperature
under the ceiling. The first set consisted of 23 K-thermocouples with the first and the last thermocouple at 5 and
27 m from the fire source, respectively. The second set
had 26 K-thermocouples with the first and the last thermocouple at 29 and 54 m from the fire source. Both sets
of thermocouples were positioned at 1 m intervals.
There were eight thermal resistors with the first three
positioned at 2 m intervals, and the other five at 4 m
intervals. The first thermal resistor was 53 m from the
fire source. All the thermocouples and thermal resistors
were positioned at about 2 cm below the central axis of
the ceiling.
Ten pairs of infrared beams, each composed of one
emitter and one receiver, were positioned at 2.45 m high
from the floor. These were installed to detect the smoke
front for deducing the velocity.
Two tests were conducted with four and eight pans of
diesel, respectively. The peak heat release rates for these
two tests were 0.8 and 1.5 MW correspondingly.
226
L.H. Hu et al. / Tunnelling and Underground Space Technology 20 (2005) 223–229
Fig. 2. A schematic of the experimental layout.
4. Results and discussion
Typical temperatures recorded at different distances
away from the fire are shown in Fig. 3, taking the 1.5
MW fire as an example. It is observed that smoke temperature reduced significantly when traveling down the
corridor away from the fire. Temperature near to the fire
source increased much faster than those at positions far
away from the fire. Both the temperature rise and
maximum temperature were detected at later times at
positions further away from the fire. A possible explana220
200
A
B
C
D
E
F
A
180
Temperature (oC)
160
140
B
5m
17m
26m
42m
59m
75m
DT =DT 0 ¼ a ebðxx0 Þ=L :
120
ð23Þ
Statistical fitting gives the following:
C
100
tion is that it took some time for the smoke to travel
down the corridor, i.e. Ôlagging behindÕ the fire source.
Maximum temperatures recorded for every three sampling points are summarized in Table 1.
The dimensionless temperature decay given by DT/
DT0 was plotted against the dimensionless distance
(x x0)/L(x0 = 5, L = 74) from the fire in Fig. 4. It
can be seen that the results predicted by Eq. (2) are similar to the full-scale data when (x x0)/L was less than
0.4 or x was less than 35. Better agreement was found
for the 0.8 MW fire. But for positions with (x x0)/L
larger than 0.4 or x larger than 35, the predicted temperature decays by Eq. (2) changed faster than the experimental data from both tests. It appeared that the
decays of temperature down the corridor in the two tests
can be fitted by an exponential equation in terms of constants a and b
80
DT =DT 0 ¼ e2:45ðxx0 Þ=L ;
ð24Þ
DT =DT 0 ¼ 0:95e2:72ðxx0 Þ=L :
ð25Þ
D
60
E
F
40
20
0
200
400
600
800
1000
Time (s)
Fig. 3. Typical temperature induced at different distances by the 1.5
MW fire.
Correlation coefficients of 0.9838 and 0.9880 were
found for the 0.8 MW fire and 1.5 MW fire, respectively.
The value of b/L can be seen as the temperature decay
speed along the distance. The fitting gave the values of b
for the two tests of 2.45 and 2.72, indicating the tem-
L.H. Hu et al. / Tunnelling and Underground Space Technology 20 (2005) 223–229
Table 1
Maximum temperature recorded at different distances from the fire
1.2
Distance from fire (m)
1.0
Maximum temperature (C)
1.5 MW
115
106
101
94
90
80
77
74
62.5
52.3
47
57.2
51.5
53.4
48.5
48
46
47.3
45.6
44.1
42.5
40
37.4
35.5
198.2
170
158.4
142.1
134.6
116.8
110.9
103.7
86.1
74.1
62.5
77.6
69.5
65.6
64
62.5
58.7
59.6
57.4
54.3
51.2
48.1
43.8
42.2
7m
39m
79m
0.8
I / I0
5
8
11
14
17
20
23
26
29
32
35
38
41
44
47
50
53
55
59
63
67
71
75
79
0.8 MW
227
0.6
0.4
0.2
0.0
05
0
100
150
Time (s)
0
u=u0 ¼ a0 eb ðxx0 Þ
ð27Þ
Four equations were achieved for the two tests with the
two different methods used to measure the arrival times
exponential fitting of 0.8 MW
exponential fitting of 1.5 MW
Bailey et al. (2002)
experimental data of 0.8 MW
experimental data of 1.5 MW
1. 0
0. 9
0. 8
∆T/T∆ 0
0. 7
0. 6
0. 5
0. 4
0. 3
0. 2
0. 1
0 .2
0 .3
0 .4
300
methods are very close to each other for the two tests.
The method based on infrared beams was acceptable
to track the smoke front.
Taking the measured arrival time at every 8 m down
the corridor, the average velocities in those locations
were calculated:
8
ui ¼
;
ð26Þ
ti ti1
where ti is the arrival time of the smoke front to position
i.
Velocity decays, defined as ui/u0, were plotted against
the distance from the fire source in Fig. 7. Exponential
fittings were also attempted to approach the experimental data by the following:
1. 1
0 .1
250
Fig. 5. Tracking the arrival of smoke front by infrared beams.
perature decay speed factor of 0.033 and 0.037,
respectively. The two values are very close to each other.
Arrival times of the smoke front were indicated by
visual observation and the abrupt decrease in optional
light density as shown in Fig. 5. The arrival times measured by these two methods are compared in Fig. 6. The
results can be used to measure the decay of average
velocity in a distance down the corridor of 8 m long.
It can be seen that the data deduced from these two
0. 0
0 .0
200
0 .5
0 .6
0 .7
0 .8
(x-x0) / L
Fig. 4. Temperature decay along the corridor.
0 .9
1 .0
1 .1
228
L.H. Hu et al. / Tunnelling and Underground Space Technology 20 (2005) 223–229
200
W
Infrared beams
0.8MW,by
1.5MW,by Infrared beams
0.8MW,by visual observation
180
Travel Time (s)
160
1.5 MW, by visual observation
140
120
100
80
60
40
20
0
0
10
20
30
40
50
60
Distance from the fire (m)
70
80
Fig. 6. Measured travel time of smoke front.
1.4
1.2
1.2
1.0
1.0
0.8
1.21e −0.006 x
u / u0
0.6
v / v0
v / v0
0.8
0.6
1.00e −0.005 x
u / u0
0.4
0.4
0.2
0.2
0.0
0
10
20
30
40
50
60
70
0.0
80
0
10
20
Distance from fire source (m)
(b)
0.8 MW, by infrared beams
1.6
1.6
1.4
1.4
1.2
1.2
1.0
1.0
0.8
u / u0
v / v0
v / v0
(a)
1.21e −0.005 x
0.6
0.4
0.4
0.2
0.2
0
10
20
30
40
50
60
70
80
0.0
50
60
70
80
60
70
80
0.8 MW, by visual observation
1.5 MW, by infrared beams
u / u0
0
10
20
1.26e −0.004 x
30
40
50
Distance from firesource (m)
Distance from firesource (m)
(c)
40
0.8
0.6
0.0
30
Distance from fire source (m)
(d)
1.5 MW, by visual observation
Fig. 7. Velocity decay along the corridor.
u=u0 ¼ 1:21e0:005ðxx0 Þ ;
0.8 MW fire by infrared beams:
u=u0 ¼ 1:21e0:006ðxx0 Þ ;
ð28Þ
u=u0 ¼ 1:00e0:005ðxx0 Þ ;
0.8 MW fire by visual observation:
1.5 MW fire by visual observation:
u=u0 ¼ 1:26e0:004ðxx0 Þ :
1.5 MW fire by infrared beams:
ð29Þ
ð30Þ
ð31Þ
The decay factors of velocity for the two sets of
experimental data were 0.006, 0.005, 0.005 and
0.004, respectively. (see Table 2).
L.H. Hu et al. / Tunnelling and Underground Space Technology 20 (2005) 223–229
229
Table 2
Fitting results of experimental data on velocity decay
Test case
Fitting results
a
0.8
1.5
0.8
1.5
MW,
MW,
MW,
MW,
by
by
by
by
infrared beams
infrared beams
visual observation
visual observation
b
Correlation coefficient
Value
Standard error
Value
Standard error
1.21
1.00
1.21
1.26
0.13
0.17
0.19
0.13
0.006
0.005
0.005
0.004
0.002
0.004
0.004
0.002
0.6988
0.4472
0.4958
0.5733
5. Conclusions
References
Two sets of full-scale burning tests were carried out
in an 88 m long corridor for studying decays of smoke
temperature and velocity. Temperature decay along
the corridor was measured directly by two sets of thermocouples and a set of thermal resistors placed under
the ceiling. Velocity decay was also calculated by the
travel time of the smoke front measured by infrared
beams and visual observation. The results showed that
temperature distribution along the corridor fell into
exponential decays with a decay factor of about
0.035. The empirical exponential equation obtained
was compared with the equation by Bailey et al.
(2002) used in CFAST. Good agreement was found
when the distance away from the fire source is less
than 35 m.
Decay of velocity along the corridor can also be
fairly well fitted by an exponential equation, indicating
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and observations by human eyes appeared to be the
same.
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Acknowledgements
This work was supported by the China National
Key Basic Research Special Funds (NKBRSF) Project
under Grant No. 2001CB409600, National Natural Science Foundation of China under Grant No. 50376061
and Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) undergroud
Grant No. 20030358051. Thanks also to the KDLIAN
Safety Technology Limited Company for providing the
technology of the infrared beam smoke detection
system.