Investigation on flow field characteristics in an open-pit coal mine

In this paper, the atmospheric flow field characteristics in a deep open-pit mine are investigated numerically and theoretically. A theoretical model on the recirculation length based on the energy equation is used, and a total variation diminishing (TVD) difference scheme with second-order accuracy is used to solve the NS equations with a standard two-equation k-ε turbulence model. The effects of elevated inner dump on the flow field characteristics of the open-pit mine are analyzed detailedly with the same inflow parameters. The results show that a recirculation zone exists in the open-pit mine due to the reflux from the high-pressure zone to the low-pressure zone. As the height of the inner dump increases, the flow becomes more complicated, and the low-pressure zone and the recirculation zone become bigger. The elevated inner dump makes it difficult for the internal fluid to flow to the outside, which results in the increase of the dust concentration. At last, the influences of key parameters on flow filed are conducted by normalizing the depth of the lowest direct current flow on the windward slope. The sensitivity analysis is done by study each influencing factor. This paper offers an effective way to study the flow field characteristics in an open-pit coal mine, which is essential to the dust pollution control of open-pit mine.


Introduction
Spraying water is commonly used for dust suppression in open-pit mines (Peng et al. 2019). A more economical approach is to spray a mixture of a suitable dust suppressant and water (Wang et al. 2019). But some open-pit mines in environmentally vulnerable areas of Northwest China are extremely short of water (Zhou et al. 2016;Hu et al. 2014). In these areas, groundwater and annual rainfall are scarce. There are no rivers or lakes on the surface and local people live by collecting rainwater. The water for these mines needs to be transported from other places; spraying water is not suitable for these extremely water-short open-pit mines.
Inner dumps are useful for reducing transportation distance in flat coal seam mining (Tang and Cai 2018). In general, the total inner space is adequate; there can be insufficient space during special periods, for example, when the mining area turns or when the mining area crosses a coal seam anticline. Elevating the inner dump is a common countermeasure, as the method is economically advantageous because it does not reselect the outside dump, which means the transportation distance is shortened. But the dust concentration increases significantly with the elevating of the inner dump. Furthermore, the concentrations of NO, SO 2 , and some other elements also increase significantly (Sosa et al. 2013). Evidently, elevating the inner dump may change the surrounding topography of the mine and have a significant influence on the air flow in and around the mine. It may also affect the dissipation efficiency of dust and other pollutants in the mine (Tian et al. 2008). The accumulation and dispersion of dust, truck tail gas, blasting products, and so on are affected. This in turn worsens air quality in the mine which not only threatens the health of the workers in the mine, but also affects operational efficiency of the equipment (Vaupel et al. 2016).
Therefore, it is necessary to study the influence of elevating the inner dump on the atmospheric flow field in the pit.
Based on the influence mechanism, corresponding measures for dust reduction are presented (Silvester et al. 2009). As these dust reduction methods are based on the variation mechanism of the airflow field and do not require water sprinkling, they are suitable for use in open-pit mines in water deficient areas. There are three methods to investigate the atmospheric flow field in the open pit, theory, numerical simulations, and experiments. Due to the limitation of experimental conditions and development of the CFD (Computational fluid dynamics) Teng et al. 2014;Teng and Jiang 2012), most of the research focuses on numerical simulation (Tartakovsky et al. 2013;Pedro et al. 2021;Wang et al. 2021;Ma et al. 2020;Li et al. 2021;Zhang et al. 2018). Tang used Fluent to study the dust move in the pit and escape rate and time out of the pit (Tang and Cai 2018). Ma investigates the effect of spraying on coal dust diffusion in a coal mine based on a numerical simulation and experimental spraying results (Ma et al. 2020). There are relative few theoretical studies on the flow field of the open pit, including flow field characteristics, recirculation zone, dust transport, and concentration distribution.
This paper presents a detailed numerical analysis of the atmospheric flow field characteristics in a deep open-pit mine. Mathematical and physical models are presented in the "Mathematical and physical models" section. In the "Results and discussion" section, both the theoretical and numerical investigations on the flow field characteristics in the pit are shown. The effects of the height of inner dump on the pressure, velocity, and structures are discussed in detail. Finally, the essential points of this paper are summarized in the "Conclusion" section. For the far-field condition, the research scope is the space within 500 m above the mine. As is shown in Figure 1, the atmospheric flow field model is formatted by expanding 500 m; the mine and dump are taken as the benchmark. Figure 2 shows the sketch map of longitudinal section with elevated inner dump. α 1 and h 1 represent the angle and height of the lee side slope, α 2 is the angle of the windward slope, and h 2 is the height of the elevated inner dump. The open pit is an abrupt expansion compared to the inner dump, usually in the vertical direction of the slope. According to previous and our investigations, as the slope angle α 1 and the height of the inner dump h 2 are large sufficient, the flow is separated and the flow field characteristics in the up far-field region remain unchanged. This problem can be treated as one problem of the open channel flow. The recirculation length is defined as L and can be solved by the energy equation. For the far-field boundary condition, the flow in the open pit has almost no influence on the far flow field characteristics. For different selected height of the theoretical model, the flow condition upon the elevated inner dump is almost the same as the inflow condition; it has no significant influence on the analytical results.

Mathematical and physical models
The flow enters the control volume in left section of area A 1 = h 0 × d, with average velocity u 0 = 2 m/s and pressure p 0 , where d is the width of the inner dump in the y direction. The head in this inflow section is thus where β 0 is the Coriolis kinetic. The flow leaves the control volume through the right section of area A 2 = h r × d, with average velocity u 1 and pressure p 1 . The head in this section is thus H 1 = 1 1 2 1 u 2 1 + p 1 . Two terms traduce the head losses from the left section to the right section, considering two independent sources of dissipation: J r accounting for the singular head loss in the recirculation and J f accounting for the linear head loss due to bottom wall friction. which can be solved by the following: where S = λ(h 1 + h 2 )/(8d), it is related to the Darcy-Weisbach head loss coefficient λ and that the equivalence λ = 4c f . The energy equation expresses the head balance through the control volume; it is based on the Bernoulli's principle and the law of conservation of fluid mechanical energy.
The recirculation length L can be obtained by the following: where R h is the expansion ratio and defined as R h = (h r − h 1 − h 2 )/h r . T 1 is related to the head loss due to wall friction, T 2 is indeed related to the pressure variation, while T 3 is related to the kinetic energy variation, and T 4 is related to the Borda-Carnot-like head loss.
This paper solves the NS equations with a TVD difference scheme of second-order accuracy Teng et al. 2014;Teng and Jiang 2012); the turbulence model uses a standard two-equation turbulence model, including a turbulent kinetic energy equation and a diffusion equation, as follows: (1) where G k is the κ generating term due to the turbulent kinetic energy caused by the mean velocity gradient; G b is the κ generating term of the turbulent kinetic energy due to buoyancy; Y M is the contribution of pulsating expansion in compressible turbulence; C 1ε , C 2σ , C μ are empirical constants; σ k , σ ε are the Prandtl numbers corresponding to the turbulent kinetic energy κ and the dissipation rate ε; and S k , S ε are the source items defined by the user according to the calculation cases.
The computational mesh uses the orthogonalized uniform structured mesh, and the mesh quantity is 5 million. As the viscosity and turbulence are considered, the wall boundary grid is densified according to the y+ criterion. Mesh independence tests are performed to ensure that all the results produced are independent of the type of mesh chosen for numerical simulations. Two numerical objects are conducted, including the inner dump elevated and not elevated. By comparing the flow field characteristics under the same inflow conditions and the pit conditions, the effects of the elevated inner dump on the flow field in the pit are investigated.

Results and discussion
The flow field in the pit Figure 3 presents the numerical results of velocity contours on the symmetry plane at y =1000 m. The velocity components are predefined as u, v, and w directions, corresponding to the x, y, and z directions, respectively. As the inflow direction is x positive, the positive value of u indicates that the direction of the air flow has no change, and the negative value represents the reflux. It can be seen from Figure 3b that the negative regions exist at the bottom of the pit and the leeward slope, and As is shown in Figure 3a, the discontinuous eddies in the bottom of the mine have been extended and communicated into a large area of vortex. The generated mechanism of vortex is the pressure discrepancy inside and outside of vortex. As the air pass through an open-pit mine, the gas in the pit will flow in the same direction, and a low-pressure area will be formed in the mine. Under the action of the high-pressure airflow, the air will flow from the high-pressure zone to the low-pressure zone and a vortex will be formed. Figure 4 shows the pressure contours and streamlines on different cross sections along the y direction. The vortex structures along the spanwise distribution at the bottom of the pit can be seen from the stream lines. At y =700 m, the main vortex structure is on the lee side slope, the pressure on the windward slope, and the pit is obviously larger than the lee side slope, which causes a recirculation and forms a vortex. As the cross section moves from 700 to 1300 m along the y direction, the vortex structure shows an increasing trend and the high-pressure zone on the windward slope becomes small. The pressure in the vortex is obviously smaller than that in the nearby area. It can be seen that only a small part of the fluid in the pit exchanges with the external fluid, and the internal dust always moves in the depression, and only a small part is taken out. Figure 5 shows the contours of the velocity component w and the pressure on cross section in the incoming direction. The blue negative value area represents the air sinking to the bottom, and the red area represents air rising at the windward slope. An obvious recirculation area is presented in Figure 5b. A big positive current area appeared on the leeward side, representing rising air flow. On the windward side, the lower part of the slope becomes the downdraft, and the upper part becomes the updraft. When the downdraft flow reaches the pit bottom, it turns into a reflux flow. The returning air reaches the leeward side and becomes updraft. Then, the returning updraft air is mixed with the direct-current air flow and a big eddy occurs in the pit. The pressure inside the pit is lower than that outside, which makes it difficult for the internal fluid to flow to the outside and results in the increase of the dust concentration.

Effects of the inner dump heightening on flow field characteristics
In order to investigate the influence of inner dump heightening on flow field characteristics, four computational cases with height of inner dump at h 2 = 30 m, 60 m, 90 m, and 120 m are conducted. The energy loss in the flow field of open   Pressure contours and streamlines on the cross section at y =1000 m. c Pressure contours and streamlines on the cross section at y =1300 m pit consists of two parts: the loss in the recirculation J r and the loss due to the bottom wall friction J f . As the height of inner dump increases, the expansion ratio R h decreases, and the energy loss due to the recirculation J r and wall friction J f increases. The increased energy loss makes the flow field more complex, including the increasing recirculation length, complex pressure, velocity, and streamline distribution. The theoretical analysis is verified by numerical simulations. Figure 6 presents the velocity component u in the x direction with different heights of inner dump on cross section at y = 1000 m. The direction of the wind is from negative x-axis to positive x-axis, and the color represents the magnitude of the wind speed. As the height of inner dump increases, the area of negative u in the pit increases, and the dark red value of u beyond the pit gets bigger, which indicate the increasing of the recirculation zone. Figure 7 shows the pressure contours with different heights of inner dump. With the elevating of the inner dump, the high-pressure zone on the left of the inner dump gets bigger, the area of low-pressure zone in the pit increases, and the vortex develops. As the inner dump elevates, the depth of the lowest direct current flow on the windward slope of the pit decreases continuously, which indicates that the proportion of dust can be spread directly getting smaller and smaller. The increasing height of inner dump changes the flow field significantly compared with the no-elevated flow field. The low-speed zone is always higher than the ground and becomes larger and larger, indicating that the fluid at the bottom of the pit has mixed with the external fluid.
In order to understand the atmospheric flow field characteristics in the deep open-pit mine clearly, the three-dimensional streamlines and pressure contours on cross section at different heights of inner dump are shown in Figure 8. As the inner dump is elevated to 30 m, the low-pressure zone begins to get bigger and the reflux region is on the negative y-axis of the open-pit mine. With the dump elevated to 60 m, the high pressure disappears on the positive y-axis and the low-pressure fills the fit; the recirculation zone exists on both sides of the y-axis and is full of the whole open-pit mine. As the height of the inner dump is increased to 90 m and 120 m, the flow becomes more complicated; the recirculation zone becomes bigger and exists both inside and outside the openpit mine. With the elevating of the inner dump, the depth of the lowest direct current flow on the windward slope of the pit decreases continuously, which is not conducive to the diffusion of the dust. According to the above numerical results and previous researches, the flow field can be divided into the direct current areas and the circumfluence areas [11][12][13]. As is shown in Figure 9, DA is the lee side slope, AB is the bottom of the pit, and BC is the lee side slope. DE is the boundary line between these two areas, the upper part is the direct current area, and the lower part is the circumfluence area. DMQC is boundary between the disturbed and undisturbed flow field by the open-pit mine. The flow filed above line DC is the far-field condition, which is the same as the inflow condition. The flow filed below line DC is very complex. φ 1 is the angle between the horizontal plane and line DM and represents the disturbed flow field above the horizontal line; φ 2 and φ 3 are the angles for disturbed flow field in the open-pit mine, which represent the flow direction that consistent with the direction of incoming flow. Some of air flow to the right slope and go outside directly; the rest air flows back and forms the vortex region. M 2 is the central point of the whole recirculation zone.

Mathematical model and sensitivity analysis
In order to study the sensitive parameters, the line DE is assumed as a straight line by connecting directly to point D and point E. As position E is the depth of the lowest direct current flow on the windward slope of the mine, it does not affect the position of E by simplifying the curve DE into a straight line.
By simple deduction, the length of each section (Fig. 10) can be obtained as follows.
The depth of the lowest direct current flow on the windward slope with non-elevated inner dump is computed as follows:  The depth of the lowest direct current flow h r on the windward slope with elevated inner dump is computed as follows: The back distance at the pithead is computed as follows: (6) EP = CD · sin 2 sin sin 2 + (7) FO = CG · sin 2 sin sin 2 + The depth of the direct current area near the windward side decreases h d due to the elevating of the inner dump: The depth of the lowest direct current flow on the windward slope is normalized in this paper. Due to the elevation of the inner dump, the change of the depth of the lowest direct current flow on the windward slope can reflect the change of the direct current range in a mine, but it cannot reflect the ventilation in different mines. Therefore, the mine depth is used to normalize the index to make it a general index to describe the ventilation condition in any open-pit mine. This standardized index is named the coefficient of ventilation ϕ, and the formula is as follows: Obviously, the range of ventilation coefficient ϕ is [0,1]. When ϕ = 0, there is no direct current region of the corresponding mine. When ϕ = 1, the corresponding direct current area can reach the bottom of the pit. Other values are between the two cases. For example, ϕ = 0.5 indicates that the bottom of the direct current zone reaches half way down the windward side. The index can be used for ventilation comparison between different mines and is very intuitive.
The main influencing factors of h d include the direct current area descent angle β, the lee side angle α 1 , the windward edge angle α 2 , and inner dump elevation h 2 .
The effect of independent lifting of each factor on h d is shown in Table 1.
As the angle of the direct current zone β decreases, or the angle of the lee side α 1 increases, or the angle of the windward side α 2 increases or elevating and increasing of inner dump h 2 , it can lead to an increase in h d .
The increase of h d means that the direct current zone shrinks, which is not conducive to the discharge of dust and other pollutants in the pit. The direct current area, the direct current area ratio, and the depth of lowest direct current flow on the windward slope and the direct current zone reach three indicators, which reflect the dust dissipation conditions in the mine. The depth of lowest direct current flow on the windward slope can be used as an important index to describe whether the flow field in the open pit leads to dust dispersion.