New Technology for Preventing and Controlling Air Leakage in Goaf Based on the Theory of Wind Flow Boundary Layer

Abstract

Air leakage in the goaf is a fundamental reason for the high-temperature heat damage of the coal mining face and the gas concentration in the upper corner exceeding the limit. Combined with the boundary layer theory, this study analyzes the airflow state of the coal mining face. We propose installing a new air curtain system to prevent air leakage in the goaf. The length of the intake air curtain is determined by solving the theoretical equation. Numerical simulation is used to study different layout schemes of air curtains, and the spatial distribution law of different air volumes inside the working face is analyzed. The simulation results are compared with the field-measured data. The results show that when the length of the air curtain on the air inlet side is 20 m, the wind flow on the working face can be approximated as a state of attached jet, and a diffuse turbulent flow area will be formed outside the air curtain. Gas concentration will increase in this area. The air leakage prevention effect is best when the air curtains with a length of 20 m for the inlet air and 10 m for the return air are arranged at both ends of the working face. This air curtain system can reduce the temperature of the working face and the gas concentration in the upper corner and has certain guiding significance for the air leakage prevention work in the goaf.

1. Introduction

Air leakage in a goaf will cause the working face’s temperature to rise, the gas in the upper corner will exceed the limit, and the coal left in the goaf will spontaneously combust [1]. For this reason, researchers worldwide have conducted much research on the air leakage law of goaves. Su Hetao et al. [2]. established a similar goaf model according to the actual goaf size at a ratio of 1:50 and studied different ventilation methods and the air leakage law of the goaf under different inclination angles. Liming Yuan [3] analyzed and studied the air leakage flow field in the goaf of different ventilation systems and obtained the flow field distribution. Li Zongxiang et al. [4]. studied and analyzed the gas seepage process in the goaf and obtained some concepts, such as some equations of state of the gas flow in the porous medium in the goaf and the initial conditions and boundary conditions for the solution, which provided reliable information for computer numerical simulation. Good theoretical basis. According to the different types of mine air leakage, Yang Yong [5] selected different air leakage detection gases, set corresponding release points and sampling points, successfully analyzed some laws of mine air leakage, and could better take some air leakage prevention measures. Chu Fangjian et al. [6]. studied the existence of two air leakage sources in the mine and released two tracer gasses, CF2ClBr and SF6, respectively, at the two air leakage sources to obtain the air leakage channel and the range of air leakage. Qin Ruxiang [7] and others used SF6 tracer gas to release the gas at the lower corner of the working face and collect it at the return air alley. Zhang Xuebo [8] established a mining model, performed a numerical simulation of air leakage, and used tracer gas to conduct field measurements. The field measurement results were consistent with the numerical simulation results, thus obtaining the goaf of the U + L ventilation system, with some air leakage laws in the area. Yang Shengqiang [9] and others analyzed the influence of the actual mine gas extraction on the air leakage in the goaf by combining on-site measurement analysis and numerical simulation and found that due to the existence of high gas drainage in the goaf, the gas in the goaf was exacerbated. Risk of air leakage and spontaneous combustion of leftover coal. Yang Ming [10] simulated the U-shaped ventilation system and the Y-shaped ventilation system, respectively, through Fluent and obtained the air leakage of the two ventilation systems. The gas accumulation in the upper corners was reduced. Lei Yanjie [11] used software to simulate the air leakage flow field in the goaf and found that in the absence of wind resistance changes, the air leakage size is symmetrical concerning the working face, and the wind speed at the inlet and return air lanes is more significant than that in the middle, but the wind speed is almost zero. Li Yunhua [12] studied the spontaneous combustion of coal in the goaf of the U-shaped ventilation system and the air leakage flow field. In the three distinct areas of the critical air leakage affected areas behind the frame, the air leakage at the upper corner represents the most severe risk of spontaneous combustion. Liu Shichun, Du Haigang, Wang Dong, and Principal Tong [13,14,15,16] all analyzed the relationship between the air intake in the working face and the air leakage in the goaf and determined the proper airflow in the working face. Zhang Ruiqing [17] found the influence of the air leakage in the goaf. Many factors increase with the increase of several variables, such as the high-drainage roadway’s gas extraction volume and the working face’s wind resistance.

Based on the theory of air leakage in goaf, researchers have made many achievements in the prevention and control of air leakage in goaf. Hao Xiaobo [18] adopted the method of auxiliary transportation along the trough, masonry, and sealing and constructed a positive pressure nitrogen injection chamber to reduce the working face effectively. Yang Jun [19] obtained the air leakage characteristic law of the goaf by monitoring the air leakage of the working face of the 110 construction method and preventing air leakage by “reducing the wind pressure and blocking the passage”. Chu Tingxiang [20], based on the analysis of the coal rock fractures in the goaf, put forward technology for increasing the resistance in the goaf to control the air leakage through the large coal pile experiment. Liu Yingxue [21] proposed technical measures to reduce wind and pressure and build air leakage walls based on air leakage distribution in the goaf. Gao Jianliang et al. [22] studied the influence of the wind curtain length on the “three zones” distribution of gas and spontaneous combustion in the goaf. Cui Chuanfa [23], Wang Xinjian [24], and others compared the influence of different lengths of air curtains on the working face. The above researchers analyzed the air leakage theory in goaf and put forward different methods to prevent air leakage in goaf.

In the existing research on the prevention and control technology of air leakage in the goaf, there is little discussion on the influence of the pressure difference at both ends of the working face on the air leakage. The air leakage in the goaf is essentially due to the pressure difference between the two ends of the working face, leading to the flow exchange between the ventilation airflow and the internal flow field of the goaf. Due to the ventilation requirements of the coal mining face, the pressure difference at both ends of the working face cannot be avoided, but the object of the pressure difference can be adjusted. Based on the air leakage mechanism of the goaf, this paper proposes to install a new type of air curtain system. This system makes the action object of the pressure difference at both ends of the working face transfer from the goaf to the coal mining face, thereby reducing air leakage in the goaf. In this study, the airflow state of the working face on the inlet side is analyzed through the boundary layer theory, and the influence of the new air curtain system on the flow field inside the working face and the goaf are analyzed. As a result, the theoretical support is provided for reducing the air leakage in the goaf, alleviating the high-temperature heat damage of the working face and the gas concentration in the upper corner.

2. Mathematical Physical Model

2.1. Geometric Model of Coal Mining Face

According to the mining situation of the 12,302 working face, a 1:1 scale physical model is established by using Solid works software, which consists of five parts: the goaf caving zone, the fissure zone, the working face, the wind curtain, and the shearer. The length of the goaf is 300 m, the length of the interface with the working face is 200 m, and the mining height is 4 m. According to the settlement of the overlying strata on the working face after mining, the caving rock’s fragmentation coefficient and compactness, the caving zone’s height, and the mining height are determined by thickness ratio. The two roadways of the working face are set as rectangular sections, with a size of 20 m × 4 m × 4 m (length × width × height), and the model built accordingly is shown in Figure 1.

2.2. Theoretical Equation of Air Leakage in Goaf

2.2.1. Determination of Goaf Void Ratio

A void ratio $n$ is a dimensionless number, and its value ranges from 0 to 1. The definition equation [25] is as follows:

$$n=(1-\frac{M}{d_0}\cdot \frac{d}{M})\times 100\%$$

(1)

where $n$ is the porosity, %; $M$ is the mass of the porous medium, kg; $d_0$ is the true density, kg/m³; $d$ is the apparent density, kg/m³.

2.2.2. Determination of Air Leakage in Goaf

The differential equation of wind flow in the goaf [26] is:

$$\frac{{\partial }^{2}H}{\partial x^2}+\frac{{\partial }^{2}H}{\partial z^2}=0,0<x<a,0<z<b$$

(2)

where $H$ is the total wind pressure of the underground air, pa; $a$ is the entire length of the working face, m; $b$ is the actual depth of the goaf, m.

Integrating the air leakage speed, the air leakage [27] $Q_g$ in the goaf is:

$$Q_g={\displaystyle {\int }_0^c{\displaystyle {\int }_0^{\frac{a}{2}}{V}_z}}{|}_{z=0}dxdy$$

(3)

Substituting Equation (2) into Equation (3), the integral [28] is solved as follows:

$$Q_g={\displaystyle \sum _{n=1}^{\infty }\frac{2k\left(P_o-P_{in}\right)}{n^2{\pi }^2}\cos \left(n\pi -1\right)\frac{sh\frac{2n\pi b}{a}}{ch\frac{2n\pi b}{a}}\sin \frac{n\pi }{2},\left(n=1,2,\dots \right)}$$

(4)

where $Q_g$ is the air leakage of the goaf, m³/s; $c$ is the height of the goaf, m; $P_{in}$ and $P_o$ are the total wind pressure at the inlet and return air corners, respectively, $\mathrm{Pa}$; $V_z$ is the air leakage velocity in the goaf, $\mathrm{m}/\mathrm{s}$; the rest of the symbols are the same as above.

2.2.3. Determination of the Length of the Air Curtain

The ventilation system of the 12,302 working face is a U-shaped retreat. Under the influence of the inclined wind curtain of the working face, the intake air flow can be approximately regarded as the discussion of the wind flow turning in the right-angle roadway [29]. The air flow state is shown in Figure 2.

It can be seen from Figure 2a that the flow process can be divided into two areas from the flow shrinkage section A-A′ to the uniform velocity C-C′ section: from the axis of the roadway to the inner side wall after the corner, namely A′B The ′O′O area is a turbulent jet area. Due to the sudden change of the wind flow direction, the wind flow itself has a violent impact, and a vortex will appear near the inner wall, also known as the vortex area. The second area is the ABCO″O′O area from the roadway axis to the rear outer wall of the corner, which is called the pipe flow boundary layer area [30].

• Eddy current region segment

At the end section B-B′ of the vortex area (Figure 2a), the wind speed of the wind flow is not uniform, the wind speed of the outer wall of the roadway is higher, and the wind speed of the inner wall is lower. That is, the B-B′ section is the end of the vortex area and the non-wind speed stable area.

According to the research data of Gaby Launay [31], the length $L$ of the vortex area is 5.2 times the maximum width $b$ of the vortex area at the minimum shrinkage section, and according to the different shrinkage degrees of the flow section after the wind turns, the width $b$ of the maximum vortex area is not greater than 0.6 times the width $D$ of the working face, from which the length of the vortex region can be obtained:

$$\begin{array}{l}L=5.2b\\ b\le 0.6D\end{array}\}\Rightarrow L\le 3.12D$$

(5)

where $L$ is the length of the eddy current region, m; $D$ is the width of the working face, m; $b$ is the width of the maximum eddy current region, m.

• Wind speed stabilization section

When the thickness $\delta$ of the boundary layer is equal to the radius $r_0$ of the roadway, i.e., the boundary layer is connected to each other and occupies the entire section of the roadway, it becomes a fully developed pipe flow state, and the subsequent fluid velocity distribution curve will remain in a stable state. According to the boundary layer theory [32], its momentum equation is:

$$\frac{d}{dX}{\displaystyle {\int }_0^{\delta }{V}_x^3}dy-V_0\frac{d}{dX}{\displaystyle {\int }_0^{\delta }{V}_x}dy=-\frac{{\tau }_0}{\rho }$$

(6)

where $V_x$ is the wind speed at any position of the roadway section, m/s; $V_0$ is the maximum wind speed at the center of the roadway, m/s; $\delta$ is the thickness of the boundary layer, m; ${\tau }_0$ is the shear stress of the roadway wall to the wind flow, N/m²; $\rho$ is the pressure acting on AB (Figure 2a).

In the roadway with high (Reynolds number) and frictional resistance, the following equations need to be used:

• The wind speed distribution equation:

  $$V_x=V\left[1-20.5\sqrt{\alpha }+31\sqrt{\alpha }\sqrt{1-{\left(\frac{\eta }{{\eta }_0}\right)}^2}\right]$$

  (7)
• The maximum wind speed $V_0$ of the axis and the average wind speed $V$ of the section:

  $$V_0=\left(1+10.5\sqrt{\alpha }\right)V$$

  (8)
• When $R\mathrm{e}$ is high, the shear stress ${\tau }_0$ of the roadway is:

  $${\tau }_0=\alpha V^2$$

  (9)

${\eta }_0$ in the pipe flow corresponds to $\delta$ in the boundary layer. In the stable stage of wind flow, there is $\delta =\frac{D}{2}$, which is substituted into the above equation and integrated, and after sorting out:

$$\frac{X_0}{D}=\frac{0.147}{\sqrt{\alpha }}+5$$

(10)

where $\eta$ is the distance from a point to the axis, m; ${\eta }_0$ is the distance between the side wall and the axis, m; $D$ is the width of the working face, m; $X_0$ is the length of the stable section of wind speed distribution after turning, m; $\alpha$ is the friction resistance coefficient of the well roadway, $\mathrm{N}\cdot {\mathrm{s}}^2/{\mathrm{m}}^4$.

• Appropriate length of air curtain

It can be seen from Figure 2b that after crossing the middle of the vortex area, the wind flow no longer blows in the direction of the goaf, that is, the wind pressure on the goaf is greatly reduced here [33]. For practical reasons, this can be taken as the optimal length $h_1$ of the air curtain. $h_1$ is expressed as the sum of the median value of the length of the vortex area and the equivalent diameter of the air inlet tunnel, and is obtained from the width $D=10 \mathrm{m}$ of the working face:

$$\begin{array}{l}\begin{array}{l}L=5.2b\\ b\le 0.6D\end{array}\}\Rightarrow L\le 3.12D\\ \\ h_1=3.12D\times 1/2+x\end{array}\}\Rightarrow h_1\approx 20 \mathrm{m}$$

(11)

In the equation, $L$ is the length of the eddy current region, m; $D$ is the width of the working face, m; $b$ is the width of the maximum eddy current region, m; $x$ is the equivalent diameter of the air inlet roadway, m.

If the length of the wind flow stable section is taken as the length of the air curtain, and the 12,302 working face adopts the support and shielding hydraulic support, it can be seen that the frictional resistance coefficient [34] of the working face is about 0.0216, so $h_2$ can be obtained in Equation (12):

$$\begin{array}{l}\frac{X_0}{D}=\frac{0.147}{\sqrt{\alpha }}+5\\ \\ h_2=X_0+x\end{array}\}\Rightarrow h_2\approx 60 \mathrm{m}$$

(12)

In the equation, $X_0$ is the length of the stable section of wind speed distribution after turning, m; $D$ is the width of the working face, m; $\alpha$ is the friction resistance coefficient of the well roadway, N·s²/m⁴; $x$ is the equivalent diameter of the air inlet roadway, m.

When the $h_2$ length is used, the total length of the working face is 200 m, and the length of the air curtain is as long as 60 m, which is difficult to ensure the tightness of the air curtain sealing, and at the same time increases the difficulty of operation and the possibility of damage to the workers. In the $h_1$ scheme, the length of the inclined air curtain is set to 20 m. Under the condition of sufficiently reducing the wind flow pressure, the length is reduced considering the actual situation of the site, which is more economical and applicable. At the $h_1$ length, the flow state of the air flow after passing through the air curtain can be approximated as an attached jet [35]. As shown in Figure 2c, the air leakage in the goaf is only generated under the action of the negative pressure of the return air tunnel and the diffusion of air flow.

2.3. Mesh Generation and Independence Check

2.3.1. Mesh Generation

Based on the goaf seepage theory, a goaf porosity custom function (User-defined functions (UDF)) was written and imported into the Fluent solver. Then, the model file Parasolid (*.x_t) was input into CFD-Mesh for mesh generation. The mesh quality and main parameters of the model are shown in Figure 3.

The physical model generates 1,974,663 mesh elements, with a maximum mesh quality of 0.957, a minimum mesh quality of 0.178, and an average mesh quality of 0.784, with no negative meshes. Among them, up to 98.4% of the total number of grids have a grid quality ≥ 0.5, indicating that the overall quality of the grid is good.

2.3.2. Mesh Independence Test

The quality of the mesh will affect the calculation accuracy and the calculation convergence. For areas with violent changes in physical quantities, local mesh refinement can improve the calculation accuracy of the area, but for non-sensitive areas, increasing the mesh density does not significantly improve the calculation accuracy but only increases the calculation time. Therefore, in meshing, it is necessary to increase the local mesh density purposefully and, at the same time, check the mesh independence. The Multizone meshing method provides high-quality mesh generation, with most volume meshes being hexahedral meshes. For non-smooth models, Multizone allows the generation of a small number of the pyramid and tetrahedral meshes by capturing geometric features. In order to verify the independence of the grid, using different grid division methods and element sizes, generate 2.14 × 106 and 1.57 × 106 element numbers. Figure 4 compares element amounts of 2.14 × 106 (Multizone) and 1.57 × 106 (Automatic). In the coal mining face, different sizes and types of grids are generated between the wind curtain and the goaf caving zone.

Figure 5 shows the temperature versus gas concentration profiles along the working face at x = 28 m, Z = 1.7 m under three different meshing conditions. It can be found that the element amount of 1.97 × 106 has a result deviation of about 1.1% compared with the element amount of 2.14 × 106, while the mesh size of 1.57 × 106 deviates by as much as 14% compared to the finest mesh. Therefore, we can conclude that using a grid of 1.97 × 106 elements for numerical simulation can ensure the accuracy of the simulation results.

2.4. Boundary Conditions and Model Verification

Since gas mainly accumulates in the caving zone and fissure zone in the goaf [36,37], it is assumed that 90% of the gas gushing comes from the caving zone and 10% comes from the fissure zone. Therefore, the primary solution condition parameters are shown in

Table 1. Boundary condition parameter settings.

Project	Name	Type	Parameter Settings
Model	Energy equation	On	/
	Turbulence equation	k-epsilon	Standard wall fn
	Component	Component delivery	Methane-air-2step
	Entry boundary	Inlet	36.81 m3/s; 298 k
	Export border	Pressure—outlet	/
Area Set up	Fissure zone	Fluid	Udf porosity; 305 k; gas source term
	Caving belt
	Coal mining face		Air
Solve Parameter	Pressure velocity coupling	Simple	/

.

Since the initial boundary conditions of the wall will affect the results, we set the length of the working face inclination monitoring line to 0–199 m. Every 20 m along the line is set as a measuring point, 11 measuring points.

A temperature sensor is placed at each measuring point along the line and connected by a waveform storage recorder Graphtec GL800. A bundle tube is suspended from the upper part of the measuring point, and gas samples are taken once every hour. Furthermore, three bags of gas samples are taken each time, and the gas volume fraction is analyzed by gas chromatography. Then, the gas concentration in the air is obtained. The average value of the measurement results of each measurement point was used as the actual measurement result (Figure 6a).

Figure 6b shows, by drawing the Fluent standard field function (Velocity Magnitude) of the working surface, the change of the wind flow velocity under the condition of the wind curtain is represented. The site was measured by Kestrel 5500 anemometer and CFJ5 mine low-speed anemometer.

It can be seen from Figure 6a that the simulation results are in good agreement with the measured average values, and the degree of dispersion is 0.1–0.6%, which is within the acceptable range. Therefore, the turbulence model, porosity parameter, and solution method are considered reliable, and the nonlinear seepage and goaf porosity models established by numerical simulation are correct. Hence, these can be used for subsequent simulation studies.

Figure 6b shows that due to the turning state of the wind flow, the wind speed of the working face reaches its peak value in the first 20 m, and the wind speed of this section has apparent differences, which is in line with the speed characteristics of the turbulent jet region. After passing through the eddy current area, the boundary layer gradually occupies the section to form a pipe flow state, and the wind speed gradually becomes stable. After 60 m, the wind speed distribution curve remains stable. The visible field function wind speed curve echoes the above mathematical model. Therefore, the solution method of this theoretical equation is considered feasible.

3. Simulation Results and Discussion

3.1. Spatial Distribution Law of Different Air Volumes inside the Working Face

According to the wind speed requirements of the working face, the wind speed is in the range of 0.25–4 m/s, and the air supply volume of the working face is set to 15.61 m³/s 36.81 m³/s, 51.67 m³/s, 63.14 m³/s, respectively.

In order to study the influence of different air supply volumes of working face on air leakage in goaf, the inclination air volume and air leakage volume of working face under different air supply volumes were analyzed and compared with the measured values. The area division method [22] is adopted along the working face, and every 10 m interval along the line is regarded as a measurement area. A positive value means that the working face has air leakage in the goaf, and the air volume of the working face is reduced, and a negative value means that the wind flows from the goaf to the working face. The total air volume and leakage air volume of the working face are shown in Figure 7.

It can be seen from Figure 7 that the difference between the calculated value and the measured value is within an acceptable range. In the figure, Q_L is the total air leakage at the working face. With the increase of air supply volume, the proportion of total air leakage Q_L in the total air volume also increases, reaching the maximum value in the middle of the working face. The total air volume in the middle and rear of the working face gradually recovered, and the Q_L also decreased. Due to the gas and other gases released by the coal and rock layers in the goaf and the increase in gas temperature, the air volume of the return airway is more significant than that of the inlet airway. The larger the air supply volume of the working face, the more extensive the leakage range of the working face, and the greater the air leakage in the same section, and the air leakage is most evident in the range of 0–20 m.

The simulated ventilation rates are the variation law of working face temperature and gas concentration under the conditions of Q₁ (15.61 m³/s), Q₂ (36.81 m³/s), Q₃ (51.67 m³/s), and Q₄ (63.14 m³/s). Monitoring lines were set with different distances from the coal wall and the working face inclination (L = 2, L = 5, L = 8, L = 10, L is the distance from the coal wall). The working face’s temperature, gas concentration, and turbulent kinetic energy were analyzed (Figure 8).

C₀ is the initial wall temperature. It can be seen from Figure 8 that with the increase in air volume, the temperature of the working face decreases significantly, and the exchange between the airflow and the flow field in the goaf is more intense. Near the side of the coal wall, the heat source mainly comes from the mechanical heat release of the coal rock. Due to the existence of the vortex area, the temperature of the inlet air at L = 2 and L = 5 has a rise-fall-rise change (Figure 8c). It can be seen from Figure 8a that under the influence of porosity, the wind flow counteracts, forming a vortex and cooling the front end of the working face again. The gas concentration at this distance is almost unaffected by the goaf’s air leakage in the early stage, and the curve is relatively stable.

As the distance from the goaf decreases, the interaction between the wind flow and the goaf becomes more and more significant. In the L = 8 and 10 areas, the wind flow is most violently mixed with the goaf convection on the air inlet side, and the leakage air volume is also the largest. So, the working face temperature and gas concentration do not change significantly on the intake side. The dynamic pressure decreases when the wind flow passes through the eddy current area. As a result, the air leakage becomes smaller, resulting in a significant temperature rise of the wind flow under the action of heat transfer in the goaf (Figure 8c). The gas concentration also increased significantly, and the difference between the temperature and gas concentration at different air volumes reached the maximum at L = 10 m.

Turbulent kinetic energy is 1/2 of the product of turbulent velocity fluctuation variance and fluid mass. In the region of L = 2 and 5, due to the existence of porosity, the wind flow is affected by the vortex region on the coal wall side (Figure 8d), and the turbulent kinetic energy presents a fluctuating state under the influence of Reynolds stress. With the increase of L, the turbulent kinetic energy exhibits an obvious hierarchy with different air supply volumes. Combined with the curve of turbulent kinetic energy and velocity in Figure 8d, the peak value of turbulent kinetic energy appears as the point where the velocity drops the fastest after the wind flow passes through the eddy region.

The discussion of air leakage in the goaf should be based on the actual situation, and the influence of other factors should be minimized. L = 8 m is the working area of the working face. It can be seen from the turbulent kinetic energy and velocity curves that this area is unaffected by the eddy current area, which has good discussion significance for the change of temperature and gas concentration.

3.2. Influence of Air Curtain System on Working Face Gas Temperature

It can be seen from the preceding that a suitable length of air inlet air curtain can effectively reduce the wind pressure of the wind flow on the goaf. However, there is still negative pressure in the return air roadway to the goaf (as shown in Figure 2c), resulting in air leakage. The working face forms a double-sided air curtain system by arranging wind curtains on the top row of the return air corners. It cuts off the air leakage passages at the upper corners, transforming the negative pressure on the goaf by the return airway into the working surface. The negative pressure on the working surface can further reduce air leakage. According to the on-site ventilation volume of 36.81 m³/s, the air curtains are divided into two layout types: one-sided (0 m, 4 m, 20 m, 60 m) and two-sided (20 + 4 m, 20 + 10 m, 20 + 20 m). According to the implementation effect of different air curtains, the cloud map of working face temperature and gas concentration is shown in Figure 9.

It can be seen that with the increase of the length of the unilateral air curtain, the width of the heat dissipation belt in the goaf decreases [11], and the position moves to the middle of the working face. As a result, the temperature in the first half of the working surface gradually decreases. At 60 m, the cooling effect is particularly significant, and the overall temperature of the working face drops significantly. In the double-sided air curtain arrangement, with the increase of the length of the return air curtain, the temperature of the upper corner is also significantly improved. It can be seen from Figure 9b that due to the action of the “O” ring [38] in the goaf, the wind flow bypasses the central compaction area and expands to both ends, resulting in the gas concentration distribution showing a forward convex shape in the middle. The wind diffused from the outside of the air curtain to the goaf makes the airflow in the nearby area turbulent, and this is called the diffused turbulent area.

The change in the total air volume of the working face and the effect of the air curtain at L = 8 m are shown in Figure 10.

When the air inlet air curtain is short, the diffused turbulent area outside the air curtain will cause the fresh air flow to exchange with the gas inside the goaf, resulting in a small peak in the gas concentration at the air inlet corner. This phenomenon occurs when the air curtain length is 4 m and 10 m, and the temperature also increases regionally. When the length increases to 20 m since the inlet airflow will not directly blow to the goaf, it will not cause the peak gas concentration on the inlet side, and the temperature is always lower than the original state. An ideal air leakage prevention effect is achieved.

It is not difficult to see from the curve that the longer the length of the air curtain, the lower the air leakage and the better the cooling effect. However, due to the limitation of cost, the practicability of the air curtain that is too long is low. While reducing a specific temperature, the double-sided wind curtain has a practical cooling effect on the corners of the working surface. With the increase in the length of the return air curtain, the temperature and gas concentration in the upper corner decreased successively, and the peak gas concentration in the upper corner was eliminated. There is little difference between the 10 m and 20 m air curtains on the return airside. Compared with the effect of the two-sided 20 + 10 m air curtain, the average temperature of the working face is reduced by 0.1℃, and the temperature of the upper corner is reduced by 0.9 ℃. The gas concentration in the upper corner decreased from 0.12% to 0.01%, a decrease of 91.7%. The air leakage of the working face is reduced by 32% compared with the original air leakage.

To sum up, it is a relatively economical and feasible solution to arrange a 20 + 10 m air curtain system in the coal mining face. This scheme can effectively reduce the air leakage in the goaf and reduce the working face’s temperature and the gas concentration in the upper corner.

4. Conclusions

The focus of this study is to analyze the state of the wind flow inside the coal mining face in conjunction with the theory of the attached face layer. In addition, the effect of different wind curtain layout options on the coal mining face is investigated. Our conclusions are summarised below.

(1)

The optimal length of the air curtain can be solved by the theoretical equation of the boundary layer. The stable length of the turning airflow velocity is negatively correlated with the friction resistance of the roadway side surface and positively correlated with the width of the working face. However, the optimal length of the air curtain is only positively correlated with the maximum width of the vortex region. Take the 12,302 coal mining face as an example. By comparing theoretical calculation, numerical simulation, and field test, it is determined that the optimal length of the air curtain on the inlet side of the 12,302 coal mining face is 20 m.

(2)

On the air inlet side of the working face, the existence of the porosity in the goaf forms a resistance to the intrusion of the wind flow, which causes the wind flow itself to have a violent impact. The coal wall is cooled for a second time, thereby forming a vortex. The dynamic pressure of the wind flow will decrease significantly after passing through the vortex region. There is a flowing exchange between the outer side of the coal working face and the inner flow field of the goaf, resulting in a significant increase in the temperature and gas concentration in this area.

(3)

The working face adopts a 20 + 10 m air curtain arrangement system, which can transfer the pressure difference at both ends of the working face from the goaf to the inside, reducing the air leakage in the goaf and enhancing the ventilation effect inside the working face. Compared with the original air leakage, the air leakage under this air curtain system is reduced by 32%, the average temperature of the working face is reduced by 0.1 °C, the temperature at the upper corner is reduced by 0.9 °C, and the gas concentration at the upper corner is reduced from 0.12% to 0.01%. As a result, the gas concentration dropped by 91.7%.

(4)

When the length of the air inlet air curtain is too short, a turbulent diffusion area will be generated outside the air curtain, resulting in local peaks of temperature and gas concentration, caused by the intrusion. The fresh airflow in this area mixes with the convection in the goaf flow field, which will lead to an increase in gas concentration and temperature in this area. As the length of the intake air curtain increases, the peak value will gradually decrease to disappear, indicating that the flow state of the airflow is gradually stabilized with the increase of the length of the air intake air curtain. Therefore, if the wind curtain is blindly installed, the length and installation method of the wind curtain will not be up to standard, which will hurt the temperature and gas concentration of the working surface. When the coal mining face adopts the 20 + 10 m air curtain arrangement system, it can effectively avoid the turbulent diffusion area and achieve an ideal effect in preventing and controlling the air leakage in the goaf.

Of course, the current research still has certain limitations and needs further development. The results of this study are based on the data of the 12,302 working faces of Jining No. 2 Mine. Different coal mining faces have different dimensional parameters, so it is necessary to analyze the research objects independently. In the future, theoretical equation solving and numerical simulation should be applied to different types of coal mining faces to provide more theoretical references for preventing and controlling air leakage in the goaf.