Study on critical velocity in the sloping tunnel fire under longitudinal ventilation

Topic: T2.1 Design and Innovation Reference number: 1088 Study on critical velocity in the sloping tunnel fire under longitudinal ventilation Xin-ling Lu 1, Miao-cheng Weng 1,2,3, *, Fang Liu 1,2,3 1. School of Urban Construction and Environment Engineering, Chongqing University, Chongqing 400045, China; 2. Key Laboratory of Three Gorges Reservoir Region s Eco-Environment, Ministry of Education, Chongqing 400045, China; 3. National Centre for International Research of Low-carbon and Green Buildings, Chongqing 400045, China. Abstract: The critical velocity and the backlayering length of smoke in the tunnel fires are the two most important parameters in longitudinal ventilation design. This paper introduced the sectional coefficient ζ to describe the geometrical characteristic of the tunnel section, and the characteristic hydraulic diameter of the tunnel H replaced the tunnel height H. Then, CFD simulations were conducted in nine tunnels with different cross sectional shapes using the proprietary software Fire Dynamic Simulator, version 5.5. With the FDS simulations, prediction models for backlayering length and critical velocity of the horizontal tunnels was proposed modified by the sectional coefficient ζ. And the effect of slope on the critical velocity was studied. Moreover, the prediction models for critical velocity on different slopes compared with the prediction models proposed by others. Key words: tunnel fire, slope tunnel, CFD simulation, backlayering length, critical velocity 1 Introduction The reverse flow of smoke in tunnel fires is one of the special smoke movements in longitudinal ventilation. The critical velocity is the minimum longitudinal ventilation velocity to prevent the reverse flow of the smoke from the fire in the upstream direction in the tunnel. The backlayering length is the length of the reversed smoke front along the upstream direction to the fire source when the ventilation velocity is lower than the critical velocity. The critical velocity is the longitudinal ventilation velocity when the backlayering length is zero. There is no smoke to the upstream direction of the fire source when the longitudinal velocity is greater than the critical velocity in the tunnel. Thus, it can prevent the hazards of smoke to blocked vehicles and personnel of the upstream direction, and also provide safe passage for the aid to firefighters. The critical velocity involves many factors, such as fire scale, slope and tunnel cross-section geometry, etc. Among them, the fire scale has the greatest impact on the critical velocity [1]. The critical velocity has been a focus of study of researchers from various countries [2, 3]. Based on the theoretical analysis, Thomas [4] proposed a prediction model for the backlayering length in case of a fire in a longitudinally ventilated tunnel. The equation of the predicted model is shown as follows: * Corresponding author at: School of Urban Construction and Environment Engineering, Chongqing University, Chongqing 400045, PR China. Tel.: +86 18623121928; fax: +86 23 65120771 E-mail address: 416540297@qq.com

L = L H gh ρ a T f C p 3 A antelon et al. [5] carried out small-scale experiments in a 1.5m long semicircular pipe with 0.15m radius. Their research showed that the dimensionless backlayering length is related to the modified Richardson number as the following formula: L Ri 0.3 (2) where Ri = g ρ a T a C p 3 H. Li et al. [6] proposed the following equation for the dimensionless backlayering length based on theoretical analysis and small-scale experiments. L = { 18.5ln(0.81 1/3 / ) 0.15 18.5(0.43/ ) > 0.15 ρ a C p T a g 1/2 H 5/2, = (gh) 1/2. Based on CFD simulations and small-scale experiments, Weng et al. [7] proposed a prediction model for the backlayering length in metro tunnel fires. L = 7.13ln ( H 3) 4.36 (4) ρ a C p T a g 1/2 H 5/2, = (gh ) 1/2. In addition to the work of these researchers there is a great deal of theoretical, numerical and experimental studies on critical velocity that can be found in literature. Thomas [8] suggested a predicted model for the critical velocity of longitudinal ventilation is based on the theory of the Froude number, which is shown as the following formula: c = k [ g 1/3 ] ρ a C p T f where k is a constant. The value of k was determined from suitable experiments. Kennedy [9, 10] derived a semi-empirically equation to calculate the critical velocity by relating the temperature rise of hot gases from a fire to the convective heat release rate from the fire. This is stated as follows: T f = c = k g k [ ρ a C p A c + T a gh 1/3 ] ρ a C p AT f where k is a constant which is set to 0.61. When the fire occurs on a horizontal or uphill tunnel k g = 1.0, and k g = 1.0 + 0.0374(tanθ) 0.8 when the fire occurs on a downhill tunnel. tanθ is the tangent of the slope angle (%). Oka and Atkinson [11] carried out a series of small-scale experiments to examine the relationship between the critical velocity and the heat release rate, taking different geometries of the fire source into account. A dimensionless equation was proposed: c = { k v ( 0.12 )1/3 < 0.12 k v 0.12 ρ a C p T a g 1/2 H 5/2, = (gh) 1/2. And k v is a constant that varies from 0.22~0.38. (5) (7) (1) (6) (3)

Weng et al. [7] also proposed a prediction model for critical velocity by 1/10 scale model experiments and CFD simulations. c = 0.82 1/3 ρ a C p T a g 1/2 H 5/2, = (gh ) 1/2. Most tunnels have a slope which can significantly affect smoke movement under fire due to buoyancy and stack effects. After the study of Oka and Atkinson [11], Atkinson and Wu [12] carried out experimental study on the critical velocity to show how this was changed by the tunnel slope and suggested the following relationship to consider the slope of inclined tunnel based on the critical velocity in the horizontal tunnel. C,θ / C,0 = (1 + 0.014θ) (9) Ko et al. [13] used experimental study to investigate the effects of a tunnel slope on the critical velocity in the tunnel fires. The relationship between the normalized critical velocity and the angle of tunnel slope was determined as: C,θ / C,0 = (1 + 0.033θ) (10) Based on experiment results, Yi et al. [14] proposed the correlation between the critical velocity and the tangent of the slope angle of the tunnel expressed as: C,β / C,0 = (1 + 0.034β) (11) Chow et al. [15] studied on smoke movement in a tilted tunnel fire with longitudinal ventilation, and an equation was produced in terms of the angle of tilt θ: C,θ / C,0 = (1 + 0.022θ) (12) A recent model tunnel has been built [7] with which experiments on tunnel ventilation and smoke extraction were carried out in succession. In this paper, through a series of numerical simulations, characteristics of smoke flow inside the tunnel are studied with different longitudinal ventilation velocities under different conditions. The effects of the tunnel sectional coefficient and the slope on the backlayering length and critical velocity are discussed based on the numerical simulation results. Then, prediction models are proposed and compared with other different models. (8) Nomenclature A cross-sectional area of the tunnel (m 2 ) C p thermal capacity of air (J/(kg K)) D characteristic fire diameter (m) g gravitational acceleration (m/s 2 ) H tunnel height (m) H characteristic hydraulic diameter of the tunnel (m) k coefficient in Eq. (5) k coefficient in Eq. (6) k g gradient correction factor in Eq. (6) k v coefficient in Eq. (7) L backlayering length (m) L dimensionless backlayering length

heat release rate (W) convective heat release rate per unit width of the tunnel (W/m) dimensionless heat release rate Ri modified Richardson number T a ambient air temperature (K) T f smoke temperature (K) velocity of longitudinal ventilation (m/s) dimensionless ventilation velocity c critical velocity (m/s) c dimensionless critical velocity C,θ critical velocity of the inclined tunnel with slope θ C,β critical velocity of the inclined tunnel with slope tangent β C,0 critical velocity of the horizontal tunnel Greek letters β tangent of the slope angle (%) δx nominal size of a mesh cell (m) ζ sectional coefficient of the tunnel θ tunnel slope in degrees (deg) ρ a ambient air density (kg/m 3 ) 2 CFD simulations and boundary conditions Tunnel height is one of the most important parameters influencing smoke movement. But, the tunnel height doesn t sufficiently reflect the impact of the geometric characteristics of the tunnel to smoke flow. The experimental results carried out by Wu and Bakar [16] clearly demonstrate that for a tunnel having the same height, the critical velocity varies with the tunnel width. The tunnel height is not suitable as the characteristic length. Therefore a new characteristic length has to be sought. In the work of De Ris [17], the characteristic length was taken as the mean hydraulic diameter of the duct. It was considered that the dynamic flow of air inside the duct was more a function of the mean hydraulic diameter of the duct (which also included the effect of duct width), rather than depending solely on the height of the duct. So our research focused on using the characteristic hydraulic diameter of the tunnel H, to replace the tunnel height H, as the characteristic length in the dimensionless analysis. The hydraulic diameter of the tunnel, H, is defined as the ratio of 4 times the cross-sectional area to the tunnel wetted perimeter. The tunnel cross sectional area and the tunnel height simultaneously affect smoke movement. Therefore, taking both the tunnel height and the cross sectional area into consideration, the sectional coefficient ζ which comprehensively considers the impacts of the width and height of tunnel on the development of smoke plume was introduced. The sectional coefficient defined as tunnel cross-sectional area divided by the square of height

is as follows: ζ = A/H 2 (13) CFD modeling of tunnel fires can be undertaken using different kinds of models from 1D models to advanced 3D models [18]. Restricted by the limited experimental conditions, CFD methods allow reseachers to achieve a deeper understanding of the influences of tunnel sectional coefficients. The CFD tools include packages such as Fluent, CFX, Phoenics, FDS, etc., and FDS (Fire Dynamics Simulator) has already been widely used to simulate tunnel fires [19]. Therefore, FDS was used to perform the CFD simulations in the present study. 2.1 The set-up of the simulation studies As ground conditions vary from soft clay to hard rock the tunnel construction methods are different. Hence, the cross-sectional shapes of tunnels are not always the same. By collecting data from the intervals between every two stations of Metro line 6 in Chongqing, China, nine typical tunnel sections were chosen to conduct CFD simulations. The schematic views of the tunnel sections are shown in Fig. 1. All the tunnels are unidirectional tubes with one track except tunnels H and I which are bidirectional tubes with two tracks. In addition, tunnels A, B, C, D, E and F have the same widths but different heights, while tunnels D and G have the same heights but different widths. Moreover, the sectional shape of all the tunnels are simplied to a rectangular shape except tunnel C which is a horseshoe shape. Fig. 1 Tunnel section (Unit:mm) The present study adopted 250 CFD simulations. As stated above, nine different sectional coefficients are included. In the simulations, two different heat release rates were imposed. For each heat release rate, five longitudinal ventilation velocities were included. In order to study the effect of the tunnel slope on the

characteristics of smoke flow, the characteristics of the tunnel sectional coefficient ζ, in typical tunnels (F and D) were chosen to be the research objects of the tunnels of the sectional coefficient ζ 1 and the tunnels of the sectional coefficient ζ < 1. The slope, β, of the tunnels was varied to include the values and zero, plus or minus 0.5%, 1%, 2%, and 3%. The specific simulation scheme is shown in Table 1. Case 1 HRR (MW) Tunnel ζ β A 0.67 0 Table 1 Scheme of FDS simulations Longitudinal ventilation velocity (m/s) Case HRR (MW) Tunnel ζ β 4 D 0.89 0 1.40,1.60,1.8 13 D 0.89 0 5 5 E 1 0 0,2.00,2.20 14 7.5 E 1 0 10 A 0.67 0 2 B 0.75 0 11 B 0.75 0 3 C 0.79 0 12 C 0.79 0 6 F 1.14 0 15 F 1.14 0 7 G 1.3 0 16 G 1.3 0 8 H 1.67 0 17 H 1.67 0 9 I 1.85 0 18 I 1.85 0 19 F 1.14 0.5% 22 F 1.14 3.0% 1.40,1.60,1.8 30 F 1.14 3.0% 5 23 F 1.14-0.5% 0,2.00,2.20 31 7.5 F 1.14-0.5% 27 F 1.14 0.5% 20 F 1.14 1.0% 28 F 1.14 1.0% 21 F 1.14 2.0% 29 F 1.14 2.0% 24 F 1.14-1.0% 32 F 1.14-1.0% 25 F 1.14-2.0% 33 F 1.14-2.0% 26 F 1.14-3.0% 34 F 1.14-3.0% 35 D 0.89 0.5% 38 D 0.89 3.0% 1.40,1.60,1.8 46 D 0.89 3.0% 5 39 D 0.89-0.5% 0,2.00,2.20 47 7.5 D 0.89-0.5% 43 D 0.89 0.5% 36 D 0.89 1.0% 44 D 0.89 1.0% 37 D 0.89 2.0% 45 D 0.89 2.0% 40 D 0.89-1.0% 48 D 0.89-1.0% 41 D 0.89-2.0% 49 D 0.89-2.0% 42 D 0.89-3.0% 50 D 0.89-3.0% Longitudinal ventilation velocity (m/s) 1.90,2.20,2.5 0,2.65,2.80 1.90,2.20,2.5 0,2.65,2.80 1.90,2.20,2.5 0,2.65,2.80 2.2 Meshes During the FDS simulations, the assumed length of the tunnels was 150 m in all the simulation cases. In order to optimize the meshes efficiency in the FDS simulations, the whole tunnel domain was divided into three continuous sub-domains. The domain close to the inlet is defined as Right Domain, the domain close to the outlet is defined as Left Domain, and the domain with fire source is defined as Middle Domain. The lengths for the three domains were 30m, 30m and 90m respectively. Because the variation of the parameters near the fire source is strong, the meshes in the Middle Domain are well refined. The meshes in the other two domains are less refined [20].

The FDS user s guide suggests that a non-dimensional expression D /δx can be used to measure how well the fire induce flow field could be resolved. The quantity D /δx can be thought of as the number of computational cells spanning the characteristic diameter of the fire, and the value of D /δx is ranged from 4 to 16 [21]. The mesh sizes for all simulation cases in this paper have been determined by this rule. D = ( 2/5 ρ a C p T a g 1/2) In addition, the meshes on the interface of the three domains were also conformed to the requirement in FDS user s guide. Fig. 2 (a) and Fig. 2 (b) shows the detail information of meshes in simulation cases C and D. In this study, X, Y and Z represented the lateral, longitudinal and vertical directions respectively. The (14) numbers and sizes of the meshes in all simulations are shown in Table 2. (a) (b) Fig. 2 The computational meshes for case C (a) and case D (b)

Table 2 The detail information of the meshes Tunnel Domain Number of meshes Mesh size (m) X Y Z X Y Z A B C D E F G H I L 150 15 24 0.30 0.32 0.30 M 400 30 48 0.15 0.16 0.15 R 150 15 24 0.30 0.32 0.30 L 150 15 20 0.30 0.32 0.32 M 400 30 40 0.15 0.16 0.16 R 150 15 20 0.30 0.32 0.32 L 20 100 20 0.30 0.30 0.30 M 40 600 40 0.15 0.15 0.15 R 20 100 20 0.30 0.30 0.30 L 150 15 18 0.30 0.32 0.30 M 400 30 36 0.15 0.16 0.15 R 150 15 18 0.30 0.32 0.30 L 150 15 16 0.30 0.32 0.30 M 400 30 32 0.15 0.16 0.15 R 150 15 16 0.30 0.32 0.30 L 150 15 15 0.30 0.32 0.28 M 400 30 30 0.15 0.16 0.14 R 150 15 15 0.30 0.32 0.28 L 150 24 18 0.30 0.29 0.30 M 400 48 36 0.15 0.15 0.15 R 150 24 18 0.30 0.29 0.30 L 100 50 30 0.45 0.40 0.40 M 300 100 60 0.20 0.20 0.20 R 100 50 30 0.45 0.40 0.40 L 100 50 30 0.45 0.40 0.36 M 300 100 60 0.20 0.20 0.18 R 100 50 30 0.45 0.40 0.36 2.3 Boundary conditions The material of the tunnel surface including walls, ceilings and floors were assumed to be concrete. Each tunnel had two opening portals. One of the opening portals was set as "SUPPLY" in FDS simulation case, and the longitudinal ventilation velocity was imposed at the opening portal. Another opening portal was set as "OPEN". The longitudinal ventilation velocity in all simulation cases are shown in Table 2. The fire source in the FDS software was set as "BURNER". According to the study of the heat release rate in the metro tunnel fire, the maximum heat release rate of the metro tunnel fire was 5MW. With the development of new technologies, metro tunnels are now usually constructed of non-combustible materials

and fire resistant materials, hence the heat release rate will be further reduced. In order to consider the risk of metro tunnel fire, 5MW and 7.5MW were adopted as the typical fire heat release rate in this study. The ambient temperature inside and outside was 20 0 C, the pressure was 101325.0 Pa, and the smoke concentration was 0 at the initial time. The simulation time was 900s. 3 Results and discussion 3.1 The backlayering length of the horizontal tunnels Previous research [7] has shown that the dimensionless backlayering length is: L = f ( H 3) (15) ρ a C p T a g 1/2 H 5/2, = (gh ) 1/2. So the backlayering length from numerical simulations have been processed as the relationship between two dimensionless parameters, L H the results of the tunnel with ζ < 1 are shown in Fig. 3(b). and 3. The results of the tunnel with ζ 1 are shown in Fig. 3(a), and 16 14 12 y = 6.41 ln(x) - 3.58 R²= 0.90 L H 10 8 6 4 Simulation results with ζ 1 2 Fitted curve 0 0.0 3.0 6.0 9.0 12.0 / 3 Fig. 3(a) Backlayering length vs. HRR and longitudinal velocity (ζ 1)

16 14 12 y = 8.32 ln(x) - 5.81 R²= 0.96 10 L H 8 6 4 Simulation results with ζ<1 2 Fitted curve 0 0.0 3.0 6.0 9.0 12.0 / 3 Fig. 3(b) Backlayering length vs. HRR and longitudinal velocity (ζ < 1) According to Fig. 3, fitted curves conform to the natural logarithmic relationship with R 2 = 0.90 when the sectional coefficient ζ 1, and R 2 = 0.96 when the sectional coefficient ζ < 1. The prediction model for the dimensionless backlayering length can be described as follows: L = {6.41ln ( 3) 3.58 ζ 1 H 8.32ln ( 3) 5.80 ζ < 1 ρ a C p T a g 1/2 H 5/2, = (gh ) 1/2. (16) 3.2 The critical velocity of the horizontal tunnels According to the definition of the critical velocity, it is the minimum longitudinal ventilation velocity that prevents the reverse flow of smoke from the fire to the upstream direction in the tunnel. This means that when the backlayering length is equal to 0, the corresponding longitudinal velocity is exactly equal to the critical velocity. Then the prediction model for the dimensionless critical velocity can be described as follows: = { 0.83 1/3 0.79 1/3 ζ 1 ζ < 1 ρ a C p T a g 1/2 H 5/2, = (gh ) 1/2 (17) 3.3 The effect of slope on the critical velocity In order to study the influence of the tunnel slope on the critical velocity, tunnel F with the sectional coefficient ζ 1 and tunnel D with ζ < 1 were chosen to be the research objects. ariations in critical velocity with the tangent of the slope angle are shown in Fig. 4. And Fig. 4 clearly demonstrates that the ratio, C,β / C,0, increase with the increase of the tunnel slope, β. Fitted curves of simulation results with ζ 1 and ζ < 1 were performed and the correlation between C,β / C,0 and β can be expressed as:

(C,β ) / (C,0) C,β / C,0 = { 1 + 1.008β ζ 1 (18) 1 + 2.355β ζ < 1 1.10 1.05 y = 1.008x + 0.999 R² = 0.938 1.00 FDS with ζ 1 0.95 FDS with ζ<1 y = 2.355x + 1.002 R² = 0.916 Fitted curve of ζ 1 Fitted curve of ζ<1 0.90-4% - 3% - 2% - 1% 0% 1% 2% 3% 4% β Fig. 4 Effect of the slope β of tunnel on C,β / C,0 with ζ 1 and ζ < 1 3.4 Comparison of the prediction for the critical velocity on different slopes In order to compare the prediction model for critical velocity obtained by this study with other models such as those proposed by Atkinson and Wu [12], Ko et al. [13], Yi et al. [14] and Chow et al. [15], Eq. (9) ~ (12) and Eq. (18) are plotted in Fig. 5. This indicates that the curve of Eq. (18) with ζ 1 is between that of the Eq. (9) and Eq. (12) respectively as proposed by Wu and Chow. This may be due to the fact that the sectional coefficient ζ of the model tunnels from Atkinson & Wu and Chow et al. are mostly greater than or equal to 1. So the curve of Eq. (18) with ζ 1 are close to the prediction models of Wu and Chow. Fig. 5 also shows that the curve of Eq. (18) with ζ < 1 is between that of the Eq. (10) proposed by Ko and the Eq. (11) proposed by Yi, and that the the curve of ζ < 1 is close to the prediction model proposed by Ko. This may be due to Ko et al. s and Yi et al. s model tunnel have a sectional coefficient ζ less than 1, respectively. Different experimental conditions or CFD boundary conditions might result in the discrepancies between these equations.

(C,β ) / (C,0) 1.15 1.10 1.05 1.00 ζ 1 0.95 ζ 1 Wu 0.90 Ko Yi Chow 0.85-4% - 3% - 2% - 1% 0% 1% 2% 3% 4% β Fig. 5 Comparison of the variation of C,β / C,0 with tunnel slope β by different models 4 Conclusions This study used the FDS simulation to research the backlayering length and the critical velocity of smoke in the metro tunnel with different sectional coefficients, longitudinal ventilation velocities, heat release rates and tunnel slopes. The following three main conclusions can be drawn: 1) The sectional coefficient ζ is introduced of an important new parameter. 2) New formulas for the backlayering length and critical velocity are proposed for the tunnels with different sectional coefficients and slopes. 3) Considering the maximum heat release rate in metro tunnel is 7.5 MW, the maximum dimensionless heat release rate of the fire source * involved in this paper is 0.1586 (the equivalent of HRR of the fire source is 7.5 MW). So the applicable range of the established prediction model is 0.01 0.16. Acknowledgements This work was supported by the Fundamental Research Funds for the Central Universities (106112015CDJXY210008), Chongqing Graduate Student Research Innovation Project Grant No. CYB14031 and the 111Project, No.B13041. References [1] Lu P, Cong BH, GX L, Study of fire smoke flow characteristics of horizontal tunnel using longitudinal ventilation, Engineering Science, 2004;6: 59-64.

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