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Critical roof opening longitudinal length for complete smoke exhaustion in subway tunnel fires
International Journal of Thermal Sciences 133 (2018) 55–61
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Critical roof opening longitudinal length for complete smoke exhaustion in subway tunnel fires
T
Kun Hea, Xudong Chenga,∗, Shaogang Zhangb, Hui Yanga, Yongzheng Yaoa, Min Penga, Wei Conga a b
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui, 230026, China College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai, 201306, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Critical opening longitudinal length Complete smoke exhaustion Smoke control Temperature distribution
A series of experiments were conducted to investigate the smoke exhaustion in a subway tunnel under natural ventilation with a wide roof opening (its width is equal to tunnel width) based on a 1/10 reduced-scale tunnel model. The effect of the roof opening longitudinal length on the smoke exhaustion was addressed both theoretically and experimentally. The results indicated that there existed a critical opening longitudinal length which allows a complete smoke exhaustion under fire conditions. The critical opening longitudinal length was related to the tunnel aspect ratio and the distance between fire source and roof opening. A theoretical model was also developed to predict the critical opening longitudinal length for subway tunnel. The research outcomes of this study provide a technical guide for the future subway tunnel design.
1. Introduction Compared to other urban public transport means, subway has the advantages of fast speed, large passenger capacity, punctuality etc. So Subway tunnel plays an important role in releasing urban traffic pressure. However, fire is one of the largest threats to the subway tunnel. Because of its long-narrow structure, a large amount of smoke and heat will be accumulated under fire conditions when there is no efficient way to exhaust the smoke. It could result in a large number of casualties and affect emergency evacuation and rescuing processes [1–3]. A statistics showed that about 85% of the casualties are due to the hot and toxic smoke [4]. Therefore, it is significantly important to design the smoke ventilation system of a subway tunnel to create a safer environment for passengers. Compared to mechanical ventilation, natural ventilation has several advantages for a subway tunnel, such as space saving, cost reduction, and no need for maintenance. It is also useful to promote the air exchange with outside environment and maintain fresh air supply [5]. Due to the reasons above, natural ventilation has attracted increasing attention for smoke exhaustion from both engineers and researchers. For example, Ji et al. [4] studied the effect of shaft height on the smoke exhaustion in an urban road tunnel. It was found that the boundary layer separation is significant with a low shaft, while a higher shaft could largely reduce the effects, but showing reduced exhaustion efficiency companied with “plug-holing phenomenon”. The opening's
∗
viability and efficiency for a tunnel fire has already been studied experimentally. Tong et al. [6] have proved the viability of roof opening in smoke exhaustion during an urban road tunnel fire based on a series of 1/10 reduced-scale experiments. Ingason et al. [7] numerically and experimentally studied a combined system of large opening extraction and longitudinal ventilation. Ura et al. [8] indicated that the smoke exhaustion based on roof opening is sufficient to maintain a safe evacuation environment for passengers using a series of 1/12 reduced-scale tunnel model experiments. Yoon et al. [9] carried out experiments in two road tunnels and found that the ratio of natural ventilation pressure induced by shaft to the mechanical ventilation pressure came to about 30%, which greatly improved the smoke exhausting efficiency. Wang et al. [10,11] conducted a series of full-scale experiments to study the longitudinal smoke propagation distance in the tunnel with vertical shafts. They found that the back-layering lengths of five cases were all less than 60 m, which confirmed the feasibility using natural ventilation in tunnel with vertical shafts. Under the limited studies on the smoke exhaustion based on roof opening or shaft in tunnels, the related studies on subway tunnels are even rare, which are more about the temperature distributions along the tunnel than how to exhaust the whole smoke through the roof opening. For example, Yuan et al. [12] studied ceiling temperature decay characteristics in subway tunnel fires under natural ventilation based on a 1/15 reduced-scale subway tunnel model. Kashef et al. [13] proposed equations to predict ceiling temperature and smoke length in
Corresponding author. E-mail address: [email protected] (X. Cheng).
https://doi.org/10.1016/j.ijthermalsci.2018.07.011 Received 27 October 2017; Received in revised form 9 July 2018; Accepted 9 July 2018 1290-0729/ © 2018 Published by Elsevier Masson SAS.
International Journal of Thermal Sciences 133 (2018) 55–61
K. He et al.
Nomenclature
A d H L m˙ out Q˙ x
ΔTmax v W α
β
area of the roof opening (m2) thickness of smoke layer (m) tunnel height (m) roof opening longitudinal length (m) mass flow rate of smoke through the roof opening (kg/s) convective heat release rate (kW) the maximum temperature beneath the ceiling above the fire source (K) average velocity of smoke through roof opening (m/s) tunnel width (m) coefficient considering the fraction for the extraction of fresh air flows
cp g k L∗ Q˙ Ta ΔTmax, B x
ρ0
subway tunnel fires under natural ventilation condition. Although subway tunnels and road tunnels are similar in long-narrow structures, they differ in aspect geometries and ratio. For example, road tunnels have an aspect ratio of 0.64–0.7 (e.g. height: 7–9 m; and width: 10–14 m), whereas for a subway tunnel it is over 1.0 (e.g. height: 5 m; and width: 4.2 m) [14]. Previous studies [6,8–11] have demonstrated that the shafts or the roof openings are viable for smoke exhaustion, while its opening width seems to be a little small, as seen in Fig. 1(a). Therefore, the smoke cannot be exhausted completely which could pass around the roof opening and continue spreading to the downstream, which is adverse for the evacuation. Therefore, in this study, a wide roof opening, whose width was equal to the tunnel width, was proposed to block the smoke movement, as seen in Fig. 1(b). A series of reduced-scale experiments were conducted to address the effects of the roof opening longitudinal length on smoke exhaustion under fire conditions in subway tunnel. Both smoke configuration and temperature underneath the ceiling were measured and analyzed. In addition, a theoretical model was developed to predict the critical roof opening longitudinal length which allows completed smoke exhaustion under fire conditions.
coefficient between average temperature rise and the max temperature specific heat capacity of air (kJ /(kg⋅K ) ) gravity acceleration (m/s2) temperature decay coefficient dimensionless roof opening longitudinal length total heat release rate (kW) ambient temperature (K) the max temperature rise behind the roof opening (K) longitudinal distance between the fire source and the roof opening (m) density of smoke gas (kg/m3) density of ambient air (kg/m3)
because, as smoke gas spread along the tunnel, the temperature difference will decrease due to the heat loss mainly caused by heat transfer from the smoke gases to the tunnel boundaries under the natural ventilation [18]. As shown in Fig. 2 (a), when the smoke gas spreads to region beneath the roof opening, part of the smoke gas (m˙ out ) will be exhausted through the roof opening owing to the buoyancy caused by the temperature difference between hot smoke gas and ambient air, which also brings heat (Q˙ out ) out of the tunnel. The remaining smoke will continue spreading downstream and its temperature is still higher than that of ambient air. If the roof opening is long enough, all of the smoke will be exhausted out through roof opening, then the temperatures measured by thermocouples behind the roof opening are equal to that of the ambient air, as shown in Fig. 2 (b). According to Li et al. [19], the maximum temperature rise of smoke ( ΔTmax ) beneath the ceiling above the fire source can be expressed by:
ΔTmax = 17.5
2/3 Q˙ H 5/3
(1)
Meanwhile, the maximum smoke temperature rise beneath the roof opening can be obtained according to previous studies [20,21]:
2. Theoretical analysis
ΔTx = e−kx / H ΔTmax
When a fire occurs in a tunnel, the plume rises rapidly due to the buoyancy. After the smoke impinges at the ceiling, it spreads radially beneath the ceiling until it hits the sidewall of the tunnel. Along the longitudinal direction, a transition from radial to one-dimensional spreading then takes place quickly and the plume keeps at it after that [15–17]. At the point of impinging, the temperature reach its maximum for the entire smoke impinging area underneath the ceiling. This is
(2)
where x is the longitudinal distance between the fire source and the roof opening, and k is the temperature decaying coefficient. On the other hand, the convective heat flow at the fire place can be also obtained from the following energy equation:
˙ Q˙ 0 = cp mβΔT max
Fig. 1. Vertical view of tunnels with (a) a narrow opening in Wang's study; and (b) a wide roof opening in this study. 56
(3)
International Journal of Thermal Sciences 133 (2018) 55–61
K. He et al.
Fig. 2. Smoke distribution in a tunnel when (a) smoke are not completely exhausted through roof opening; and (b) roof opening can completely exhaust all the smoke.
where Q˙ 0 is the convective heat flow at the fire place, which is expressed as:
1 2 ρ v = Δp 2 s
Q˙ 0 = Q˙ (1 − χ )
where v is the average velocity of smoke through roof opening. As the heat losses of the smoke underneath the ceiling are due to radiation and convection heat transfer during the transportation, the temperature difference of smoke in a regional area can be ignored [23]. It is then assumed that the smoke temperature beneath the roof opening is uniform. A relationship can be obtained based on the ideal gas law:
(4)
where Q˙ is the fire size, and χ is the proportion of the radiation heat loss, which can be estimated to be 0.3 [22]. The convective heat flow (Qx ) at the distance x from the fire source can be got as follows:
Q˙ x = cp m˙ x βΔTx
ρ0 − ρs ΔTx = ρs Ta
(5)
where m˙ x is fire smoke mass flow rate at the distance x from the fire source. Under natural ventilation, the fire smoke mass flow rate on both side of the fire source is equal to each other, and the air entrainment can be ignored as the smoke spread in the tunnel because the entrainment coefficient is very small, about 0.00015 [16]. Therefore, m˙ x is assumed to be half of the total mass flow at the fire source, namely m˙ x = 0.5m˙ . According to Eqs. (2)–(5), the relationship between Q˙ and Qx can be given by:
Q˙ x = 0.5Q˙ (1 − χ ) e−kx / H
v=
(6)
(7)
(14)
where H and W are the height and width of the tunnel, respectively. Because the roof opening is rectangular, its area can be calculated by: (15)
A = LW
where L is the roof opening longitudinal length. Combining the Eq. s (8)–(15), the mass flow rate of the smoke through the roof opening can be got:
(8)
m˙ out = αρs LW
2βΔTx g 0.2128H (0.5W / H )−1/3 Ta
(16)
Combing Eq. (1), Eq. (2), Eq. (7) and Eq. (16), and using the Boussinesq approximation ( ρs ≈ ρa ), in which the density difference is often ignored except concerning the buoyancy, the heat of smoke exhausted from the opening (Q˙ out ) that can be got as:
(9)
where the h′ is the distance between the neutral plane and the bottom of the opening, which is approximate equal to the thickness of smoke layer in our study. So the above Eq. (9) can be rewritten as follows:
Δp = (ρ0 − ρs ) gd
(13)
d 0.5W −1/3 ⎞ = 0.2128 ⎛ H ⎝ H ⎠
where A is the area of roof opening; α is the coefficient to consider the fraction for the extraction of fresh air flows; and v is the average velocity of smoke flowing out thought the roof opening. The pressure difference at the bottom of the opening between inside and outside of the opening can be got:
Δp = (ρ0 − ρs ) gh′
2βΔTx gd Ta
where β is the conversion coefficient between average temperature rise and maximum temperature rise. Oka et al. [24] proposed an empirical model to predict the thickness of the smoke layer in tunnel, when the ratio of x/H is greater than 1.671. The thickness of smoke can be noted below:
where β is the conversion coefficient between average temperature rise and maximum temperature rise, and m˙ out is the mass flow rate of the smoke through the roof opening:
m˙ out = αρs vA
(12)
Combining the Eq. s (9)–(12), the velocity of the smoke exhausted through the roof opening can be got:
And the heat of smoke exhausted from the opening (Q˙ out ) that can be described as follows:
Q˙ out = cp m˙ out βΔTx
(11)
5/6 g ˙ −3/2kx / H ρ0 L ⎛ W ⎞ Q˙ out = 53.6cp αβ 3/2Qe H⎝H ⎠ Ta
(10)
(17)
As the longitudinal length of roof opening increases, more and more smoke and heat will be exhausted. When the opening longitudinal
Based on the Bernoulli equation, we have 57
International Journal of Thermal Sciences 133 (2018) 55–61
K. He et al.
length is long enough, all the heat under the roof opening can be exhausted though the roof opening. A shortest opening longitudinal length, which is able to exhaust all heat, is defined as the critical opening longitudinal length, and in this situation, Q˙ x is equal to Q˙ out : 5/6 g ˙ −3/2kx / H ρ0 L ⎛ W ⎞ 0.5Q˙ (1 − χ ) e−x / H = 53. 6cp αβ 3/2Qe H⎝H ⎠ Ta
Table 1 Experimental scenario in this study.
(18)
We define L∗ and As as the dimensionless length of the roof opening and the aspect ratio of a tunnel, respectively:
L∗ =
L H
Scenario No.
Fire source (kW)
Longitudinal distance between fire source and roof opening, x (m)
Roof opening longitudinal length, L (m)
1–8 9–16 17–24 25–32 33–40 41–48
5.5 11.0 16.6 22.1 11.0 11.0
2 2 2 2 3 4
0, 0.04, 0.08, 0.12 0.16,0.20,0.24,0.28
(19) (20)
As = W / H
5/2 Q˙ s l = ⎛ s⎞ Q˙ F ⎝ lF ⎠ ⎜
Therefore, the critical dimensionless opening longitudinal length is:
Lc∗
=
153.1αβ 3/2cp ρ0
1 g / Ta As5/6 e−0.5kx / H
⎟
(22)
In this study, four different gas flow rates of 0.2, 0.4, 0.6, 0.8 m3/h were chosen, and the corresponding heat release rate are 5.5, 11.0, 16.6, 22.1 kW. According to Froude's scaling law, they are equivalent to 1.8, 3.5, 5.3, 8.8 MW fires in full-scale tunnel. A total of 48 experimental tests were conducted, as shown in Table 1.
(21)
3. Experiments A series of experiments were carried out in a 1/10 reduced-scale tunnel model. As shown in Fig. 3, the model is 8 m long, 0.4 m wide and 0.5 m high. The roof, floor and one sidewall are made of fireproof panels, while the other sidewall is made of fire-resistant glass for observation purpose. To address the effect of roof opening longitudinal length, in this study, the opening longitudinal length was adjusted in a range of 0–0.28 m with an interval of 0.04 m, while the width of the opening was fixed at 0.4 m. During the adjustment of the opening longitudinal length, the center of the roof opening was always located in the centerline of the tunnel. Besides, the two entrances of the model keep opened in all experiments. And under natural ventilation, the heat and smoke on the right side of the fire source will be equal to that of the left side of the fire source. If the smoke and heat on the right side of the fire source can be completely exhausted out of the tunnel, the other half of the smoke and heat can be also completely exhausted out of the tunnel when another roof opening is set up at the left side of the fire source. Hence, we only focus on smoke temperature on the right of fire source. To obtain the temperature of smoke at the ceiling, a number of type K thermocouples were placed for the measurement during the experiments. These thermocouples were installed 0.02 m underneath the ceiling from one end of the tunnel to the other with an interval of 0.25 m. A propane gas burner (0.15 m square) was located at the centerline of the tunnel floor, as the fire source. It was positioned 1.5 m away from the left end of the tunnel, as seen in Fig. 3. A gas flow rate meter with an error of 0.01 m3/h was used to control the fire size by monitoring gas flow rate supplied to the gas burner. The heat release rate can be calculated by effective heat of combustion and the propane flow rate. The heat of combustion of propane was 46.45 MJ/kg and the combustion efficiency was usually assumed to be 1 [14,25]. Froude's scaling law has been widely used in reduced-scale fire experiments [22]. According to Froude's scaling law, the temperature fields are equal to each other. The heat release rate relationship between small-scale model tunnel and the full-scale tunnel can be expressed as follows:
4. Results and discussions 4.1. Distribution of temperature rise Fig. 4 presents the distribution of temperature rise located 0.02 m beneath and along the centerline of the ceiling when different longitudinal lengths of the roof opening (L) are utilized. The temperature rise is the temperature difference between the smoke and ambient air. It can be observed from the figure that the influences of the longitudinal lengths on the temperature rises before the roof opening are very limited. However, after the smoke spreads to the roof opening, part of the smoke is exhausted directly through it. The temperature of the smoke drops due to the heat losses, which is lower than that of the scenario without any roof opening. Therefore, the scenario without any roof opening could show the highest temperature rise when comparing to those with roof openings. This phenomenon is evidenced by the temperature outputs shown in Fig. 4. Under a larger longitudinal length, more of the smoke can be exhausted through the roof opening, companied with a lower temperature rise for those smoke spread behind the roof opening. It can be also seen from Fig. 4 that the temperature rise behind the roof opening approaches to zero when the longitudinal length exceeds 0.24 m for a fire source of 5.5 kW. It is indicated that almost all the smoke are exhausted through the roof opening, showing very limited smoke behind it. For the other fire sources used in this study, namely 11.0–22.1 kW, their situations are similar that 0.24 m can be considered as the critical length of the tunnel which can exhaust almost all the smoke produced by the fires. The related finding can be also evidenced by the smoke configuration recorded during the experiments. During the experiment, a method of combining a laser beam with DV (digital video) was used to record the movement of smoke gas inside the tunnel. For a fire source of 11.0 kW, the configurations of smoke beneath the roof opening under various longitudinal lengths are shown in Fig. 5. Without roof opening, a large number of smoke can be observed through the whole tunnel, as Fig. 3. The schematic diagram of experimental set-up.
58
International Journal of Thermal Sciences 133 (2018) 55–61
K. He et al.
Fig. 4. Temperature rises along the center line beneath the ceiling with fire sources of: (a) 5.5 kW; (b) 11.0 kW; (c) 16.6 kW; and (d) 22.1 kW.
Moreover, for a specific longitudinal length, the maximum temperature rise increases under a greater fire size. Fig. 7 presents the maximum temperature rise behind the roof opening under different longitudinal distances (2–4 m) between the fire source and the roof opening. For a specific dimensionless length of the roof opening, the maximum temperature rise is higher with a shorter distance. And for a specific distance (x), the maximum temperature rise is lower with a longer opening length, which indicates more smoke is exhausted out of the tunnel. A residual rate φ is proposed and defined to describe the smoke attenuation by the roof opening based on the temperature rise, which is expressed by:
seen in Fig. 5(a). For the situations with roof opening, smoke layer behind it becomes thinner under a larger longitudinal length, as shown in Fig. 5(b)-(d). A longer roof opening is greatly beneficial to the smoke exhaustion. It can be seen that when the longitudinal length exceeds 0.24 m, very limited smoke can be observed behind the roof opening. It should be noted that when the roof opening is relatively small (L = 0.04 m), the change of the smoke layer thickness is also not obvious. This phenomenon can be also evidenced by the measured temperature rises shown in Fig. 3. It is known that the smoke could easily pass the roof opening and continues spreading with a relatively narrow one. 4.2. Critical longitudinal length
φ=
Fig. 6 shows the maximum temperature rise behind the roof opening under various fire sizes (5.5–22.1 kW) when the longitudinal distance between the fire source and the roof opening is 2 m. The dimension temperature rise represents the dimension temperature difference for all the measured temperatures from the thermocouples on the right of the roof opening (or the location for the situation without roof opening). The maximum temperature rise shows a decreasing trend with a greater dimensionless roof opening longitudinal length (L* in Eq. (16)). The decreasing rate seems to be greater for a larger fire size.
ΔTmax, B ΔTmax, N
(23)
where ΔTmax, B is the maximum temperature rise behind the roof opening, and ΔTmax, N is the temperature rise of the same point when where is no roof opening. The residual rate can describe the relative attenuation rate. More smoke can be exhausted out through the roof opening with the increase of the opening longitudinal length, which will lead to lower smoke temperature behind the roof opening and lower residual rate. When all the heat can be exhausted out of the tunnel, the residual rate will be zero. So the critical smoke exhaustion is 59
International Journal of Thermal Sciences 133 (2018) 55–61
K. He et al.
Fig. 5. Smoke configurations of a fire source of 11.0 kW with various long roof openings.
estimated as residual rate being equal to zero in our study. Fig. 8 shows the residual rates calculated by Eq. (23) based on experimental data. The relationship can be seen in Fig. 8, which can be expressed as:
1.073 − 16.267x x ≤ 0.066 y=⎧ 0 x > 0.066 ⎨ ⎩
(24)
A correlation coefficient of 0.9629 can be obtained, representing a good correlation. Critical smoke exhaustion can be estimated according to Eq. (24), and the critical dimensionless roof opening longitudinal length can be got as following with the value of αβ 3/2 equal to 0.10:
Lc∗ =
1 15.2cp ρ0 g / Ta As5/6 e−0.5kx / H
(25)
When dimensionless longitudinal length is greater than the critical dimensionless longitudinal length, the smoke gas can be completely exhausted out of the tunnel through the roof opening, and favorable conditions for evacuation can be achieved.
Fig. 6. The maximum temperature rise behind the roof opening under different fire sizes when the vertical distance between the fire source and the roof opening is 2 m. 60
International Journal of Thermal Sciences 133 (2018) 55–61
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described as Eq. (25), was developed to predict the critical roof opening longitudinal length, which can make the smoke completely flow out of the tunnel through the roof opening. This model be used for ventilation openings in tunnels with no shafts or very short shafts. Acknowledgment This work was supported by National Key Research and Development Program of China (No.2016YFC0800603), National Natural Science Foundation of China (No.51776192) and Fundamental Research Funds for the Central Universities under Grant (No. WK2320000035). We sincerely appreciate these supports. Appendix A. Supplementary data Supplementary data related to this article can be found at https:// doi.org/10.1016/j.ijthermalsci.2018.07.011. References Fig. 7. The maximum temperature rise behind the roof opening under different longitudinal distances between the fire source and the roof opening with a fire size of 11.0 kW.
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Fig. 8. The residual rate calculated by Eq. (18) using experiment data.
5. Conclusions A series of experiments were conducted to investigate influence of the longitudinal length of a wide roof opening (its width is equal to tunnel width) on the smoke exhaustion based on a 1/10 reduced-scale subway tunnel model. Several conclusions can be addressed based on experimental and theoretical analysis: (1) There is a critical roof opening longitudinal length that allows the smoke gas to be exhausted completely through the roof opening. Therefore, there is no smoke gas behind the opening and the max temperature behind the opening will be equal to the ambient temperature, which is quite beneficial for the passengers' evacuation. (2) The critical opening longitudinal length is related to the tunnel aspect ratio and the distance between fire source and roof opening. (3) A theoretical model with new idea of remaining fire source,
61
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Critical roof opening longitudinal length for complete smoke exhaustion in subway tunnel fires
T
Kun Hea, Xudong Chenga,∗, Shaogang Zhangb, Hui Yanga, Yongzheng Yaoa, Min Penga, Wei Conga a b
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui, 230026, China College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai, 201306, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Critical opening longitudinal length Complete smoke exhaustion Smoke control Temperature distribution
A series of experiments were conducted to investigate the smoke exhaustion in a subway tunnel under natural ventilation with a wide roof opening (its width is equal to tunnel width) based on a 1/10 reduced-scale tunnel model. The effect of the roof opening longitudinal length on the smoke exhaustion was addressed both theoretically and experimentally. The results indicated that there existed a critical opening longitudinal length which allows a complete smoke exhaustion under fire conditions. The critical opening longitudinal length was related to the tunnel aspect ratio and the distance between fire source and roof opening. A theoretical model was also developed to predict the critical opening longitudinal length for subway tunnel. The research outcomes of this study provide a technical guide for the future subway tunnel design.
1. Introduction Compared to other urban public transport means, subway has the advantages of fast speed, large passenger capacity, punctuality etc. So Subway tunnel plays an important role in releasing urban traffic pressure. However, fire is one of the largest threats to the subway tunnel. Because of its long-narrow structure, a large amount of smoke and heat will be accumulated under fire conditions when there is no efficient way to exhaust the smoke. It could result in a large number of casualties and affect emergency evacuation and rescuing processes [1–3]. A statistics showed that about 85% of the casualties are due to the hot and toxic smoke [4]. Therefore, it is significantly important to design the smoke ventilation system of a subway tunnel to create a safer environment for passengers. Compared to mechanical ventilation, natural ventilation has several advantages for a subway tunnel, such as space saving, cost reduction, and no need for maintenance. It is also useful to promote the air exchange with outside environment and maintain fresh air supply [5]. Due to the reasons above, natural ventilation has attracted increasing attention for smoke exhaustion from both engineers and researchers. For example, Ji et al. [4] studied the effect of shaft height on the smoke exhaustion in an urban road tunnel. It was found that the boundary layer separation is significant with a low shaft, while a higher shaft could largely reduce the effects, but showing reduced exhaustion efficiency companied with “plug-holing phenomenon”. The opening's
∗
viability and efficiency for a tunnel fire has already been studied experimentally. Tong et al. [6] have proved the viability of roof opening in smoke exhaustion during an urban road tunnel fire based on a series of 1/10 reduced-scale experiments. Ingason et al. [7] numerically and experimentally studied a combined system of large opening extraction and longitudinal ventilation. Ura et al. [8] indicated that the smoke exhaustion based on roof opening is sufficient to maintain a safe evacuation environment for passengers using a series of 1/12 reduced-scale tunnel model experiments. Yoon et al. [9] carried out experiments in two road tunnels and found that the ratio of natural ventilation pressure induced by shaft to the mechanical ventilation pressure came to about 30%, which greatly improved the smoke exhausting efficiency. Wang et al. [10,11] conducted a series of full-scale experiments to study the longitudinal smoke propagation distance in the tunnel with vertical shafts. They found that the back-layering lengths of five cases were all less than 60 m, which confirmed the feasibility using natural ventilation in tunnel with vertical shafts. Under the limited studies on the smoke exhaustion based on roof opening or shaft in tunnels, the related studies on subway tunnels are even rare, which are more about the temperature distributions along the tunnel than how to exhaust the whole smoke through the roof opening. For example, Yuan et al. [12] studied ceiling temperature decay characteristics in subway tunnel fires under natural ventilation based on a 1/15 reduced-scale subway tunnel model. Kashef et al. [13] proposed equations to predict ceiling temperature and smoke length in
Corresponding author. E-mail address: [email protected] (X. Cheng).
https://doi.org/10.1016/j.ijthermalsci.2018.07.011 Received 27 October 2017; Received in revised form 9 July 2018; Accepted 9 July 2018 1290-0729/ © 2018 Published by Elsevier Masson SAS.
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Nomenclature
A d H L m˙ out Q˙ x
ΔTmax v W α
β
area of the roof opening (m2) thickness of smoke layer (m) tunnel height (m) roof opening longitudinal length (m) mass flow rate of smoke through the roof opening (kg/s) convective heat release rate (kW) the maximum temperature beneath the ceiling above the fire source (K) average velocity of smoke through roof opening (m/s) tunnel width (m) coefficient considering the fraction for the extraction of fresh air flows
cp g k L∗ Q˙ Ta ΔTmax, B x
ρ0
subway tunnel fires under natural ventilation condition. Although subway tunnels and road tunnels are similar in long-narrow structures, they differ in aspect geometries and ratio. For example, road tunnels have an aspect ratio of 0.64–0.7 (e.g. height: 7–9 m; and width: 10–14 m), whereas for a subway tunnel it is over 1.0 (e.g. height: 5 m; and width: 4.2 m) [14]. Previous studies [6,8–11] have demonstrated that the shafts or the roof openings are viable for smoke exhaustion, while its opening width seems to be a little small, as seen in Fig. 1(a). Therefore, the smoke cannot be exhausted completely which could pass around the roof opening and continue spreading to the downstream, which is adverse for the evacuation. Therefore, in this study, a wide roof opening, whose width was equal to the tunnel width, was proposed to block the smoke movement, as seen in Fig. 1(b). A series of reduced-scale experiments were conducted to address the effects of the roof opening longitudinal length on smoke exhaustion under fire conditions in subway tunnel. Both smoke configuration and temperature underneath the ceiling were measured and analyzed. In addition, a theoretical model was developed to predict the critical roof opening longitudinal length which allows completed smoke exhaustion under fire conditions.
coefficient between average temperature rise and the max temperature specific heat capacity of air (kJ /(kg⋅K ) ) gravity acceleration (m/s2) temperature decay coefficient dimensionless roof opening longitudinal length total heat release rate (kW) ambient temperature (K) the max temperature rise behind the roof opening (K) longitudinal distance between the fire source and the roof opening (m) density of smoke gas (kg/m3) density of ambient air (kg/m3)
because, as smoke gas spread along the tunnel, the temperature difference will decrease due to the heat loss mainly caused by heat transfer from the smoke gases to the tunnel boundaries under the natural ventilation [18]. As shown in Fig. 2 (a), when the smoke gas spreads to region beneath the roof opening, part of the smoke gas (m˙ out ) will be exhausted through the roof opening owing to the buoyancy caused by the temperature difference between hot smoke gas and ambient air, which also brings heat (Q˙ out ) out of the tunnel. The remaining smoke will continue spreading downstream and its temperature is still higher than that of ambient air. If the roof opening is long enough, all of the smoke will be exhausted out through roof opening, then the temperatures measured by thermocouples behind the roof opening are equal to that of the ambient air, as shown in Fig. 2 (b). According to Li et al. [19], the maximum temperature rise of smoke ( ΔTmax ) beneath the ceiling above the fire source can be expressed by:
ΔTmax = 17.5
2/3 Q˙ H 5/3
(1)
Meanwhile, the maximum smoke temperature rise beneath the roof opening can be obtained according to previous studies [20,21]:
2. Theoretical analysis
ΔTx = e−kx / H ΔTmax
When a fire occurs in a tunnel, the plume rises rapidly due to the buoyancy. After the smoke impinges at the ceiling, it spreads radially beneath the ceiling until it hits the sidewall of the tunnel. Along the longitudinal direction, a transition from radial to one-dimensional spreading then takes place quickly and the plume keeps at it after that [15–17]. At the point of impinging, the temperature reach its maximum for the entire smoke impinging area underneath the ceiling. This is
(2)
where x is the longitudinal distance between the fire source and the roof opening, and k is the temperature decaying coefficient. On the other hand, the convective heat flow at the fire place can be also obtained from the following energy equation:
˙ Q˙ 0 = cp mβΔT max
Fig. 1. Vertical view of tunnels with (a) a narrow opening in Wang's study; and (b) a wide roof opening in this study. 56
(3)
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Fig. 2. Smoke distribution in a tunnel when (a) smoke are not completely exhausted through roof opening; and (b) roof opening can completely exhaust all the smoke.
where Q˙ 0 is the convective heat flow at the fire place, which is expressed as:
1 2 ρ v = Δp 2 s
Q˙ 0 = Q˙ (1 − χ )
where v is the average velocity of smoke through roof opening. As the heat losses of the smoke underneath the ceiling are due to radiation and convection heat transfer during the transportation, the temperature difference of smoke in a regional area can be ignored [23]. It is then assumed that the smoke temperature beneath the roof opening is uniform. A relationship can be obtained based on the ideal gas law:
(4)
where Q˙ is the fire size, and χ is the proportion of the radiation heat loss, which can be estimated to be 0.3 [22]. The convective heat flow (Qx ) at the distance x from the fire source can be got as follows:
Q˙ x = cp m˙ x βΔTx
ρ0 − ρs ΔTx = ρs Ta
(5)
where m˙ x is fire smoke mass flow rate at the distance x from the fire source. Under natural ventilation, the fire smoke mass flow rate on both side of the fire source is equal to each other, and the air entrainment can be ignored as the smoke spread in the tunnel because the entrainment coefficient is very small, about 0.00015 [16]. Therefore, m˙ x is assumed to be half of the total mass flow at the fire source, namely m˙ x = 0.5m˙ . According to Eqs. (2)–(5), the relationship between Q˙ and Qx can be given by:
Q˙ x = 0.5Q˙ (1 − χ ) e−kx / H
v=
(6)
(7)
(14)
where H and W are the height and width of the tunnel, respectively. Because the roof opening is rectangular, its area can be calculated by: (15)
A = LW
where L is the roof opening longitudinal length. Combining the Eq. s (8)–(15), the mass flow rate of the smoke through the roof opening can be got:
(8)
m˙ out = αρs LW
2βΔTx g 0.2128H (0.5W / H )−1/3 Ta
(16)
Combing Eq. (1), Eq. (2), Eq. (7) and Eq. (16), and using the Boussinesq approximation ( ρs ≈ ρa ), in which the density difference is often ignored except concerning the buoyancy, the heat of smoke exhausted from the opening (Q˙ out ) that can be got as:
(9)
where the h′ is the distance between the neutral plane and the bottom of the opening, which is approximate equal to the thickness of smoke layer in our study. So the above Eq. (9) can be rewritten as follows:
Δp = (ρ0 − ρs ) gd
(13)
d 0.5W −1/3 ⎞ = 0.2128 ⎛ H ⎝ H ⎠
where A is the area of roof opening; α is the coefficient to consider the fraction for the extraction of fresh air flows; and v is the average velocity of smoke flowing out thought the roof opening. The pressure difference at the bottom of the opening between inside and outside of the opening can be got:
Δp = (ρ0 − ρs ) gh′
2βΔTx gd Ta
where β is the conversion coefficient between average temperature rise and maximum temperature rise. Oka et al. [24] proposed an empirical model to predict the thickness of the smoke layer in tunnel, when the ratio of x/H is greater than 1.671. The thickness of smoke can be noted below:
where β is the conversion coefficient between average temperature rise and maximum temperature rise, and m˙ out is the mass flow rate of the smoke through the roof opening:
m˙ out = αρs vA
(12)
Combining the Eq. s (9)–(12), the velocity of the smoke exhausted through the roof opening can be got:
And the heat of smoke exhausted from the opening (Q˙ out ) that can be described as follows:
Q˙ out = cp m˙ out βΔTx
(11)
5/6 g ˙ −3/2kx / H ρ0 L ⎛ W ⎞ Q˙ out = 53.6cp αβ 3/2Qe H⎝H ⎠ Ta
(10)
(17)
As the longitudinal length of roof opening increases, more and more smoke and heat will be exhausted. When the opening longitudinal
Based on the Bernoulli equation, we have 57
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length is long enough, all the heat under the roof opening can be exhausted though the roof opening. A shortest opening longitudinal length, which is able to exhaust all heat, is defined as the critical opening longitudinal length, and in this situation, Q˙ x is equal to Q˙ out : 5/6 g ˙ −3/2kx / H ρ0 L ⎛ W ⎞ 0.5Q˙ (1 − χ ) e−x / H = 53. 6cp αβ 3/2Qe H⎝H ⎠ Ta
Table 1 Experimental scenario in this study.
(18)
We define L∗ and As as the dimensionless length of the roof opening and the aspect ratio of a tunnel, respectively:
L∗ =
L H
Scenario No.
Fire source (kW)
Longitudinal distance between fire source and roof opening, x (m)
Roof opening longitudinal length, L (m)
1–8 9–16 17–24 25–32 33–40 41–48
5.5 11.0 16.6 22.1 11.0 11.0
2 2 2 2 3 4
0, 0.04, 0.08, 0.12 0.16,0.20,0.24,0.28
(19) (20)
As = W / H
5/2 Q˙ s l = ⎛ s⎞ Q˙ F ⎝ lF ⎠ ⎜
Therefore, the critical dimensionless opening longitudinal length is:
Lc∗
=
153.1αβ 3/2cp ρ0
1 g / Ta As5/6 e−0.5kx / H
⎟
(22)
In this study, four different gas flow rates of 0.2, 0.4, 0.6, 0.8 m3/h were chosen, and the corresponding heat release rate are 5.5, 11.0, 16.6, 22.1 kW. According to Froude's scaling law, they are equivalent to 1.8, 3.5, 5.3, 8.8 MW fires in full-scale tunnel. A total of 48 experimental tests were conducted, as shown in Table 1.
(21)
3. Experiments A series of experiments were carried out in a 1/10 reduced-scale tunnel model. As shown in Fig. 3, the model is 8 m long, 0.4 m wide and 0.5 m high. The roof, floor and one sidewall are made of fireproof panels, while the other sidewall is made of fire-resistant glass for observation purpose. To address the effect of roof opening longitudinal length, in this study, the opening longitudinal length was adjusted in a range of 0–0.28 m with an interval of 0.04 m, while the width of the opening was fixed at 0.4 m. During the adjustment of the opening longitudinal length, the center of the roof opening was always located in the centerline of the tunnel. Besides, the two entrances of the model keep opened in all experiments. And under natural ventilation, the heat and smoke on the right side of the fire source will be equal to that of the left side of the fire source. If the smoke and heat on the right side of the fire source can be completely exhausted out of the tunnel, the other half of the smoke and heat can be also completely exhausted out of the tunnel when another roof opening is set up at the left side of the fire source. Hence, we only focus on smoke temperature on the right of fire source. To obtain the temperature of smoke at the ceiling, a number of type K thermocouples were placed for the measurement during the experiments. These thermocouples were installed 0.02 m underneath the ceiling from one end of the tunnel to the other with an interval of 0.25 m. A propane gas burner (0.15 m square) was located at the centerline of the tunnel floor, as the fire source. It was positioned 1.5 m away from the left end of the tunnel, as seen in Fig. 3. A gas flow rate meter with an error of 0.01 m3/h was used to control the fire size by monitoring gas flow rate supplied to the gas burner. The heat release rate can be calculated by effective heat of combustion and the propane flow rate. The heat of combustion of propane was 46.45 MJ/kg and the combustion efficiency was usually assumed to be 1 [14,25]. Froude's scaling law has been widely used in reduced-scale fire experiments [22]. According to Froude's scaling law, the temperature fields are equal to each other. The heat release rate relationship between small-scale model tunnel and the full-scale tunnel can be expressed as follows:
4. Results and discussions 4.1. Distribution of temperature rise Fig. 4 presents the distribution of temperature rise located 0.02 m beneath and along the centerline of the ceiling when different longitudinal lengths of the roof opening (L) are utilized. The temperature rise is the temperature difference between the smoke and ambient air. It can be observed from the figure that the influences of the longitudinal lengths on the temperature rises before the roof opening are very limited. However, after the smoke spreads to the roof opening, part of the smoke is exhausted directly through it. The temperature of the smoke drops due to the heat losses, which is lower than that of the scenario without any roof opening. Therefore, the scenario without any roof opening could show the highest temperature rise when comparing to those with roof openings. This phenomenon is evidenced by the temperature outputs shown in Fig. 4. Under a larger longitudinal length, more of the smoke can be exhausted through the roof opening, companied with a lower temperature rise for those smoke spread behind the roof opening. It can be also seen from Fig. 4 that the temperature rise behind the roof opening approaches to zero when the longitudinal length exceeds 0.24 m for a fire source of 5.5 kW. It is indicated that almost all the smoke are exhausted through the roof opening, showing very limited smoke behind it. For the other fire sources used in this study, namely 11.0–22.1 kW, their situations are similar that 0.24 m can be considered as the critical length of the tunnel which can exhaust almost all the smoke produced by the fires. The related finding can be also evidenced by the smoke configuration recorded during the experiments. During the experiment, a method of combining a laser beam with DV (digital video) was used to record the movement of smoke gas inside the tunnel. For a fire source of 11.0 kW, the configurations of smoke beneath the roof opening under various longitudinal lengths are shown in Fig. 5. Without roof opening, a large number of smoke can be observed through the whole tunnel, as Fig. 3. The schematic diagram of experimental set-up.
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Fig. 4. Temperature rises along the center line beneath the ceiling with fire sources of: (a) 5.5 kW; (b) 11.0 kW; (c) 16.6 kW; and (d) 22.1 kW.
Moreover, for a specific longitudinal length, the maximum temperature rise increases under a greater fire size. Fig. 7 presents the maximum temperature rise behind the roof opening under different longitudinal distances (2–4 m) between the fire source and the roof opening. For a specific dimensionless length of the roof opening, the maximum temperature rise is higher with a shorter distance. And for a specific distance (x), the maximum temperature rise is lower with a longer opening length, which indicates more smoke is exhausted out of the tunnel. A residual rate φ is proposed and defined to describe the smoke attenuation by the roof opening based on the temperature rise, which is expressed by:
seen in Fig. 5(a). For the situations with roof opening, smoke layer behind it becomes thinner under a larger longitudinal length, as shown in Fig. 5(b)-(d). A longer roof opening is greatly beneficial to the smoke exhaustion. It can be seen that when the longitudinal length exceeds 0.24 m, very limited smoke can be observed behind the roof opening. It should be noted that when the roof opening is relatively small (L = 0.04 m), the change of the smoke layer thickness is also not obvious. This phenomenon can be also evidenced by the measured temperature rises shown in Fig. 3. It is known that the smoke could easily pass the roof opening and continues spreading with a relatively narrow one. 4.2. Critical longitudinal length
φ=
Fig. 6 shows the maximum temperature rise behind the roof opening under various fire sizes (5.5–22.1 kW) when the longitudinal distance between the fire source and the roof opening is 2 m. The dimension temperature rise represents the dimension temperature difference for all the measured temperatures from the thermocouples on the right of the roof opening (or the location for the situation without roof opening). The maximum temperature rise shows a decreasing trend with a greater dimensionless roof opening longitudinal length (L* in Eq. (16)). The decreasing rate seems to be greater for a larger fire size.
ΔTmax, B ΔTmax, N
(23)
where ΔTmax, B is the maximum temperature rise behind the roof opening, and ΔTmax, N is the temperature rise of the same point when where is no roof opening. The residual rate can describe the relative attenuation rate. More smoke can be exhausted out through the roof opening with the increase of the opening longitudinal length, which will lead to lower smoke temperature behind the roof opening and lower residual rate. When all the heat can be exhausted out of the tunnel, the residual rate will be zero. So the critical smoke exhaustion is 59
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Fig. 5. Smoke configurations of a fire source of 11.0 kW with various long roof openings.
estimated as residual rate being equal to zero in our study. Fig. 8 shows the residual rates calculated by Eq. (23) based on experimental data. The relationship can be seen in Fig. 8, which can be expressed as:
1.073 − 16.267x x ≤ 0.066 y=⎧ 0 x > 0.066 ⎨ ⎩
(24)
A correlation coefficient of 0.9629 can be obtained, representing a good correlation. Critical smoke exhaustion can be estimated according to Eq. (24), and the critical dimensionless roof opening longitudinal length can be got as following with the value of αβ 3/2 equal to 0.10:
Lc∗ =
1 15.2cp ρ0 g / Ta As5/6 e−0.5kx / H
(25)
When dimensionless longitudinal length is greater than the critical dimensionless longitudinal length, the smoke gas can be completely exhausted out of the tunnel through the roof opening, and favorable conditions for evacuation can be achieved.
Fig. 6. The maximum temperature rise behind the roof opening under different fire sizes when the vertical distance between the fire source and the roof opening is 2 m. 60
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described as Eq. (25), was developed to predict the critical roof opening longitudinal length, which can make the smoke completely flow out of the tunnel through the roof opening. This model be used for ventilation openings in tunnels with no shafts or very short shafts. Acknowledgment This work was supported by National Key Research and Development Program of China (No.2016YFC0800603), National Natural Science Foundation of China (No.51776192) and Fundamental Research Funds for the Central Universities under Grant (No. WK2320000035). We sincerely appreciate these supports. Appendix A. Supplementary data Supplementary data related to this article can be found at https:// doi.org/10.1016/j.ijthermalsci.2018.07.011. References Fig. 7. The maximum temperature rise behind the roof opening under different longitudinal distances between the fire source and the roof opening with a fire size of 11.0 kW.
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Fig. 8. The residual rate calculated by Eq. (18) using experiment data.
5. Conclusions A series of experiments were conducted to investigate influence of the longitudinal length of a wide roof opening (its width is equal to tunnel width) on the smoke exhaustion based on a 1/10 reduced-scale subway tunnel model. Several conclusions can be addressed based on experimental and theoretical analysis: (1) There is a critical roof opening longitudinal length that allows the smoke gas to be exhausted completely through the roof opening. Therefore, there is no smoke gas behind the opening and the max temperature behind the opening will be equal to the ambient temperature, which is quite beneficial for the passengers' evacuation. (2) The critical opening longitudinal length is related to the tunnel aspect ratio and the distance between fire source and roof opening. (3) A theoretical model with new idea of remaining fire source,
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