Smoke back-layering flow length in longitudinal ventilated tunnel fires with vertical shaft in the upstream

Accepted Manuscript Smoke back-layering flow length in longitudinal ventilated tunnel fires with vertical shaft in the upstream Yongzheng Yao, Xudong Cheng, Shaogang Zhang, Kai Zhu, Long Shi, Heping Zhang PII: DOI: Reference:

S1359-4311(16)31156-5 http://dx.doi.org/10.1016/j.applthermaleng.2016.07.027 ATE 8625

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

27 May 2016 1 July 2016 4 July 2016

Please cite this article as: Y. Yao, X. Cheng, S. Zhang, K. Zhu, L. Shi, H. Zhang, Smoke back-layering flow length in longitudinal ventilated tunnel fires with vertical shaft in the upstream, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.07.027

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Smoke back-layering flow length in longitudinal ventilated tunnel fires with vertical shaft in the upstream Yongzheng Yao1, Xudong Cheng1, Shaogang Zhang1, Kai Zhu1, Long Shi2, Heping Zhang1 1. State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, China 2. Centre for Environmental Safety and Risk Engineering, Victoria University, Melbourne, VIC 8001, Australia

ABSTRACT： Smoke back-layering flow length is the length of the reversed smoke flow upstream of the fire when the longitudinal ventilation velocity is lower than the critical velocity. This paper experimentally investigates the smoke back-layering flow length of longitudinal ventilated tunnel fires with a vertical shaft in the upstream (0.5-4.0 m from the fire source) using a 1/10 reduced-scale subway tunnel model. Experimental results show that the vertical shaft in the upstream can control the smoke back-layering flow length within a relatively limited range, compared to the tunnel without vertical shaft. Moreover, for the cases that the fire source is not located exactly below the vertical shaft, the most appropriate dimensionless distance between the vertical shaft and fire source is 3, resulting in the shortest smoke back-layering flow length. By introducing a concept of virtual fire source below vertical shaft, a new empirical model was further deduced to predict the smoke back-layering flow length. Its predictions fit reasonably well when the dimensionless longitudinal flow velocity is less than 0.19. Beyond that, the predictions are little higher than the experiments, which is because some of the assumptions in this model are invalid under higher longitudinal ventilation velocity.

Keywords:

Tunnel fire;

Longitudinal ventilation;

Vertical shaft;

Virtual fire source;

Smoke back-layering flow length

1. Introduction As an effective way to relieve the traffic pressure, tunnels have got fast development worldwide. However, due to its special long-narrow building structure, in the event of a fire, the hot and toxic smoke gas spreads fast and widely, which prohibits the safe evacuation of occupants and the firefighters from extinguishing the fire [1]. The tunnel fires could result in a large number of casualties, especially in the subway tunnel fire due to the high density of people. For example, the Baku subway tunnel fire in Azerbaijan happened in 1995 with 289 people killed [2], that in Kaprun Austria in 2001 and Dague Korea in 2003 killed 155 and 198 people, respectively [3,4]. A statistics show that smoke is the most fatal factor in fires, and about 75-85% of victims result from the hot and toxic smoke [5]. Hence, mastering effective smoke control methods is of great

significance to reduce casualties in tunnel fires. Longitudinal ventilation and transverse exhausting are the most common method of smoke control in tunnel fires [6]. In the past several years, a large number of studies on smoke flow characteristics in the tunnel fires with longitudinal ventilation have been reported [7-17], mainly involving the parameters of smoke back-layering flow length. By analyzing the Froude number, Thomas [7] firstly suggested that the buoyancy and inertial force should be equal at the critical condition. He also has firstly proposed an equation to predict the smoke back-layering flow length as following:

l 

L gHQ  H 0c pT f V 3 A

(1)

Hu et al. [8] thought the static pressure difference between the smoke front and the ambient should be equal to the hydraulic pressure of incoming air at the position where the upstream back-layering front stops propagating. Based on this, an equation to predict the smoke back-layering flow length was given as follows:    Q 2 3  C K H  L  ln  g    1 3   2  0.019   Fr  V 

(2)

Li et al. [9] correlated the smoke back-layering flow length with other parameters such as heat release rate and longitudinal ventilation velocity based on a dimensional analysis and reduced-scale tunnel experiments:





18.5ln 0.81Q1 3 V  , Q  0.15  L   Q  0.15 18.5ln  0.43 V  , 

(3)

with

Q 

Q a C pTa g 1 2 H 5 2

V V

gH

(4)

(5)

Zhang et al. [10] investigated the influence of metro train on the smoke back-layering in the subway tunnel fires. A new physical model including the factor of metro train length was developed to predict the length of smoke back-layering flow in the tunnel based on the smoke gas temperature distribution and fire dynamics theory: 

Corresponding author. Tel.: +86 551 63606957. E-mail address: [email protected]; [email protected]

L  1.712Q1 3  1 3 1 3   6.956 ln    , Q  QL  LT H V 1       L    0.935Qb1T3  1 3  LT  LU LT 1 3   19.432 ln   , Q  QL  LT   H H V   

(6)

with

QL1 3LT  0.584 

V  LT   exp   1  6.956 H 

Where H is hydraulic diameter of tunnel, m;

(7)

 is the blockage ratio; LU is the smoke

back-layering flow length in the upstream region of tunnel without blockage, m; LT is the metro 1 3

train length, m; QL  LT is the dimensionless number when the smoke back-layering flow length is equal to the metro train length. However, strong longitudinal ventilation will destroy the smoke stratification structure in tunnel fires, then make great threat to human evacuation and rescue works in the tunnel [18]. Currently, transverse exhausting in tunnel fires has attracted much attention from engineers and researchers [6, 19-25]. Ji et al. [19] studied the effects of shaft height on natural ventilation performance in tunnel fires. They found that when shaft height is relatively small, the boundary layer separation is significant, preventing the throughflow of the smoke. With the increasing of shaft height, the boundary layer separation becomes inconspicuous but showing plug-holing, which can strongly decrease the smoke exhaust efficiency. Ji et al. [20] investigated the effects of vertical shaft geometry on natural ventilation performance during tunnel fires. They replaced the right-angle connection between vertical shaft and ceiling with the bevel-angle connection to split one separation point into two separation points, which attenuates the negative effect of boundary layer separation and improves smoke exhaustion capacity. Du et al. [6] evaluated the performance of longitudinal and transverse ventilation for smoke control in a looped urban traffic link tunnel, respectively. They found that for longitudinal ventilation, the critical velocities, as the minimal air velocities for preventing smoke infiltrating into the regions upstream of the fire and entering the downstream tunnel branches that are adjacent to the smoke discharge route, should be guaranteed. For transverse ventilation, an effective exhaust flow rate could be twice the smoke production rate to confine the smoke in the tunnel branch where fire occurs. Vauquelin et al. [21-22] addressed the control effect of smoke when a fire source is confined and extracted between two exhaust vents located on both sides of the fire source. The smoke layer propagation downstream the vent can been prevented by increasing vent extraction flow rate.

Through the above studies, we can find the longitudinal ventilation and transverse exhausting with vertical shaft or extraction fan were always investigated separately. There are a few attentions on smoke control of tunnel fires by combining longitudinal ventilation and transverse exhausting, especially involving the issues of smoke back-layering flow length. In fact, this mode may be very meaningful and practical to guide smoke control and protect smoke stratification structure in tunnel fires. Ingason et al. [26] proposed the concept of single-point extraction system and two-point extraction system combining with longitudinal ventilation from both sides of tunnel to constrain the smoke within limits. Wang et al. [27] studied how the shaft dimension and the distance between shafts influence smoke back-layering flow length in longitudinal ventilated tunnel when fire source is under a group of vertical shafts. A prediction formula for calculating back-layering length is deduced based on dimensional analysis as follows:

L  1.9388 108  EQ  where EQ and

0.0623

 FT 

2.213

a

0.94

b 

0.4475

 d1

0.302

 d 2

0.021

 h

0.3328

 D

1.3763

(8)

FT are the dimensionless number; a is the length of shaft, m; b is the width of

shaft, m; d1 is the distance between two shafts, m; d2 is the distance between two groups of shaft, m; h is the height of shaft, m; and D is the equivalent diameter, m. However, the fire scenarios and prediction formula is too complex, which may not be convenient to guide the smoke control in the practical engineering applications. Chen et al. [28] carried out small-scale experiments in model tunnels to study the smoke back-layering flow length with the combination of longitudinal ventilation and extraction fan at difference distance from fire source in tunnel fires, as shown in Fig.1, where the extraction fan is in the downstream and the smoke back-layering flow length is obtained through the modified actual heat release rate, which is equal to the difference between the total heat release rate and exhausted heat from extraction fan. In addition, the longitudinal ventilation velocity is also modified by adding the induced velocity due to extraction fan. The following relationship is proposed [28]:





18.5ln 0.81Q1 3 v , Q  0.15  L   Q  0.15  18.5ln  0.43 v  , 



Q 

v 

Q  C p d Tm a ex  kd

a C pTa g1 2H v  d wS 2 Aa gH

5 2

    

(9)

(10)

(11)

where S is the cross-sectional area of vertical shaft, m2; and A is the cross-sectional area of tunnel,

m2. In Chen et al.’s work [28], they only considered the smoke back-layering flow length in tunnel fires with extraction fan in the downstream, but another case with extraction fan in the upstream was ignored. Moreover, the extraction fan is more expensive, and it is usually replaced by vertical shaft in the practical engineering applications. Therefore, the issue about the smoke back-layering flow length in longitudinal ventilated tunnel fires with vertical shaft in the upstream should also be worth considering and researching.

Fig.1. A schematic of smoke back-layering flow length under the combination of both longitudinal ventilation and downstream ceiling extraction.

2. Theoretical analysis A virtual fire source with the virtual heat release rate is assumed to predict the smoke back-layering flow length. As shown in Fig. 2, the virtual heat release rate is obtained based on the convection heat remained beyond vertical shaft, which is integrated into a total heat release rate of virtual fire source exactly below the vertical shaft. Therefore, the smoke back-layering flow length includes a part beyond vertical shaft and another part between fire source and vertical shaft. In addition, we considered the additional flow velocity induced by the vertical shaft, which was proposed in Chen et al.’s study [28].

Fig.2. A schematic of smoke back-layering flow length under the combination of both longitudinal ventilation and upstream vertical shaft

Shown in Fig. 2, when a fire occurs, the plume rises vertically from the fire source and spreads radially beneath ceiling until it reaches the sidewalls of the tunnel, then a transition from

radial to one-dimensional spreading toward both sides takes place [29]. When the hot smoke spreads to the area beneath the vertical shaft, part of the heat, Qexhaust , will be exhausted from vertical shaft under the effect of the vertical inertial force induced by stack effect. The remained smoke can spread sequentially toward the upstream with less heat, so a lower longitudinal ventilation velocity is needed to stop the incoming smoke, comparing with the situation without vertical shaft. In addition, the heat of path loss, Qloss , from fire source to the vertical shaft cannot be ignored. We assume that the heat of smoke spreading upstream and downstream is equal to the half of the convective heat release rate of the fire source under a lower longitudinal ventilation velocity:

Qup  Qdown 

1   r  Q 2

(12)

where  r is the proportion of the radiation heat loss; and Q is the total heat release rate, kW. The convective heat beyond vertical shaft can be expressed based on the conservation of energy:

Qremain  Qup  Qexhaust  Qloss

(13)

The virtual heat release rate of the virtual fire source below the vertical shaft can be integrated by combining the convective heat beyond vertical shaft with radiation heat loss:

Qvirtual  2 Qup  Qexhaust  Qloss  1  r 

(14)

The heat of smoke exhausted from the vertical shaft can be expressed as follows:

Qexhaust  C p mshaft Td

(15)

mshaft  Swd

(16)

with

where mshaft is the mass flux of smoke through the vertical shaft, kg/s. It should be noted that the heat of smoke exhausted from the vertical shaft and the heat of path loss are mainly related to the average temperature rise of smoke layer, not the maximum smoke temperature rise. And β is the conversion coefficient between average temperature rise and maximum temperature rise. The driving force of smoke through vertical shaft comes from the stack effect caused by temperature difference between the smoke below the vertical shaft and the ambient fresh air. The temperature difference means the density difference, which eventually leads to the smoke move upward under the effect of buoyancy [24]. According to Bernoulli’s principle, the buoyancy can be

expressed by:

Fv   ghS

(17)

  a  d

(18)

with

where h is the height of the vertical shaft, m. The buoyancy can be expressed in another way according to the Momentum Theorem:

Fv  mshaft w

(19)

Combining Eqs. (16)-(19), we can get the velocity of smoke through the vertical shaft.

w



d

gh

(20)

Assuming the smoke below the vertical shaft has a uniform temperature, we can obtain this relationship according to the ideal gas equation of state:

d a  Ta Td

(21)

So, Eq. (20) can have a further conversion:

w

Td Ta

gh

(22)

The maximum smoke temperature rise beneath the vertical shaft can be calculated by the model proposed by Hu et al. [30]:

Td  e kd Tm a x

(23)

where Tmax is the maximum smoke temperature rise near the fire, K; k is the attenuation coefficient of the smoke; and d is the horizontal distance from fire source to the vertical shaft, m. Li et al. [31] proposed an empirical model to predict the maximum temperature of smoke beneath the ceiling near the fire source under various longitudinal ventilation velocities in a reduced-scale tunnel model. The relationship is further modified by adding the induced velocity due to vertical shaft:

Tmax

with

 Q  13 53 ,  ub H ef  23 17.5 Q ,  H ef5 3 

u   0.19 u   0.19

(24)

13

u  V  d wS 2 Aa  

 gQc     b a CpTa 

(25)

where b is the radius of the fire source, m; and Qc is the convective heat release rate, kW. The smoke layer exchanges heat with tunnel surface and the environment. The heat loss has been described in Hu’s previous study about the longitudinal decay theory of tunnel fire smoke temperature [32]:

qloss   DTx

(26)

where  is the heat transfer coefficient; D is the part of the perimeter of the smoke layer cross-section that contacts the tunnel surface, m; and Tx is the maximum temperature rise of smoke layer at the horizontal distance of

x

relative to fire source, K. Therefore, the total heat of

path loss from fire source to vertical shaft can be expressed in the form of integral:

Qloss  

d

0

1  e kd  DTx d x   D  Tmax  k

(27)

Based on Eqs. (3)-(5), after replacing the heat release rate of the fire source and longitudinal ventialtion velocity with the modified one, the dimensionless smoke back-layering flow length beyond vertical shaft can be calculated by:





1 3   l  18.5ln 0.81Qvirtual U , Qvirtual  0.15 l    H 18.5ln  0.43 U   , Qvirtual  0.15  

(28)

with

2 Qup  Qexhaust  Qloss  1   r   Qvirtual   aC pTa g 1 2 H 5 2

U 

V  d wS 2 Aa gH

(29)

(30)

Finally, the dimensionless smoke back-layering flow length in a longitudinal ventilated tunnel fires with a vertical shaft in the upstream can be calculated as follows:

L  l   d  

l d  H H

(31)

where d  is the dimensionless distance between the fire source and vertical shaft, m; and H is the tunnel height, m.

3. Reduced-scale experiments A series of experiments were carried out in a 1/10 reduced-scale subway tunnel model, as shown in Fig.3. The length, width and height of this tunnel are 14 m, 0.4 m and 0.5 m, respectively. A 0.35 m high bracket was fixed under the tunnel. One sidewall of the tunnel is made up of 5 mm thick fire-resistant glass for observation. The top, bottom and the other sidewalls were all made by 7 mm thick fire-proofing board. In addition, the vertical shaft with dimension of 0.25 m (length) × 0.25 m (width) × 0.2 m (height) was placed at the longitudinal center line of ceiling. A multi blade fan was placed on left side of the tunnel. A 0.5 m long rectifier box, with thin tubes filled, was fixed between the multi blade fan and tunnel to smooth the turbulence of the ventilated flow from the fan. The longitudinal ventilation velocity from the fan can be controlled through a frequency inverter with a velocity range of 0-1 m/s with an accuracy of 1%. Five different longitudinal ventilation velocities of 0.15, 0.20, 0.25, 0.30 and 0.35 m/s were chosen in this study, which are equivalent to 0.47, 0.63, 0.79, 0.95 and 1.11 m/s in a full-scale tunnel based on the Froude Scaling Law. A series of thermocouples were positioned 1 cm below the ceiling along the longitudinal centerline with an interval of 0.25 m, shown in Fig. 3.

Fig.3. A schematic of the experimental apparatus

For fire source, a porous propane gas burner was designed, and the top surface is 35 cm higher than the floor. The gas burner was welded by 4 mm thick steel plates, constructing a space of 0.15 m (long)×0.15 m (wide)×0.1 m (high). And the space was filled with sand to make an even and stable propane flame. The gas fuel flow rate was controlled and monitored by a gas flow rate meter with an error of 0.01 m3/h. Heat release rate is calculated by fuel supply and its effective heat of combustion. Five different flow rates of 0.2, 0.3, 0.4, 0.5 and 0.6 m3/h were chosen in this study, representing fire sources of 5.52, 8.28, 11.04, 13.8 and 16.56 kW, respectively, which are equivalent to 1.75, 2.62, 0.63, 3.49, 4.36 and 5.25 MW in a full-scale tunnel. During all the tests, the dimensionless heat release rate was lower than 0.15 and the smoke back-layering flow was beyond the vertical shaft. The gas burner was set along the longitudinal central line of the tunnel with six horizontal distances from the vertical shaft in the downstream, including 0.5, 1, 1.5, 2, 3 and 4 m, which are equivalent to 5, 10, 15, 20, 30, and 40 m in a full-scale tunnel. For comparison purposes, the cases without vertical shaft were also studied. In

total, 175 cases were carried out, as summarized in Table 1. Table 1 A summary of experimental scenarios Test no.

Distance

between

fire

Longitudinal

source and vertical shaft

ventilation

(m)

velocities (m/s)

Heat release rates (kW)

1-5

0.15

5.52

8.28

11.04

13.8

16.56

6-10

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

16-20

0.30

5.52

8.28

11.04

13.8

16.56

21-25

0.35

5.52

8.28

11.04

13.8

16.56

26-30

0.15

5.52

8.28

11.04

13.8

16.56

31-35

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

41-45

0.30

5.52

8.28

11.04

13.8

16.56

46-50

0.35

5.52

8.28

11.04

13.8

16.56

51-55

0.15

5.52

8.28

11.04

13.8

16.56

56-60

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

66-70

0.30

5.52

8.28

11.04

13.8

16.56

71-75

0.35

5.52

8.28

11.04

13.8

16.56

76-80

0.15

5.52

8.28

11.04

13.8

16.56

81-85

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

91-95

0.30

5.52

8.28

11.04

13.8

16.56

96-100

0.35

5.52

8.28

11.04

13.8

16.56

101-105

0.15

5.52

8.28

11.04

13.8

16.56

106-110

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

116-120

0.30

5.52

8.28

11.04

13.8

16.56

121-125

0.35

5.52

8.28

11.04

13.8

16.56

126-130

0.15

5.52

8.28

11.04

13.8

16.56

131-135

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

141-145

0.30

5.52

8.28

11.04

13.8

16.56

146-150

0.35

5.52

8.28

11.04

13.8

16.56

151-155

0.15

5.52

8.28

11.04

13.8

16.56

156-160

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

166-170

0.30

5.52

8.28

11.04

13.8

16.56

171-175

0.35

5.52

8.28

11.04

13.8

16.56

11-15

36-40

61-65

86-90

111-115

136-140

161-165

No vertical shaft

0.5

1.0

1.5

2.0

3.0

4.0

4. Results and discussion 4.1. Smoke back-layering flow length Fig. 4 reflects the longitudinal temperature distribution of smoke beneath the ceiling in the tunnel. The smoke back-layering flow length is determined by the first measuring station in the upstream of fire source indicating the ambient temperature value, as shown in Fig. 4. Table 2 summarizes the experimental results of smoke back-layering flow length in each case. 160

Smoke back-layering flow length=7.5 m

140 120

T (℃)

100

Thermocouple indicating ambient temperature value

80 60 40

Back-layering flow length 20 -10

-8

-6

-4

-2

0

x (m)

Fig. 4. The temperature distribution of smoke underneath the ceiling along the central line

Fig. 5 shows the difference between the smoke back-layering flow length in the tunnel with vertical haft in the upstream and without vertical shaft. It is shown that the vertical shaft in the upstream can control the smoke back-layering flow within a relatively limited range, compared to the tunnel without vertical shaft.

Smoke back-layering flow length (m)

12

0.5 m 1.0 m 1.5 m 2.0 m 3.0 m 4.0 m No vertical shaft

10

8

6

4

2 0.15

0.20

0.25

0.30

0.35

Longitudinal ventilation velocity (m/s)

Fig.5. Smoke back-layering flow length for a 5.52 kW fire source

Table 2 A summary of experimental results of smoke back-layering flow length Distance

between

source

and

fire

vertical

shaft(m)

longitudinal ventilation

Heat release rates(kW) 5.52

velocities(m/s)

No vertical shaft

0.5

1.0

1.5

2.0

3.0

4.0

8.28

11.04

13.8

16.56

Smoke back-layering flow length (m)

0.15

11.5

____

____

____

____

0.20

9.5

10.0

11.25

____

____

0.25

8.0

9.0

9.5

10.5

11.5

0.30

7.0

7.5

8.0

9.0

10.25

0.35

5.75

6.5

7.25

8.5

9.75

0.15

7. 5

8.5

9.25

9.75

11.0

0.20

6.25

7.25

7.75

8.5

9.75

0.25

5.25

6.25

7.0

8.25

9.0

0.30

4.75

5.25

6.0

7.25

8.0

0.35

4.0

4. 5

5.25

6.0

6.75

0.15

6.0

6.0

7.5

8.25

9.5

0.20

4.75

5.5

6.25

7.25

8.0

0.25

4.0

4.75

5.75

6.5

7.0

0.30

2.75

4.0

4.25

5.75

6.25

0.35

1.75

2.75

3.75

4.5

5.25

0.15

5.25

6.0

6.5

7.25

8.25

0.20

4.5

5.0

6.0

6.75

7.25

0.25

3.5

4.0

5.25

5.75

6.5

0.30

2.75

3.5

4.0

5.0

5.5

0.35

2.0

2.75

3.25

4.0

4.75

0.15

5.75

6.5

7.5

8.25

9.25

0.20

5.25

5.75

6.75

7.5

8.5

0.25

4.25

4.75

6.0

6.75

7.25

0.30

3.25

4.0

5.0

5.5

6.75

0.35

2.5

3.25

4.5

4.5

5.5

0.15

7.5

8.5

9.75

10.0

11.5

0.20

6.5

7.25

8.75

9.75

10.75

0.25

5.25

6.5

7.5

8.5

9.75

0.30

4.5

5.5

6.25

7.5

8.25

0.35

3.75

4.75

5.5

6.25

7.0

0.15

9.0

9.75

11.0

____

____

0.20

7.5

9.0

9.75

11.0

11.75

0.25

6.25

7.5

9.0

9.75

10.75

0.30

5.25

6.5

7.75

8.0

9.5

0.35

4.0

6.0

6.5

7. 5

8.75

Fig. 6(a-e) presents the dimensionless smoke back-layering flow length for all the tested cases in this study. It can be observed that: (a) the dimensionless smoke back-layering flow length decreases with the increase of ventilation velocity but increases with a higher heat release rate;

and (b) the dimensionless smoke back-layering flow length decreases when fire source is moving away from the vertical shaft (within dimensionless distance for 3), Which is probably related to the strong induced effect of vertical shaft on the hot smoke. When a fire occurs in the free space, the smoke rises vertically under the effect of buoyancy. However, the upward buoyancy has to translate into forward driving force beneath ceiling in tunnel due to the limit of ceiling. So, if the fire source was very close to a vertical shaft for nature ventilation, such as the dimensionless distance for 1 or 2, the vertical shaft would induce extra smoke into it to keep its previous kinestate. Accordingly, more smoke flows into upstream and beyond the vertical shaft, resulting in a longer smoke back-layering flow length. Meanwhile, the dimensionless distance for 3 is the first location where the smoke plume isn't influenced directly by the induced effect of vertical shaft. Therefore, the smoke back-layering flow length is the shortest of all the tested cases. However, when the dimensionless distance is larger than 3, the dimensionless smoke back-layering flow length was observed to increase. This is because the longer the distance between fire source and vertical shaft is, the less the heat exhausted from the vertical shaft is. Furthermore, the influence of the vertical shaft on smoke back-layering flow length is limited when it is far from the fire source. 24

0.15 m/s 0.25 m/s 0.35 m/s

20

0.2 m/s 0.3 m/s

0.15 m/s 0.25 m/s 0.35 m/s

20

0.2 m/s 0.3 m/s

16 16

L*

L*

12 12

8 8

4

Heat release rate of fire source 5.52 kW

Heat release rate of fire source 8.28 kW

4

0 0

2

4

6

8

10

0

2

4

6

(a) 0.15 m/s 0.25 m/s 0.35 m/s

24

10

(b)

0.2 m/s 0.3 m/s

0.15 m/s 0.25 m/s 0.35 m/s

24

20

0.2 m/s 0.3 m/s

20

16

16

L*

L*

8

d*

d*

12

12 8 8

Heat release rate of fire source 11.04 kW

4

Heat release rate of fire source 13.8 kW

4 0

2

4

6 *

d

(c)

8

10

0

2

4

6

d*

(d)

8

10

28 0.15 m/s 0.25 m/s 0.35 m/s

24

0.2 m/s 0.3 m/s

L*

20

16

12 Heat release rate of fire source 16.56 kW

8 0

2

4

6

8

10

d*

(e) Fig. 6. Dimensionless smoke back-layering flow length at different dimensionless fire source-vertical shaft distance under the combination of both longitudinal ventilation and vertical shaft in the upstream.

It should be noted that this paper did not consider an extreme condition, where fire source is just located beneath vertical shaft. In this condition, a lot of smoke will be exhausted directly through the vertical shaft and the smoke back-layering flow length may be the shortest. However, it is more practical that there is a distance between the fire source and the vertical shaft. In this study, the most appropriate dimensionless distance between the vertical shaft and fire source is 3, resulting in the shortest smoke back-layering flow length.

4.2. Comparison of model predictions with experiments The cases from the experiments where the dimensionless distance between the fire source and the vertical shaft is less than 3 have not been chosen for comparison with the predictions by the model. This is because the induced effect of vertical shaft on smoke plume occurs for these cases, but the model in this paper did not consider this condition. Fig. 7 shows the regression between the experiments ( d   3 ) and the prediction calculated from Eq. (31) when u  0.19 . It can be seen from this figure that the dimensionless smoke back-layering flow length correlates reasonably well with Eq. (31).

28

L* by the experiments

24 20 16 12 8 4 0 0

4

8

12

16

20

24

28

L* predicted by Eq.(31)

Fig.7. A comparison between the experimental results in this study and the predictions obtained from Eq. (31) when u  0.19 .

Fig. 8 shows the correlation between the experiments ( d   3 ) and the prediction by Eq. (31) under the condition when u  0.19 . It is known that the empirical model slightly overestimates the prediction. This is because when u  0.19 , the ventilated flow has a significant effect on fire plume and the flame starts to deflect toward downstream [31], Meanwhile, more hot smoke spread downstream than upstream under higher longitudinal ventilation velocities. In fact, it should be noted that equal treatment about the convective heat of smoke spreading upstream and downstream is considered in this model, causing the initial assumption in this model is invalid. Overall, this model overestimates the convective heat of smoke spreading upstream in higher longitudinal ventilation velocities, which results in a high prediction about the smoke back-layering flow length. 20 V=0.3 m/s V=0.35 m/s V=0.35 m/s V=0.35 m/s

L* by the experiments

16

Q=5.52 kW Q=5.52 kW Q=8.28 kW Q=11.04 kW

12

8

4

0 0

4

8

12

16

20

L* predicted by Eq.(31)

Fig.8. A comparison between the experimental results in this study and the predictions obtained from Eq. (31) when u  0.19 .

5. Conclusions This paper experimentally investigates the smoke back-layering flow length in longitudinal ventilated tunnel fires with a vertical shaft in the upstream. Several conclusions can be addressed: (1) The vertical shaft in the upstream can control the smoke back-layering flow length within a relatively limited range, compared to the tunnel without vertical shaft. Moreover, when fire source is close to vertical shaft, the induced effect of vertical shaft on smoke plume will seriously increase the convective heat of smoke spreading upstream. So, the distance between the fire source and the vertical shaft has a significant effect on the smoke back-layering flow length, which keep decreasing when fire source is moving away from the vertical shaft (within dimensionless distance for 3). However, when the dimensionless distance is larger than 3, the smoke back-layering flow length was observed to increase. (2) By introducing a concept of virtual fire source below the vertical shaft, an empirical model was developed to predict the smoke back-layering flow length in longitudinal ventilated tunnel fires with a vertical shaft in the upstream. It is known from the comparison that the prediction fit reasonably well with the experimental data when the dimensionless longitudinal air flow velocity is less than 0.19. However, the empirical model slightly overestimates prediction when the dimensionless longitudinal air flow velocity is beyond 0.19, which is because some of the assumptions in this model are invalid under higher longitudinal ventilation velocity.

Acknowledgements This work was supported by National Natural Science Foundation of China (No. 51323010) and Fundamental Research Funds for the Central Universities under Grant (No. WK2320000033)

References [1] J. Ji, Z.H. Gao, C.G. Fan, J.H. Sun, Large Eddy Simulation of stack effect on natural smoke exhausting effect in urban road tunnel fires, Int. J. Heat Mass Transf. 66 (2013) 531-542. [2] A.R. Nilsen, T. Log, Results from three models compared to full-scale tunnel fires tests, Fire Saf. J. 44(1) (2009) 33-49. [3] A. Beard, R. Carvel, The Handbook of Tunnel Fire Safety, Thomas Telford Publishing. (2005). [4] L.H. Hu, L.F. Chen, L. Wu, Y.F. Li, J.Y. Zhang, N. Meng, An experimental investigation and correlation on buoyant gas temperature below ceiling in a slopping tunnel fire, Appl. Therm. Eng. 51(1-2) (2013) 246-254.

[5] D. Yang, R. Huo, X.L. Zhang, X.Y. Zhao, Comparison of the distribution of carbon monoxide concentration and temperature rise in channel fires: Reduced-scale experiments, Appl. Therm. Eng. 31(4) (2011) 528-536. [6] T. Du, D. Yang, S.N. Peng, Y.L Li, Y.M. Xiao, Performance evaluation of longitudinal and transverse ventilation for thermal and smoke control in a looped urban traffic link tunnel, Appl. Therm. Eng. 96 (2016) 490-500. [7] P. Thomas, The movement of buoyant fluid against a stream and the venting of underground fires. Fire Res. (1958) 351. [8] L.H. Hu, R. Huo, W.K. Chow, Studies on buoyancy-driven back-layering flow in tunnel fires, Exp. Therm. Fluid Sci. 32(8) (2008) 1468-1483. [9] Y.Z. Li, B. Lei, H. Ingason, Study of critical velocity and backlayering length in longitudinally ventilated tunnel fires, Fire Saf. J. 45(6-8) (2010) 361-370. [10] S.G. Zhang, X.D. Cheng, Y.Z. Yao, K. Zhu, K.Y. Li, S. Lu, R.F. Zhang, H.P. Zhang, An experimental investigation on blockage effect of metro train on the smoke back-layering in subway tunnel fires, Appl. Therm. Eng. 99 (2016) 214-223. [11] W. Tang, L.H. Hu, L.F. Chen, Effect of blockage-fire distance on buoyancy driven back-layering length and critical velocity in a tunnel: An experimental investigation and global correlations, Appl. Therm. Eng. 60 (1-2) (2013) 7-14. [12] H. Ingason, Y.Z. Li, Model scale tunnel fire tests with longitudinal ventilation, Fire Saf. J. 45(6-8) (2010) 371-384. [13] X.P. Guo, Q.H. Zhang, Measuring fire size in tunnels, Appl. Therm. Eng. 59 (1-2) (2013) 101-105. [14] L.H. Hu, W. Tang, L.F. Chen, L. Yi, A non-dimensional global correlation of maximum gas temperature beneath ceiling with different blockage-fire distance in a longitudinal ventilated tunnel, Appl. Therm. Eng. 56 (1-2) (2013) 77-82. [15] M.C. Weng, X.L. Lu, F. Liu, C.X. Du, Study on the critical velocity in a sloping tunnel fire under longitudinal ventilation, Appl. Therm. Eng. 94 (2016) 422-434. [16] C.G. Fan，Y.Z. Li, H. Ingason, A. Lönnermark, Effect of tunnel cross section on gas temperatures and heat fluxes in case of large heat release rate, Appl. Therm. Eng. 93 (2016) 405-415. [17] S.G. Zhang, Y.Z. Yao, K. Zhu, K.Y. Li, R.F. Zhang, S. Lu, X.D. Cheng, Prediction of smoke back-layering length under different longitudinal ventilations in the subway tunnel with metro train, Tunn. Undergr. Space Technol. 53 (2016) 13-21.

[18] L.F. Chen, L.H. Hu, W. Tang, L. Yi, Studies on buoyancy driven two-directional smoke flow layering length with combination of point extraction and longitudinal ventilation in tunnel fires, Fire Saf. J. 59 (2013) 94-101. [19] J. Ji , Z.H. Gao, C.G. Fan, W. Zhong, J.H. Sun, A study of the effect of plug-holing and boundary layer separation on natural ventilation with vertical shaft in urban road tunnel fires, Int. J. Heat Mass Transf. 55(21-22) (2012) 6032-6041. [20] J. Ji , C.G. Fan, Z.H. Gao, J.H. Sun, Effects of vertical shaft geometry on natural ventilation in urban road tunnel fires, J. Civ. Eng. Manag. 20(4) (2014) 466-476. [21] O. Vauquelin, D. Telle, Definition and experimental evaluation of the smoke ‘‘confinement velocity’’ in tunnel fires, Fire Saf. J. 40(4) (2005) 320-330. [22] O. Vauquelin, O. Megret, Smoke extraction experiments in case of fire in a tunnel, Fire Saf. J. 37(5) (2002) 525-533. [23] C.G. Fan, J. Ji, W. Wang, J.H. Sun, Effects of vertical shaft arrangement on natural ventilation performance during tunnel fires, Int. J. Heat Mass Transf. 73 (2014) 158-169. [24] J. Ji, J.Y. Han, C.G. Fan, Z.H. Gao, J.H. Sun, Influence of cross-sectional area and aspect ratio of shaft on natural ventilation in urban road tunnel, Int. J. Heat Mass Transf. 67 (2013) 420-431. [25] R. Harish, K. Venkatasubbaiah, Effects of buoyancy induced roof ventilation systems for smoke removal in tunnel fires, Tunnel. Undergr. Space Technol. 42 (2014), 195-205. [26] H. Ingason, Y. Z. Li, Model scale tunnel fire tests with point extraction ventilation, J. Fire Prot. Eng. 21(1) (2011) 5-36. [27] Y.F. Wang, P.N. Yan, B. Zhang, J.C. Jiang, Thermal buoyant smoke back-layering length in a naturally ventilated tunnel with vertical shafts, Appl. Therm. Eng. 93 (2016) 947-957. [28] L.F. Chen, L.H. Hu, X.L. Zhang, X.Z. Zhang, X.C. Zhang, L.Z. Yang, Thermal buoyant smoke back-layering flow length in a longitudinal ventilated tunnel with ceiling extraction at difference distance from heat source, Appl. Therm. Eng. 78 (2015) 129-135. [29] J. Ji, W. Zhong, K.Y. Li, X.B. Shen, Y. Zhang, R. Huo, A simplified calculation method on maximum smoke temperature under the ceiling in subway station fires, Tunn. Undergr. Space Technol. 26 (2011) 490-496. [30] L.H. Hu, R. Huo, W.K. Chow, H.B. Wang, R.X. Yang, Decay of buoyant smoke layer temperature along the longitudinal direction in tunnel fires, J. Appl. Fire Sci. 13(1) (2004) 53-77. [31] Y.Z. Li, B. Lei, H. Ingason, The maximum temperature of buoyancy-driven smoke flow beneath the ceiling in tunnel fires, Fire Saf. J. 46(4) (2011) 204-210.

[32] L.H. Hu, Study on the thermophysics characteristics of smoke movement during tunnel fires. PhD Dissertation, University of Science and Technology of China, Hefei, Anhui, China. (2006).

Nomenclature g : gravity acceleration ( m / s2 ) C p : specific heat capacity of air at constant pressure (kJ/kg K)

 : heat transfer coefficient

K : attenuation coefficient of smoke layer temperature Ck : a constant in Eq. (2)  and  : constant in Eq. (2) Ta : ambient air temperature (K) Tmax : maximum smoke temperature rise near the fire source (K) Td : maximum smoke temperature rise beneath the vertical shaft (K) T f :flame temperature (K) Q : total heat release rate (kW) Qc : convective heat release rate (kW)

mshaft : mass flux of smoke through the vertical shaft (kg/s) b : radius of the fire source (m)

d : distance between the fire source and vertical shaft (m) d  dimensionless distance between the fire source and vertical shaft (m) l : smoke back-layering flow length beyond vertical shaft (m) l * : dimensionless smoke back-layering flow length beyond vertical shaft (m) L : smoke back-layering flow length (m) L : dimensionless smoke back-layering flow length (m) h : height of vertical shaft (m) H : tunnel height (m) H ef : effective tunnel height (m)

D : part of the perimeter of the smoke layer cross-section that contacts the tunnel surface (m) S : cross-sectional area of vertical shaft ( m 2 ) A : cross-sectional area of tunnel ( m 2 ) w : flow velocity of smoke into vertical shaft (m/s)

V : longitudinal ventilation velocity (m/s)

V  : dimensionless longitudinal ventilation velocity (m/s)

U  : dimensionless modified air flow velocity at the upstream of virtual fire source (m/s) u  : dimensionless modified air flow velocity at the downstream of virtual fire source (m/s)

Greek symbols

 a : ambient air density ( kg / m3 )  d : density of smoke below vertical shaft ( kg / m3 )  r : proportion of the radiation heat loss

Fig.1. A schematic of smoke back-layering flow length under the combination of both longitudinal ventilation and downstream ceiling extraction. Fig.2. A schematic of smoke back-layering flow length under the combination of both longitudinal ventilation and upstream vertical shaft Fig.3. A schematic of the experimental apparatus Fig.4. The temperature distribution of smoke underneath the ceiling along the central line Fig.5. Smoke back-layering flow length for a 5.52 kW fire source Fig. 6. Dimensionless smoke back-layering flow length at different dimensionless fire source-vertical shaft distance under the combination of both longitudinal ventilation and vertical shaft in the upstream. Fig.7. A comparison between the experimental results in this study and the predictions obtained from Eq. (31) when u  0.19 . Fig.8. A comparison between the experimental results in this study and the predictions obtained from Eq. (31) when u  0.19 .

Fig. 1

Fig. 2

Fig. 3

160

Smoke back-layering flow length=7.5 m

140 120

T (℃)

100 80

Thermocouple indicating ambient temperature value

60 40

Back-layering flow length 20 -10

-8

-6

-4

x (m)

Fig. 4

-2

0

Smoke back-layering flow length (m)

12

0.5 m 1.0 m 1.5 m 2.0 m 3.0 m 4.0 m No vertical shaft

10

8

6

4

2 0.15

0.20

0.25

0.30

Longitudinal ventilation velocity (m/s)

Fig. 5

0.35

0.15 m/s 0.25 m/s 0.35 m/s

20

0.2 m/s 0.3 m/s

16

L*

12

8

4

Heat release rate of fire source 5.52 kW

0 0

2

4

6

d*

Fig. 6 (a)

8

10

24 0.15 m/s 0.25 m/s 0.35 m/s

20

0.2 m/s 0.3 m/s

L*

16

12

8 Heat release rate of fire source 8.28 kW

4 0

2

4

6

d*

Fig. 6 (b)

8

10

0.15 m/s 0.25 m/s 0.35 m/s

24

0.2 m/s 0.3 m/s

20

L*

16 12 8 Heat release rate of fire source 11.04 kW

4 0

2

4

6

d*

Fig. 6 (c)

8

10

0.15 m/s 0.25 m/s 0.35 m/s

24

0.2 m/s 0.3 m/s

20

L*

16

12

8

Heat release rate of fire source 13.8 kW

4 0

2

4

6

d*

Fig. 6 (d)

8

10

28 0.15 m/s 0.25 m/s 0.35 m/s

24

0.2 m/s 0.3 m/s

L*

20

16

12 Heat release rate of fire source 16.56 kW

8 0

2

4

6

d*

Fig. 6 (e)

8

10

28

L* by the experiments

24 20 16 12 8 4 0 0

4

8

12

16

20

L* predicted by Eq.(31)

Fig. 7

24

28

20 V=0.3 m/s V=0.35 m/s V=0.35 m/s V=0.35 m/s

L* by the experiments

16

Q=5.52 kW Q=5.52 kW Q=8.28 kW Q=11.04 kW

12

8

4

0 0

4

8

12

L* predicted by Eq.(31)

Fig. 8

16

20

Table 1 A summary of experimental scenarios Table 2 A summary of experimental results of smoke back-layering flow length

Test no.

Table 1

Distance

between

fire

Longitudinal

source and vertical shaft

ventilation

(m)

velocities (m/s)

Heat release rates (kW)

1-5

0.15

6-10 Distance between fire longitudinal 11-15 No vertical shaft source and vertical ventilation 16-20 shaft(m) velocities(m/s) 21-25

5.52

0.20 0.25 0.30 0.35

5.52

8.28

11.04

13.8

16.56

5.52 8.28 11.04 13.8 16.56 Heat release rates(kW) 5.52 8.28 11.04 13.8 16.56 8.28 11.04 13.8 16.56 5.52 8.28 11.04 13.8 16.56 Smoke back-layering flow length (m) 5.52 8.28 11.04 13.8 16.56

26-30

0.15

5.52

8.28

11.04

13.8

16.56

31-35

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

41-45

0.30

5.52

8.28

11.04

13.8

16.56

46-50

0.35

5.52

8.28

11.04

13.8

16.56

51-55

0.15

5.52

8.28

11.04

13.8

16.56

56-60

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

66-70

0.30

5.52

8.28

11.04

13.8

16.56

71-75

0.35

5.52

8.28

11.04

13.8

16.56

76-80

0.15

5.52

8.28

11.04

13.8

16.56

81-85

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

91-95

0.30

5.52

8.28

11.04

13.8

16.56

96-100

0.35

5.52

8.28

11.04

13.8

16.56

101-105

0.15

5.52

8.28

11.04

13.8

16.56

106-110

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

116-120

0.30

5.52

8.28

11.04

13.8

16.56

121-125

0.35

5.52

8.28

11.04

13.8

16.56

126-130

0.15

5.52

8.28

11.04

13.8

16.56

131-135

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

141-145

0.30

5.52

8.28

11.04

13.8

16.56

146-150

0.35

5.52

8.28

11.04

13.8

16.56

151-155

0.15

5.52

8.28

11.04

13.8

16.56

156-160

0.20

5.52

8.28

11.04

13.8

16.56

0.25

5.52

8.28

11.04

13.8

16.56

166-170

0.30

5.52

8.28

11.04

13.8

16.56

171-175

0.35

5.52

8.28

11.04

13.8

16.56

36-40

61-65

86-90

111-115

136-140

161-165

Table 2

0.5

1.0

1.5

2.0

3.0

4.0

No vertical shaft

0.5

1.0

1.5

2.0

3.0

4.0

0.15

11.5

____

____

____

____

0.20

9.5

10.0

11.25

____

____

0.25

8.0

9.0

9.5

10.5

11.5

0.30

7.0

7.5

8.0

9.0

10.25

0.35

5.75

6.5

7.25

8.5

9.75

0.15

7. 5

8.5

9.25

9.75

11.0

0.20

6.25

7.25

7.75

8.5

9.75

0.25

5.25

6.25

7.0

8.25

9.0

0.30

4.75

5.25

6.0

7.25

8.0

0.35

4.0

4. 5

5.25

6.0

6.75

0.15

6.0

6.0

7.5

8.25

9.5

0.20

4.75

5.5

6.25

7.25

8.0

0.25

4.0

4.75

5.75

6.5

7.0

0.30

2.75

4.0

4.25

5.75

6.25

0.35

1.75

2.75

3.75

4.5

5.25

0.15

5.25

6.0

6.5

7.25

8.25

0.20

4.5

5.0

6.0

6.75

7.25

0.25

3.5

4.0

5.25

5.75

6.5

0.30

2.75

3.5

4.0

5.0

5.5

0.35

2.0

2.75

3.25

4.0

4.75

0.15

5.75

6.5

7.5

8.25

9.25

0.20

5.25

5.75

6.75

7.5

8.5

0.25

4.25

4.75

6.0

6.75

7.25

0.30

3.25

4.0

5.0

5.5

6.75

0.35

2.5

3.25

4.5

4.5

5.5

0.15

7.5

8.5

9.75

10.0

11.5

0.20

6.5

7.25

8.75

9.75

10.75

0.25

5.25

6.5

7.5

8.5

9.75

0.30

4.5

5.5

6.25

7.5

8.25

0.35

3.75

4.75

5.5

6.25

7.0

0.15

9.0

9.75

11.0

____

____

0.20

7.5

9.0

9.75

11.0

11.75

0.25

6.25

7.5

9.0

9.75

10.75

0.30

5.25

6.5

7.75

8.0

9.5

0.35

4.0

6.0

6.5

7. 5

8.75

HIGHLIGHTS

 Combined effect of longitudinal ventilation and an upstream vertical shaft was addressed.  Vertical Shaft distance from fire source showed big effect on smoke back-layering flow length.  The most appropriate dimensionless distance between vertical shaft and fire source is 3 in this study.

 Empirical model was developed to predict smoke back-layering flow length with a vertical shaft.