Numerical simulation of airflow distribution in mine tunnels

Numerical simulation of airflow distribution in mine tunnels

International Journal of Mining Science and Technology xxx (2017) xxx–xxx Contents lists available at ScienceDirect International Journal of Mining ...

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International Journal of Mining Science and Technology xxx (2017) xxx–xxx

Contents lists available at ScienceDirect

International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst

Numerical simulation of airflow distribution in mine tunnels Ding Cui a,⇑, He Xueqiu b,c, Nie Baisheng c a

Department of Safety Engineering, China University of Labor Relations, Beijing 100048, China School of Civil and Environment Engineering, University of Science and Technology Beijing, Beijing 100083, China c School of Resource & Safety Engineering, China University of Mining & Technology, Beijing 100083, China b

a r t i c l e

i n f o

Article history: Received 1 November 2016 Received in revised form 18 December 2016 Accepted 23 January 2017 Available online xxxx Keywords: Mine tunnel Turbulence Airflow distribution Three-center arch Average velocity

a b s t r a c t Based on 3D modelling of typical tunnels in mines, the airflow distribution in a three-center arch-section tunnel is investigated and the influence of air velocity and cross section on airflow distribution in tunnels is studied. The average velocity points were analyzed quantitatively. The results show that the airflow pattern is similar for the three-center arch section under different ventilation velocities and cross sectional areas. The shape of the tunnel cross section and wall are the critical factors influencing the airflow pattern. The average velocity points are mainly close to the tunnel wall. Characteristic equations are developed to describe the average velocity distribution, and provide a theoretical basis for accurately measuring the average velocity in mine tunnels. Ó 2017 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction Mine ventilation is the process of continually inputting fresh air and outputting polluted air. The ventilation system is the basic system in mines. It is estimated that many mine disasters, including fire, coal gas and dust explosions, occur because of failures of the ventilation systems [1]. Nowadays, the airflow velocity and volume in tunnels are detected by on-line monitoring systems. However, because of the non-uniform distribution of airflow, the velocity measured by sensors is not the average velocity in section. As such, it is quite necessary to study the airflow pattern especially the average velocity distribution to calculate the airflow volume accurately. At present, the airflow distribution on the cross-section is macroscopically described with numerical simulation in several studies [2–5]. Only a few have studied the average velocity distribution in circular and rectangular tunnels quantitatively, by experimental and theoretical methods [6–11]. However, the relations between the airflow distribution, the average velocity and the cross-sectional shape and size have not been developed and described successfully. The characteristic equations of average velocity distribution close to the roof have been developed in three-center arch section tunnels and trapezoidal cross section tunnels [12,13]. But the other areas of the average velocity distribution on three-center arch section were not developed quantitatively. Thus, this study aims to present the ⇑ Corresponding author. E-mail address: [email protected] (C. Ding).

airflow distribution and develop the characteristic equations of the average velocity distribution in three-center arch section tunnels. 2. Numerical simulation 2.1. Physical model of the tunnel The numerical analysis method, which is proven to be accurate enough by experiments in the previous study, was adopted to simulate the airflow distribution in three-center arch section tunnels [12]. In this paper, the tunnel length is 8 m, the width is 260 mm, and the wall height is 113 mm. The small arch radius is 66 mm, and the large arch radius is 183 mm, as shown in Figs. 1 and 2. To analyze the airflow distribution in tunnels quantitatively, the model in Fig. 1 is amplified to 2, 3, 4 and 5 times respectively. The sizes of the five three-center arch section tunnels are shown in Table 1. The airflow in the tunnels was set to be turbulent, which is like actual ventilation conditions. The airflow distribution was then studied under different airflow velocities and different tunnel sizes.

2.2. Mathematical model and assumptions Per the fluid dynamics theory, the airflow in tunnels can be described by using the following equations:

http://dx.doi.org/10.1016/j.ijmst.2017.05.017 2095-2686/Ó 2017 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Ding C et al. Numerical simulation of airflow distribution in mine tunnels. Int J Min Sci Technol (2017), http://dx.doi.org/ 10.1016/j.ijmst.2017.05.017

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C. Ding et al. / International Journal of Mining Science and Technology xxx (2017) xxx–xxx

where Y M is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, and Y M ¼ 2qeM2t ; and lt the turbulent viscosity, and lt ¼ qC l ke . C 1e , C 2e and C l are constants. C 1e ¼ 1:44, C 2e ¼ 1:92, C l ¼ 0:09. rk and re are the turbulent Prandtl numbers for k and e, respectively. rk ¼ 1:0, and re ¼ 1:3. q is the density in kg/m3. u is the velocity, m/s. k is the turbulence kinetic energy, kJ/kg. e is the turbulence kinetic energy dissipation rate in m2/s3. l is the molecular (dynamic) viscosity, Pas. t is the time, s, and h is the static enthalpy, k. Ch is the transport coefficient. When developing the mathematical model, the following assumptions were made: the airflow is incompressible, the wall is adiabatic, there are neither workers nor vehicles in the tunnel, and the presence of smoke and dust is ignored. 2

Fig. 1. Three-center arch-section of the physical model.

2.3. Boundary conditions and parameters The tunnel inlet was set to be the velocity-inlet and the airflow velocity was set to 1, 2, 3, 4 and 5 m/s respectively. The tunnel outlet was set to be the pressure-outlet and the relative pressure was 0 Pa. The airflow distribution in the three-center arch section tunnels of five sizes were simulated under the different airflow velocities. 3. Analysis of the airflow pattern in tunnels

Fig. 2. Physical model of the tunnel.

The continuity equation

@ q @ðquj Þ ¼0 þ @xj @t

ð1Þ

The momentum equations (i direction)

  @ðqui Þ @ðuj ui Þ @ @uj þ ¼ u @t @xj @xj @xj

ð2Þ

The energy equation

  @ðqhÞ @ðquj hÞ @ @h þ ¼ Ch @t @xj @xj @xj

ð3Þ

The standard k  e model was used to calculate the turbulence and diffusion of the airflow. k equation

@ @ @ ðqkÞ þ ðqkui Þ ¼ @t @xi @xj

e equation @ @ @ ðqeÞ þ ðqeui Þ ¼ @t @xi @xj











lt @k þ Gk  qe  Y M rk @xj



lt @ e e e2 þ G1e Gk  C 2e q re @xj k k



ð4Þ



4. Analysis of average velocity distribution

ð5Þ

In the above-mentioned equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients,

Gk ¼ ql0I l0J

@ lj @xi

The airflow distribution on fully developed turbulence cross sections were studied. In this paper, the distance between the cross sections analyzed and the tunnel inlet was set according to fluid mechanics theory. The distance between the cross sections analyzed and the tunnel inlet was 5.6(Z1), 11.2(Z2), 16.8(Z3), 22.4(Z4), 28(Z5) respectively. The velocity profiles on the above five cross sections (Z1, Z2, Z3, Z4, Z5) were analyzed as shown in Fig. 3. It can be concluded from Fig. 3 that the airflow distribution shows a circular distribution which is like the shape of threecenter arch section under different ventilation velocities and cross section sizes. The shape of the cross section was the critical factor influencing the airflow pattern. The airflow velocity reached its maximum value in the center of the tunnel and decreased from the center to the tunnel wall. The average velocity points were mainly close to the tunnel wall under different airflow velocities and the airflow velocity which was smaller than the average velocity would decrease more quickly when it was closer to the tunnel wall. According to the above analysis, the tunnel wall is also a critical factor influencing the airflow distribution.

ð6Þ

The average velocity points are quite critical to achieve an accurate measurement and monitoring of ventilation volumes in tunnels. According to Ding, the distribution of the average velocity points in any three-center arch section tunnel shows as an annular ring and the ventilation velocity has little influence on the above distribution feature[12]. In order to further analyze the

Table 1 Dimensions of three-center arch tunnels. Tunnel number

1 2 3 4 5

Tunnel parameter Large arch radius (mm)

Small arch radius (mm)

Width (mm)

Wall height (mm)

Length (m)

183 366 549 732 915

66 132 198 264 330

260 520 780 1040 1300

113 226 339 452 565

8 16 24 32 40

Please cite this article in press as: Ding C et al. Numerical simulation of airflow distribution in mine tunnels. Int J Min Sci Technol (2017), http://dx.doi.org/ 10.1016/j.ijmst.2017.05.017

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Fig. 3. Velocity profiles on fully developed turbulence sections in five tunnels.

distribution of the average velocity points and develop its characteristic equations, the distribution curve has been separated into six parts as shown in Fig. 4. According to reference, the characteristic equation of the first part can be described by Eq. (7). And in this paper, the characteristic equations of the other five parts have been developed [12].

 3:2819r 2 x 1

d 2

where r 1 = radius of the top circular arc, m; and d = width of the tunnel, m. As shown in Fig. 3, the curve is symmetrical, so the feature of the fourth, fifth and sixth parts will be analyzed quantitatively. (1) The fourth part

2 þ 8:408r 11:84 ðy  0:6142r1 þ 0:0138Þ2 ¼ 1 ð7Þ

Fig. 4. Average distribution curve on three-center arch cross-section.

Based on analysis of relationships between the length of the fourth part, the width of the tunnel and the distance from tunnel floor to part 4, it has been found that the length of the fourth part and the distance from the tunnel floor to part 4 had perfect linear relations with the width of the tunnel respectively, as shown in Figs. 5 and 6.

Fig. 5. Relationship between the distance from the tunnel floor to part 4 and the tunnel width.

Please cite this article in press as: Ding C et al. Numerical simulation of airflow distribution in mine tunnels. Int J Min Sci Technol (2017), http://dx.doi.org/ 10.1016/j.ijmst.2017.05.017

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C. Ding et al. / International Journal of Mining Science and Technology xxx (2017) xxx–xxx

Fig. 8. Relationship between the distance from part6 to the left edge and the height of the wall.

Fig. 6. Relationship between the length of part 4 and the tunnel width.

Based on the above analysis, the characteristic equations of the fourth part can be described as Eqs. (8) and (9).

d1 ¼ 0:085d  0:0034

ð8Þ

d2 ¼ 0:5324d  0:0728

ð9Þ

where d = width of the tunnel, m; d1 = distance between the fourth part curve and the tunnel floor, m; and d2 = length of the fourth part curve, m. (2) The fifth part

Fig. 9. Relationship between the length of part6 and the height of tunnel wall.

Numerical fitting methods have been used to develop the characteristic equations of the fifth part as shown in Fig. 7. By combining the above five equations and the width of different tunnels, the five equations can be normalized into one equation, as Eq. (10). 1:965 1

y ¼ 0:0236d

ð10Þ

x

where d = width of the tunnel, m; x = x-coordinate, m, and x 2 ½0:2219h  0:0014; 0:2338d þ 0:0364; and y = y-coordinate, m. (3) The sixth part The feature of the sixth part has been studied by using the above method. The length of the curve and the distance between

Fig. 7. Part 5 curve fitting diagrams for three-center arch-sections in five tunnels.

Table 2 Characteristic equations of three-center arch section tunnel. Part number

Characteristic equation

1

3:2819r 2 1

2 3 4 5 6

 d 2 2

Range of parameter

8:408r1:84 ðy 1

x þ x ¼ d  0:2219h þ 0:0014 1:965

1

ðd  xÞ f ðxÞ ¼ 0:0236d f ðxÞ ¼ 0:085d  0:0034 1:965

f ðxÞ ¼ 0:0236d x1 x ¼ 0:2219h  0:0014

2

 0:6142r 1 þ 0:0138Þ ¼ 1

y P 0:9932h  0:0087 y 2 ½0:5053h þ 0:0096; 0:9932h  0:0087 x 2 ð0:7662d  0:0364; d  0:2219h þ 0:0014Þ x 2 ½0:2338d þ 0:0364; 0:7662d  0:0364 x 2 ð0:2219h  0:0014; 0:2338d þ 0:0364Þ y 2 ½0:5053h þ 0:0096; 0:9932h  0:0087

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the curve and the left wall have a perfect linear relation with the height of the tunnel wall, as shown in Figs. 8 and 9. Based on the above analysis, the characteristic equations of the sixth part can be represented by Eqs. (11) and (12).

h1 ¼ 0:2219h  0:0014

ð11Þ

h2 ¼ 0:4879h  0:0183

ð12Þ

where h = height of the tunnel wall, m; h1 = distance between the sixth part curve and the left wall, m; and h2 = length of the curve, m. Based on the above analysis, the characteristic equations of all the six parts have been developed as shown in Table 2. 5. Conclusions To understand the airflow distribution in tunnels and measure the average velocity and ventilation volume accurately, the airflow pattern and the average velocity points were investigated in different sizes of three-center arch section tunnels. The conclusions are as follows: (1) The airflow distribution shows a circular distribution which is similar to the shape of three-center arch section under different ventilation velocities and cross section sizes. The shape of the cross section was the critical factor influencing the airflow distribution. The airflow velocity reaches its maximum value in the center of the tunnel and decreases from the center to the tunnel wall. (2) The average velocity points were mainly close to the tunnel wall under different airflow velocities and the airflow velocity which was smaller than the average velocity would decrease more quickly when it was closer to the tunnel wall. The tunnel wall is also a critical factor influencing the airflow distribution. (3) Characteristic equations were developed to describe the average velocity distribution, which provides the theoretical basis for accurately measuring the average velocity and ventilation flow rates in mine tunnels.

5

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Please cite this article in press as: Ding C et al. Numerical simulation of airflow distribution in mine tunnels. Int J Min Sci Technol (2017), http://dx.doi.org/ 10.1016/j.ijmst.2017.05.017