A study for predicting the maximum gas temperature beneath ceiling in sealing tactics against tunnel fire

Tunnelling and Underground Space Technology xxx (xxxx) xxxx

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A study for predicting the maximum gas temperature beneath ceiling in sealing tactics against tunnel fire Changkun Chen, Yulun Zhang , Peng Lei, Weibing Jiao ⁎

Institute of Disaster Prevention Science & Safety Technology, Central South University, Changsha 410075, PR China

ARTICLE INFO

ABSTRACT

Keywords: Tunnel fire Sealing tactics Maximum temperature Critical sealing Ceiling

Sealing the tunnel portal is one of practical strategies for tunnel fire extinguishing. In order to better comprehend the sealing effects on tunnel fire and help with sealing strategies scientifically, the maximum gas temperature beneath ceiling in a sealing fire was investigated theoretically, experimentally and numerically in this paper. The results show that maximum ceiling gas temperature is greatly affected by sealing ratio, which probably due to the comprehensive effect between fresh air supply and the reduction of heat loss significantly related to vent area of tunnel portal. Moreover, there always exists a critical sealing ratio, at which ceiling temperature would reach the maximum, and when beyond the critical sealing ratio, maximum gas temperature would drop gradually, which is expected in firefighting. Also, it is found that critical sealing ratio is a function of dimensionless heat release rate, and the greater the heat release rate is, the smaller the critical sealing ratio would be. Finally, an empirical model determining maximum ceiling gas temperature is developed to modify the current models by taking sealing effect into account. The predictions calculated by modified equations agree well with experimental and numerical date in maximum ceiling gas temperature.

1. Introduction Nowadays, tunnel fire is one of the most serious accidents in the transportation industry (Fan et al., 2013; Meng et al., 2018), which has attracted more and more attention due to its catastrophic consequences such as enormous casualties, tunnel structure damage, and huge economic loss (Zhong et al., 2013; Li et al., 2011). For instance; the fire in a subway tunnel in Daegu Korea on February 18, 2003 caused 198 deaths and 146 injures (Chen et al., 2017). And the Yanhou Tunnel Fire Accident in China on March 1, 2014 has claimed as many as 40 lives and left 82 million direct economic loss (Ingason et al., 2014). Usually, large tunnel fire is difficult for firefighters to get inside tunnel to extinguish fire because of the high-density combustibles and complex fire environment (Chen et al., 2017; Chen et al., 2016). Thus, it would be a good choice to extinguish fire by sealing the two tunnel portals simultaneously, which could reduce oxygen supply of internal combustion so as to achieve the purpose of smothering fire. As a typical case, the train carrying oil with 13 carriage in the Baoji-Chengdu railway tunnel of China derailed and caused an intense fire in May 2008 (Chen et al., 2017; Huang et al., 2018), and firefighters couldn't get into the tunnel to fight the fire directly. Eventually, the large fire was extinguished by the approach of sealing tunnel portals. However, it is

worth noting that despite the fire was put out successfully, the process still lasted for 9 days and caused huge economic losses. And this extends the contact time between tunnel structure and fire temperature to some extent, which probably cause destructive damage to tunnel lining structure. Therefore, it is strongly necessary to study the temperature distribution inside tunnel in a sealing fire, especially for the maximum ceiling gas temperature related to the tunnel fire safety design. During the past few years, a series of theories and models for the characteristics of tunnel fires and high-rise building fires have been widely developed by experiments and numerical simulations (Gannouni and Ben Maad, 2016; Gao et al., 2015; Huang et al., 2018; Zhou et al., 2018). Full-scale experiments of tunnel fire can describe more objectively and explain the main characteristics of fire development in long and narrow space, and is one of effective test approaches. For instance, the EUREKA EU499-tunnel fire experiments in Repparfjord (Hammerfest, Norway) in 1990–1992 (Grant and Drysdale, 1995; Haack et al., 1995)and the Runehamar fire tests in 2003 (Ingason et al., 2015), obtained many significant research findings and provided the foundation for the later study. However, the full-scale experiments couldn’t usually be promoted application duo to its high cost, long time and destructive effect. Therefore, the model scale experiment and numerical simulation are widely used to investigate tunnel fire. Ingason (2008)

⁎ Corresponding author at: Institute of Disaster Prevention Science and Safety Technology, Railway Campus, Central South University, Changsha, Hunan 410075, PR China. E-mail address: [email protected] (Y. Zhang).

https://doi.org/10.1016/j.tust.2019.103275 Received 12 August 2019; Received in revised form 3 December 2019; Accepted 23 December 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Changkun Chen, et al., Tunnelling and Underground Space Technology, https://doi.org/10.1016/j.tust.2019.103275

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Nomenclature Cp g Hef H hs K mp mp,s Q Qc Q* R ΔTaverage ΔTaverage,s

ΔTmax ΔTmax,s T∞ V V* β βc ρ∞ χ η, ψ ∞ ss sg sl F M

specific heat capacity (kJ/kg/K) gravity acceleration (m/s2) ceiling clearance above fire source (m) portal height of tunnel (m) sealing height of tunnel portal (m) sealing coefficient mass flow rate of fire plume (kg/s) mass flow rate of fire plume under sealing (kg/s) heat release rate of fire source (kW) convective heat release rate (kW) dimensionless heat release rate radius of the fire source (m) average ceiling excess temperature (K) average ceiling excess temperature under sealing (K)

maximum ceiling excess temperature (K) maximum ceiling excess temperature under sealing (K) ambient temperature (K) longitudinal ventilation velocity (m/s) dimensionless longitudinal ventilation velocity sealing ratio critical sealing ratio density of ambient air (kg/m3); combustion efficiency proportional coefficient in Eqs. (9) and (10) ambient small fire general size fire large fire full scale model scale

incombustible material is an important approach for tunnel fire extinguishing. When the tunnel portals were sealed, the original balance of the combustion and temperature distribution inside tunnel would be broken due to the restriction of fresh air supply and heat loss, and the maximum ceiling temperature differs from general tunnel fire apparently. Chen et al. (2017, 2016) conducted liquid pool fire tests in a 1:9 model scale tunnel with different symmetrical and asymmetrical sealing ratios at tunnel portals to study the combustion process and temperature distribution characteristic from the perspectives of experimental and qualitative. The results shown ceiling temperature inside tunnel varies versus sealing ratio and exist a critical sealing ratio related to the heat release rate, at which the temperature beneath ceiling would reach the maximum. Yao et al. (2017) theoretically and experimentally investigated the fire development characteristic and the maximum ceiling gas temperature in a fully enclosed channel. Huang et al. (2018) studied the maximum gas temperature and longitudinal temperature attenuation beneath ceiling with different sealing ratios by FDS numerical simulation and proposed a temperature prediction model taking the sealing rate into account. Yao et al. (2018a) experimentally investigated the influence of initial sealing time on fire behaviors in a reduced-scale channel model under different sealing rates. Additionally, Lönnermark et al. (2010) summarized the guidelines and solutions for fire safety of underground facilities in the course of construction, including the sealing. In summary, the special study on tunnel firefighting, especially the effect of sealing on fire temperature characteristics inside tunnel is relatively less at present. Hence, more attention should be paid to this aspect for tunnel fire. Considering this, in this paper, a series of model scale experiments and full-scale numerical simulations about tunnel fire were carried out to investigate the gas temperature beneath ceiling with different sealing ratios at tunnel portals. And combined the theoretical analysis to some extent, a modified model correlating the sealing ratio and maximum ceiling gas temperature is proposed. This work is expected to provide some valuable references for actual tunnel sealing strategies and fire extinguishing.

investigated the extinguishing efficiency of water mist on heavy goods vehicle fire in tunnel by the 1:23 model scale experiments. Tang et al. (2013) carried out the fire tests in 1:5 model tunnel to study the effect of a vehicular blockage at the upstream of fire source on the backlayering length driven by buoyancy and critical velocity under longitudinal ventilation. And some other model scale experiments were conducted to investigate tunnel fire characteristics including exhaust smoke, temperature distribution, heat release rate, etc. (Fan et al., 2013; Zhao et al., 2019). In addition, the numerical simulation about tunnel fire also have been widely reported to study the smoke movement (Ji et al., 2015), critical velocity (Weng et al., 2016), temperature distribution (Ji et al., 2017) and other characteristic parameters. The main simulation software used in tunnel fire is FDS and its feasibility has been widely verified by many scholars (Gannouni and Ben Maad, 2016), which is known as a practical tool to simulate fire-induced environment. And the numerical simulations were carried out in this paper as a supplement to the experimental conditions. The maximum gas temperature beneath the tunnel ceiling during tunnel fire is a key parameter which determines to the fire protection design of tunnel structure (Huang et al., 2018). Much work has been done to investigate the maximum ceiling gas temperature in tunnel fire. Tang et al. (2017) experimentally investigated the effect of blockagefire source distance on maximum ceiling temperature of buoyancy induced smoke flow in a longitudinal ventilated tunnel. Results show that with upstream blockage of fire source and different blockage-fire source distance considered, the maximum ceiling temperature firstly increases to the maximum value under the blockage-fire source distance of 0.5 m, then decreases as blockage-fire source distance continues to increase. Yao et al. (2018b) studied the smoke movement and maximum temperature distribution below tunnel ceiling under the condition of completely sealed portals, and the influence of fire source location and fuel area was analyzed. A corresponding empirical model considering different fire sources locations and sizes is proposed. Ye et al. (2019) studied the attenuation law of longitudinal maximum smoke temperature induced by strong plume. A theoretical correlation is derived by incorporating the approximate boundary layer thickness and related coefficients is determined in the full-scale fire experiments, and the correlation could be well applied to the estimation of fire detection time, assessment of thermal environment and heat exposure in engineering practice. Tang et al. (2018, 2019) theoretically and experimentally investigated the distribution of maximum smoke temperature below ceiling and air entrainment characteristics of tunnel fire under different smoke extraction systems. Although many scholars have studied the maximum gas temperature of tunnel fire from multiple perspectives (Li et al., 2011; Zhao et al., 2019; Ji et al., 2015; Kurioka et al., 2003; Li and Ingason, 2012; Yao et al., 2017), the existing theories and models have little taken into account the effect of sealing on the temperature inside tunnel. Sealing tunnel portals with

2. Theoretical considerations 2.1. Previous model of maximum ceiling temperature The heat produced by fire can easily accumulate beneath the tunnel ceiling due to the space characteristics of long-narrow and confined, and then the fire-induced high temperature drove by ventilation and thermal buoyancy would spread horizontally and vertically. The high temperature of smoke acting on the structure surface could seriously damage the tunnel lining. In particular, the maximum smoke temperature beneath the ceiling, as a key parameter to the tunnel fire 2

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protection design, has a great impact on the structural safety of tunnel. Kurioka et al. (2003) proposed the following empirical model for maximum gas excess temperature beneath tunnel ceiling based on a series of model scale experiments under longitudinal ventilation:

Q 2/3 Fr 1/3

Tmax = T

= 1.77,

= 1.2

Q 2/3 Fr 1/3

= 2.54,

=0

1.35,

where Q* is the dimensionless heat release rate defined as:

2

Q cp T g1/2Hef5/2

Q =

mp, s = K1 0.20

(2)

Fr is the Froude number given by:

V2 Fr = gHef

Taverage, s = (3)

Tmax =

V =

5/3 VR1/3Hef

17.5

(Qc g /

Tmax, s =

Q2/3

,V

0.19

V cp T R)1/3

cp T

(4)

Tmax, s =

(9)

(10)

Taverage, s

K2 (1 2g

cp T

1/3

)Q (1

) Q1/3Hef5/3

(11)

K2 Q 2/3 17.5 5/3 K1 Hef

(12)

The dimensionless coefficients K1 and K2 are related to the sealing ratio at tunnel portals. And in order to quantitatively investigate the effect of sealing on maximum gas temperature beneath ceiling, sealing ratio is defined as the proportion of the sealing height over the tunnel portal height (Chen et al., 2016), which is expressed as follows:

(5)

=

hs (0 H

1)

(13)

where hs is sealing height at tunnel portal, H is the tunnel portal height. Therefore, for a specific fire scenario, the heat release rate is fixed, and the K2 is a function of sealing ratio , and Eq. (12) can be expressed K1 as:

Tmax, s = f ( )17.5

Q2/3 Hef5/3

(14)

In a tunnel fire, when the tunnel portals are sealed, the fresh air supply inside the tunnel will be restricted, and the combustion is suppressed due to the lack of oxygen to maintain, so as to achieve the purpose of fire extinguishing. In addition, the sealing will also cause heat and high temperature produced by combustion to accumulate rapidly inside the tunnel and lose heat difficultly, which means increasing the maximum temperature to some extent. The maximum gas temperature beneath tunnel ceiling is determined by the relative prevailingness of oxygen supply restriction and heat accumulation, and both the two factors are related to the sealing ratio. Based on the above considerations and combined with the limit concept, f ( ) can be analyzed as follows. When the fire size is very

1/3

Q1/3z 5/3

(8)

Substituting the known parameters of a specific tunnel fire scenario gives:

In general, the vertical fire plume of tunnel fire is similar with ideal flame plume before impinging on the ceiling. Based on the assumption of point source and top hat profile, the mass flow rate mp and average excess temperature Taverage at vertical height z of ideal flame plume can be obtained from Eqs. (6) and (7) (Karlsson and Quintiere, 2000).

g

K2 (1 )Q cp mp

K1 cp 0.20

2.2. Maximum ceiling temperature in sealing strategy

2

) Q1/3z 5/3

(1

cp T

Tmax, s =

where R is the radius of fire source (m); Qc is the convective heat release rate (kW). Kurioka's and Li's models are the classical models to predict maximum gas excess temperature beneath tunnel ceiling, which provide great convenience for tunnel fire safety design. However, the above models do not consider the influence of sealing at tunnel portals, which couldn't be directly applied to the prediction of maximum smoke temperature in the process of sealing and fire extinguishing. Previous studies have shown that in some fire scenarios, sealing the tunnel portals will result in a larger maximum smoke temperature. It is obviously beyond the prediction of the current model for maximum gas temperature. Therefore, it is necessary to establish a prediction model that takes the sealing factors into account.

mp = 0.20

1/3

Substituting Eqs. (8) and (9) into Eq. (10) gives:

, V > 0.19

5/3 Hef

g

where mp, s and Taverage, s is the mass flow rate and average excess temperature of fire plume in the sealing tunnel fire. Usually, the maximum excess temperature is proportional to the average temperature rise, and the proportional coefficient of 1.59 is a reasonable value according to Li's study (Li et al., 2011), so the maximum gas temperature rise below ceiling concerned in this paper can be expressed as:

where Tmax is the maximum excess temperature (K); T is the ambient temperature; Q is the heat release rate (kW); is density of ambient air (kg/m3); cP is specific heat capacity (kJ/kg/K); Hef is the ceiling clearance above fire source (m); V is the longitudinal ventilation velocity in tunnel (m/s). The Kurioka's model can't be applied to the fire scenario at low 2/3 longitudinal ventilation velocity, otherwise the Q 1/3 would be much Fr larger than 1.35 and bring a constant Tmax in spite of HRR. Li et al. (2011) considered the scenario of low longitudinal ventilation velocity and proposed another model included the region of low ventilation velocity to predict the maximum gas excess temperature: Q

(7)

For an actual tunnel fire, the sealing at portal will not only reduce the opening area to directly affect the mass flow rate of plume entrainment, but also indirectly affect the heat released rate of fire source by limiting oxygen supply. We assume that the effect of sealing on the mass flow rate of plume entrainment and heat release rate can be simply characterized by dimensionless coefficients K1 and K2. In addition, considering that the heat loss caused by thermal radiation is not taken into account in the ideal plume, we adopt the proportional coefficient to modify the heat released rate, which accounts for about 20%-40% of the total energy released from many common fuel sources. The Eqs. (6) and (7) can be transformed into Eqs. (8) and (9).

(1)

Q 2/3 < 1.35, Fr 1/3

Q cp mp

Taverage =

(6) 3

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small, the fresh air inside tunnel is enough to support the combustion of fire source, and sealing at portals can only reduce the heat loss. The larger the sealing ratio is, the more heat accumulation is and the higher the maximum temperature rise is. This means f ( ) is an increasing function in this situation (marked as Kss). When the fire size is very large, fire plume will hit the tunnel ceiling, and under the situation of no-sealing at portals, the maximum temperature rise below ceiling will be close to a constant (marked as Co). At this point, the combustion is completely controlled by the ventilation conditions. As long as the portal is sealed, the opening area will be reduced and fire source combustion will be suppressed, which leads to the maximum temperature rise decrease. This means f ( ) is a decreasing function in this situation (marked as Ksl). Specially, for a general size fire, the combustion suppression and heat accumulation induced by sealing at tunnel portals both play an important role in the maximum ceiling temperature rise, which means that there is a critical sealing ratio ( c ) in the sealing process. When the sealing ratio β is equal to the c , the oxygen supply restriction is not enough to make the combustion fully extinguish and the heat released by fire source is difficult to lose heat due to the sealing at portals, and the maximum gas temperature below ceiling will reach another peak. Only beyond critical sealing ratio, the maximum gas temperature will decrease all along to a lower temperature, which is desired in firefighting. Especially, the critical sealing ratio closely related to the heat released rate of fire source, which can be expressed as Eq. (15), and the larger heat released rate is, the lower critical sealing ratio would be. c

The Kss, Ksg1, Ksg2, Ksl, C0 and βc are deduced from the experimental and numerical results. 3. Model scale experiments for fire sealing In order to verify the above theoretical analysis and obtain sealing coefficients of the modified model, a series of experiments about fire sealing were carried out in a scaled tunnel. The detailed experimental procedures were shown below. 3.1. Model tunnel system and parameters of the experiments The 1/9 reduced-scale model tunnel used in this paper is arched, 8 m long, 0.6 m wide and 0.8 m high, as shown in Fig. 1. The side walls with the height of 0.5 m and floor are made of brick and concrete. The height of tunnel vault is 0.3 m, and the main materials are steel structure and fire asbestos. Moreover, the inner and outer sides of vault are covered by a layer of asbestos to ensure the heat insulation and sturdiness. Figs. 1 and 2 present the stereogram and sectional view of the tunnel, respectively. There are several reserve holes distributed at the tunnel floor, and the electronic balances with an error tolerance of 0.1 g used to measure the mass loss rate are placed in these holes and protected by the asbestos simultaneously. Also, several holes are reserved for igniting. And once fuel was ignited, the reserve holes were filled up with bricks and sealed by fire-proof plates immediately. Methanol, a typical fuel, is used as fire source with the purity of 99.9% in this paper (Fan et al., 2013; Kurioka et al., 2003) and loaded into the identical rectangular steel pans (0.6 m × 0.3 m × 0.1 m) to simulate carriages filled with liquid fuels. The fuel pans are located in the middle of tunnel and along the longitudinal centerline with a 0.1 m horizontal spacing, and the fuel pan number is marked No. 1 to No. 3 in the direction from portal A to B, as shown in Fig. 1. And each fuel pan is filled with 4 kg methanol before each test. In addition, experimental heat release rate was obtained from Eq. (17):

(15)

= f (Q )

The critical sealing ratio c is determined by the experimental and numerical simulation data. And considering the above analysis results into Eq. (14), this study on the maximum gas temperature beneath ceiling in a sealing tunnel fire can be divided into four regions briefly. The following equation can be obtained:

K ss 17.5 Tmax,s =

Q2/3 5/3 Hef

K sg1 17.5 K sg2 17.5

,

Q2/3 5/3 Hef

relatively small fire , general size fire ,

Q2/3

, general size fire , 5/3

>

Hef

K sl C0,

N

c

Q= ·

mi · H

c

where N is the fuel pan quantity of 1, 2, 3; mi is average mass lost rate of corresponding fuel pan in relatively steady stage of combustion (g/s),

(16)

relatively large fire

Centerline 0.1 0.3 Portal A Fuel pan 0.15

0.3

0.15

0.15 0.6 0.15

8.0 Portal B 0.2

Ignition hole

0.5

(17)

i=1

0.1

No.1

0.15

0.2 Fuel pans

Balance holes

0.6

Fig. 1. Sectional layout of the model tunnel (Unit: m).

Symmetricall seal

Portal A

Balance hole

Thermocouple tree

Tunnel portal is sealed with fireproof plates at a certain value

Ignition hole

Fuel pans

Portal B

Electronic balance

Fig. 2. Three-dimensional layout and photos of the model tunnel (Unit: m). 4

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appeared. Therefore, combined with the overall layout of points, the thermocouples for measuring maximum ceiling smoke temperature were finally determined to be installed 5 cm below the ceiling surface under the current experimental conditions. In the formal experiments, there are 13 thermocouple trees were fixed from 0.2 to 0.75 m above the floor to measure the vertical temperature. And 19 thermocouples were located 50 mm beneath the ceiling to measure the ceiling temperature. All temperature date was recorded by a dynamic data acquisition system, which was connected to a host computer through a date cable so that the acquired data could be uploaded to the PC for display and storage. The detailed layout of thermocouples is shown in Fig. 3.

Table 1 Average mass loss rate of single/multiple fuel pan fire. Fuel pan quantity

1 2 3

Fuel area (m2)

0.18 0.36 0.54

Fuel pan location

Total HRR (kW)

No.1

No.2

No.3

3.9 5.8 6.6

/ 5.7 7.3

/ / 6.5

78 228.5 400

and the average mass loss rates of each pan measured in single/multiple fuel pan fire is shown in Table 1; is the combustion efficiency, for clean liquid fuel such as ethanol, = 1.0 is acceptable value (Karlsson and Quintiere, 2000; Zhou et al., 2019; Ji et al., 2012); H is the heat of combustion (kJ/kg). The temperature distribution inside tunnel in experiments was tested with a series of 0.3 mm diameter K-type stainless steel sheathed thermocouples, which were mounted along the tunnel longitudinal centerline. Due to the heat transfer from fire smoke to cold ceiling, the location of maximum ceiling temperature was not tightly close to tunnel ceiling surface, but at a certain distance. Usually, in many previous studies, this distance was 1 cm, 1.5 cm, 2 cm, 3 cm, 5 cm, etc. Actually, this distance is related to specific experimental conditions, especially the thermal characteristics of ceiling materials. In current model tunnel, the ceiling consists of the steel frame and multiple layers fire asbestos, which thermal performance is similar to the concrete ceiling of actual tunnel. In order to determine the location of maximum ceiling temperature under current experimental condition, a set of preliminary tests were conducted before the formal experiments. In preliminary tests, the thermocouple tree composed of 7 temperature measuring points was positioned below tunnel ceiling and the distance between measuring points and ceiling surface was 1 cm, 2 cm, 3 cm, 4 cm, 5 cm and 6 cm, respectively. The distance between the thermocouple tree and fire source was change to 0.35 m, 0.5 m, 0.7 m, 1.0 m, 1.5 m, 2.0 m and 2.5 m, respectively, which the practice is mentioned in ji's research (Fan et al., 2013; Ji et al., 2012). It was found that when the distance between the fire source and measuring point was less than 1.0 m, the location of maximum ceiling temperature was about 4–6 cm below the ceiling. When the distance was greater than or equal to 1.0 m, maximum ceiling temperature firstly increased, then stabilized and slightly decreased at last. When the measuring point was about 3–5 cm below the ceiling, the maximum ceiling gas temperature

3.2. Experimental conditions Tunnel portals are sealed with asbestos and fire-proof plates symmetrically, and five types of sealing ratio used in experiments are illustrated in Fig. 4. Actually, due to the geographical characteristics of tunnel and the complex fire environment, it is difficult for the firefighters to arrive on the fire spot and complete the sealing immediately. Considering this, the initial sealing time was set to 300 s after ignition, representing the response time before sealing in the actual tunnel fire. The specific conditions of tests are summarized in Table 2. In this work, 3 groups of tests with different heat release rates were carried out under the natural ventilation of 0–0.2 m/s and each group has 5 cases according to different sealing ratios. The ambient temperature is about 20 °C and the fuel depth of each fire pan is approximate to 3 cm. Moreover, to ensure the reliability and repeatability of the data, each test is repeated two times. 3.3. Scaling law For turbulent buoyancy-driven flow generated by a fire, general characteristic of flow does not depend on the scale (McCaffrey et al., 1977). Hence, experimental investigations can be performed with reduced-scale model on smoke movement in fire situation based on Froude modeling (Yi et al., 2014). The Froude number, which means the ratio of inertia force to gravitational force (Quintiere, 1989); could be preserved in this paper:

Fr =

2 VM V2 = F gLM gLF

(18)

Centerline

0.5

0.5

0.5

0.5

0.5

8.0 0.5 0.3 0.350.35 0.35 0.35 0.3 0.5

0.5

0.5

Fuel pans

Electronic balance Unit: m

0.5

0.5

0.5

0.05 0.05 0.1 0.1 0.1 0.8 0.1 0.1 0.2

Thermocouple (Error: ±0.3%* T; Range: -50~1200 oC) Fig. 3. The thermocouples arrangement under tunnel ceiling. Fig. 4. Layout of different sealing ratios.

5

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Table 2 Experimental conditions set. Test No.

Number of fuel pan

Fuel depth

Fuel area 2

HRR

Sealing ratio

Ambient temperature

Ventilation condition

78 kW

0% 25% 50% 75% 100%

293 K

Natural ventilation

1 2 3 4 5

1

3 cm

0.18 m

6 7 8 9 10

2

3 cm

0.36 m2

228.5 kW

0% 25% 50% 75% 100%

293 K

Natural ventilation

11 12 13 14 15

3

3 cm

0.54 m2

400 kW

0% 25% 50% 75% 100%

293 K

Natural ventilation

*The HRR is average value at stable combustion stage acquired by mass loss rate measured in cases of no sealing.

where g is the gravitational acceleration, V is the characteristic velocity, L is the characteristic length. The subscript ‘F’ and ‘M’ represent the full and model scale parameters, respectively. The scaling relationships for heat release rate (Q) and temperature (T) are:

QM L = M QF LF

kLES =

5/2

(19)

µLES cp Pr

, ( D)LES =

1/2

(21)

µLES Sc

4.2. Fire scenarios

(20)

TM = TF

2 ( ·u¯)2 3

µLES = (Cs )2 2S¯ij: S¯ij

Based on the Froude scaling law, a full-scale simulation tunnel model is established correspondingly to the experimental model and the similarity ratio is 1/9. The tunnel ceiling, sidewalls and floor of simulation model set as 1.0 m thickness concrete structure, whose main physical properties, such as the conductivity, density and specific heat are respective 1.2 W/(m·K), 2200 kg/m3 and 0.88 kJ/(kg·K) (Ji et al., 2019). Moreover, the 3 m extended computational region was added at every tunnel portal with 4 m long in the longitudinal direction of tunnel, which is usually believed to bring better results (Huang et al., 2018). The design of fire source is a key factor affecting the accuracy of fire simulation. In current simulation works, the design of fire source is determined by setting physical parameters of fuel (density, heat of combustion, specify heat, heat of vaporization, etc.) into FDS, to allow the fire burn freely to the greatest extent, which this design method is closer to the real fire than adopting the designed fire with the constant heat release rate. The fuel area of fire source and the arrangement of temperature measuring points is consistent with the experimental configuration. The both tunnel portals are opened with no initial air velocity, which is natural ventilation condition. When fire source burning 300 s, the two tunnel entrances were sealed symmetrical with different sealing ratios. The ambient temperature and ambient pressure is respective 293 K and 101.32 kPa. 21 sealing ratios and 10 heat release rates were considered. And total 210 tests were conducted, as shown in Table 3.

where Q is the heat release rate (HRR), and LM/LF is the similarity ratio. 4. Numerical simulations for fire sealing Compared with experiments, the numerical simulation was also carried out more tests due to its low cost, and it is a valuable supplement and verification to the investigation of tunnel fire sealing in this paper. The detailed numerical simulation settings were shown below. 4.1. Brief introduction to FDS FDS, which is developed by NIST (National Institute of Standards and Technology), is regarded as a classic tool for simulating fire-induced environment by solving numerically a set of the Navier-Stokes equations for thermally-driven (Ji et al., 2015; Ji et al., 2013). In this paper, FDS is used to simulate fire scenarios in tunnel with different sealing ratios. Large eddy simulation model is applied due to the fact that it disposes turbulence and buoyancy well (Huang et al., 2018). And the Smagorinsky model was adopted to deal with the turbulence (Zhang et al., 2002). The turbulence viscosity, thermal conductivity, material diffusivity in FDS is expressed as follows (McGrattan et al., 2010): Table 3 Numerical simulations set. Test no.

HRR (MW)

Sealing ratio (%)

1–21 22–42 43–63 64–84 85–105 106–126 127–147 148–168 169–189 190–210

3.65 7.3 12 19 29 38 48.6 57 73 97

0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

5, 5, 5, 5, 5, 5, 5, 5, 5, 5,

10, 10, 10, 10, 10, 10, 10, 10, 10, 10,

15, 15, 15, 15, 15, 15, 15, 15, 15, 15,

20, 20, 20, 20, 20, 20, 20, 20, 20, 20,

25, 25, 25, 25, 25, 25, 25, 25, 25, 25,

30, 30, 30, 30, 30, 30, 30, 30, 30, 30,

35, 35, 35, 35, 35, 35, 35, 35, 35, 35,

40, 40, 40, 40, 40, 40, 40, 40, 40, 40,

45, 45, 45, 45, 45, 45, 45, 45, 45, 45,

50, 50, 50, 50, 50, 50, 50, 50, 50, 50,

55, 55, 55, 55, 55, 55, 55, 55, 55, 55,

60, 60, 60, 60, 60, 60, 60, 60, 60, 60,

*The HRR is average value at stable combustion stage acquired by the simulation results in cases of no sealing. 6

65, 65, 65, 65, 65, 65, 65, 65, 65, 65,

70, 70, 70, 70, 70, 70, 70, 70, 70, 70,

75, 75, 75, 75, 75, 75, 75, 75, 75, 75,

80, 80, 80, 80, 80, 80, 80, 80, 80, 80,

85, 85, 85, 85, 85, 85, 85, 85, 85, 85,

90, 90, 90, 90, 90, 90, 90, 90, 90, 90,

95, 95, 95, 95, 95, 95, 95, 95, 95, 95,

100 100 100 100 100 100 100 100 100 100

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4.3. Grid system sensitive test

rate (78 kW and 400 kW) have been compared with the model-scale experimental results based on Froude scaling law, as shown in Fig. 6. The comparisons indicated that the gas temperatures simulated by FDS were in good agreement with experimental data. Therefore, the current numerical simulation tests could be regard as a good supplement and extension to the experimental conditions in this paper.

The grid size is a key factor to determine the accuracy of result and computation time (Huang et al., 2018); and the optimal grid size should not only guarantee the accuracy of simulation results, but also save the computational cost as much as possible. For a specific fire scenario, the optimal grid size can usually be derived by the fire source characteristic diameter D∗, and the D∗ can be expressed as:

D =

Q cp T

5. Results and discussion

2/5

g

The maximum gas temperature beneath the ceiling for a typical case is shown in Fig. 7, and it can be seen that the temperature curve reaches a steady state from about 370 s to 630 s. After then, the curve drop rapidly due to the fuel is nearly exhausted. Therefore, in the further analysis, the averaged value between 370 s and 630 s is taken as the average maximum gas temperature beneath the ceiling. In other cases, the time intervals may be different, but the principle is also applied (Zhao et al., 2019; Ji et al., 2011).

(22)

When the ratio of fire characteristic diameter to grid size ( D ) range x from 4 to 16, the deviation between simulation and experimental results is within the acceptable range, and when the ratio is 10, the relatively reliable results can be obtained, which has been verified by many studies. In addition, the Eq. (22) implies that the optimal grid size is related to the heat release rate of specific fire scenario, and the smaller the heat release rate is, the smaller the optimal grid size is. The heat release rate in current study range from 3.65 to 73 MW, so the case with minimum heat release rate of 3.65 MW was chosen for grid sensitive tests before starting the formal simulation work. Six grid sizes from 0.10 to 0.40 m were selected to conduct simulation cases for comparison. The comparison results of the vertical temperature distribution and longitudinal ceiling temperature distribution in tunnel downstream were shown in Fig. 5. It can be seen from Fig. 5 that when grid size is less than or equal to 0.15 m, the vertical temperature distribution curves right above fire source and longitudinal ceiling temperature distribution in tunnel downstream is basically coincident. To further refine mesh does not bring higher accuracy, but increases the computational cost. Hence, under such a fire scenario with 3.65 MW heat release rate, the optimal grid size is determined to be 0.15 m, which the D is close to 10. After x checking, the commended grid size of 0.15 m could also ensure the accuracy of simulation results in other cases with large heat release rate. Finally, a grid size of 0.15 m was chosen to apply to all simulation conditions in the current study.

5.1. Critical sealing ratio in tunnel fire The maximum ceiling gas temperature under different sealing ratios is shown in Fig. 8, and it can be seen, except for the conditions that heat release rate is relatively large or small, the maximum gas temperature beneath ceiling increases first and then decreases with the increase of sealing ratio. As analyzed in Section 2, there is a critical value for the sealing effect on the fire temperature field beneath ceiling inside the tunnel indeed. And when the sealing ratio at tunnel portal reached the critical value, the gas temperature peaked the maximum correspondingly. Especially, similar as the analysis in Section 2, the critical sealing ratio is closely related to heat release rate of fire source and shows a decreasing tendency with the increase of heat release rate. Additionally, when the heat release rate is relatively large, maximum gas temperature decreases continuously with the increase of sealing ratio. The reason revealed is that when the heat release rate of the fire source is relatively large, the combustion is mainly controlled by the ventilation condition (Zhao et al., 2019). And sealing the tunnel portal would significantly restrict the air absorption, which made more difficult for fire source to maintain heat release rate at a high level. As a result, the maximum gas temperature inside tunnel decreases gradually. At this situation, the critical sealing ratio is considered as 0 ( c = 0 ). On the contrary, when the heat release rate is relatively small, the combustion is mainly controlled by the fuel inside tunnel, and sealing the tunnel portal mainly reduces the heat loss and the ventilation restriction is relatively little effect on combustion of fire source. Hence, the maximum gas temperature beneath ceiling always increases with the

4.4. Simulation results validation The feasibility of using FDS in numerical simulation for fire environment of tunnel has been extensively validated by experiments and theories (Huang et al., 2018; Ji et al., 2015, 2017). In current numerical work, FDS simulation results for the maximum gas temperature distribution along the longitudinal and vertical of tunnel under the typical cases with representative sealing ratio (0% and 100%) and heat release

Fig. 5. Temperature distribution at typical location in tunnel downstream with different grid sizes (HRR = 3.65 MW, 7

= 0 ).

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Fig. 6. Comparison of FDS simulation results with experimental data based on the Froude scaling law.

critical sealing ratio can be expressed as:

1, c

2.13Q + 1.07

= 0,

Q 0.06, 0.06 < Q Q >0.48,

0.48, (23)

Moreover, the above analysis also indicates that the larger fires are more suitable for use of sealing strategy, while smaller fires are more suitable for taking extinguishing actions on fire source directly due to the smaller heat release rate and thermal radiation threat. 5.2. Maximum excess gas temperature beneath the ceiling The maximum excess gas temperatures beneath ceiling obtained experimentally and numerically are compared with Li's model as shown in Fig. 10. It can be seen that when the heat release rate is more than 57 MW, the maximum ceiling gas temperature almost no longer increases and is close to constant. According to the Li and Ingason’s report (Li and Ingason, 2012), the constant value is associated with tunnel scale, which 950–1150 °C for model scale tunnel tests and 1150–1350 °C for large scale tunnel tests. In this paper, model scale test and large scale numerical simulation are involved, and combined the results shown in Fig. 10, the constant value is taken as C0 = 1150 °C. It should be noted that effect of sealing on tunnel fire was not taken into

Fig. 7. Times averaged section for maximum gas temperature beneath ceiling.

sealing ratio increase. In this case, critical sealing ratio is considered as 1 ( c = 1). Fig. 9 shows the correlation of the critical sealing ratio with the dimensionless heat release rate and it can be seen that two parameters have a good linear relationship. The fitting formula for calculating the 8

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Fig. 8. Maximum gas temperature under different sealing ratios.

temperature in tunnel fire extinguishing. The f ( ) representing the sealing factor in Eq. (14), which is deduced from the measured date in this paper and previous theoretical analysis, can be calculated as follows:

Tmax,s Tmax,s = Q 2/3 Tmax 17.5 5/3

f( )=

(24)

Hef

where Tmax, s is the maximum excess gas temperature beneath ceiling obtained in experiments and simulations;

Tmax = 17.5

Q2/3

5/3 Hef

is the pre-

diction by Li's model. According to the analysis in Section 2, the dimensionless coefficient Kss, Ksg1, Ksg2, Ksl are related to the sealing ratio. And firstly, the sealing coefficients for relatively small fire (Kss) and large fire (Ksl) can be fitted as the function of sealing ratio, as shown in Fig. 11. From the above fitting results, the relation equations of sealing 0.06) and large fire coefficients Kss and Ksl for relatively small fire (Q (Q > 0.48) could be obtained as:

Fig. 9. Fitting relationship of critical sealing ratio.

Kss = 0.11e

Ksl =

/0.61

(25)

+ 0.66

0.096 + 1.0 14.9e

/0.13

0.55

+ 0.7,

> 0.55

(26)

Especially, for the general size fire, there exists similar trend to some extent in the variation of maximum gas temperature with sealing ratio except for specific values, as shown in Fig. 8(b). The gas temperature below ceiling obviously increase with the increase of heat release rate and sealing ratio when c , and obviously decrease with the increase of sealing ratio and decrease of heat release rate at > c . Hence, it can be concluded that the sealing coefficient for general size fire, Ksg, is a function of both sealing ratio and dimensionless heat release rate, which could be extended to the following equation for the general size fire: Fig. 10. Maximum gas temperature beneath tunnel ceiling.

(27)

Ksg = f ( , Q )

The fitting of Ksg with dimensionless heat release rate Q is shown in Fig. 12. It is found from Fig. 12 that the index b in fitting with a power function for different cases are very close and the fitted value of b is summarized in Table 4. R is the Pearson correlation coefficient (Ji et al., 2015) between the fitted curves and the simulated results, whose square value exceeding 0.9661 supports the accuracy of fitting curves. It can be seen clearly that the difference of two fitting coefficient b values is very small, so using the average value of b, in following Eq. (28) gives:

account in Li's model. It can be observed that the experimental and numerical data for relatively small sealing ratio or heat release rate in this work agree well with the predictions by Li's model, and the maximum gas temperature beneath ceiling increases with the increases of heat release rate. The maximum gas temperature beneath ceiling does not vary monotonously with the sealing ratio, except when the heat release rate of fire source is relatively large ( c = 0 ) or small ( c = 1) as analyzed previously. Obviously, the sealing ratio of tunnel portal has great influence on the maximum gas temperature inside tunnel, and the current models cannot effectively predict the fire temperature field inside tunnel after sealing. Therefore, it is necessary to propose the model (e.g. Eq. (14)) taking the sealing factor into account to predict the maximum gas

Ks g1

Q

0.171

and Ks g2

Q

( 0.271)

(28)

Combining with the above analysis and Eq. (27), the following relationships can be obtained: 9

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Fig. 11. Correlation of sealing coefficient in small and large fire.

Ks g1· Q

( 0.171)

0.271

= f1 ( ) and Ksg2·Q

(29)

= f2 ( )

Table 4 The fitted value of b.

Using Eq. (29), the values of Ksg1 and Ksg2 can be incorporated in one equation to some extent, respectively, as shown in Fig. 13. The formula of sealing coefficient Ksg1 and Ksg2 for general size fire 0.48 ) can be expressed as: (0.06 < Q

Ksg1 = Q Ksg 2 =

0.171 (0.086e /0.34

Q *( Q*

0.271) (

+ 1.082),

256e

/0.433

(30)

c

0. 083 + 0. 876),

( 0.271) (1.

0. 55

+ 0. 482),

Ksg1 fitting curve

> 0. 55

>

c

(31)

Summing up the above, by substituting Eqs. (25), (26), (30) and (31) into Eq. (16), the modified model considering sealing factor can be obtained, which is applied to predict the maximum excess gas temperature beneath ceiling in tunnel fire, and expressed as follows in this paper. 0.06): For the relatively small fire (Q

Tmax,s = (0.11e

/0.61

+ 0.66)·17.5

Q2/3 ,V Hef5/3

For the general size fire (0.06 < Q When the sealing ratio c:

Tmax,s = Q

0.171 (0.086e /0.34

0.19

β

b

β

0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65%

0.17624 0.18107 0.18118 0.1873 0.20105 0.17414 0.17526 0.15368 0.15258 0.16296 0.1592 0.15536 0.17664 0.162

45% 0.34383 50% 0.27374 55% 0.30566 60% 0.32237 65% 0.23203 70% 0.27539 75% 0.24225 80% 0.24806 85% 0.24952 90% 0.2516 95% 0.26633 100% 0.24432 b average for Ksg1: 0.1713 b average for Ksg2: 0.2713

When the sealing ratio

(32)

0.48 ):

Q Tmax,s =

+ 1.082)·17.5

Q 2/3 ,V Hef5/3

Q

0.19

Ksg2 fitting curve

(33)

( 0.271) (

>

c:

0.083 + 0.876)·17.5

( 0.271) (1.256e

/0.433

b

Q2/3 , H 5/3 ef

+ 0.482)·17.5

Q 2/3 H 5/3 ef

For the relatively large fire (Q > 0.48):

Fig. 12. Correlation of sealing coefficient with dimensionless heat release rate. 10

0.55, V

0.19

> 0.55, V

0.19

(34)

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Fig. 13. Correlation of sealing coefficient with sealing ratio.

Tmax,s =

( 0.096 + 1.0)·1150, (14.9e

/0.13

+ 0.7)·1150,

0.55 V > 0.55, V

of fire source. The modified model considering sealing ratio of tunnel portal is proposed, which could be used to predict the maximum ceiling gas temperature inside tunnel. The major conclusions are as follows: For tunnel pool fire, the sealing will have a totally different effect depending on the heat release rate of fire source. When the fire is relatively small, maximum ceiling gas temperature inside tunnel will continuously increase with the increase of tunnel portal sealing. For the large fires, the sealing strategy can well limit the development of fire. Compared to the small fire, large fire is more suitable for use of sealing strategy, while taking extinguishing actions on fire source directly is a better choice for the small fire. For the general size fire, there exists a critical sealing ratio closely related to the heat release rate of fire source, at which the ceiling gas temperature inside tunnel would peak the maximum. An empirical formula for calculating the critical sealing ratio at different heat release rates is presented in this paper, which correlation analysis suggests that the effect of heat release rate on critical sealing ratio is approximately linear. And, the larger the heat release rate is, the lower the critical sealing ratio would be. The sealing ratio of tunnel portal has a great influence on the characteristics of fire temperature filed inside tunnel, which lies on the relative prevailingness of restricting fresh air supply and reducing heat loss. And a modified model taking the sealing factor into account is proposed to predict the maximum gas temperature beneath tunnel ceiling. And the predictions by the modified model are in good

0.19 0.19

(35)

It could be clearly found that the results of fitting correlation are consistent with the theoretical analysis results in essence. There does exist a critical sealing ratio in the sealing process of tunnel fire, at which the maximum ceiling gas temperature is obtained, and the study of effect of sealing ratio on the maximum gas temperature in a sealing tunnel fire could be divided into two regions accordingly: increase region and decrease region. The rate of increase or decrease in different regions shows different trends, mainly due to the influence of heat release rate of fire source. When the fire is relatively small, the sealing coefficient is mainly related to the sealing ratio. And when the fire is relatively large, the combustion inside tunnel is mainly control by ventilation opening, and the effect of sealing ratio on restricting fresh air supplement is far greater than the heat release rate of fire source, which leads to the sealing coefficient still mainly related to the sealing ratio. When the fire is general size, both heat release rate and sealing ratio have significant influences on the sealing coefficient. Specifically, sealing ratio 0.55 is a special point for the decrease region in the larger tunnel fire, at which the rate of decrease varies greatly. This special point may be related to the structure characteristics of tunnel cross section used in this paper. Usually, the sealing ratio is defined by the sealing height rather than the sealing area, allowing for the more convenient applications in practical tunnel sealing projects. And when the sealing ratio exceeds 0.55, sealing area is nearly from the rectangular part to arc part of tunnel cross section. Then, if the sealing continues, the available ventilation area supporting the internal combustion of tunnel will be reduced faster than the rectangular part, so that the tunnel fire with larger heat released rate mainly controlled by ventilation conditions will be more restrained, and the maximum ceiling gas temperature inside tunnel will drop rapidly. At last, the comparison of experimental and numerical simulation results of maximum excess gas temperature beneath ceiling with the model prediction is shown in Fig. 14. It can be easily found that the model prediction by modified model agree well with the experimental and numerical date. Therefore, the modified model proposed in this paper can be successfully applied to predict the maximum gas temperature beneath tunnel ceiling after sealing tunnel portal. 6. Conclusions A series of experiments and numerical simulations were carried out in this work to investigate the influence of sealing ratio on the maximum gas temperature beneath ceiling under different heat release rate

Fig. 14. Comparison of measured results in experiments and simulations with predictions by modified model. 11

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agreement with experimental and numerical results. Finally, the modified model based on a series of experimental and numerical tests proposed in this paper mainly focused on the feature of maximum gas temperature beneath ceiling in tunnel fire under sealing symmetrically, and it is expected to be a complement including the sealing factor to the existing prediction models. However, the sealing of tunnel fire is a complex process involving many factors actually and only sealing ratio is considered in this work by scale model experiments and numerical simulations. In the future, more factors related to sealing and the full or large-scaled tests should be considered.

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CRediT authorship contribution statement Changkun Chen: Funding acquisition, Methodology, Investigation. Yulun Zhang: Conceptualization, Methodology, Investigation, Data curation, Writing - original draft. Peng Lei: Software, Methodology. Weibing Jiao: Software, Methodology. Declaration of Competing Interest The authors declared no potential conflicts of interest with respect to the research, authorship, and publication of this article. Acknowledgements This work was supported by the National Natural Science Foundation of China (Nos. 51576212 and 71790613). The authors appreciate the supports deeply. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.tust.2019.103275. References Chen, C.K., Zhu, C.X., Liu, X.Y., Yu, N.H., 2016. Experimental investigation on the effect of asymmetrical sealing on tunnel fire behavior. Int. J. Heat Mass Transf. 92, 55–65. Chen, C.K., Xiao, H., Wang, N.N., Shi, C.L., Zhu, C.X., Liu, X.Y., 2017. Experimental investigation of pool fire behavior to different tunnel-end ventilation opening areas by sealing. Tunn. Undergr. Space Technol. 63, 106–117. Fan, C.G., Ji, J., Gao, Z.H., Sun, J.H., 2013. Experimental study on transverse smoke temperature distribution in road tunnel fires. Tunn. Undergr. Space Technol. 37 (6), 89–95. Gannouni, S., Ben Maad, R., 2016. Numerical analysis of smoke dispersion against the wind in a tunnel fire. J. Wind Eng. Ind. Aerodyn. 158, 61–68. Gao, Z.H., Ji, J., Wan, H.X., Li, K.Y., Sun, J.H., 2015. An investigation of the detailed flame shape and flame length under the ceiling of a channel. Proc. Combust. Inst. 35 (3), 2657–2664. Grant, G.B., Drysdale, D.D., 1995. Estimating heat release rates from large-scale tunnel fires. Fire Saf. J. 5, 1213–1224. Haack, A., Casale, E., Ingason, H., 1995. EUREKA-Project EU 499: FIRETUN-Fires in Transport Tunnels, Report on Full Scale Tests. Studiengesellschaft Stahlanwendung e. V., D-40213 Dusseldorf, Germany. Huang, Y., Li, Y., Dong, B., Li, J., Liang, Q., 2018. Numerical investigation on the maximum ceiling temperature and longitudinal decay in a sealing tunnel fire. Tunn. Undergr. Space Technol. 72, 120–130. Ingason, H., 2008. Model scale tunnel tests with water spray. Fire Saf. J. 43 (7), 512–528. Ingason, H., Li, Y.Z., Lönnermark, A., 2014. Tunnel Fire Dynamics. Springer. Ingason, H., Li, Y.Z., Lönnermark, Anders, 2015. Runehamar tunnel fire tests. Fire Saf. J. 71, 134–149. Ji, J., Zhong, W., Li, K.Y., Shen, X.B., Zhang, Y., Huo, R., 2011. A simplified calculation method on maximum smoke temperature under the ceiling in subway station fires. Tunn. Undergr. Space Technol. 26 (3), 490–496. Ji, J., Fan, C.G., Zhong, W., Shen, X.B., Sun, J.H., 2012. Experimental investigation on influence of different transverse fire locations on maximum smoke temperature under

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