Effect of a Double-Machine Parallel Air Curtain on Wind Flow in an Underground Roadway of a Coal Mine

Abstract

In order to study the effect of a double-machine parallel circulation air curtain in intercepting wind flow in a mine roadway, the air curtain jet angle and full fan pressure were analyzed. Taking a metal mine roadway as the engineering background, Fluent numerical simulation technology was used to establish an equi-proportional physical model of the original roadway, and a K45-6 axial flow fan was selected to numerically simulate the flow field inside the original roadway, which was analyzed from three aspects: isolation pressure difference, air leakage volume and wind choke rate. The results show that when the full pressure of the fan is fixed, with an increase in the jet angle of the air curtain, the separation pressure difference and the wind choke rate show a trend of first increasing and then decreasing, and the air leakage volume shows a trend of first decreasing and then increasing. With an increase in the air curtain jet angle, the air curtain convergence gradually forms a complete air curtain, but when the air curtain jet angle continues to increase, the air curtain cannot effectively block the wind flow due to the transverse pressure from the roadway. When the jet angle is too small or the full pressure of the fan is too large, the phenomenon of induced air flow will occur, and the two-machine parallel air curtain will direct the air downstream of the roadway to upstream and no longer intercept the roadway air flow. After comprehensive analysis, the effect of wind control is obvious to set up a double-parallel air curtain in the roadway, and the optimal combination of the roadway air curtain is 30° for the full pressure blade of the fan and 30° for the jet angle.

1. Introduction

Intelligent ventilation in mines refers to the operation of realizing on-demand air supply through intelligent control, continuously transporting fresh air to a mine stably and economically, providing personnel with air for breathing, diluting and discharging harmful gases and dust, improving mine climatic conditions, and having certain intelligent control of wind flow during disaster relief. Traditional wind flow control measures include manual or semi-manual regulations, which have difficulty meeting the requirements of intelligent ventilation in mines, and the regulation of wind flow cannot be realized in a roadway with special conditions, or the regulation cannot achieve the expected effect. Mining air curtains are a new type of wind flow control technology that can realize intelligent regulation of wind flow in a roadway with more complex conditions without affecting the transportation of equipment and personnel work in the roadway. During the transportation of materials, pedestrians and driving frequency are high and easily deform the roadway; thus, wind flow regulation is of great significance to the improvement of mine safety at the production management level. This is the advantage of air curtains, which cannot be replaced with dampers and other wind flow control technologies [1,2,3].

In the 1960s of the 20th Century, China began to introduce air curtain technology. Xu et al. [4,5] took the lead in deriving the effective pressure theory of air curtains and developed a mining air curtain that can replace the damper to block air leakage in the transportation roadway. However, most of the work carried out by our predecessors is limited to experimental research, and the design of air curtains mainly relies on empirical formulas, and the shunt flow field in air curtains is not clear, so designed air curtains inevitably have some unreasonable factors. Therefore, Liu et al. [6] applied numerical simulation technology to the study of mine air curtains, which is of great significance in studying the flow of air curtains and their internal fluid. Wang et al. [7,8] used multivariate methods combined with numerical simulations and found that air curtains with high Reynolds numbers had better effects. Zhao et al. [9,10] used Fluent simulation and showed that the air supply angle of a circulating air curtain should be 10~30°. Tao et al. [11,12,13] used FDS (Fire Dynamics Simulator) to analyze fire in a subway tunnel and obtained the influence of the air curtain jet angle and jet velocity on the temperature and flow field distribution in the subway tunnel.

In summary, domestic and foreign research mainly carries out theoretical research and technical applications for single-fan air curtains. However, it is difficult for a stand-alone air curtain to efficiently cut off and divert air flow, and it is not easy to realize wind flow control. Gupta et al. [14] discussed the blocking efficiency of a bilateral air curtain by experimentally changing the jet angle and exhaust air speed of the air curtain and found that the effect of controlling the roadway air flow with a dual-machine parallel connection was significantly better than that of the stand-alone air curtain, which could realize the adjustment of barrier, emission, and drag increase in the roadway air flow.

At present, there is a lack of research on the influencing factors of the working conditions of the double-machine parallel compound air curtain. In this study, the influence and law of the full pressure of the fan and the jet angle, outlet width, initial velocity of the jet and other factors of an air curtain in a roadway were studied using a numerical simulation method. In addition, the condition range of the fan full pressure and jet angle when the double-machine parallel double air curtain had the strongest wind flow isolation ability in the roadway were explored, so as to provide a reference for the best working conditions of the air curtain.

Part One of this paper provides a contextual backdrop concerning the application of air curtains within mine tunnels. The ensuing section, Part Two, elucidates the numerical simulation methodologies used for the development of a comprehensive physical replica of the initial tunnel. Part Three unveils the outcomes of our investigation into parameters encompassing isolation pressure differentials, air leakage, and drag rates. Part Four undertakes an in-depth analysis of these findings and engages in a comprehensive discourse regarding the efficacy of dual-machine parallel air curtains in mitigating wind flow within mine tunnels. Finally, Part Five encapsulates this study’s key discoveries and underscores their significance in concluding remarks.

2. Numerical Simulation Model Establishment

China’s metal mines mostly use shafts and ramps for joint development [15]. Under the combined action of multiple factors such as long-term ground pressure and frequent driving, dampers are seriously damaged, and their management and maintenance are extremely inconvenient, so it is necessary to set up an air curtain to regulate the air flow [16]. In this paper, the simulation parameters of the studied roadway are set to 4.2 m wide, 3.5 m high, and a 14.7 m² cross-sectional area.

2.1. Roadway Model Establishment

By analyzing the actual situation of the air curtain, roadway, and chamber, the roadway and air curtain were simplified, and the basic parameters and morphological characteristics that had an impact on the simulation research results were retained [17].

Using the pre-processing software GAMIDT Gambit 2.4 for modeling, a 3D physical model of the roadway with a length of 60.0 m, a width of 4.2 m, and a height of 3.5 m was established under the Cartesian coordinate system. Among them, the chamber is located in the middle of the roadway, respectively placed on both sides of the roadway, each side of the chamber is 4.0 m long, 2.0 m wide, and 3.5 m high. The air curtain fan is placed in the chamber on both sides of the roadway, the air outlet and the roadway wind flow are arranged at an angle of α, and the jet angle α is 5~60°, as shown in Figure 1. The diameter of the single fan is 1.0 m and the height is 1.7 m; the overall length of the air curtain is 1.6 m; the width of the bar gap is 0.3 m and the length is 1.7 m; the width of the air outlet is 0.08~0.40 m; and the longitudinal arrangement of the double fan is shown in Figure 2. Figure 3 is meshing of the air curtain model.

Using an independent mesh test of the simulation, testing time–pressure curves at 1,500,000, 2,500,000, and 3,500,000 meshes, it was concluded that the number of meshes did not distinctly change the results of the experimental analysis, as shown in Figure 4.

2.2. Mathematical Models

In order to study the interaction between air curtain jet and roadway wind flow in the roadway based on the theory of wind flow movement in the mine, the characteristics of the air curtain intercepted wind flow field were obtained using a numerical simulation analysis [18,19].

The Navier–Stokes equation for a turbulent motion incompressible fluid is

$$\frac{\partial \mathrm{U}}{\partial t}+\mathrm{U}\cdot \nabla \mathrm{U}=-\frac{1}{\rho }\nabla p+v{\nabla }^2\mathrm{U}+\mathrm{f}$$

(1)

where $\frac{\partial \mathrm{U}}{\partial t}$ represents the rate of change in the velocity field $\mathrm{U}$ with respect to time; $\mathrm{U}\cdot \nabla \mathrm{U}$ describes the convective term, which accounts for motion caused by the velocity field itself; $-\frac{1}{\rho }\nabla p$ represents the pressure gradient term, which describes the motion caused by the velocity field itself; $v{\nabla }^2\mathrm{U}$ represents the viscous term, where $v$ is dynamic viscosity; ${\nabla }^2\mathrm{U}$ is the Laplacian gradient of the velocity field; and $\mathrm{f}$ denotes external forces, such as gravity or other external forces.

Next, expand and transform the above equation, and time-average each parameter. After sorting, the differential equation or Reynolds turbulent motion equation for the turbulent motion of the incompressible viscous fluid can be obtained. After simplification, we obtain:

$$-\frac{\partial \overline{P}}{\partial x}+2\frac{\partial }{\partial x}(\mu \frac{\partial \overline{u}}{\partial z}-\rho \overline{\dot{u}}\overline{\dot{w}})=0$$

(2)

$$-\frac{\partial \overline{P}}{\partial y}+2\frac{\partial }{\partial y}(\rho \overline{\dot{v}}\overline{\dot{v}})=0$$

(3)

$$-\rho g-\frac{\partial \overline{P}}{\partial z}-2\frac{\partial }{\partial z}(\rho \overline{\dot{w}}\overline{\dot{w}})=0$$

(4)

The last two equations in this system of equations show that the distribution pattern of hydrostatic pressure in the y-axis and z-axis directions is different from the hydrostatic pressure distribution. However, a large number of test results show that the difference between the distribution law of time-averaged static pressure and the distribution law of hydrostatic pressure is very small. Therefore, in actual calculations, it is advisable that:

$$\frac{\partial \overline{P}}{\partial y}=0,\rho g+\frac{\partial \overline{P}}{\partial z}=0$$

(5)

The momentum conservation equation is:

$$\frac{\partial \mathrm{U}}{\partial t}+(\mathrm{U}\cdot \nabla )\mathrm{U}=-\frac{1}{\rho }\nabla p+v{\nabla }^2\mathrm{U}+\mathrm{f}$$

(6)

where $\frac{\partial \mathrm{U}}{\partial t}$ represents the rate of change in velocity with respect to time; $\mathrm{U}$ represents the rate of change in velocity with respect to time, m/s²; $\nabla$ is the gradient operator; $\rho$ is the fluid density, kg/m³; $p$ is the pressure, Pa; $v$ is the kinematic viscosity of the fluid, m²/s; and $\mathrm{f}$ represents external body forces per unit volume, N (e.g., gravity).

According to the standard $k-\epsilon$ equation, the turbulent transport equation is:

$$\frac{\partial (\rho k)}{\partial t}+\frac{\partial (\rho u_{i}k)}{\partial x_i}=\frac{\partial }{\partial x_j}[(\mu +\frac{{\mu }_t}{{\sigma }_k})\frac{\partial k}{\partial x_j}]+G_k-\rho \epsilon$$

(7)

$$\frac{\partial (\rho \epsilon )}{\partial t}+\frac{\partial (\rho u_i\epsilon )}{\partial x_i}=\frac{\partial }{\partial x_j}[(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }})\frac{\partial \epsilon }{\partial x_j}]+C_{1\epsilon }{G}_k\frac{\epsilon }{k}-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}$$

(8)

where $k$ is the turbulent flow energy of the unit mass fluid (m²/s²); $\epsilon$ is the dissipation rate of $k$ (m²/s²); ${\mu }_t$ is the viscosity of turbulent flow force (Pa·s); $G_k$ is the generation term of turbulent energy $k$ due to the average velocity gradient; $C_{1\epsilon }$ and $C_{2\epsilon }$ are empirical constants; and ${\sigma }_{\epsilon }$ and ${\sigma }_k$ are the Prandtl numbers corresponding to the turbulent kinetic energy $k$ and the dissipation rate $\epsilon$, respectively.

2.3. Meshing

The size of the mesh is one of the most important factors affecting the accuracy of the operation, and the model is meshed using ANSYS [20]. Comprehensively considering the computer computing power and simulation effect, a tetrahedral grid is used for non-structural division, and the air curtain and the smaller parts of the surrounding area are partially meshed [21,22]. The mesh quality in the simulation is as high as possible to reduce the error that can be caused by mesh accuracy on the simulation results. The total number of meshes is 3,568,500, as shown in Figure 5.

2.4. Boundary Condition Setting

(1)

Numerical simulation conditions

In order to meet the simulation requirements of this paper, jet theory and roadway wind flow motion theory, as well as various parameters of the roadway and air curtain combined with the meshing situation, determine the relevant parameter settings in Fluent [23,24]. For specific numerical simulation conditions and boundary conditions, see

Table 1. Numerical simulation condition settings.

Modle	Define
Solve	Segregated
Viscous model	K-epsilon
Specious model	Implicit
Speed	Absolute
Time	Steady

and

Table 2. Boundary condition settings.

Set Conditions	Boundary Condition Type
roadway walls, air curtain walls	wall
fan inlet	fan
air curtain exit	interior
roadway entrance	velocity inlet
roadway exit	pressure outlet

. The number of time steps is 150; the time step size(s) is 0.008; the max iterations/time step is 20; and the reporting interval is 1.

(2)

Convergence tolerance settings

The default convergence criteria in Fluent consider that convergence is achieved when the residual values of all variables, including velocity, pressure, etc., drop below 10⁻³, except for the energy residual, which should be below 10⁻⁶. However, the actual convergence status also depends on whether the inlet and outlet flow rates have reached a stable balance. Confirmation of convergence should take into account these factors, but it should also be adjusted based on specific circumstances. For specific parameter settings, please refer to

Table 3. The calculation convergence criteria settings in Fluent.

Calculate Residual Items	Calculate the Residual Settings
continuity	10−3
energy	10−6
x-velocity	10−3
y-velocity	10−3
z-velocity	10−3
k	10−3
epsilon	10−3

.

(3)

Operating condition settings

The settings related to the model running conditions in Fluent are as shown in

Table 4. The operating condition settings in Fluent.

Set Up the Project	Unit	The Parameter Value
Work pressure	Pa	101,325
Reference velocity coordinates	m	x = 0, y = 0, y = 0
Acceleration due to gravity	N/kg	9.81
Operating temperature	K	298

.

(4)

Fan boundary condition setting

In the fan boundary of this simulation, the corresponding wind pressure interval parameters need to be entered, and the corresponding flow rate will also change at each full pressure value. Therefore, the whole of this fan characteristic curve function can be used as a boundary condition as a variable input. In this paper, the K45-6 axial fan is simulated and selected, and the fan characteristic curve functions of the fan blade angle are 20°, 25°, 30°, 35°, and 40°, respectively. As is shown in

Table 5. Fan characteristic curve function under different fan blade angles.

Fan Blade Angle/°	Fan Characteristic Curve Function
20	$y_1=-7.69x^2+136.91x-225.03$
25	$y_2=-7.50x^2+171.14x-461.43$
30	$y_3=-4.29x^2+109.20x-74.79$
35	$y_4=-3.15x^2+88.04x+85.58$
40	$y_5=-2.96x^2+90.73x+102.96$

.

The fan characteristic curve is shown in Figure 6.

2.5. Model Validation

In order to verify the established model, the on-site measurement uses a combination of a tilting differential pressure meter and precision barometer to reduce measurement error. The measured data are sorted and analyzed, and the results are shown in

Table 6. Measured data of the roadway.

Roadway Name	Sectional Area/m2	Blade Angle/(°)	Jet Angle/(°)	Differential Pressure/Pa	Analog Differential Pressure/Pa
The upper side of the air curtain of the main inclined well	14.694	30	30	52.7	49.6
The underside of the air curtain of the main inclined well	14.486	30	30
1000 air curtain upper side	14.830	35	30	58.6	58.3
1000 air curtain underside	14.326	35	30

. As can be seen from Table 4, the maximum error between the measured data and the model is 6.3%, which proves the accuracy of the model.

3. Numerical Simulation Results and Analysis

Isolation differential pressure, often referred to as pressure drop, denotes the decrease in pressure attributed to friction and resistance losses when a fluid traverses pipes, pipe fittings, or other elements within a fluid system. The isolation pressure drop is typically determined using the Darcy–Weisbach equation:

$$\Delta P=\frac{4\cdot fL\rho V^2}{2D}$$

(9)

• where $\Delta P$—isolation pressure difference, Pa;
• $f$—resistance coefficient (determined based on fluid and pipe conditions);
• $L$—pipeline length, m;
• $\rho$—fluid density, kg/m³;
• $V$—fluid velocity, m/s;
• $D$—pipe diameter, m.

Air leaks are commonly associated with the sealing performance of containers, pipes, and other systems. Calculating air leakage typically involves taking into account factors such as the leakage area, pressure difference, and other relevant parameters. The rate of air leakage can be estimated using the following formula:

$$Q=C\cdot A\cdot \Delta P$$

(10)

• where $Q$—air leakage rate, m³/s;
• $C$—leakage coefficient (usually determined based on the characteristics of the system and leakage port);
• $A$—leakage area, m²;
• $\Delta P$—pressure difference, Pa.

The drag rate refers to the resistance encountered by structures when subjected to wind forces. The calculation of wind resistance typically considers factors such as the shape of the structure and the velocity of the wind. The drag rate can be estimated using the following formula:

$$F=0.5\cdot {\rho }^{\prime }\cdot A^{\prime }\cdot C_d\cdot {V^{\prime }}^2$$

(11)

• where $F$—wind resistance, N;
• ${\rho }^{\prime }$—air density, kg/m³;
• $A^{\prime }$—the area of the structure, m²;
• $C_d$—drag coefficient;
• $V^{\prime }$—wind velocity, m/s.

3.1. The Influence of Jet Angle on the Isolation Pressure Difference

As one of the main factors affecting the efficiency of a multi-machine parallel circulation air curtain, the jet air supply angle directly determines the strength of its air flow ability to partition a roadway [25]. When an air curtain works to isolate the air flow of a roadway, the static pressure difference generated before and after it is called the effective pressure of the air curtain, that is, the partition pressure difference of the air curtain [26]. This indicator can directly reflect the barrier capacity of the air curtain. The simulation is divided into five parts, which are the numerical simulation of different jet angles under the full pressure of the fan blade at 20°, 25°, 30°, 35°, and 40°, from which the relationship between the full pressure of the fan and the pressure difference of the separator can be judged. The jet angle at each fan blade angle is set to 5°, 15°, 30°, 45°, and 60°. The outlet width is set to 0.16 m, and the outlet height is 1.7 m. The simulation results of different jet angles under different full pressures of different fans are analyzed and compared by intercepting Y = 0.86 m sections.

Figure 7, Figure 8 and Figure 9 show pressure clouds of the fan blade angles of the air curtain at 20°, 25°, and 30° and the jet working at different angles. It can be seen that under the action of the air curtain, the pressure distribution of the roadway undergoes a very obvious change. The roadway pressure cloud map where the air curtain is located can be divided into three parts, namely, the chamber position and upstream and downstream of the roadway wind flow. As shown in the figure, it can be seen that the upstream position of the roadway is green, and the downstream is light blue. This is due to the action of the air curtain, which causes the pressure upstream of the roadway wind flow to be significantly greater than that downstream of the roadway, resulting in a partition pressure difference.

The blue area at the chamber location is significantly deeper than downstream of the roadway, and the pressure is negative. This is due to the rotation of the fan blades of the air curtain fan, which extracts the roadway air, and the inhaled air flow is ejected through the air supply to form a high-speed jet. And because of the influence of the lateral pressure from the roadway wind flow, the jet bends and shifts, and flows downstream of the roadway air flow, so that the air flow forms a circulation between the inlet and outlet of the air curtain.

It can also be seen from Figure 7, Figure 8 and Figure 9 that when the air curtain is 5°, 15°, and 30°, the jets ejected by the air curtain on both sides of the chamber position collide and merge in the middle of the roadway, forming a closed air curtain, and the ability to resist the roadway wind flow is strong. When the jet angle is 45° and 60°, the blue color of the chamber position is lighter, indicating that the local negative pressure formed is small, and the jets ejected by the air curtains on both sides also collide in the middle of the roadway.

From Figure 10 and Figure 11, it can be seen that the color of the chamber position is close to downstream of the roadway wind flow, and there is no obvious difference. This shows that there is no circulating air flow between the inlet and outlet of the air curtain on both sides of the chamber, that basically no completely closed air curtain is formed, and that the effect of isolating the air flow of the roadway is not exerted. Comparing the results of the same angle in Figure 7, Figure 8 and Figure 9 shows that when the fan blade angle of the air curtain fan is 35° and 40°, the working nature changes, and the air curtain may show the phenomenon of excessive partition, which needs to be further analyzed and determined from the specific data.

Since the model adopts a large-section roadway, the pressure of each Y axial height plane is close to but not exactly the same under the action of the air curtain and the roadway wind flow. The jet of the air curtain collides with the roadway wind flow, and a vortex will be formed locally, resulting in large changes in wind flow disturbance, and the position where the wind flow disturbance changes greatly. It is necessary to avoid the position where the wind flow disturbance changes greatly.

According to the relationship between power, pressure difference, and air volume, combined with the above simulation data, it can be calculated that under the conditions of different fan full pressure and different jet angles, the effective power generated by the air curtain is between 840.8 and 2043.3 W. The result of calculating the isolation pressure difference is shown in Figure 12.

As can be seen from Figure 12, the size of the isolation pressure difference depends on two variables: one is the angle and the other is the full pressure of the fan. When the full pressure of the air curtain fan is at a blade angle of 20°, when the jet is shot out at different angles, the overall isolation pressure difference is small. At a jet angle of 5°, the isolation pressure difference reaches 36 Pa. As the angle increases to 15°, the rate of differential isolation pressure rises steeper. When the jet angle reaches 30°, the isolation pressure difference reaches the maximum, but the upward trend between 15° and 30° is smoother than the upward trend of 5~15°. At the jet angle of 45°, the isolation pressure difference drops very significantly. As the jet angle continues to increase to 60°, the isolation pressure difference continues to fall, and the rate of decline is reduced compared with the previous section when the isolation pressure difference reaches the minimum value. By analyzing the polyline when the fan blade is 25°, 30°, 35°, and 40°, it can be found that it has the same change law as described above. When the jet angle is fixed, with the increase in the full pressure of the fan, the partition pressure difference also continues to increase, showing a positive correlation. This law is the same in the jet angle of 5~60°, indicating that the ability of the multi-machine parallel circulating air curtain to isolate the air flow of the roadway is enhanced with the increase in the full pressure of the fan. Since the jet angle is in the range of 15~30°, the rate of increase in the isolation pressure difference is gentler than that of the previous section and basically reaches the maximum value.

This shows that the optimal jet angle range of the multi-machine parallel circulation air curtain is 15~30°. When the angle is greater than 30°, the isolation pressure difference drops sharply. When the angle increases to 45°, the isolation pressure difference continues to decrease, but the angle has less effect on the isolation pressure difference.

When the jet angle is greater than 30°, two jets erupt from the air curtain outlet. Sufficient air is not sucked up in a relatively short time, and the boundaries and sections of the jet are not sufficiently enlarged to a certain extent. Under the action of the lateral pressure of the roadway wind flow, it bends and flows downstream of the roadway wind flow, so that the two jets do not collide to form a wind curtain or the formed wind curtain is not completely closed. The air curtain is not completely intercepted, resulting in some roadway air flow through, resulting in a certain degree of air leakage, resulting in a small partition pressure difference.

3.2. The Influence of Jet Angle on Air Leakage Volume and Wind Choke Rate

In order to explore the influence of the jet angle of the air curtain on the wind flow of the partition roadway, the velocity cloud and velocity vector plot of the jet ejected at each angle when the full pressure of the fan is 25° are listed below. Due to the large number of models, the specific situation of wind turbine blade angles of 20°, 30°, 35°, and 40° is represented in Figure 13.

The inlet wind speed of the roadway is 4 m/s, and the total air volume is 58.8 m³/s. When the air curtain is closed, because the cross-sectional area of the two roadways is the same, the natural distribution of the components of both roadways in the parallel wind network is 29.4 m³/s, that is, the wind speed is equal to 2 m/s. It is clear from the velocity cloud plots in Figure 13, Figure 14, Figure 15, Figure 16 and Figure 17 that the color difference between the two roadways is large. The color of the roadway with the air curtain is dark, and the display speed is about 0.0~1.0 m/s. The roadway without the air curtain is lighter in color, and the speed is displayed at 3.0~4.0 m/s. This shows that under the action of the multi-machine parallel circulation air curtain, some roadway air flow is effectively intercepted and plays a significant role. Figure 13 shows a clear high-speed wind flow passing between the two jets because the air curtain on both sides of the roadway is at 5°. The jets ejected at 5° are close to the roadway wall, so the jets will rub against the roadway wall, and the friction position will form a vortex, which has a more obvious wall effect. In the case of a certain amount of jet flow, as the jet ejected from the outlet moves forward and continuously sucks the air in the roadway, the momentum of the jet gradually decreases, and after reaching a certain distance, the momentum decreases to 0. However, at this time, the two jets of the air curtain have not collided and merged in the middle of the roadway to form a closed air curtain, more roadway wind flows through, and the air leakage is large, so the ability to intercept the roadway wind flow is poor.

From Figure 14, Figure 15 and Figure 16, it can be found that when the jet angle is 15°, 30°, and 45°, a circulating air flow is formed between the air curtain outlet and the inlet at the chamber position, and the colors of the upper and lower reaches of the roadway in the velocity cloud diagram are close to the same, indicating that the effect of intercepting the roadway wind flow is better. In Figure 15, when the jet angle is 30°, the wind velocity distribution at the chamber position is the most uniform, the wind curtain formed is the most complete, and the wind flow disorder is good. It can be seen from Figure 17 that due to the excessive angle of the jet, after the jet is ejected and before the air flow is sucked up enough to further convert the momentum, it is subjected to lateral pressure from the roadway wind flow, resulting in bending and shifting. The two jets cannot collide and merge in the middle of the roadway, so more roadway wind flows through, the air leakage is large, and the ability to intercept the roadway wind flow is very poor.

In order to accurately judge the air leakage volume and wind choke rate at various angles, we obtain the change trend between 5° and 60° and the angle interval with the best effect of isolating the roadway wind flow, intercept the roadway section 20 m downstream of the chamber, and use Fluent to calculate the average air volume of the entire section as the air leakage volume. Then, we subtract the air leakage from the original total air volume of the roadway to be the air volume intercepted by the air curtain and then divide it by the total air volume of the roadway to determine the wind choke rate at various angles. The calculation results are shown in Figure 17 and Figure 18.

As shown in Figure 18, it can be seen that there are positive and negative values in the air leakage volume. Positive values indicate that the air curtain is not intercepted by the roadway wind flow, whereas negative values mean that the partition is excessive, no roadway air flow passes through the air curtain, and the function of the air curtain is no longer a barrier. According to the positive and negative air leakage volume, the diagram can be divided into two parts: upper and lower. When the fan blade angle is 30° and the jet angle is 30°, the air leakage at this time is minimal, and only 2.5 m³/s of roadway wind flow is not intercepted. When the jet angle is 45°, the air leakage increases to 4.8 m³/s, and the partition capacity deteriorates significantly. When the jet angle continues to increase to 60°, the air leakage reaches a maximum of 6.8 m³/s. At this time, the ability of the multi-machine parallel circulating air curtain to isolate the roadway air flow is the worst, the rate of air leakage increase at 45~60° is significantly faster than that at 30~45°, and the slope becomes steeper, as intuitively reflected in Figure 18. It shows that when the jet angle reaches 45° and continues to increase, the blocking capacity will be sharply reduced.

When the jet angle is 5~15°, the air leakage volume is negative. At this time, the section of the roadway taken for the leakage air volume not only does not have the wind flow from upstream of the roadway but the air volume downstream of the roadway is led upstream under the action of the air curtain, resulting in the reverse wind phenomenon. This shows that the isolation effect of the multi-machine parallel air curtain has reached its best when the full pressure of the fan is 30°, and reducing the angle will make the air curtain lose its ability to block the air flow in the roadway and start to drain the air flow.

When the fan blade angles are 20° and 25°, respectively, the air leakage volume in the range of 5~60° is positive, indicating that there is air leakage at any angle, and the air curtain is blocking the air flow. When the jet angle is 5~15°, the air leakage volume is significantly reduced. In the angle range of 15~30°, the air leakage volume still continues to decrease, and the decline rate begins to slow down compared with the rate of the previous angle range, indicating that the air curtain isolation capacity increases in this angle range and gradually approaches the optimal angle. When the jet angle increases to 30~45°, the air leakage volume begins to increase at a faster rate, and the isolation capacity decreases rapidly. When the angle increases to 60°, the air leakage volume increases to the maximum value at the full pressure of the corresponding fan, and the isolation capacity is the worst. When the fan blade angle is 35° and 40°, it can see that most of the air leakage is negative, indicating that the air curtain directs air flow at this time.

When the fan blade angle is 35° and the jet angle is 45° and when the fan blade angle is 40° and the jet angle is 60°, the air leakage volume is positive, indicating that the air curtain under these conditions is in the isolation roadway air flow, and the relationship between partition capacity and angle is consistent with the law when the angle of the fan blade is 20° and 25°. However, when you want to achieve the same partition effect, you can use a lower fan full pressure by setting different installation angles, whereas using a larger full pressure will undoubtedly increase power consumption. In the folded line when the fan blade angle is 40°, when the jet angle is 5°, the air leakage reaches the minimum value within the angle range of the taken angle range of −12.2 m³/s. When the jet angle gradually increases, the air leakage volume increases. This indicates that the emissive capacity of the air curtain decreases with the increase in the jet angle.

Figure 19 visually shows the relationship between the choke rate, the full fan pressure, and the air curtain jet angle. It can be seen from the figure that the wind choke rate exceeds 100%, which is due to the phenomenon of excessive partition when the full pressure of the air curtain fan is too large, and the partition is generated at a certain jet angle. With the wind choke rate of 100% as the boundary, the graph can be divided into two parts for analysis: upper and lower. When the blade angle of the air curtain fan is 30° and the jet angle is 30°, the wind choke rate of the multi-machine parallel air curtain reaches 91.4%, which achieves the best isolation effect under this full pressure condition. When the jet angle increases to 60°, the wind choke rate shows a clear downward trend. When the blade angle is 20° and 25°, the wind choke rate is in the range of 61.6~85.7%, which is lower than 100%. It is shown that under the conditions of these two full pressure values, any jet angle has a greater influence on the wind flow of the partition roadway, and with the increase in the jet angle, it shows the law of first increasing and then decreasing. When the fan blade angle is 35° and 40° and the jet angle is 45~60°, the wind choke rate is 81.0~89.1%, and the wind flow capacity of the isolation roadway is strong, but due to the large full pressure of the fan, it will produce more power consumption. When the angle is within 5~30°, the wind choke rate is greater than 100%, indicating that the air curtain is educating air flow at this time, and with the increase in the angle, the emissive capacity is weakened.

3.3. The Influence of Air Curtain Outlet Width on the Isolation Pressure Difference

Numerous studies have shown that the air curtain outlet is also one of the important factors affecting the ability of air curtain partitioning. In order to explore the relationship between the outlet width of the multi-machine parallel circulation air curtain and the air flow capacity of the partition roadway, five air curtain models with different outlet widths were made using GAMBIT software [27,28]. Under the condition of maintaining the jet angle for a certain amount, the isolation pressure difference generated under different models is calculated. The full pressure of the fan is also one of the influencing factors affecting the air curtain’s ability to intercept the air flow in the roadway, so the full pressure of multiple sets of fans is set for different situations, and the specific simulation setting data conditions are shown in

Table 7. Simulation parameters.

Fan Blade Angle	Exit Width/m	Exit Height/m	Jet Angle/°	Fan Blade Angle	Exit Width/m	Exit Height/m	Jet Angle/°
20°	0.08	1.7	30°	30°	0.08	1.7	30°
	0.12	1.7	30°		0.12	1.7	30°
	0.16	1.7	30°		0.16	1.7	30°
	0.20	1.7	30°		0.20	1.7	30°
	0.24	1.7	30°		0.24	1.7	30°
	0.28	1.7	30°		0.28	1.7	30°
	0.32	1.7	30°		0.32	1.7	30°
	0.36	1.7	30°		0.36	1.7	30°
	0.40	1.7	30°		0.40	1.7	30°
25°	0.08	1.7	30°	35°	0.08	1.7	30°
	0.12	1.7	30°		0.12	1.7	30°
	0.16	1.7	30°		0.16	1.7	30°
	0.20	1.7	30°		0.20	1.7	30°
	0.24	1.7	30°		0.24	1.7	30°
	0.28	1.7	30°		0.28	1.7	30°
	0.32	1.7	30°		0.32	1.7	30°
	0.36	1.7	30°		0.36	1.7	30°
	0.40	1.7	30°		0.40	1.7	30°

.

The jet angle remains unchanged under 30°, and the simulation results for different air curtain outlet widths under different full pressure of different fans are analyzed and compared when Y = 0.86 m is intercepted. Since there are many simulation figures, the range of 0.16~0.32 m is selected to obtain a conclusive picture of the middle part for further analysis.

It can be seen from Figure 20, Figure 21, Figure 22 and Figure 23 that the multi-machine parallel circulation air curtain makes the pressure value at both ends of the chamber of the roadway significantly different. Thus, the color upstream of the roadway is significantly darker than downstream, that is, the pressure value upstream of the roadway is greater than that of the valve downstream, resulting in a partition pressure difference.

The pressure at the chamber position is negative, which is due to the rotation of the fan blade of the air curtain fan, sucking the roadway air, generating local negative pressure, and causing the inhaled air flow through the air supply to form a high-speed jet ejection. Because of the influence of the lateral pressure from the roadway wind flow, the jet bends and shifts and flows downstream of the roadway air flow, so that the airflow forms a cycle between the inlet and outlet of the air curtain [29].

It can be seen in Figure 20 that when the fan blade angle is 20° and the air curtain width is 0.16 m, the color upstream of the roadway is a very dark green and the pressure value is positive. As the width of the air curtain gradually increases to 0.32 m, the color upstream of the roadway gradually changes from dark green to light green and finally to yellow, but the color downstream also gradually warms, so the resulting partition pressure difference changes. In Figure 21, Figure 22 and Figure 23, the colors of the upper and lower reaches of the roadway also show the same change pattern as in Figure 20. Since the model adopts a three-dimensional large-section roadway, there will be local wind flow disorder. In order to reduce the error, the entire section of the roadway is taken 20 m upstream and downstream of the chamber, and the pressure average of the entire section is calculated using Fluent, and then the partition pressure difference generated by the air curtain is calculated.

From the calculation results of the above isolation pressure difference, it can be seen that the effective power made under different outlet widths and different fan full pressures is in the range of 1126.0~1425.9 W. The calculation result of the isolation pressure difference is shown in Figure 24.

As shown in Figure 24, we can see the relationship between the isolation pressure difference, the full pressure of the fan, and the outlet width of the air curtain. The different outlet widths and the full pressures of the fan determine the partition pressure difference of different sizes produced by the multi-machine parallel circulation air curtain.

When the fan blade angle is 20° and the air curtain outlet width is 0.08 m, the partition pressure difference generated by the air curtain is 38.3 Pa, and the partition effect is the worst. When the outlet width increases to 0.20 m, the isolation pressure difference increases to a certain extent, and the growth rate is large. As the outlet width continues to increase, so does the isolation pressure difference. When the outlet width is increased to 0.24 m, the partition pressure difference reaches the maximum, and the multi-machine parallel air curtain at this time has the strongest ability to resist the roadway air flow and the isolation effect is the best. As the outlet width continues to increase, the isolation pressure differential begins to decrease. By analyzing the folded lines at the angle of the fan blade of 25°, 30°, and 35° and different outlet widths, the same law as above can be obtained. This shows that under the full pressure of any fan, with the increase in the outlet width of the air curtain, the isolation pressure difference shows a trend of first increasing and then decreasing, and the ability to intercept the air flow of the roadway is first enhanced and then weakened. The partition effect reaches its best when it is 0.20~0.24 m.

3.4. The Influence of Air Curtain Outlet Width on Air Leakage Volume and Wind Choke Rate

In order to explore the influence of the outlet width of the air curtain and the full pressure of the fan on the air leakage volume and wind choke rate when the air flow of the roadway is isolated, a numerical simulation is made under the condition that the jet angle is unchanged by 30°, and different air curtain outlet width and different fan full pressure are selected as variables.

Due to the large number of models, only the velocity clouds and velocity vectors of the air curtain at different widths at a fan blade angle of 20° are listed here. The results are shown in Figure 25.

The wind speed at the inlet of the roadway is 4 m/s, and when the air curtain is closed, the frictional wind resistance, local resistance, roadway break area, and other conditions of the two roadways are equal. Thus, the natural allocation of the components of the two roadways is 29.4 m³/s, that is, the wind speed is equal to 2 m/s. From the velocity cloud figures in Figure 25, Figure 26, Figure 27, Figure 28 and Figure 29, it can be seen that the wind speed distribution of the roadway has changed significantly under the action of air curtains with different outlet widths. Downstream of the roadway with the air curtain is dark blue and the speed is about 0.0~1.0 m/s, whereas the roadway without the air curtain is light blue and the speed is about 3.0~4.0 m/s. From the velocity vector diagram, it can be seen that the two jets of the air curtain form a closed air curtain in the middle of the roadway, and a circulating air flow is formed between the outlet and the inlet of the air curtain, which effectively intercepts part of the roadway air flow. However, it can also be seen that part of the air volume from upstream of the roadway is pumped away by the air curtain fan, and the remaining part flows downstream of the roadway, all with different degrees of air leakage.

In comparison, the downstream position of the chamber in Figure 25, Figure 28, and Figure 29 is lighter in color, indicating that when the air curtain outlet width is 0.16 m, 0.28 m, and 0.32 m, the air leakage volume is larger and the ability to intercept the roadway air flow is weak. When the air curtain outlet width is 0.20 m and 0.24 m, the air leakage volume is small, and the ability to intercept the roadway air flow is strong. As can be seen from Figure 27, when the air curtain outlet width is 0.24 m, the air flow through the air curtain is minimal.

A roadway section is taken 20 m downstream of the chamber, the average air volume of the entire section is calculated using FLUENT to be the air leakage volume, and then the wind choke rate under different air curtain outlet widths is calculated.

As shown in Figure 30, it can be seen that there are two positive and negative values in the air leakage volume, and most of the positive values exist when the fan blade angle is 20°, 25°, and 30°. When the outlet width of the air curtain is 0.08~0.40 m, a negative value exists in the case that the full pressure of the fan is 35° and the outlet width is 0.24~0.32 m. When the full pressure of the fan is 20°, the air leakage is positive at any outlet width. This shows that the outlet width of the multi-machine parallel air curtain at this time is within 0.08~0.40 m, which has a certain effect on intercepting the air flow of the roadway, and with the increase in the outlet width, the air leakage volume first decreases and then increases.

In the process of increasing the width of the air curtain outlet, the resistance in the air curtain formed by the two jets of the air curtain to the lateral pressure of the roadway wind flow gradually increases, and the effect of intercepting the roadway wind flow becomes better and better. When the outlet width is increased to 0.24 m, the interception effect is best. When the outlet width continues to increase, the air leakage volume begins to increase and the interception effect begins to weaken. This shows that when the outlet width is 0.24 m, the energy loss in the multi-machine parallel air curtain is the smallest, and the interception effect is the strongest. The same variation law can be obtained by analyzing the broken lines with fan blade angles of 25° and 30°. When the angle of the fan blade is 35° and the outlet width is 0.20 m, the air leakage volume is positive, and the air leakage decreases with the increase in the outlet width, indicating that the effect of intercepting the air flow in the roadway increases, which is in line with the law of the air curtain when it exerts the effect of intercepting the air flow. When the outlet width is 0.24~0.32 m, the air leakage volume is negative, and it decreases first and then increases with the increase in outlet width, indicating that this node is the critical point of the isolation and drainage air flow.

Figure 31 shows the relationship between the multi-machine parallel circulation air curtain, outlet width, and wind choke rate. The efficiency of the air curtain intercepting roadway air flow can be intuitively seen. When the choke rate exceeds 100%, it indicates that the air curtain has changed from a state of intercepting wind flow to an induced air flow. When the angle of the fan blade is 20°, 0.08~0.40 m, the corresponding wind choke rate is 67.0~74.1%. The wind choke rate is lowest when the outlet width is 0.08 m, and the maximum value is reached at a width of 0.24 m. As the outlet width continues to increase, the choke rate begins to decrease. At the fan blade angles of 25° and 30°, the wind choke rate is less than 100%. This shows that under the conditions of full pressure and outlet width, the multi-machine parallel air curtain can effectively intercept the wind flow, and the interception effect first increases and then weakens with the increase in outlet width, which is the same as when the blade angle is 20°.

When the fan blade angle is 35°, it can be seen that the choke rate increases with the increase in the outlet width. When the outlet width is increased to 0.24 m, the wind choke rate reaches 101.7%, and the wind flow from intercepting roadway to draining air flow begins to change.

From Figure 31, it can be seen that when the full pressure of the fan is small, the ability to intercept the wind flow can be improved by increasing the width of the air curtain outlet. Although increasing the full pressure of the fan can also improve the air flow capacity of the partition roadway of the multi-machine parallel air curtain, it will increase additional power consumption and cause unnecessary waste. According to the relationship between the full pressure of the fan, the width of the air curtain outlet, and the wind choke rate, by combining the actual needs, the design of the air curtain outlet width can provide certain guidance for the practical application of multi-machine parallel air curtains, reduce energy consumption and enhance economic value.

4. Conclusions

In this paper, the effects of full pressure, air curtain outlet width, and jet angle of a double-machine parallel double-unit axial fan on the interception of wind flow in a mine roadway of double-machine parallel circulation air curtain are mainly studied. The following conclusions are obtained:

(1)

The air curtain of the double-machine parallel compound axial fan in the roadway can effectively block the air flow in the roadway and realize the control of the air flow. The main factors that affect the air flow in the roadway are the air curtain outlet width, the jet angle, and the full fan pressure.

(2)

Using numerical simulation, when the outlet width of the air curtain is fixed, the air curtain with different jet angles is simulated under different fan full pressure values. It can be found that when the full pressure of the fan is fixed, as the jet angle of the air curtain increases, the partition pressure difference and wind choke rate also increase. The growth rate is faster between 5~15° and 15° at the jet angle, and the same growth rate is 15~30°, but the growth rate tends to be flat. When the jet angle reaches 30°, the isolation pressure difference and wind choke rate reach a stage high. When the jet angle continues to increase, the isolation pressure difference and wind choke rate begin to decrease, and the overall trend increases first and then decreases. When the jet angle is unchanged, the isolation pressure difference and wind choke rate will increase with the increase in the full pressure of the fan. However, when the full pressure exceeds a critical point, the isolation surplus phenomenon occurs, and the multi-machine parallel circulation air curtain at this time no longer intercepts the roadway air flow but drains the air flow. The simulation results show that when the jet angle is between 15° and 30°, the multi-machine parallel circulation air curtain has the strongest ability to block air flow.

(3)

When keeping the jet angle constant, different fan full pressure values, i.e., blade angles, are simulated by setting different fan full pressure values for air curtains with different outlet widths. It can be seen from the analysis that when the full pressure of the fan remains unchanged, the isolation pressure difference and wind choke rate first increase and then decrease with the increase in the width of the air curtain outlet. However, when a certain outlet width is reached, the choke rate exceeds 100%, indicating that the multi-machine parallel air curtain at this time begins to change from blocking wind flow to diversion air flow. When the width of the air curtain outlet remains unchanged, the isolation pressure difference and wind choke rate increase with the increase in the full pressure of the fan. When the wind choke rate exceeds 100%, the air flow is initiated, and the emission capacity increases with the increase in full pressure. In summary, it can be concluded that the air flow capacity of the multi-machine parallel circulation air curtain blocking the roadway increases with the increase in the width of the air curtain outlet. When increased to 0.20~0.24 m, the energy loss in the air curtain is the smallest and the interception efficiency is the best.

(4)

In order to more simply and clearly judge the effect of the multi-machine parallel air curtain isolation roadway wind flow, as well as the transition critical point of blocking and diversion air flow, an air leakage index is introduced. When the air leakage volume is positive, it means that the air curtain is blocking the air flow. When the air leakage volume is negative, it means that the blocking of air flow begins to shift to the pilot air flow. When the jet angle, outlet width, and full pressure of the air curtain change, the critical point of intercepting the wind flow and the transition of the induced wind flow can be directly judged.