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Effect of tunnel cross section on gas temperatures and heat fluxes in case of large heat release rate
Accepted Manuscript Title: Effect of tunnel cross section on gas temperatures and heat fluxes in case of large heat release rate Author: Chuan Gang Fan, Ying Zhen Li, Haukur Ingason, Anders Lönnermark PII: DOI: Reference:
S1359-4311(15)00968-0 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.09.048 ATE 7040
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
16-7-2015 16-9-2015
Please cite this article as: Chuan Gang Fan, Ying Zhen Li, Haukur Ingason, Anders Lönnermark, Effect of tunnel cross section on gas temperatures and heat fluxes in case of large heat release rate, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.09.048. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of tunnel cross section on gas temperatures and heat fluxes in case of large heat release rate Chuan Gang Fan1,*, Ying Zhen Li2, Haukur Ingason2, Anders Lönnermark2
1. School of Transportation Engineering, Hefei University of Technology, China 2. Fire Research, SP Technical Research Institute of Sweden, Sweden
Corresponding Author: Chuan Gang Fan. Address: School of Transportation Engineering, Hefei University of Technology, Hefei 230009, Anhui, China. Tel: +86-551-0551-62901960 (Office), +86-18255170802(Mobile) Email: [email protected]
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Highlights
Effect of tunnel cross section together with ventilation velocity was studied.
Ceiling temperature varies clearly with tunnel height, but little with tunnel width.
Downstream temperature decreases with increasing tunnel dimensions.
HRR is an important factor that influences decay rate of excess gas temperature.
An equation considering both tunnel dimensions and HRR was developed.
Abstract
Tests with liquid and solid fuels in model tunnels (1:20) were performed and analyzed in order to study the effect of tunnel cross section (width and height) together with ventilation velocity on ceiling gas temperatures and heat fluxes. The model tunnel was 10 m long with varying width (0.3 m, 0.45 m and 0.6 m) and height (0.25 m and 0.4 m). Test results show that the maximum temperature under the ceiling is a weak function of heat release rate (HRR) and ventilation velocity for cases with HRR more than 100 MW at full scale. It clearly varies with the tunnel height and is a weak function of the tunnel width. With a lower tunnel height, the ceiling is closer to the base of continuous flame zone and the temperatures become higher. Overall, the gas 2
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temperature beneath the ceiling decreases with the increasing tunnel dimensions, and increases with the increasing longitudinal ventilation velocity. The HRR is also an important factor that influences the decay rate of excess gas temperature, and a dimensionless HRR integrating HRR and other two key parameters, tunnel cross-sectional area and distance between fuel center and tunnel ceiling, was introduced to account for the effect. An equation for the decay rate of excess gas temperature, considering both the tunnel dimensions and HRR, was developed. Moreover, a larger tunnel cross-sectional area will lead to a smaller heat flux. Key words: model scale, tunnel cross section, gas temperature, heat flux, longitudinal ventilation
Nomenclature
A
tunnel cross-sectional area (m2)
B
decay rate of temperature downstream of fuel
bfo
radius of the fuel (m)
Cheat,β=1/3
lumped heat capacity coefficient (J/m2 K)
cp
heat capacity (kJ/kg K)
d
characteristic tunnel hydraulic diameter (m)
Fr
Froude number
g
gravity acceleration (m/s2)
H
tunnel height (m)
Hf
distance between fuel center and tunnel ceiling (m)
hc,PT
convective heat transfer coefficient for plate thermometers (W/m2 K)
Kcond
conduction correction factor (W/m2 K)
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k
decay coefficient in fire section
kn
decay coefficient in non-fire section
L
length scale (m)
m
mass flow rate (kg/s)
Q
heat release rate (kW)
q
incident heat flux (kW/m2)
To
ambient temperature or surrounding gas temperature (K)
T cf
ceiling gas temperature (K)
Tc , m ax
maximum gas temperature under tunnel ceiling (°C)
TPT
measured temperature by plate thermometer (K)
Tc
excess gas temperature under tunnel ceiling (K)
Tc , m ax
maximum excess gas temperature under tunnel ceiling (K)
Tc , ref
reference temperature (K)
Tnref
reference temperature in non-fire section (K)
T ref
reference temperature in fire section (K)
Tx
excess gas temperature with a distance from reference location (K)
t
time (s)
u
gas velocity (m/s)
uo
longitudinal ventilation velocity at ambient conditions (m/s)
V
dimensionless ventilation velocity
W
tunnel width (m)
w*
characteristic plume velocity (m/s) 4
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x
distance from fuel centre (m)
xmax
position of maximum ceiling gas temperature (m)
xref
reference position (m)
Greek
density (kg/m3)
Stephan–Boltzmann constant (kW/m2 K4)
PT
surface emissivity of plate thermometer
Subscript F
full scale
M
model scale
max
maximum value
o
ambient
1. Introduction
The characteristics of ceiling jet, such as heat transfer and temperature profile, have attracted extensive attentions in certain thermal engineering research [1-8]. In tunnels, gas temperatures beneath the ceiling and heat fluxes are important factors in the study of risk of fire spread, evacuation and rescue service. The key factors that influence gas temperatures and heat fluxes include heat release rate (HRR), fuel type, vertical distance between fuel and tunnel ceiling, ventilation, and distance from fuel [9-11]. There are three focus points presented here, the nearby maximum ceiling temperature, the varying downstream ceiling gas temperature and the
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corresponding heat flux towards the floor level. All three focus points are investigated as a function of the tunnel cross section. The first focus point, i.e. the maximum ceiling gas temperature, has attracted special attention due to its importance in protection of tunnel structure. Kurioka et al. [12] proposed an empirical model to predict the maximum gas temperature under the tunnel ceiling based on model scale experiments. Li et al. [13] conducted a theoretical analysis of maximum gas temperature under the tunnel ceiling based on the plume theory and validated the theoretical model using a large amount of test data. The results show that the maximum excess gas temperature under the ceiling can be divided into two regions. Under high ventilation, i.e. when the dimensionless ventilation velocity, V uo / w
*
( w* (
Qg b fo o c p T o
)
1/ 3
), is greater than 0.19, the maximum excess gas temperature
under the tunnel ceiling is proportional to the HRR and inversely proportional to the longitudinal ventilation velocity. Under lower ventilation, the maximum excess gas temperature under the ceiling varies as the two-thirds power of the dimensionless HRR, independent of the longitudinal ventilation velocity. Ji et al. [14] carried out a series of model scale experiments to investigate the influence of transverse fuel location on maximum smoke temperature under the tunnel ceiling, and found that the maximum smoke temperature rise above the fuel keeps almost unchanged with the fuel moving closer to the tunnel sidewall at the beginning and then increases significantly after the distance between the fuel and the sidewall decreases to a certain value. Oka et al. [15] carried out a series of experiments of ceiling jets in an inclined tunnel. A new correlation for predicting the maximum gas temperature rise of ceiling jet in an inclined tunnel was developed and it is confirmed that the correlation for predicting the maximum gas temperature position in a horizontal tunnel with longitudinal ventilation can be applied to an inclined tunnel. Note that most of the 6
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work mentioned above is only suitable for small HRRs where the flame has not reached the tunnel ceiling. For a large HRR in the tunnel, the flame impinges on the ceiling and the continuous flame volume (combustion zone) extends along the ceiling [16, 17]. Therefore, the maximum gas temperature under the ceiling should be the flame temperature, and the longitudinal temperature distribution should also be influenced. Li and Ingason [16] extends their previous work [13] to account for large HRR and proposed robust equations to estimate maximum ceiling gas temperatures under different ventilation conditions. A large amount of model scale and full scale test data was gathered and used in the validation of their equations. According to their study, the effect of tunnel width on the maximum ceiling gas temperature is insignificant. Despite this, a parametric study could be necessary to support it. This is one of the objectives of the work presented here. The second focus point, distribution of gas temperature along the tunnel ceiling, has also been in focus in the tunnel community. This is mainly for easy use in estimation of gas temperature at a certain location downstream of the fuel, given that rather accurate estimation of the maximum ceiling gas temperature at the fuel site has already been possible. Ingason and Li [18] proposed a simple correlation to estimate the excess gas temperature distribution for both small and large HRRs, which was validated using both model and full scale test data. The equation is expressed as: Tc T c , m ax
0.57 e
( 0.13
x
)
H
0.43 e
( 0.021
x H
)
(1)
Based on a numerical study with Fire Dynamics Simulator, Li et al. [19] developed a simple correlation for the temperature distribution of smoke flow along the ceiling under natural
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ventilation. The numerical results indicate that the correlation could be utilized for all tunnels but with separate fitting constants for different tunnel aspect ratios:
Tc T c , ref
( 0.00733 ( x x ref ) / d ) e e ( 0.00406 ( x x ref ) / d )
H
1
W H
(2) 1
W
where H
d 2(
H
) 20.3(
W
W
)
H
Kashef et al. [20] conducted a series of tests in two 1/15 reduced-scale tunnels to investigate the ceiling temperature distribution with natural ventilation shafts. Based on experimental results and the one-dimensional theory, formulas to predict the temperature distribution were developed. The smoke temperature can be expressed using the temperature decay formula and reference temperature formula. The ceiling gas temperature decay can be expressed as: Tx T ref Tx T nref
e
( kx )
e
in fire section
( kn x )
in non-fire section
(3)
(4)
Bailey et al. [21] proposed a correlation after a series of CFD (Computational Fluid Dynamics) simulations: Tx T ref
1
( ) 2
x 16.7
(5)
Obviously, all the above equations follow the exponential correlation. However, until now, no experimental work on how tunnel cross section interacts with the temperature distribution along the tunnel ceiling with large HRR under longitudinal ventilation (the most popular ventilation scheme) has been reported. 8
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The last focus point is heat fluxes from the hot ceiling gas temperatures. Several experimental studies have been performed to quantify the heat transfer from flame and smoke to the ceiling and wall [22-25], while less studies have focused on the heat flux at the floor level. In fact, based on heat flux at the floor level downstream of the fuel, it will be convenient to estimate the conditions for a material to ignite at a certain distance from the fuel and partly determine whether the environment in the tunnel is tenable for evacuees [18]. The heat flux to an object includes both convection and electromagnetic radiation [26] from the ambient environment, which are related closely with gas temperature. Due to the small effect of convection on total heat flux at floor level, convection can be neglected. Ingason and Li [27] proposed a simple equation to predict the heat flux at floor level downstream of the fuel, where the convection has been neglected: q 0.68 (Tcf To ) 4
4
(6)
The heat flux at floor level can be easily estimated if the gas temperature beneath the tunnel ceiling, Tcf, and the surrounding (ambient) temperature, To, are known. Moreover, how the heat flux at the floor level downstream of the fuel varies with the tunnel cross section is still unknown. In summary, this study investigates the effect of tunnel cross section, i.e. tunnel height and width, on the ceiling gas temperatures and heat fluxes in case of large heat release rate. The effects of the cross section on these parameters have not been investigated in any details in previous studies.
2. Scale modelling
When using scale modelling, it is important that the similarity between full scale and model scale is well defined. A complete similarity involves both gas flow conditions and material
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properties. The gas flow conditions can be described by a number of non-dimensional numbers, e.g. the Froude number, the Reynolds number and the Richardson number. For a perfect scaling, all of these numbers should be kept the same in the model scale as in the full scale. This is, however, in most cases not possible and it is often enough to focus on the Froude number: Fr
u
2
gL
(7)
This so-called Froude scaling has been used in the present study. General information about scaling theories can be obtained from [28, 29]. The model scale tunnel used in the study was built in scale 1:20, which means that the size of the tunnel is scaled geometrically according to this ratio. The key parameters considered in the study and how they are scaled between the model scale and the full scale are presented in Table 1. The influence of the thermal inertia of the involved material is neglected. Previous studies have proved that model scale studies can give interesting results and important information when different parameters are varied [30-36].
3. Experimental set-up
The tunnel, as shown in Fig. 1, was 10 m long and the tunnel width and height were varied during the test series.. The widths were 0.3, 0.45 and 0.6 m, and the heights were 0.25 and 0.4 m. The widths correspond to 6, 9 and 12 m in real scale, while the heights correspond to 5 and 8 m, respectively. Thus, for the six tunnels, the aspect ratios (W/H) are 0.75, 1.1, 1.2, 1.5, 1.8 and 2.4. The ceiling, floor and one of the walls were made of 15 mm thick Promatect H boards. The other wall was comprised of 15 windows of 5 mm thick fireproof glass set in steel frames.
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A longitudinal ventilation system was established in the upstream end of the tunnel. The swirls created by the axial fan was hampered by filling a mixing box consisting of 10 mm thick Promatect H boards with straw fibres and wooden wool. This mixing box created a smooth flow profile in the tunnel with a maximum velocity of 1.3 m/s. Four different ventilation velocities were used: 0.22, 0.45, 0.67 and 1.12 m/s, corresponding to 1, 2, 3 and 5 m/s at full scale, respectively. Moreover, test under natural ventilation was also conducted. It should be noticed that in cases with the 0.6 m wide and 0.4 m high tunnel, the highest velocity reached was 0.5 m/s. The fuel was positioned at the tunnel centre, i.e. 5 m from the inlet and outlet of the tunnel, as shown in Fig. 2. This position is denoted “0” and different positions in the tunnel are related to this zero position with negative values in the upstream direction and positive values in the downstream direction. For convenience, metres have been used to name different positions. The wood crib was constructed of four layers of long sticks (0.5 m) with four sticks in each layer and three layers of short sticks (0.15 m) with three sticks in each layer. The sides of the square cross section of the sticks were 0.015 m. This gave a total height of 0.105 m. The porosity of wood crib 2
[37] was 2.1 mm and the exposed fuel surface was 0.54 m . In some tests, all short wood sticks
were replaced by plastic (polyethene) with the same dimensions. The weight was in a range of 756-882 g for wood cribs and 908-1004 g for wood/plastic cribs. Each crib was manufactured by hand. The cribs were placed on four 0.05 m high piles with pieces of Promatect H boards standing on a Promatect H board connected by metals rods to a digital weighing scale (load cell) under the tunnel floor. In heptane tests, an almost square pool (0.155 m × 0.160 m), standing directly on the Promatect H board connected to the weighing scale, was used. The initial fuel surface was 0.07 m above the tunnel floor and the fuel weight was in a range of 852-876 g. 11
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Gas temperatures were measured under the ceiling longitudinally, as shown in Fig. 2. Bare thermocouples Type K, 0.25 mm in diameter were used. Type K is suitable for continuous measurements within the temperature range from -250 °C to 1260 °C. The ambient temperature was around 20 °C in all tests. The gas velocity was measured with bi-directional probes [38] connected to differential pressure instruments at the tunnel centreline at two different positions: -2.75 and +3.65 m. The pressure transducers were calibrated before the test series and checked again in the middle of the test series. The heat radiation to the tunnel floor was measured with two different devices: traditional heat flux meters (Schmidt-Boelter) [39] and plate thermometers (PTs) [40-42]. The PT consists of a stainless steel plate with an insulation pad on the backside. A thermocouple is welded to the plate centre. The PTs and the heat flux meters were mounted at the centreline of the floor at +0.75 and +3.75 m. The incident heat flux using data from the PT can be obtained with aid of the following equation [40-42]: P T [T P T ] ( hc , P T K cond )([T P T ] [T o ] ) C heat , 1/ 3 4
[ q ]
i 1
i
i
PT
i
[T P T ] t
i 1
[T P T ]
i 1
t
i
i
(8)
where the surface emissivity of Plate thermometer P T =0.8, the convective heat transfer coefficient
hc , PT
=8 W/m2 K, the conduction correction factor Kcond=8.43 W/m2 K and the lumped
heat capacity coefficient Cheat,β=1/3 =4202 J/m2 K. In Table 2, the values of heat flux were determined using Schmidt-Boelter gauges. A total of 26 tests in tunnels were performed, as shown in Table 2 with details on the test series and how the parameters were varied. All measurements were started two minutes before ignition to register background conditions and to ensure that everything was running. No test was
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manually extinguished, but the fuel was let burn until only glowing embers were left or the heptane was totally consumed. More details about the test setup can be found in [43] In Table 2, the values of HRR were determined using the method of fuel weight loss [18, 44]. For heptane, the HRR was calculated from the mass signal assuming a combustion enthalpy of 44.56 MJ/kg and a combustion efficiency of 0.92. The effective combustion enthalpy for the crib material was calculated based on oxygen consumption calorimetry in free burn tests. For wood crib, the HRR was calculated from the mass signal using a effective combustion enthalpy of 15 MJ/kg. For wood/plastic crib, the effective combustion enthalpy is 20.8 MJ/kg. Oxygen consumption calorimetry was also used to check the HRR. Test results show that the HRRs based on these two different methods agree very well. For all tests, the HRRs are between 63 kW and 214.8 kW, and their corresponding values in the real tunnel are between 112.7 MW and 384.2 MW.
4. Results and discussion
4.1 Maximum ceiling gas temperature
Figure 3 shows the maximum gas temperature beneath the ceiling as a function of tunnel width and height. The maximum gas temperature lies mainly in a range of 900-1150 °C. Combining with Table 2, it seems that the maximum gas temperature under the tunnel ceiling is a weak function of the HRR and the ventilation velocity for large HRR more than 100 MW at full scale. Moreover, the maximum gas temperature varies slightly with the tunnel width but is affected evidently by the tunnel height. As shown in Fig. 3, there exists a clear stratification for the data points with different heights, solid data points represent lower ceiling height (H=0.25 m), and open data points 13
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the higher ceiling height (H=0.4 m). In fact, the gas temperature beneath the ceiling in all these cases represents the continuous flame zone temperature. In cases with lower tunnel heights, the ceiling is closer to the base of continuous flame zone, thus leading to a higher gas temperature under the ceiling.
4.2 Ceiling gas temperature distribution for heptane tests
Figure 4 represents the gas temperatures measured along the tunnel ceiling for heptane tests (uo=0.67 m/s). The position x=0 represents the position above the fuel. The longitudinal ventilation flow inclines the flame and the position of the maximum temperature under the tunnel ceiling lies in a range of 0.5-0.75 m downstream of the fuel. In cases with the same tunnel height, the temperature decreases with the increasing tunnel width at distant positions from the fuel (x>xmax). This is mainly due the fact that a wider tunnel result in a greater heat loss of the downstream smoke flows. Further, in Fig. 4 it can be observed that the gas temperature increases with the tunnel width near the fuel (xxmax, the gas temperature decreases with the increasing tunnel height, as a higher tunnel height indicates better entrainment and a shorter ceiling flame length. For x
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however, greater at x=0. The reason is also due to the backlayering, as for a given velocity, a higher tunnel height indicates a longer backlayering [45], corresponding to a higher gas temperature. Overall, the ceiling gas temperature downstream of the fuel decreases with the increasing tunnel cross sections.
4.3 Ceiling gas temperature distribution for crib tests
Figure 5 shows the temperatures measured along the tunnel ceiling with different ventilation velocities for wood crib (H=0.25 m, W=0.45 m). It is shown that a larger ventilation velocity leads to a slightly higher gas temperature downstream of the fuel (x>1.5 m in Fig. 5). This could be due to the fact that at a low ventilation velocity (0 and 0.22 m/s), the HRR is slightly lower (as shown in Table 2) and these cases are actually under ventilation controlled. For a velocity over 0.45 m/s, the maximum HRR is approximately of the same value. This suggests that these cases are fuel controlled and under this condition the effect of ventilation on the HRR is negligible. Further, less heat is blown to downstream of the fuel as more heat is lost to the tunnel structure upstream of the fuel due to the existence of the smoke backlayering. Figure 6 shows the temperatures measured along the tunnel ceiling for crib tests. Despite different longitudinal ventilation velocities and fuel types, in cases with the same tunnel height, the ceiling gas temperature downstream of the fuel decreases with the increasing tunnel width for x>xmax, but increases with the tunnel width near the fuel for x
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4.4 Decay rate of ceiling gas temperature
For engineering applications, an equation on the decay of ceiling gas temperature downstream of the fuel considering the tunnel dimension is very useful. Fig. 7 shows the relationship between the dimensionless excess gas temperature under the ceiling, ΔTc/ΔTc,max, and the dimensionless distance from the point of the maximum temperature, (x-xmax)/H, along with the calculated results by Eq. (1). Here, x in Eq. (1) is replaced by (x-xmax), as under the longitudinal ventilation the position of the maximum temperature under the tunnel ceiling is at a certain distance downstream of the fuel. For all tests with different fuels, ventilation velocities and tunnel cross sections, the predicted values by Eq. (1) are more or less higher than the test results, and the degree of difference between them seems to be dependent on the tunnel cross section. In fact, it is not surprising to find this difference as Eq. (1) is fitted mainly based on large scale tunnel tests, without considering the influence of cross section specifically. The comparison of measured dimensionless excess ceiling gas temperature with Eq. (2) is shown in Fig. 8. In some cases (heptane tests with W/H of 0.75 and 1.2, wood crib test with W/H of 0.75, 1.2 and 2.4, and wood/plastic crib test with W/H of 1.2), data lie close to the equal line, indicating good correlation. However, data with different tunnel cross sections apparently deviate from the equal line in different patterns. This indicates the effect of tunnel cross section on ceiling gas temperatures in large HRR cannot be expressed by Eq. (2). The reason could be that Eq. (2) was developed based on results from numerical simulations of model scale tunnel under natural ventilation (without longitudinal ventilation), and the HRRs simulated (at full scale) were relatively small and the ceiling gas temperatures obtained were less than 300 °C.
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Both Eq. (1) and Eq. (2) neglect the effect of HRR, however, in this work on large HRR more than 100 MW at full scale, the HRR could have an important influence on the gas temperature under the ceiling, which will be investigated in the following. It is also shown in Fig. 7 that the decay rate of dimensionless excess gas temperature is influenced significantly by the tunnel dimensions. For each test, the dimensionless excess gas temperature under the ceiling with the dimensionless distance can be correlated well with an exponential equation (similar to the form of Eqs. (3) and (4)) as: Tc T c , m ax
e
( B
( x x m ax ) H
)
(9)
At first, it is of interest to check whether the test results within the measurement range can be represented using Eq. (15). Fig. 9 shows the correlation coefficients obtained using the above exponential equation to fit the data for all the tests. Note that for each test only one correlation coefficient was obtained. Clearly, most of the correlation coefficients are about 0.95, indicating the reasonability of the use of this exponential equation. It should be noticed that in Fig. 7, the dimensionless distance is expressed as ( x x m ax )
H
, where the tunnel height is chosen to be the
characteristic length in the expression. In fact, we have tried to use the tunnel width and hydraulic diameter as the characteristic length, however, the fitting results are not as satisfactory as that using the tunnel height. Therefore in the following analysis, the tunnel height will be used by default. The decay rate of dimensionless excess gas temperature against the tunnel cross-sectional area is shown in Fig. 10, which demonstrates that the decay rate generally increases with the tunnel cross-sectional area, for every fuel. This may also indicate that the influence of ventilation condition on the decay rate is relatively small. Moreover, for a certain tunnel cross-sectional area, 17
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the decay rate in the wood crib tests is evidently higher than that in heptane and wood/plastic crib tests. In fact, the HRR in the wood crib tests was from 63 to 106.8 kW, evidently smaller than that in both heptane (from 139.4 to 214.8 kW) and wood/plastic crib (from 145.6 to 172.2 kW) tests. Therefore, the HRR is also an important factor that can influence the decay rate, and a dimensionless HRR is introduced here [18]: Q
Q
*
o c p To g
1/ 2
AH
1/ 2
(10)
f
The decay rate of dimensionless excess gas temperature against the dimensionless HRR is shown in Fig. 11, where all experimental data correlate well with the proposed line as: B 0.2 Q
* ( 0.52 )
(11)
Eqs. (15), (16) and (17) could be used for estimation of ceiling gas temperature at a given location downstream of the fuel in case of large heat release rate. However, it should be kept in mind that most data points corresponds to Q * >0.75. Therefore the above equation is only suitable in this range. As all the test data come from model scale tests, further validation is required using large scale test data.
4.5 Heat flux on the floor downstream of the fuel
Figure 12 shows the maximum heat flux downstream of the fuel measured by Schmidt-Boelter gauge as a function of tunnel cross-sectional area for heptane tests. In general, a larger tunnel cross-sectional area will lead to a smaller heat flux downstream of the fuel. This is mainly due to that the gas temperature decreases with the increasing cross-sectional area, as shown in Sect. 4.2 and Sect. 4.3 and Fig. 4 to Fig. 6. As indicated by Eq. (6), the heat flux downstream of the fuel decreases with the decreasing ceiling gas temperature. In Eq. (6), the ceiling gas temperature, Tcf, 18
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is considered as the maximum ceiling gas temperature above the heat flux meter in the test and the surrounding temperature, To, is the ambient temperature recorded before conducting the test. Figure 13 shows the maximum heat flux downstream of the fuel measured by Schmidt-Boelter gauge as a function of tunnel cross-sectional area for wood crib tests. Despite the position and ventilation velocity, the maximum heat flux decreases with the increase of tunnel cross-sectional area at first and then reaches a level with a little change. The change trend in the wood/plastic crib tests is similar, thus the data are not shown. Figure 14 shows the comparison of measured maximum heat fluxes using Schmidt-Boelter gauges to the calculated values using Eq. (14) (Plate thermometer) and Eq. (6) for all tests. It is shown that the heat fluxes measured by PTs with the aid of Eq. (14) correlate well with the values measured by the Schmidt-Boelter gauges. Results from Eq. (6) using the ceiling gas temperature appear a little higher than the measured values closer to the fuel. This could be due to that the ceiling gas temperature, considered as the maximum ceiling gas temperature above the heat flux meter, is much higher than the average temperature of the whole smoke layer in the vicinity of the fuel. Despite this, the comparison shows that the heat flux at the floor level can be estimated relatively well using the ceiling gas temperature by Eq. (6), especially at higher ranges.
5. Conclusion
The study investigated the effect of tunnel cross section on the ceiling gas temperatures and heat fluxes in case of large heat release rate. The major conclusions are: 1. The maximum gas temperature under the tunnel ceiling lies mainly in a range of 900-1150 °C in the tests. It appears that the maximum temperature is a weak function of the HRR
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and the longitudinal ventilation velocity for large HRRs. Moreover, the maximum temperature varies rather slightly with the tunnel width but is affected clearly by the tunnel height. This is probably due to the fact that in cases with the lower tunnel height, the ceiling is closer to the base of continuous flame zone, thus leading to a higher temperature below the ceiling. 2. For both crib and heptane tests, the ceiling gas temperature downstream of the fuel decreases with the increasing tunnel cross sections. Further, the ceiling gas temperature downstream of the fuel increases with the increasing ventilation velocity. 3. In tunnels with large HRR, the HRR is also an important factor that influences the decay rate of excess gas temperature, and a dimensionless HRR was introduced to account for the effect. An equation for the decay rate of excess gas temperature downstream of the fuel, considering both the tunnel dimensions and HRR, was developed. 4. A larger tunnel cross-sectional area leads to a smaller heat flux downstream of the fuel. The heat flux downstream of the fuel has a close relationship with the local temperature under the ceiling. In practical engineering application, the heat flux at the floor level can be estimated using the ceiling gas temperature by Eq. (6).
Acknowledgements
The authors would like to acknowledge SP Tunnel and Underground Safety Center for the financial support to the study. The experimental work was financed by the Swedish Research Council (FORMAS) which is gratefully acknowledged. Chuan Gang Fan was also financially supported by National Natural Science Foundation of China (NSFC) under Grant No. 51376173
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and China Scholarship Council under Program for Ph.D. Student Overseas Study Scholarship 2013.
References
[1] J. Wang, S. Lu, Y. Guan, S. Lo, H. Zhang, Experiment investigation on the influence of low pressure on ceiling temperature profile in aircraft cargo compartment fires, Appl Therm Eng, 89 (2015) 526-533. [2] X. Zhang, L. Hu, W. Zhu, X. Zhang, L. Yang, Flame extension length and temperature profile in thermal impinging flow of buoyant round jet upon a horizontal plate, Appl Therm Eng, 73(1) (2014) 15-22. [3] R. Harish, K. Venkatasubbaiah, Effects of buoyancy induced roof ventilation systems for smoke removal in tunnel fires, Tunn Undergr Sp Tech, 42 (2014) 195-205. [4] L.H. Hu, R. Huo, H.B. Wang, R.X. Yang, Experimental and numerical studies on longitudinal smoke temperature distribution upstream and downstream from the fire in a road tunnel, J Fire Sci, 25(1) (2007) 23-43. [5] G.H. Ko, S.R. Kim, H.S. Ryou, An Experimental Study on the Effect of Slope on the Critical Velocity in Tunnel Fires, J Fire Sci, 28(1) (2010) 27-47. [6] R. Harish, K. Venkatasubbaiah, Numerical simulation of turbulent plume spread in ceiling vented enclosure, European Journal of Mechanics-B/Fluids, 42 (2013) 142-158. [7] J. Ji, W. Zhong, K.Y. Li, X.B. Shen, Y. Zhang, R. Huo, A simplified calculation method on maximum smoke temperature under the ceiling in subway station fires, Tunn Undergr Sp Tech, 26(3) (2011) 490-496. [8] D. Yang, R. Huo, X.L. Zhang, X.Y. Zhao, On the front velocity of buoyancy-driven transient ceiling jet in a horizontal corridor: Comparison of correlations with measurements, Appl Therm Eng, 31(14-15) (2011) 2992-2999. [9] L.H. Hu, L.F. Chen, L. Wu, Y.F. Li, J.Y. Zhang, N. Meng, An experimental investigation and correlation on buoyant gas temperature below ceiling in a slopping tunnel fire, Appl Therm Eng, 51(1-2) (2013) 246-254. [10] D. Yang, R. Huo, X. Zhang, X. Zhao, Comparison of the distribution of carbon monoxide concentration and temperature rise in channel fires: Reduced-scale experiments, Appl Therm Eng, 31(4) (2011) 528-536. [11] J. Ji, H. Wan, K. Li, J. Han, J. Sun, A numerical study on upstream maximum temperature in inclined urban road tunnel fires, Int J Heat Mass Tran, 88 (2015) 516-526. [12] H. Kurioka, Y. Oka, H. Satoh, O. Sugawa, Fire properties in near field of square fire source with longitudinal ventilation in tunnels, Fire Safety J, 38(4) (2003) 319-340. [13] Y.Z. Li, B. Lei, H. Ingason, The maximum temperature of buoyancy-driven smoke flow beneath the ceiling in tunnel fires, Fire Safety J, 46(4) (2011) 204-210. [14] J. Ji, C.G. Fan, W. Zhong, X.B. Shen, J.H. Sun, Experimental investigation on influence of different transverse fire locations on maximum smoke temperature under the tunnel ceiling, Int J Heat Mass Tran, 55(17-18) (2012) 4817-4826. 21
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[15] Y. Oka, N. Kakae, O. Imazeki, K. Inagaki, Temperature Property of Ceiling Jet in an Inclined Tunnel, Procedia Engineering, 62 (2013) 234-241. [16] Y.Z. Li, H. Ingason, The maximum ceiling gas temperature in a large tunnel fire, Fire Safety J, 48 (2012) 38-48. [17] Z. Gao, J. Ji, H. Wan, K. Li, J. Sun, An investigation of the detailed flame shape and flame length under the ceiling of a channel, P Combust Inst, 35(3) (2015) 2657–2664. [18] H. Ingason, Y.Z. Li, Model scale tunnel fire tests with longitudinal ventilation, Fire Safety J, 45(6-8) (2010) 371-384. [19] L.M. Li, X.D. Cheng, X.G. Wang, H.P. Zhang, Temperature distribution of fire-induced flow along tunnels under natural ventilation, J Fire Sci, 30(2) (2012) 122-137. [20] A. Kashef, Z. Yuan, B. Lei, Ceiling temperature distribution and smoke diffusion in tunnel fires with natural ventilation, Fire Safety J, 62 (2013) 249–255. [21] J. Bailey, G.P. Forney, P. Tatem, W. Jones, Development and validation of corridor flow submodel for CFAST, J Fire Prot Eng, 12(3) (2002) 139-161. [22] A. Andreozzi, N. Bianco, M. Musto, G. Rotondo, Influence of wall emissivity and convective heat transfer coefficient on the adiabatic surface temperature as thermal/structural parameter in fire modeling, Appl Therm Eng, 51(1-2) (2013) 573-585. [23] D. Kontogeorgos, M. Founti, Numerical investigation of simultaneous heat and mass transfer mechanisms occurring in a gypsum board exposed to fire conditions, Appl Therm Eng, 30(11-12) (2010) 1461-1469. [24] L.J. Li, J. Ji, W.X. Shi, Z.H. Gao, J.H. Sun, J.P. Zhu, A modified turbulent mixing model with the consideration of heat transfer between hot buoyant plume and sidewalls in a closed stairwell, Int J Heat Mass Tran, 84 (2015) 521-528. [25] W.X. Shi, J. Ji, J.H. Sun, S.M. Lo, L.J. Li, X.Y. Yuan, Influence of staircase ventilation state on the airflow and heat transfer of the heated room on the middle floor of high rise building, Applied Energy, 119 (2014) 173-180. [26] R. Karadag, New approach relevant to total heat transfer coefficient including the effect of radiation and convection at the ceiling in a cooled ceiling room, Appl Therm Eng, 29(8-9) (2009) 1561-1565. [27] H. Ingason, Y.Z. Li, Model scale tunnel fire tests with point extraction ventilation, J Fire Prot Eng, 21(1) (2011) 5-36. [28] G. Heskestad, Modeling of Enclosure Fires, in:
Proceedings of the Fourteenth Symposium
(International) on Combustion, The Combustion Institute, The Pennsylvania State University, USA, 1972, pp. 1021-1030. [29] J.G. Quintiere, Scaling Applications in Fire Research, Fire Safety Journal, 15 (1989) 3-29. [30] H. Ingason, U. Wickström, P. van Hees, The Gothenburg Discoteque Fire Investigation, in:
9th
International Fire Science & Engineering Conference (Interflam 2001), Interscience Communications, Edinburg, Scotland, 2001, pp. 965-976. [31] H. Ingason, Model Scale Railcar Fire Tests, SP REPORT 2005:48, SP Swedish National Testing and Research Institute, Borås, 2005. [32] A. Lönnermark, H. Ingason, Fire Spread in Large Industrial Premises and Warehouses, SP Report 2005:21, SP Swedish National Testing and Research Institute, Borås, Sweden, 2005. [33] J. Ji, X. Yuan, K. Li, J. Sun, Influence of the external wind on flame shapes of n-heptane pool fires in long passage connected to a shaft, Combust Flame, 162(5) (2015) 2098-2107. 22
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[34] W. Weng, Experimental study of back-draft in a compartment with openings of different geometries, Combust Flame, 132(4) (2003) 709-714. [35] P. Zhu, X. Wang, C. Tao, Experiment study on the burning rates of ethanol square pool fires affected by wall insulation and oblique airflow, Exp Therm Fluid Sci, 61 (2015) 259-268. [36] J. Ji, M. Li, Y. Li, J. Zhu, J. Sun, Transport characteristics of thermal plume driven by turbulent mixing in stairwell, Int J Therm Sci, 89 (2015) 264-271. [37] H. Ingason, Model Scale Tunnel Fire Tests - Longitudinal ventilation, SP REPORT 2005:49, SP Swedish National Testing and Research Institute, Borås, Sweden, 2005. [38] B.J. McCaffrey, G. Heskestad, Brief Communications: A Robust Bidirectional Low-Velocity Probe for Flame and Fire Application, Combustion and Flame, 26 (1976) 125-127. [39] B. Persson, I. Wetterlund, Tentative Guidelines for Calibration and Use of Heat Flux Meters, SP Report 1997:33, SP Swedish National Testing and Research Institute, 1997. [40] H. Ingason, U. Wickström, Measuring incident radiant heat flux using the plate thermometer Fire Safety Journal, Vol. 42(2) (2007) 161-166. [41] A. Häggkvist, The plate thermometer as a mean of calculating incident heat radiation - a practical and theoretical study, Luleå University of Technology, 2009. [42] H. Andreas, S. Johan, U. Wickström, Using plate thermometer measurements to calculate incident heat radiation, Journal of Fire Sciences, 31(2) (2013) 166-177. [43] A. Lönnermark, H. Ingason, The Effect of Cross-sectional Area and Air Velocity on the Conditions in a Tunnel during a Fire, SP Swedish National Testing and Research Institute: Borås, Sweden., 2007. [44] J. Jie, L. Kaiyuan, Z. Wei, H. Ran, Experimental investigation on influence of smoke venting velocity and vent height on mechanical smoke exhaust efficiency, J Hazard Mater, 177(1-3) (2010) 209-215. [45] Y.Z. Li, B. Lei, H. Ingason, Study of critical velocity and backlayering length in longitudinally ventilated tunnel fires, Fire Safety Journal, 45 (2010) 361 - 370.
23
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Figure captions Fig. 1 A photo of the 1:20 model scale tunnel [36]. Fig. 2 Side view of the model scale tunnel with positions of measurements (Dimensions in mm). Fig. 3 Maximum gas temperature below the ceiling as a function of tunnel width and height. Fig. 4 Temperatures measured along the tunnel ceiling for heptane tests (uo=0.67 m/s). Fig. 5 Temperatures measured along the tunnel ceiling with different ventilation velocities for wood crib tests (H=0.25 m, W=0.45 m). Fig. 6 Temperatures measured along the tunnel ceiling for crib tests. Fig. 7 Dimensionless excess ceiling gas temperature as a function of the dimensionless distance. Fig. 8 Comparison of measured dimensionless excess ceiling gas temperature with Eq. (2). Fig. 9 Correlation coefficients obtained using Eq. (15) to fit the data. Fig. 10 Decay rate of dimensionless excess gas temperature as a function of tunnel cross-sectional area. Fig. 11 Decay rate of dimensionless excess gas temperature as a function of dimensionless HRR. Fig. 12 Maximum heat flux downstream of the fuel as a function of tunnel cross-sectional area for heptane tests. Fig. 13 Maximum heat flux downstream of the fuel as a function of cross-sectional area for wood crib tests. Fig. 14 Measured and calculated maximum heat fluxes for all tests. 24
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Table captions
Table 1 A list of scaling correlations for the model tunnel. Equation Type of unit
Scaling model number
Heat Release Rate (kW)
Q F Q M ( LF / LM )
5/ 2
(12)
Mass flow rate (kg/s)
m F m M ( LF / LM )
5/2
(13)
Velocity (m/s)
u F u M ( LF / LM )
Time (s)
t F t M ( LF / LM )
Temperature (K)
TF TM
Heat flux (kW/m2)
q F q M ( L F / L M )
1/2
(14)
1/2
(15) (16)
1/2
(17)
Table 2 Description of the test conditions in tunnels.
uo Test
H
W
A
Q m ax
(m)
(m)
(m2)
(kW)
q m ax
(kW/m2)
(kW/m2)
x=0.75 m
x=3.75m
Tc,max
Fuel (m/s)
q m ax
Notea
(°C)
25
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1
Heptane
0.67
0.25
0.3
0.08
185.3
1063.4
119.7
10.4
19
2
Heptane
0.67
0.25
0.45
0.11
172.2
1052.5
99.4
7.0
1
3
Heptane
0.67
0.25
0.6
0.15
214.8
1025.2
85.5
5.3
15
4
Heptane
0.67
0.4
0.3
0.12
155.8
968.9
85.8
6.8
22
5
Heptane
0.67
0.4
0.45
0.18
139.4
961.7
73.3
3.4
27
6
Heptane
0.5
0.4
0.6
0.24
162.4
979.3
59.7
1.8
33
7
Wood
0
0.25
0.45
0.11
76.8
1056.2
13.8
0.9
11
8
Wood
0.22
0.25
0.3
0.08
63.0
1007.3
12.7
1.5
17
9
Wood
0.22
0.25
0.45
0.11
67.8
1104.6
10.0
0.9
3
10
Wood
0.22
0.25
0.6
0.15
71.4
1039.4
6.4
0.8
13
11
Wood
0.22
0.4
0.3
0.12
82.2
886.5
9.3
0.9
21
12
Wood
0.22
0.4
0.45
0.18
79.8
964.8
6.9
0.8
25
13
Wood
0.22
0.4
0.6
0.24
65.4
1016.0
6.7
0.8
32
14
Wood
0.45
0.25
0.45
0.11
106.8
1132.8
18.6
1.3
4
15
Wood
0.67
0.25
0.3
0.08
97.2
1047.9
58.7
3.8
16
16
Wood
0.67
0.25
0.45
0.11
103.8
1133.7
28.9
2.2
2
17
Wood
0.67
0.25
0.6
0.15
105.6
1139.2
20.1
1.3
12
18
Wood
0.67
0.4
0.3
0.12
92.4
843.6
17.7
2.7
20
19
Wood
0.67
0.4
0.45
0.18
102.6
971.4
16.7
1.6
23
20
Wood
0.5
0.4
0.6
0.24
103.2
936.7
10.8
0.8
31
21
Wood
1.12
0.25
0.45
0.11
101.4
984.0
22.9
2.3
5
22
Wood
0.67
0.25
0.3
0.08
153.9
1016.0
64.9
5.1
18
26
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+plasticb Wood 23
0.67
0.25
0.45
0.11
150.6
1137.6
48.3
3.7
10
0.67
0.25
0.6
0.15
172.2
1121.9
39.6
2.4
14
0.67
0.4
0.45
0.18
172.2
1011.1
39.9
2.8
24
0.5
0.4
0.6
0.24
145.6
908.5
26.5
1.4
35
+plastic Wood 24 +plastic Wood 25 +plastic Wood 26 +plastic a
The numbers given in the last column represent the test numbers in the technical report [43].
b
The wood/plastic crib contains some plastics, which have a higher heat of combustion than absolute wood.
Table 3 Backlayering length with different tunnel widths and heights.
Test
uo
H
W
A
Backlayring length
(m/s)
(m)
(m)
(m2)
(m)
Fuel
1
Heptane
0.67
0.25
0.3
0.08
0-0.25
2
Heptane
0.67
0.25
0.45
0.11
0-0.25
3
Heptane
0.67
0.25
0.6
0.15
0.5-0.75
4
Heptane
0.67
0.4
0.3
0.12
0.5-0.75
5
Heptane
0.67
0.4
0.45
0.18
2.5-2.75
6
Heptane
0.5
0.4
0.6
0.24
>3.75
27
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28
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S1359-4311(15)00968-0 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.09.048 ATE 7040
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
16-7-2015 16-9-2015
Please cite this article as: Chuan Gang Fan, Ying Zhen Li, Haukur Ingason, Anders Lönnermark, Effect of tunnel cross section on gas temperatures and heat fluxes in case of large heat release rate, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.09.048. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of tunnel cross section on gas temperatures and heat fluxes in case of large heat release rate Chuan Gang Fan1,*, Ying Zhen Li2, Haukur Ingason2, Anders Lönnermark2
1. School of Transportation Engineering, Hefei University of Technology, China 2. Fire Research, SP Technical Research Institute of Sweden, Sweden
Corresponding Author: Chuan Gang Fan. Address: School of Transportation Engineering, Hefei University of Technology, Hefei 230009, Anhui, China. Tel: +86-551-0551-62901960 (Office), +86-18255170802(Mobile) Email: [email protected]
1
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Highlights
Effect of tunnel cross section together with ventilation velocity was studied.
Ceiling temperature varies clearly with tunnel height, but little with tunnel width.
Downstream temperature decreases with increasing tunnel dimensions.
HRR is an important factor that influences decay rate of excess gas temperature.
An equation considering both tunnel dimensions and HRR was developed.
Abstract
Tests with liquid and solid fuels in model tunnels (1:20) were performed and analyzed in order to study the effect of tunnel cross section (width and height) together with ventilation velocity on ceiling gas temperatures and heat fluxes. The model tunnel was 10 m long with varying width (0.3 m, 0.45 m and 0.6 m) and height (0.25 m and 0.4 m). Test results show that the maximum temperature under the ceiling is a weak function of heat release rate (HRR) and ventilation velocity for cases with HRR more than 100 MW at full scale. It clearly varies with the tunnel height and is a weak function of the tunnel width. With a lower tunnel height, the ceiling is closer to the base of continuous flame zone and the temperatures become higher. Overall, the gas 2
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temperature beneath the ceiling decreases with the increasing tunnel dimensions, and increases with the increasing longitudinal ventilation velocity. The HRR is also an important factor that influences the decay rate of excess gas temperature, and a dimensionless HRR integrating HRR and other two key parameters, tunnel cross-sectional area and distance between fuel center and tunnel ceiling, was introduced to account for the effect. An equation for the decay rate of excess gas temperature, considering both the tunnel dimensions and HRR, was developed. Moreover, a larger tunnel cross-sectional area will lead to a smaller heat flux. Key words: model scale, tunnel cross section, gas temperature, heat flux, longitudinal ventilation
Nomenclature
A
tunnel cross-sectional area (m2)
B
decay rate of temperature downstream of fuel
bfo
radius of the fuel (m)
Cheat,β=1/3
lumped heat capacity coefficient (J/m2 K)
cp
heat capacity (kJ/kg K)
d
characteristic tunnel hydraulic diameter (m)
Fr
Froude number
g
gravity acceleration (m/s2)
H
tunnel height (m)
Hf
distance between fuel center and tunnel ceiling (m)
hc,PT
convective heat transfer coefficient for plate thermometers (W/m2 K)
Kcond
conduction correction factor (W/m2 K)
3
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k
decay coefficient in fire section
kn
decay coefficient in non-fire section
L
length scale (m)
m
mass flow rate (kg/s)
Q
heat release rate (kW)
q
incident heat flux (kW/m2)
To
ambient temperature or surrounding gas temperature (K)
T cf
ceiling gas temperature (K)
Tc , m ax
maximum gas temperature under tunnel ceiling (°C)
TPT
measured temperature by plate thermometer (K)
Tc
excess gas temperature under tunnel ceiling (K)
Tc , m ax
maximum excess gas temperature under tunnel ceiling (K)
Tc , ref
reference temperature (K)
Tnref
reference temperature in non-fire section (K)
T ref
reference temperature in fire section (K)
Tx
excess gas temperature with a distance from reference location (K)
t
time (s)
u
gas velocity (m/s)
uo
longitudinal ventilation velocity at ambient conditions (m/s)
V
dimensionless ventilation velocity
W
tunnel width (m)
w*
characteristic plume velocity (m/s) 4
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x
distance from fuel centre (m)
xmax
position of maximum ceiling gas temperature (m)
xref
reference position (m)
Greek
density (kg/m3)
Stephan–Boltzmann constant (kW/m2 K4)
PT
surface emissivity of plate thermometer
Subscript F
full scale
M
model scale
max
maximum value
o
ambient
1. Introduction
The characteristics of ceiling jet, such as heat transfer and temperature profile, have attracted extensive attentions in certain thermal engineering research [1-8]. In tunnels, gas temperatures beneath the ceiling and heat fluxes are important factors in the study of risk of fire spread, evacuation and rescue service. The key factors that influence gas temperatures and heat fluxes include heat release rate (HRR), fuel type, vertical distance between fuel and tunnel ceiling, ventilation, and distance from fuel [9-11]. There are three focus points presented here, the nearby maximum ceiling temperature, the varying downstream ceiling gas temperature and the
5
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corresponding heat flux towards the floor level. All three focus points are investigated as a function of the tunnel cross section. The first focus point, i.e. the maximum ceiling gas temperature, has attracted special attention due to its importance in protection of tunnel structure. Kurioka et al. [12] proposed an empirical model to predict the maximum gas temperature under the tunnel ceiling based on model scale experiments. Li et al. [13] conducted a theoretical analysis of maximum gas temperature under the tunnel ceiling based on the plume theory and validated the theoretical model using a large amount of test data. The results show that the maximum excess gas temperature under the ceiling can be divided into two regions. Under high ventilation, i.e. when the dimensionless ventilation velocity, V uo / w
*
( w* (
Qg b fo o c p T o
)
1/ 3
), is greater than 0.19, the maximum excess gas temperature
under the tunnel ceiling is proportional to the HRR and inversely proportional to the longitudinal ventilation velocity. Under lower ventilation, the maximum excess gas temperature under the ceiling varies as the two-thirds power of the dimensionless HRR, independent of the longitudinal ventilation velocity. Ji et al. [14] carried out a series of model scale experiments to investigate the influence of transverse fuel location on maximum smoke temperature under the tunnel ceiling, and found that the maximum smoke temperature rise above the fuel keeps almost unchanged with the fuel moving closer to the tunnel sidewall at the beginning and then increases significantly after the distance between the fuel and the sidewall decreases to a certain value. Oka et al. [15] carried out a series of experiments of ceiling jets in an inclined tunnel. A new correlation for predicting the maximum gas temperature rise of ceiling jet in an inclined tunnel was developed and it is confirmed that the correlation for predicting the maximum gas temperature position in a horizontal tunnel with longitudinal ventilation can be applied to an inclined tunnel. Note that most of the 6
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work mentioned above is only suitable for small HRRs where the flame has not reached the tunnel ceiling. For a large HRR in the tunnel, the flame impinges on the ceiling and the continuous flame volume (combustion zone) extends along the ceiling [16, 17]. Therefore, the maximum gas temperature under the ceiling should be the flame temperature, and the longitudinal temperature distribution should also be influenced. Li and Ingason [16] extends their previous work [13] to account for large HRR and proposed robust equations to estimate maximum ceiling gas temperatures under different ventilation conditions. A large amount of model scale and full scale test data was gathered and used in the validation of their equations. According to their study, the effect of tunnel width on the maximum ceiling gas temperature is insignificant. Despite this, a parametric study could be necessary to support it. This is one of the objectives of the work presented here. The second focus point, distribution of gas temperature along the tunnel ceiling, has also been in focus in the tunnel community. This is mainly for easy use in estimation of gas temperature at a certain location downstream of the fuel, given that rather accurate estimation of the maximum ceiling gas temperature at the fuel site has already been possible. Ingason and Li [18] proposed a simple correlation to estimate the excess gas temperature distribution for both small and large HRRs, which was validated using both model and full scale test data. The equation is expressed as: Tc T c , m ax
0.57 e
( 0.13
x
)
H
0.43 e
( 0.021
x H
)
(1)
Based on a numerical study with Fire Dynamics Simulator, Li et al. [19] developed a simple correlation for the temperature distribution of smoke flow along the ceiling under natural
7
Page 7 of 28
ventilation. The numerical results indicate that the correlation could be utilized for all tunnels but with separate fitting constants for different tunnel aspect ratios:
Tc T c , ref
( 0.00733 ( x x ref ) / d ) e e ( 0.00406 ( x x ref ) / d )
H
1
W H
(2) 1
W
where H
d 2(
H
) 20.3(
W
W
)
H
Kashef et al. [20] conducted a series of tests in two 1/15 reduced-scale tunnels to investigate the ceiling temperature distribution with natural ventilation shafts. Based on experimental results and the one-dimensional theory, formulas to predict the temperature distribution were developed. The smoke temperature can be expressed using the temperature decay formula and reference temperature formula. The ceiling gas temperature decay can be expressed as: Tx T ref Tx T nref
e
( kx )
e
in fire section
( kn x )
in non-fire section
(3)
(4)
Bailey et al. [21] proposed a correlation after a series of CFD (Computational Fluid Dynamics) simulations: Tx T ref
1
( ) 2
x 16.7
(5)
Obviously, all the above equations follow the exponential correlation. However, until now, no experimental work on how tunnel cross section interacts with the temperature distribution along the tunnel ceiling with large HRR under longitudinal ventilation (the most popular ventilation scheme) has been reported. 8
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The last focus point is heat fluxes from the hot ceiling gas temperatures. Several experimental studies have been performed to quantify the heat transfer from flame and smoke to the ceiling and wall [22-25], while less studies have focused on the heat flux at the floor level. In fact, based on heat flux at the floor level downstream of the fuel, it will be convenient to estimate the conditions for a material to ignite at a certain distance from the fuel and partly determine whether the environment in the tunnel is tenable for evacuees [18]. The heat flux to an object includes both convection and electromagnetic radiation [26] from the ambient environment, which are related closely with gas temperature. Due to the small effect of convection on total heat flux at floor level, convection can be neglected. Ingason and Li [27] proposed a simple equation to predict the heat flux at floor level downstream of the fuel, where the convection has been neglected: q 0.68 (Tcf To ) 4
4
(6)
The heat flux at floor level can be easily estimated if the gas temperature beneath the tunnel ceiling, Tcf, and the surrounding (ambient) temperature, To, are known. Moreover, how the heat flux at the floor level downstream of the fuel varies with the tunnel cross section is still unknown. In summary, this study investigates the effect of tunnel cross section, i.e. tunnel height and width, on the ceiling gas temperatures and heat fluxes in case of large heat release rate. The effects of the cross section on these parameters have not been investigated in any details in previous studies.
2. Scale modelling
When using scale modelling, it is important that the similarity between full scale and model scale is well defined. A complete similarity involves both gas flow conditions and material
9
Page 9 of 28
properties. The gas flow conditions can be described by a number of non-dimensional numbers, e.g. the Froude number, the Reynolds number and the Richardson number. For a perfect scaling, all of these numbers should be kept the same in the model scale as in the full scale. This is, however, in most cases not possible and it is often enough to focus on the Froude number: Fr
u
2
gL
(7)
This so-called Froude scaling has been used in the present study. General information about scaling theories can be obtained from [28, 29]. The model scale tunnel used in the study was built in scale 1:20, which means that the size of the tunnel is scaled geometrically according to this ratio. The key parameters considered in the study and how they are scaled between the model scale and the full scale are presented in Table 1. The influence of the thermal inertia of the involved material is neglected. Previous studies have proved that model scale studies can give interesting results and important information when different parameters are varied [30-36].
3. Experimental set-up
The tunnel, as shown in Fig. 1, was 10 m long and the tunnel width and height were varied during the test series.. The widths were 0.3, 0.45 and 0.6 m, and the heights were 0.25 and 0.4 m. The widths correspond to 6, 9 and 12 m in real scale, while the heights correspond to 5 and 8 m, respectively. Thus, for the six tunnels, the aspect ratios (W/H) are 0.75, 1.1, 1.2, 1.5, 1.8 and 2.4. The ceiling, floor and one of the walls were made of 15 mm thick Promatect H boards. The other wall was comprised of 15 windows of 5 mm thick fireproof glass set in steel frames.
10
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A longitudinal ventilation system was established in the upstream end of the tunnel. The swirls created by the axial fan was hampered by filling a mixing box consisting of 10 mm thick Promatect H boards with straw fibres and wooden wool. This mixing box created a smooth flow profile in the tunnel with a maximum velocity of 1.3 m/s. Four different ventilation velocities were used: 0.22, 0.45, 0.67 and 1.12 m/s, corresponding to 1, 2, 3 and 5 m/s at full scale, respectively. Moreover, test under natural ventilation was also conducted. It should be noticed that in cases with the 0.6 m wide and 0.4 m high tunnel, the highest velocity reached was 0.5 m/s. The fuel was positioned at the tunnel centre, i.e. 5 m from the inlet and outlet of the tunnel, as shown in Fig. 2. This position is denoted “0” and different positions in the tunnel are related to this zero position with negative values in the upstream direction and positive values in the downstream direction. For convenience, metres have been used to name different positions. The wood crib was constructed of four layers of long sticks (0.5 m) with four sticks in each layer and three layers of short sticks (0.15 m) with three sticks in each layer. The sides of the square cross section of the sticks were 0.015 m. This gave a total height of 0.105 m. The porosity of wood crib 2
[37] was 2.1 mm and the exposed fuel surface was 0.54 m . In some tests, all short wood sticks
were replaced by plastic (polyethene) with the same dimensions. The weight was in a range of 756-882 g for wood cribs and 908-1004 g for wood/plastic cribs. Each crib was manufactured by hand. The cribs were placed on four 0.05 m high piles with pieces of Promatect H boards standing on a Promatect H board connected by metals rods to a digital weighing scale (load cell) under the tunnel floor. In heptane tests, an almost square pool (0.155 m × 0.160 m), standing directly on the Promatect H board connected to the weighing scale, was used. The initial fuel surface was 0.07 m above the tunnel floor and the fuel weight was in a range of 852-876 g. 11
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Gas temperatures were measured under the ceiling longitudinally, as shown in Fig. 2. Bare thermocouples Type K, 0.25 mm in diameter were used. Type K is suitable for continuous measurements within the temperature range from -250 °C to 1260 °C. The ambient temperature was around 20 °C in all tests. The gas velocity was measured with bi-directional probes [38] connected to differential pressure instruments at the tunnel centreline at two different positions: -2.75 and +3.65 m. The pressure transducers were calibrated before the test series and checked again in the middle of the test series. The heat radiation to the tunnel floor was measured with two different devices: traditional heat flux meters (Schmidt-Boelter) [39] and plate thermometers (PTs) [40-42]. The PT consists of a stainless steel plate with an insulation pad on the backside. A thermocouple is welded to the plate centre. The PTs and the heat flux meters were mounted at the centreline of the floor at +0.75 and +3.75 m. The incident heat flux using data from the PT can be obtained with aid of the following equation [40-42]: P T [T P T ] ( hc , P T K cond )([T P T ] [T o ] ) C heat , 1/ 3 4
[ q ]
i 1
i
i
PT
i
[T P T ] t
i 1
[T P T ]
i 1
t
i
i
(8)
where the surface emissivity of Plate thermometer P T =0.8, the convective heat transfer coefficient
hc , PT
=8 W/m2 K, the conduction correction factor Kcond=8.43 W/m2 K and the lumped
heat capacity coefficient Cheat,β=1/3 =4202 J/m2 K. In Table 2, the values of heat flux were determined using Schmidt-Boelter gauges. A total of 26 tests in tunnels were performed, as shown in Table 2 with details on the test series and how the parameters were varied. All measurements were started two minutes before ignition to register background conditions and to ensure that everything was running. No test was
12
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manually extinguished, but the fuel was let burn until only glowing embers were left or the heptane was totally consumed. More details about the test setup can be found in [43] In Table 2, the values of HRR were determined using the method of fuel weight loss [18, 44]. For heptane, the HRR was calculated from the mass signal assuming a combustion enthalpy of 44.56 MJ/kg and a combustion efficiency of 0.92. The effective combustion enthalpy for the crib material was calculated based on oxygen consumption calorimetry in free burn tests. For wood crib, the HRR was calculated from the mass signal using a effective combustion enthalpy of 15 MJ/kg. For wood/plastic crib, the effective combustion enthalpy is 20.8 MJ/kg. Oxygen consumption calorimetry was also used to check the HRR. Test results show that the HRRs based on these two different methods agree very well. For all tests, the HRRs are between 63 kW and 214.8 kW, and their corresponding values in the real tunnel are between 112.7 MW and 384.2 MW.
4. Results and discussion
4.1 Maximum ceiling gas temperature
Figure 3 shows the maximum gas temperature beneath the ceiling as a function of tunnel width and height. The maximum gas temperature lies mainly in a range of 900-1150 °C. Combining with Table 2, it seems that the maximum gas temperature under the tunnel ceiling is a weak function of the HRR and the ventilation velocity for large HRR more than 100 MW at full scale. Moreover, the maximum gas temperature varies slightly with the tunnel width but is affected evidently by the tunnel height. As shown in Fig. 3, there exists a clear stratification for the data points with different heights, solid data points represent lower ceiling height (H=0.25 m), and open data points 13
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the higher ceiling height (H=0.4 m). In fact, the gas temperature beneath the ceiling in all these cases represents the continuous flame zone temperature. In cases with lower tunnel heights, the ceiling is closer to the base of continuous flame zone, thus leading to a higher gas temperature under the ceiling.
4.2 Ceiling gas temperature distribution for heptane tests
Figure 4 represents the gas temperatures measured along the tunnel ceiling for heptane tests (uo=0.67 m/s). The position x=0 represents the position above the fuel. The longitudinal ventilation flow inclines the flame and the position of the maximum temperature under the tunnel ceiling lies in a range of 0.5-0.75 m downstream of the fuel. In cases with the same tunnel height, the temperature decreases with the increasing tunnel width at distant positions from the fuel (x>xmax). This is mainly due the fact that a wider tunnel result in a greater heat loss of the downstream smoke flows. Further, in Fig. 4 it can be observed that the gas temperature increases with the tunnel width near the fuel (x
14
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however, greater at x=0. The reason is also due to the backlayering, as for a given velocity, a higher tunnel height indicates a longer backlayering [45], corresponding to a higher gas temperature. Overall, the ceiling gas temperature downstream of the fuel decreases with the increasing tunnel cross sections.
4.3 Ceiling gas temperature distribution for crib tests
Figure 5 shows the temperatures measured along the tunnel ceiling with different ventilation velocities for wood crib (H=0.25 m, W=0.45 m). It is shown that a larger ventilation velocity leads to a slightly higher gas temperature downstream of the fuel (x>1.5 m in Fig. 5). This could be due to the fact that at a low ventilation velocity (0 and 0.22 m/s), the HRR is slightly lower (as shown in Table 2) and these cases are actually under ventilation controlled. For a velocity over 0.45 m/s, the maximum HRR is approximately of the same value. This suggests that these cases are fuel controlled and under this condition the effect of ventilation on the HRR is negligible. Further, less heat is blown to downstream of the fuel as more heat is lost to the tunnel structure upstream of the fuel due to the existence of the smoke backlayering. Figure 6 shows the temperatures measured along the tunnel ceiling for crib tests. Despite different longitudinal ventilation velocities and fuel types, in cases with the same tunnel height, the ceiling gas temperature downstream of the fuel decreases with the increasing tunnel width for x>xmax, but increases with the tunnel width near the fuel for x
15
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4.4 Decay rate of ceiling gas temperature
For engineering applications, an equation on the decay of ceiling gas temperature downstream of the fuel considering the tunnel dimension is very useful. Fig. 7 shows the relationship between the dimensionless excess gas temperature under the ceiling, ΔTc/ΔTc,max, and the dimensionless distance from the point of the maximum temperature, (x-xmax)/H, along with the calculated results by Eq. (1). Here, x in Eq. (1) is replaced by (x-xmax), as under the longitudinal ventilation the position of the maximum temperature under the tunnel ceiling is at a certain distance downstream of the fuel. For all tests with different fuels, ventilation velocities and tunnel cross sections, the predicted values by Eq. (1) are more or less higher than the test results, and the degree of difference between them seems to be dependent on the tunnel cross section. In fact, it is not surprising to find this difference as Eq. (1) is fitted mainly based on large scale tunnel tests, without considering the influence of cross section specifically. The comparison of measured dimensionless excess ceiling gas temperature with Eq. (2) is shown in Fig. 8. In some cases (heptane tests with W/H of 0.75 and 1.2, wood crib test with W/H of 0.75, 1.2 and 2.4, and wood/plastic crib test with W/H of 1.2), data lie close to the equal line, indicating good correlation. However, data with different tunnel cross sections apparently deviate from the equal line in different patterns. This indicates the effect of tunnel cross section on ceiling gas temperatures in large HRR cannot be expressed by Eq. (2). The reason could be that Eq. (2) was developed based on results from numerical simulations of model scale tunnel under natural ventilation (without longitudinal ventilation), and the HRRs simulated (at full scale) were relatively small and the ceiling gas temperatures obtained were less than 300 °C.
16
Page 16 of 28
Both Eq. (1) and Eq. (2) neglect the effect of HRR, however, in this work on large HRR more than 100 MW at full scale, the HRR could have an important influence on the gas temperature under the ceiling, which will be investigated in the following. It is also shown in Fig. 7 that the decay rate of dimensionless excess gas temperature is influenced significantly by the tunnel dimensions. For each test, the dimensionless excess gas temperature under the ceiling with the dimensionless distance can be correlated well with an exponential equation (similar to the form of Eqs. (3) and (4)) as: Tc T c , m ax
e
( B
( x x m ax ) H
)
(9)
At first, it is of interest to check whether the test results within the measurement range can be represented using Eq. (15). Fig. 9 shows the correlation coefficients obtained using the above exponential equation to fit the data for all the tests. Note that for each test only one correlation coefficient was obtained. Clearly, most of the correlation coefficients are about 0.95, indicating the reasonability of the use of this exponential equation. It should be noticed that in Fig. 7, the dimensionless distance is expressed as ( x x m ax )
H
, where the tunnel height is chosen to be the
characteristic length in the expression. In fact, we have tried to use the tunnel width and hydraulic diameter as the characteristic length, however, the fitting results are not as satisfactory as that using the tunnel height. Therefore in the following analysis, the tunnel height will be used by default. The decay rate of dimensionless excess gas temperature against the tunnel cross-sectional area is shown in Fig. 10, which demonstrates that the decay rate generally increases with the tunnel cross-sectional area, for every fuel. This may also indicate that the influence of ventilation condition on the decay rate is relatively small. Moreover, for a certain tunnel cross-sectional area, 17
Page 17 of 28
the decay rate in the wood crib tests is evidently higher than that in heptane and wood/plastic crib tests. In fact, the HRR in the wood crib tests was from 63 to 106.8 kW, evidently smaller than that in both heptane (from 139.4 to 214.8 kW) and wood/plastic crib (from 145.6 to 172.2 kW) tests. Therefore, the HRR is also an important factor that can influence the decay rate, and a dimensionless HRR is introduced here [18]: Q
Q
*
o c p To g
1/ 2
AH
1/ 2
(10)
f
The decay rate of dimensionless excess gas temperature against the dimensionless HRR is shown in Fig. 11, where all experimental data correlate well with the proposed line as: B 0.2 Q
* ( 0.52 )
(11)
Eqs. (15), (16) and (17) could be used for estimation of ceiling gas temperature at a given location downstream of the fuel in case of large heat release rate. However, it should be kept in mind that most data points corresponds to Q * >0.75. Therefore the above equation is only suitable in this range. As all the test data come from model scale tests, further validation is required using large scale test data.
4.5 Heat flux on the floor downstream of the fuel
Figure 12 shows the maximum heat flux downstream of the fuel measured by Schmidt-Boelter gauge as a function of tunnel cross-sectional area for heptane tests. In general, a larger tunnel cross-sectional area will lead to a smaller heat flux downstream of the fuel. This is mainly due to that the gas temperature decreases with the increasing cross-sectional area, as shown in Sect. 4.2 and Sect. 4.3 and Fig. 4 to Fig. 6. As indicated by Eq. (6), the heat flux downstream of the fuel decreases with the decreasing ceiling gas temperature. In Eq. (6), the ceiling gas temperature, Tcf, 18
Page 18 of 28
is considered as the maximum ceiling gas temperature above the heat flux meter in the test and the surrounding temperature, To, is the ambient temperature recorded before conducting the test. Figure 13 shows the maximum heat flux downstream of the fuel measured by Schmidt-Boelter gauge as a function of tunnel cross-sectional area for wood crib tests. Despite the position and ventilation velocity, the maximum heat flux decreases with the increase of tunnel cross-sectional area at first and then reaches a level with a little change. The change trend in the wood/plastic crib tests is similar, thus the data are not shown. Figure 14 shows the comparison of measured maximum heat fluxes using Schmidt-Boelter gauges to the calculated values using Eq. (14) (Plate thermometer) and Eq. (6) for all tests. It is shown that the heat fluxes measured by PTs with the aid of Eq. (14) correlate well with the values measured by the Schmidt-Boelter gauges. Results from Eq. (6) using the ceiling gas temperature appear a little higher than the measured values closer to the fuel. This could be due to that the ceiling gas temperature, considered as the maximum ceiling gas temperature above the heat flux meter, is much higher than the average temperature of the whole smoke layer in the vicinity of the fuel. Despite this, the comparison shows that the heat flux at the floor level can be estimated relatively well using the ceiling gas temperature by Eq. (6), especially at higher ranges.
5. Conclusion
The study investigated the effect of tunnel cross section on the ceiling gas temperatures and heat fluxes in case of large heat release rate. The major conclusions are: 1. The maximum gas temperature under the tunnel ceiling lies mainly in a range of 900-1150 °C in the tests. It appears that the maximum temperature is a weak function of the HRR
19
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and the longitudinal ventilation velocity for large HRRs. Moreover, the maximum temperature varies rather slightly with the tunnel width but is affected clearly by the tunnel height. This is probably due to the fact that in cases with the lower tunnel height, the ceiling is closer to the base of continuous flame zone, thus leading to a higher temperature below the ceiling. 2. For both crib and heptane tests, the ceiling gas temperature downstream of the fuel decreases with the increasing tunnel cross sections. Further, the ceiling gas temperature downstream of the fuel increases with the increasing ventilation velocity. 3. In tunnels with large HRR, the HRR is also an important factor that influences the decay rate of excess gas temperature, and a dimensionless HRR was introduced to account for the effect. An equation for the decay rate of excess gas temperature downstream of the fuel, considering both the tunnel dimensions and HRR, was developed. 4. A larger tunnel cross-sectional area leads to a smaller heat flux downstream of the fuel. The heat flux downstream of the fuel has a close relationship with the local temperature under the ceiling. In practical engineering application, the heat flux at the floor level can be estimated using the ceiling gas temperature by Eq. (6).
Acknowledgements
The authors would like to acknowledge SP Tunnel and Underground Safety Center for the financial support to the study. The experimental work was financed by the Swedish Research Council (FORMAS) which is gratefully acknowledged. Chuan Gang Fan was also financially supported by National Natural Science Foundation of China (NSFC) under Grant No. 51376173
20
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and China Scholarship Council under Program for Ph.D. Student Overseas Study Scholarship 2013.
References
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Figure captions Fig. 1 A photo of the 1:20 model scale tunnel [36]. Fig. 2 Side view of the model scale tunnel with positions of measurements (Dimensions in mm). Fig. 3 Maximum gas temperature below the ceiling as a function of tunnel width and height. Fig. 4 Temperatures measured along the tunnel ceiling for heptane tests (uo=0.67 m/s). Fig. 5 Temperatures measured along the tunnel ceiling with different ventilation velocities for wood crib tests (H=0.25 m, W=0.45 m). Fig. 6 Temperatures measured along the tunnel ceiling for crib tests. Fig. 7 Dimensionless excess ceiling gas temperature as a function of the dimensionless distance. Fig. 8 Comparison of measured dimensionless excess ceiling gas temperature with Eq. (2). Fig. 9 Correlation coefficients obtained using Eq. (15) to fit the data. Fig. 10 Decay rate of dimensionless excess gas temperature as a function of tunnel cross-sectional area. Fig. 11 Decay rate of dimensionless excess gas temperature as a function of dimensionless HRR. Fig. 12 Maximum heat flux downstream of the fuel as a function of tunnel cross-sectional area for heptane tests. Fig. 13 Maximum heat flux downstream of the fuel as a function of cross-sectional area for wood crib tests. Fig. 14 Measured and calculated maximum heat fluxes for all tests. 24
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Table captions
Table 1 A list of scaling correlations for the model tunnel. Equation Type of unit
Scaling model number
Heat Release Rate (kW)
Q F Q M ( LF / LM )
5/ 2
(12)
Mass flow rate (kg/s)
m F m M ( LF / LM )
5/2
(13)
Velocity (m/s)
u F u M ( LF / LM )
Time (s)
t F t M ( LF / LM )
Temperature (K)
TF TM
Heat flux (kW/m2)
q F q M ( L F / L M )
1/2
(14)
1/2
(15) (16)
1/2
(17)
Table 2 Description of the test conditions in tunnels.
uo Test
H
W
A
Q m ax
(m)
(m)
(m2)
(kW)
q m ax
(kW/m2)
(kW/m2)
x=0.75 m
x=3.75m
Tc,max
Fuel (m/s)
q m ax
Notea
(°C)
25
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1
Heptane
0.67
0.25
0.3
0.08
185.3
1063.4
119.7
10.4
19
2
Heptane
0.67
0.25
0.45
0.11
172.2
1052.5
99.4
7.0
1
3
Heptane
0.67
0.25
0.6
0.15
214.8
1025.2
85.5
5.3
15
4
Heptane
0.67
0.4
0.3
0.12
155.8
968.9
85.8
6.8
22
5
Heptane
0.67
0.4
0.45
0.18
139.4
961.7
73.3
3.4
27
6
Heptane
0.5
0.4
0.6
0.24
162.4
979.3
59.7
1.8
33
7
Wood
0
0.25
0.45
0.11
76.8
1056.2
13.8
0.9
11
8
Wood
0.22
0.25
0.3
0.08
63.0
1007.3
12.7
1.5
17
9
Wood
0.22
0.25
0.45
0.11
67.8
1104.6
10.0
0.9
3
10
Wood
0.22
0.25
0.6
0.15
71.4
1039.4
6.4
0.8
13
11
Wood
0.22
0.4
0.3
0.12
82.2
886.5
9.3
0.9
21
12
Wood
0.22
0.4
0.45
0.18
79.8
964.8
6.9
0.8
25
13
Wood
0.22
0.4
0.6
0.24
65.4
1016.0
6.7
0.8
32
14
Wood
0.45
0.25
0.45
0.11
106.8
1132.8
18.6
1.3
4
15
Wood
0.67
0.25
0.3
0.08
97.2
1047.9
58.7
3.8
16
16
Wood
0.67
0.25
0.45
0.11
103.8
1133.7
28.9
2.2
2
17
Wood
0.67
0.25
0.6
0.15
105.6
1139.2
20.1
1.3
12
18
Wood
0.67
0.4
0.3
0.12
92.4
843.6
17.7
2.7
20
19
Wood
0.67
0.4
0.45
0.18
102.6
971.4
16.7
1.6
23
20
Wood
0.5
0.4
0.6
0.24
103.2
936.7
10.8
0.8
31
21
Wood
1.12
0.25
0.45
0.11
101.4
984.0
22.9
2.3
5
22
Wood
0.67
0.25
0.3
0.08
153.9
1016.0
64.9
5.1
18
26
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+plasticb Wood 23
0.67
0.25
0.45
0.11
150.6
1137.6
48.3
3.7
10
0.67
0.25
0.6
0.15
172.2
1121.9
39.6
2.4
14
0.67
0.4
0.45
0.18
172.2
1011.1
39.9
2.8
24
0.5
0.4
0.6
0.24
145.6
908.5
26.5
1.4
35
+plastic Wood 24 +plastic Wood 25 +plastic Wood 26 +plastic a
The numbers given in the last column represent the test numbers in the technical report [43].
b
The wood/plastic crib contains some plastics, which have a higher heat of combustion than absolute wood.
Table 3 Backlayering length with different tunnel widths and heights.
Test
uo
H
W
A
Backlayring length
(m/s)
(m)
(m)
(m2)
(m)
Fuel
1
Heptane
0.67
0.25
0.3
0.08
0-0.25
2
Heptane
0.67
0.25
0.45
0.11
0-0.25
3
Heptane
0.67
0.25
0.6
0.15
0.5-0.75
4
Heptane
0.67
0.4
0.3
0.12
0.5-0.75
5
Heptane
0.67
0.4
0.45
0.18
2.5-2.75
6
Heptane
0.5
0.4
0.6
0.24
>3.75
27
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28
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