Introduction

With the continuous improvement of mechanization, the mining depth and mining intensity of the mine are increasing. Due to the low permeability of deep coal seams, the mining environment of high gas mines is very complex and dangerous (Xu et al. 2018; Tong et al. 2019; Chen et al. 2019). During excavation, great amounts of gaseous and solid pollutants (mainly gas and dust particles) are produced, which severely threaten the health of workers and pollute the construction environment (Cheriyan and Choi 2020; Wang et al. 2020; Liu et al. 2019). According to statistics from the National Health and Family Planning Commission of the People’s Republic of China, gas accidents accounted for approximately 30% of all kinds of mine accidents from 2009 to 2018. In particular, because gas accidents mainly take the form of explosions, they have an extremely high mortality; the related casualties account for approximately 10% of all casualties caused by mine accidents (Fittschen et al. 2013; Ebrahimi-Moghadam et al. 2018; Chen et al. 2016). Moreover, owing to the increasing engineering capacity, the number of new pneumoconiosis cases due to the inhalation of great amounts of dust has increased year by year (Niu et al. 2021; Peng et al. 2022; Nie et al. 2022a). According to the latest data in the statistical bulletin on the development of China’s health undertakings, issued by the National Health Commission, in the 5 years from 2016 to 2020, the cumulative number of new cases of occupational diseases in China reached 118,534 including 100,426 cases of pneumoconiosis, accounting for more than 84%. Pneumoconiosis represents the largest problem for the prevention and control of occupational diseases in China (Nie et al. 2022b; Chen et al. 2022a; Nie et al. 2022c). Thus, gas and dust are the main disaster-inducing pollutants. In most cases, gas and dust exhibit co-occurrence and mutual effects to form a complex environmental phenomenon (Alden et al. 2020; Liu et al. 2021a; Nie et al. 2022d).

Researchers worldwide have thoroughly investigated dual-disaster-inducing pollutants (gas and dust) in terms of their properties, diffusion and distribution rules, and corresponding treatment measures (Nie et al. 2022e; Liu et al. 2021b; Sun et al. 2021). Regarding gaseous pollutants, Zhou et al. (2017) combined scanning electron microscopy and energy dispersive spectroscopy and discovered that the gas contents were unevenly distributed at different positions in the mine; moreover, the coal’s gas-adsorbing capacity was related to the density of the filling material in the pores. Li et al. (2020) established a model based on the lattice Boltzmann method (LBM) and large-eddy simulation for the gas diffusion and distribution and found that the LBM can be used for simulating the gas flow through a comparison. Moreover, Toraño (2009) conducted 450 measurements to determine the airflow velocity and gas concentration in six measuring sections. The researcher reported that the gas mainly accumulated in the top region of the tunnel. For a more effective gas control, Fang et al. (2016) found dead zones in the cross-channel in a double tunnel where the airflow velocity was low and gas accumulated extremely easily. The dead zone problem can be effectively addressed by adding jet fans. Furthermore, by combining simulations and experimental data, Sasmito et al. (2013) proposed multiple supplementary ventilation schemes and selected the effect and cost as the evaluation indexes for the optimization of the schemes. Kurnia et al. (2014) focused on the relationship between the gas diffusion state and gas release source and proposed a novel diverter, which can divert the fresh airflow to the gas accumulation region.

Regarding the dust pollutants, Yu et al. (2020) used molecular dynamic simulations to investigate the dust aggregation and clustering process; they discovered that dust settling could be effectively promoted by reducing the environmental temperature and increasing the moisture content. To study thoroughly the characteristics of dust diffusion and distribution, Goldasteh et al. (2013) employed the Monte Carlo method to simulate the suspension effect of the turbulent flow field on dust particles of different sizes at different airflow velocities. In addition, Zhang et al. (2008) improved the high Reynolds number k-ε turbulent model and found that the dust concentration gradually increased from the vortex center to the surrounding space; moreover, a coarse wall surface resulted in a stronger dust retention effect than a smooth wall. By using the discrete element method, Schulz et al. (2019) examined the collision among dust particles and the dust diffusion behavior in combination with computational fluid dynamics (CFD) simulations. To control the dust more effectively, Wang et al. (2019) changed the existing dust remover and stated that the arrangement of the inlet of the dust remover and scrubber on opposite sides promoted dust control; the results provide guidance for ventilation dust removal. Furthermore, Zhu et al. (2014) focused on the arrangement position of the press-in air duct and suggested that a height of 3 m of the air duct center above the floor was the optimal dust removal height. Wang et al. (2020a, b) analyzed the used surfactants in spraying and concluded that the spraying dust suppression efficiency first increased and then decreased with increasing surfactant concentration.

The previously presented studies have deficiencies regarding the following two aspects: first, the researchers only focused on single disaster-inducing pollutants. Our understanding of the complex interaction of multiple pollutants with airflow is limited, which will limit our ability to improve the cleanliness of the environment. Second, ventilation is the main dust control technology in the process of tunneling. Researchers have less research on the pollution laws of coupled gas–dust pollutants in tunnel under different distances between the air duct and cutting face. Only few theoretical cases are available on how to minimize the dust concentration while ensuring gas safety .

To fill the knowledge gaps identified above, this work conducted computational fluid dynamics (CFD) numerical simulations to study the diffusion characteristics of dual-disaster-inducing pollutants in the No. 3417 excavation tunnel, which is a typical tunnel in the Xinyuan Coal Mine. The spatiotemporal evolution rules of the pollutant diffusion in some key areas and the coupling mechanism among the airflow, gas, and dust fields were determined. Subsequently, the optimal pollution-controlling distance of the air duct was determined. Field measurements of gas and dust concentrations in the tunnel were carried out, and the results obtained were compared with the simulation data to validate the accuracy of the CFD simulations.

Establishment of physical model and selection of mathematical model

Establishment of physical model

By consulting the related information and field survey data of the No. 3417 excavation tunnel, a full-scale physical model was established with SOLIDWORKS (version 2010, a three-dimensional parametric design software developed by SolidWorks Corporation, America) and used to simulate the field conditions in the tunnel (Nie et al. 2022f; Mo and Liu, 2018; Nagaosa 2014). The established physical model mainly consists of the excavation tunnel, tunneling machine, bridge stage loader, belt conveyor, and flexible air duct, as shown in Fig. 1a. To obtain more targeted research results, the region 110 m from the cutting face was selected for the in-depth analysis.

Fig. 1
figure 1

Physical model construction and meshing. a Schematic diagram of the physical model composition. b Mesh quality measurement index distribution map

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Subsequently, the established physical model was meshed with the ICEM-CFD (version 16.0, a pre-processing software developed by ANSYS Corporation, America, which acts as a standard mesh generation software built in Fluent) post-processing software (Nie et al. 2022g; Li et al. 2022; Guan et al., 2016). The model was meshed into unstructured grids that are suitable for a fluid domain, and some local regions were more densely meshed. After the optimization, the mesh quality distribution pattern was plotted (Fig. 1b). Based on the analysis, 3,519,603 meshes were generated; the maximum mesh quality, minimum mesh quality, and average mesh quality were 0.9978, 0.0261, and 0.7070, respectively. The number of meshes with mesh quality ≥0.5 was accounted for 87.52% of the total meshes. Overall, the mesh quality was stably distributed with a high forming degree, which meets the simulation requirements of the airflow, gas, and dust fields .

Selection of mathematical model

The migration characteristics of the airflow, gas, and dust in the tunnel fall under the research category of two-phase flow. During the simulation, the airflow and gas can be treated as continuous phases, while the dust particles can be regarded as a solid discrete phase. In general, when the volume fraction of the discrete phase in the continuous phase is 10% to 12%, the interaction between particles could be ignored, and the motion of the two-phase flow can be studied with the Eulerian–Lagrangian method (Nie et al. 2022h; Chen et al. 2022b; Song and Zhang 2019):

  1. (1)

    Motion equations of gaseous airflow and gas

Under the Euler framework, the airflow and gas movement in the gas phase are described by the Navier–Stokes equation, considering the momentum and energy source in the presence of the solid phase. The flow conditions of the airflow and gas were described with the Realizable k-ε model because it can well describe the complex flow of the rotational shear flow and circular jet. Moreover, the Realizable k-ε model can accurately predict the divergence ratio of the circular jet (Mitchell et al. 2015; Huang et al. 2021; Cardoso-Saldana and Allen, 2020).

In the Realizable k-ε model, the transport equations of the turbulent kinetic energy and turbulent dissipation rate can be written as follows:

$$\rho \frac{Dk}{Dt}=\frac{\partial }{\partial {x}_j}\left[\left(\mu +\frac{\mu_t}{\sigma_k}\right)\frac{\partial k}{\partial {x}_j}\right]+{G}_k+{G}_b-\rho \varepsilon -{Y}_M$$
(1)
$$\rho \frac{D\varepsilon}{D t}=\frac{\partial }{\partial {x}_j}\left[\left(\mu +\frac{\mu_t}{\sigma_t}\right)\frac{\partial \varepsilon }{\partial {x}_j}\right]+\rho {C}_1 S\varepsilon -\rho {C}_2\frac{\varepsilon^2}{k+\sqrt{\nu \varepsilon}}+{C}_{1\varepsilon}\frac{\varepsilon }{k}{C}_{3\varepsilon }{G}_b$$
(2)

where \({C}_1=\max \left[0.43,\frac{\eta }{\eta +5}\right]\); η = Sk/ε, where k denotes the turbulent kinetic energy, ε the turbulent kinetic dissipation rate, μ represents the dynamic viscosity coefficient of air, μt os the eddy viscosity, ρ is the fluid density, and η the dissipative scale. Gk represents the generated turbulent kinetic energy induced by the mean velocity gradient, Gb is the generated turbulent kinetic energy under buoyancy, YM is the effect of the compressible turbulent fluctuating expansion on the total dissipation rate, C2 and C1ε are two constants, and σk and σε denote the turbulent Prandtl numbers of the turbulent kinetic energy and dissipation rate, respectively. In Fluent, C1ε = 1.44, C2 = 1.9, σk = 1.0, and σε = 1.2.

In addition, Cμ is a function of the mean strain rate and vorticity:

$${\mathrm{C}}_{\upmu}=\frac{1}{{\mathrm{A}}_0+{\mathrm{A}}_{\mathrm{s}}\frac{{\mathrm{U}}^{\ast}\mathrm{K}}{\upvarepsilon}}$$
(3)

where \({U}^{\ast }=\sqrt{S_{ij}{S}_{ij}+{\overset{\sim }{\varOmega}}_{ij}{\overset{\sim }{\varOmega}}_{ij}}\) (\({\overset{\sim }{\varOmega}}_{ij}={\varOmega}_{ij}-2{\varepsilon}_{ij k}{\omega}_k\) and \({\varOmega}_{ij}={\overline{\varOmega}}_{ij}-{\varepsilon}_{ij k}{\omega}_k\)); \({\overline{\varOmega}}_{ij}\) denotes the time-averaged rotation rate tensor derived from the reference coordinate system at the angular velocity ωk; A0 and As are two model constants (A0 = 4.04 and \({A}_s=\sqrt{6}\mathit{\cos}\varphi\)). Furthermore, \(\varphi =\frac{1}{3}\mathit{\operatorname{arccos}}\left(\sqrt{6}W\right)\), in which \(W=\frac{S_{ij}{S}_{jk}{S}_{kj}}{\overset{\sim }{S}}\), \(\overset{\sim }{S}=\sqrt{S_{ij}{S}_{ij}}\), and \({S}_{ij}=\frac{1}{2}\left(\frac{\mathit{\partial}{u}_j}{\mathit{\partial}{x}_i}+\frac{\mathit{\partial}{u}_i}{\mathit{\partial}{x}_j}\right)\).

By assuming that the gas is uniformly emitted from the cutting face, the mixed transportation process of the gas and airflow can be simulated with the component transfer model (Cui et al. 2014; Cowie et al. 2012; Ding et al. 2019):

$$\frac{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}{\mathrm{\partial t}}+\frac{\partial }{\mathrm{\partial x}}\left({\mathrm{q}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}\right)+\frac{\partial }{\mathrm{\partial y}}\left({\mathrm{q}}_{\mathrm{i}}{\mathrm{v}}_{\mathrm{i}}\right)+\frac{\partial }{\mathrm{\partial z}}\left({\mathrm{q}}_{\mathrm{i}}{\mathrm{w}}_{\mathrm{i}}\right)=\frac{\partial }{\mathrm{\partial x}}\left({\mathrm{D}}_{\mathrm{i},\mathrm{j}}\frac{\partial {\mathrm{q}}_{\mathrm{i}}}{\mathrm{\partial x}}\right)+\frac{\partial }{\mathrm{\partial y}}\left({\mathrm{D}}_{\mathrm{i},\mathrm{j}}\frac{\partial {\mathrm{q}}_{\mathrm{i}}}{\mathrm{\partial y}}\right)+\frac{\partial }{\mathrm{\partial z}}\left({\mathrm{D}}_{\mathrm{i},\mathrm{j}}\frac{\partial {\mathrm{q}}_{\mathrm{i}}}{\mathrm{\partial z}}\right)+{\mathrm{S}}_{\mathrm{i}}$$
(4)

where \({D}_{i,j}={D}_{j,i}=\frac{0.0101{T}^{1.75}\sqrt{1/{M}_i+1/{M}_j}}{P{\left[{\left(\sum {v}_i\right)}^{1/3}+{\left(\sum {v}_j\right)}^{1/3}\right]}^2}\); qi denotes the mass concentration of the infinitesimal component i in the fluid; μi, vi, and wi are the components of the velocity of the infinitesimal component i in the x-, y-, and z-axis directions, respectively; Di, j denotes the mass diffusion coefficient of the infinitesimal component i in the fluid; si is the production rate of the infinitesimal component i per unit volume in unit time, T, the fluid infinitesimal, and p, the pressure acting on the fluid infinitesimal; Mi and Mj are the molar masses of the components i and j; and vi and vj are the diffusion volumes of the components i and j, respectively.

  1. (2)

    Motion equation of solid–solid dust particles

According to the results of an actual measurement, the volume fraction of the dust particles in the tunnel was far below 10% (Nie et al. 2022i; Ding et al. 2019). For the movement of dust particles in the solid phase, a single dust particle is tracked in the Lagrange framework, and the motion characteristics of each particle in the system are obtained according to the force on each particle. At the same time, using the Fluent (version 16.0, a commercial software developed by ANSYS Corporation, America, for complex fluid simulation) numerical simulation software, when calculating the coupling of airflow, gas, and dust, we clicked and selected the option in the software, to consider the coupling and interaction of the discrete phase and the continuous phase.

According to the principle that the forces acting on the dust particles are balanced, the equation of motion in a Lagrangian coordinate system can be derived as follows (Huang et al. 2022; Shen et al. 2019):

$$\frac{d{u}_p}{dt}={F}_D\left(u-{u}_p\right)+\frac{g_x\left({\rho}_p-\rho \right)}{\rho_p}+{F}_x$$
(5)

where FD denotes the drag force and can be expressed as \({F}_D=\frac{18\mu }{\rho_p{D}_p^2}\frac{C_D\mathit{\operatorname{Re}}}{24}\); u is the continuous phase velocity; up is the particle velocity; μ is the molecular viscosity coefficient of the fluid; and ρ and ρp are the densities of the fluid and the particles, respectively.

In equation for FD, Dp is the particle diameter and Re is the relative Reynolds number, defined as

$$\operatorname{Re}=\frac{\rho {D}_p\mid {u}_p-u\mid }{\mu }$$
(6)

The resistance coefficient is \({C}_D={\alpha}_1+\frac{\alpha_2}{\operatorname{Re}}+\frac{\alpha_3}{{\operatorname{Re}}^2}\), where α1, α2, and α3 are constants and are obtained based on the experimental results of smooth spherical particles. The shape factor is ϕ = s/S, where s is the surface area of a sphere with the same volume as the particle and S is the actual surface area of the particle.

When the particle size was in the order of one um or less, the Stokes’ resistance formula was used:

$${F}_D=\frac{18\upmu}{{\mathrm{D}}_{\mathrm{p}}^2{\uprho}_{\mathrm{p}}{\mathrm{C}}_{\mathrm{c}}}$$
(7)

where Cc is the Cunningham correction factor \({C}_c=1+\frac{2\lambda }{D_p}\left(1.257+0.4{e}^{\frac{1.1{D}_p}{2\lambda }}\right)\) and λ is the mean free path of the molecule (Geng et al. 2019).

Simulation of multi-field coupling migration and investigation of interaction mechanism

As both gas and airflow are in the gas phase, they can mix rapidly. Therefore, we first realized the single-phase coupling simulation between airflow and gas and then added dust particles to realize the multi-phase coupling simulation of airflow, gas mixture, and dust, to explore the interaction mechanisms among all three.

CFD simulations were performed to obtain the migration characteristics and coupling pattern of the airflow, gas, and dust fields in the excavation tunnel when the air duct was located 4 m away from the cutting face (Fig. 2).

Fig. 2
figure 2

Multi-field coupling simulation results. a Airflow–gas–dust field coupling diffusion pattern. b Migration of airflow field. c Diffusion of gas field. d Diffusion of dust field

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The particle size range set in our simulation process was 4.58 to 586 μm, and the proportion of the corresponding particle size was set. The specific steps were to first obtain coal lumps from the mining process in the field, pack them appropriately, and bring them back to the laboratory. A ball mill was used to grind and crush the coal lumps, and then a 400-mesh sieve was used to sort the ground coal powder and produce experimental coal powder. A Mastersizer 3000 laser particle size analyzer was then used to determine that the particle size range of the on-site dust was 4.58 to 586 μm and that the particle size distribution conformed to the Rosin–Rammler distribution.

Analysis of simulation results of airflow field

During the excavation, the airflow migration is represented by airflow migration trajectories. Based on the simulation results in Fig. 3, the migration rules and local characteristics of the flow field were analyzed in detail:

  1. (1)

    Because the air duct was near the tunnel wall surface, a free wall-attachment jet was formed along the wall surface after the airflow was ejected from the air-out surface at a velocity of 11 m/s. Owing to the great velocity difference between the formed jet and underground air, the surrounding air with the low velocity was constantly inhaled when the jet was ejected toward the cutting face. This led to a constant increase in the jet cross-section and along-the-way flow rate. Accordingly, a wall-attachment jet flow was formed 0–4 m from the cutting face on the left wall surface of the tunnel, as shown in Fig. 3a. Because of the limited tunnel space, after the jet hit the cutting face, a back-airflow with a velocity of 4.3m/s was produced, which moved toward the back along the right wall of the tunnel.

  2. (2)

    Part of the back-airflow gradually moved toward the jet zone owing to entrainment, thereby forming an entrainment vortex field at the tunnel center 0–15 m from the cutting face (Fig. 3c). After accumulating a lot of kinetic energy, the entrainment airflow moved together with the primary jet, and the secondary jet was formed and re-ejected toward the cutting face. The other part of the back-airflow moved toward and around the air duct, which formed an arc fan-shaped airflow. Owing to airflow continuity and gravity, the arc fan-shaped airflow moved downward and backward along the left wall of the tunnel at a velocity of 0.76 m/s and met the back-airflow produced near the cutting face after the collision with the tunnel floor, thereby forming a multi-direction vortex field 15–40 m from the cutting face (Fig. 3b).

  3. (3)

    The airflow was basically unaffected by the jet and vortex fields 40 m from the cutting face and gradually stabilized with a slight change in its energy. Finally, the airflow flowed toward the outlet of the tunnel at 0.5 m/s to form a stable airflow field (Fig. 3d).

Fig. 3
figure 3

Airflow trajectories and local characteristics

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Simulation of coupling diffusion of gas–dust dual-disaster-inducing pollutants

Based on the airflow field simulation results, the coupled pollution and diffusion rules of the gas and dust were simulated to determine the spatiotemporal evolution laws of their diffusion in the high-risk region.

Simulation of gas diffusion

  1. (1)

    Figure 4a displays the pollution and diffusion characteristics in the tunnel with a cloud chart. Apparently, the gas produced near the cutting face moved together with the jet toward the two sides on the bottom of the cutting face and continued to move toward the back of the tunnel with the back-airflow after hitting the floor and side wall of the tunnel. During the diffusion, the gas concentration increased along the jet direction. Overall, the gas concentration was higher on the left than on the right side of the tunnel. The gas distributed in the entire tunnel with a mean gas concentration of up to 0.40% at T = 129 s. Moreover, at T = 261 s, the gas concentration in the tunnel remained at 0.54%.

  2. (2)

    The gas easily accumulated in the top region of the tunnel near the cutting face, where a high-risk region with a high gas concentration of over 0.80% was formed. More specifically, the high-risk region was located around the cutting face and near the top of the tunnel. During the backflow diffusion, the gas followed the airflow and entered the entrainment vortex field due to entrainment. A great amount of gas accumulated in this region because it could not be transported to the back of the roadway in time, which aggravated the effect of the vortex field. Accordingly, more airflow and gas were inhaled in this region, as shown in Fig. 4b.

Fig. 4
figure 4

Illustration of gas diffusion characteristics and the position of high-risk region. a Schematic diagram of overall gas pollution diffusion. b Schematic diagram of the formation of high-risk region

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According to the simulation results, the top of the tunnel was a high-risk region in which the gas accumulated most easily. Therefore, the top of the tunnel 0.5 m from the roof was studied to investigate thoroughly the spatiotemporal evolution rules of the gas diffusion, as shown in Fig. 5. Evidently, the gas diffusion distance increased steadily, while the gas diffusion velocity decreased gradually with time. At T = 132 s, the gas was distributed in the entire tunnel; at that moment, the gas diffusion velocity was 0.83 m/s, and the mean gas concentration was 0.52%. The gas diffusion distance and time can be fitted with the following equation: Lg = 0.005t3 − 0.2764t2 + 7.8249t + 1.8842.

Fig. 5
figure 5

Spatiotemporal evolutions of gas diffusion in the top region of the tunnel

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Simulation of dust diffusion rules

  1. (1)

    As shown in Fig. 6a, a dust diffusion chart was plotted to study the dust pollution and diffusion conditions in the tunnel. Because it was generated around the cutting face, the dust moved with the back-airflow, hit the right wall of the tunnel, and gradually spread toward the back of the tunnel along the roof. During the diffusion, the dust concentration near the air inlet was significantly lower than that near the air-return passage, while the dust concentration in the top region was lower than that in the bottom region. At T = 125 s, the dust was distributed in the entire tunnel, and the mean dust concentration was 273.68 mg/m3; at T = 264 s, the dust concentration in the tunnel stabilized at 408.7 mg/m3.

  2. (2)

    Because the excavation tunnel served as an air-inlet and air-return passage, the dust particles were extremely easily distributed, and a high-risk region with a high dust concentration of over 200 mg/m3 was formed. Because a great amount of dust moved with the backflow and hit the right wall of the tunnel (i.e., the dust could not be transported to the back of the tunnel in time), some dust was attached to the intersection corner between the cutting face and tunnel wall. Because the airflow velocity in the bottom region of the tunnel was low, the attached dust particles settled easily and accumulated. At T = 25s, the high-risk region was formed, the range of which gradually expanded with time, as shown in Fig. 6b.

Fig. 6
figure 6

Illustration of dust diffusion characteristics and the position of high-risk region. a Schematic diagram of overall dust pollution diffusion. b Schematic diagram of the formation of high-risk region

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The height of the respiratory zone is the main height at which dust can enter the worker’s respiratory system. Therefore, the dust concentration monitoring section was installed 1.55 m above the tunnel floor to investigate the spatiotemporal evolution laws of the dust diffusion. As shown in Fig. 7, the dust diffusion distance and velocity were similar to those of the gas. At T = 128 s, the dust was distributed in the entire tunnel at a diffusion velocity of 0.86 m/s, and the dust concentration was 279.65 mg/m3. Based on data fitting, the dust diffusion distance and time can be expressed with the following equation: Ld = 0.0047t3 − 0.2583t2 + 7.8433t − 3.1899.

Fig. 7
figure 7

Spatiotemporal evolution of dust diffusion at respiratory height

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Airflow–gas–dust multi-field coupling mechanism

After determining the airflow–gas–dust coupling migration laws, two groups of comparative simulations were conducted in which only the airflow field and airflow–gas coupling field were simulated, respectively. Two airflow velocity monitoring sections (i.e., A1 (Y = 2.7 m) and A2 (Y = 0.5 m)) were set to compare the variations in the airflow velocity at different heights in the tunnel and to investigate the coupling interaction mechanisms among the three fields.

Figure 8 displays the real-time monitoring curves of the airflow velocity with respect to time at different positions corresponding to different heights. When only the airflow field was simulated, the overall airflow velocity in the tunnel was high, and the gas and dust reduced the overall airflow velocity to a certain degree. After the addition of gas to the airflow migration field, the airflow velocity in the top region of the tunnel was lower than the values under the two other conditions (the airflow field and the airflow–gas–dust coupling field) at the initial stage. At T = 85 s, the airflow velocity began to increase significantly; at T = 215 s, it stabilized at 0.66 m/s. After the addition of dust to the airflow and gas migration, the airflow velocity in the bottom region of the tunnel was also lower than the values under the other two conditions (the airflow field and the airflow–gas coupling field). At T = 56 s, the airflow velocity decreased to its minimum and then increased; at T = 350 s, the airflow velocity stabilized at 0.56 m/s.

Fig. 8
figure 8

Spatiotemporal variation curves of airflow velocity at different heights

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Based on the previously presented comparative research results, the multi-field coupling mechanism of the airflow, gas, and dust can be concluded. The properties and motion characteristics of the gas and dust affected the structure and velocity of the airflow field. In addition, the change in the airflow field affected the migration of the gas and dust and concentration distributions. The interaction among the three fields finally contributed to the equilibrium state. During the migration, the gas floated up because of the change in the concentration. Subsequently, it flowed against the wind after arriving at the roof and met the vortex field, thereby leading to a constant expansion of the entrainment range and an increase in the airflow velocity in the top region of the tunnel. Owing to self-gravity, the dust particles diffused or settled on the bottom of the tunnel. In the meantime, the surrounding air was transported toward the lower part of the tunnel. The overall kinetic energy in the lower part of the tunnel was increased owing to the collisions among the dust particles. In contrast to the strong driving force of the gas, the dust particles imposed a less violent effect. Therefore, the flow velocity in the lower part of the tunnel slightly increased.

Determination of optimal pollution-controlling distance of air duct

The diffusion and concentration distribution rules of dual-disaster-inducing pollutants in the tunnel when the air duct was arranged at different distances from the cutting face (i.e., the distance between the air duct and cutting face (denoted by Lp) was varied) were simulated to determine the optimal conditions.

Analysis of gas simulation results for different L p

Figure 9a displays the simulation results of the gas field in the tunnel for different Lp values. When Lp = 2 m, the gas concentration in the tunnel reached a maximum of 0.67%. The gas diffusion velocity gradually increased with increasing Lp. Simultaneously, the gas concentration in the stable state decreased gradually. When Lp = 7 m, the gas concentration reached the minimum of 0.42%. As Lp increased to 8 m, the gas diffusion velocity gradually decreased, and the gas concentration in the stable state slightly increased to 0.44%.

Fig. 9
figure 9

Simulation results of gas pollution and diffusion characteristics for different values of Lp. a Gas concentration after reaching the stability. b Gas concentration distribution patterns in the top region of tunnel

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Figure 9b presents the simulation results of the gas concentration distribution in the top region of the tunnel. When Lp ≤ 7 m, the high gas concentration in the high-risk region decreased gradually with increasing Lp. When Lp = 2, 3, 4, and 5 m, the high-risk regions were at 12, 8.8, 4.5, and 2.3 m. As Lp increased to 6 and 7 m, the high-risk region almost disappeared. For Lp = 8 m, the high-risk region expanded again.

Analysis of dust simulation results for different values of L p

Figure 10a presents the simulation results of the dust field in the tunnel for different Lp values. Evidently, the diffusion velocities and concentrations of the dust and gas followed similar trends. When Lp ≤ 6 m, the dust concentration reached its minimum of 287.5 mg/m3. Moreover, when Lp > 6 m, the dust concentration increased slightly. When Lp = 7 and 8 m, the dust concentrations reached 312.7 and 359.7 mg/m3, respectively.

Fig. 10
figure 10

Simulation results of dust pollution and diffusion characteristics for different values of Lp. a Dust concentration after reaching the stability. b Dust concentration distribution patterns at the height of the respiratory zone

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Figure 10b displays the simulation results of the dust concentration distributions at the height of the respiratory zone. When Lp < 5 m, the high-risk region with the high dust concentration was located in the narrow space between the cutting face and right wall of the tunnel; the area significantly decreased with increasing Lp. When Lp = 2, 3, and 4 m, the distribution range of the high-risk region reached 47, 21, and 8 m, respectively. When Lp = 5 and 6 m, the high-risk region almost disappeared, thereby causing low damage to humans.

Determination of optimal pollution-controlling distance of air duct

For different values of Lp, the airflow velocity in the vortex field in the top region of the tunnel was the main factor affecting the gas concentration distribution. When Lp ≤ 7 m, the distance of the attached jet under restriction increased constantly with increasing Lp, while more and more back-airflow entered the entrainment-induced vortex field when passing through the air-out surface of the air duct. This generated a wider range of influence and increased the dilution effect on the gas, particularly in the top region of the tunnel. When Lp > 7 m, the air quantity arriving at the cutting face could not effectively transport the gas to the back of the tunnel. This was accompanied with a decrease in the dilution effect of the gas and a slight increase in the gas concentration.

For different values of Lp, the airflow velocity at the intersection corner between the cutting face and tunnel wall was also a main factor affecting the dust concentration distribution. When Lp ≤ 6 m, the time required for the jet to arrive at the cutting face decreased with decreasing Lp. Accordingly, the jet section decreased with decreasing divergence degree, and the formed back-airflow became more concentrated. Consequently, less and less airflow entered the bottom region of the tunnel, which aggravated the accumulation of dust particles and increased the dust concentration in the tunnel. When Lp > 6 m, a small amount of airflow arrived at the cutting face, and the dust could not be transported to the back of the tunnel in time, which slightly increased the dust concentration. The variation trend was similar to that of the gas.

Subsequently, the optimal pollution-controlling distance between the air dust and cutting face (Lp) was determined. Based on the previously presented contrastive analysis, when Lp = 5–8 m, the gas concentration in the tunnel remained below 0.50%. When Lp = 6 m, the dust concentration reached a minimum of 287.5 mg/m3. Therefore, the optimal value of Lp was 6 m. According to the comparison with the conditions corresponding to the maximal gas and dust concentrations (Lp = 2 m), the decrease ratios of the gas and dust were 32.84% and 47.02% (Lp = 6 m), respectively. As shown in Fig. 11, when Lp = 6 m, the gas concentration remained within a safe range, while the dust concentration could be minimized to ensure the workers’ respiratory health.

Fig. 11
figure 11

Decrease ratios of gas and dust concentrations for different values of Lp

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Field measurement

Finally, the gas and dust concentrations in the tunnel for different Lp were measured and compared with the previously presented simulation data to validate the accuracy of the simulation results.

Based on the actual field conditions, the corresponding measuring points were arranged based on the diffusion and distribution characteristics of the gas and dust. The measuring points were located at X, Y, and Z, where X denotes the distance from the cutting face, Y denotes the height above the tunnel floor, and Z denotes the distance from the left wall of the tunnel. For the gas measurement, the measuring points were set near the cutting face and tunnel roof (i.e., X = 1, 3, 8, 15, and 30 m; Y = 2.7 m); for the dust measurement, X was set to 5, 10, 30, 60, and 90 m to determine the dust concentration in the entire tunnel, and Y was the height of the respiratory zone (Y = 1.55 m). To be specific, as shown in Fig. 12, Point #A (X, 2.7, 1.6) and Point #B (X, 2.7, 4.5) were chosen for the gas measurement, while Point #C (X, 1.55, 1.6) and Point #D (X, 1.55, 4.5) were chosen for the dust measurement.

Fig. 12
figure 12

Field measurements of gas and dust concentrations

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The gas concentration was measured with the CJG10 optical interference methane detector, while the dust was sampled with the AKFC-92A mine dust sampler; its concentration was measured in the laboratory. Tables 1,2,3,4 compare the measured concentrations and numerical simulation data for the different measuring points for different Lp. Overall, the relative errors between the measured and simulated gas and dust concentrations were 1.23% to 18.52% and 0.24% to 19.73%, respectively. As shown in Fig. 13, the error was mostly below 5%, which proves that the diffusion and distribution rules of the gas and dust pollutants determined with the numerical simulations represented the actual field conditions.

Table 1 Gas concentration at the gas measuring point A (X, 2.7, 1.6)
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Table 2 Gas concentration at the gas measuring point B (X, 2.7, 4.5)
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Table 3 Dust concentration at the dust measuring point C (X, 1.55, 1.6)
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Table 4 Dust concentration at the dust measuring point D (X, 1.55, 4.5)
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Fig. 13
figure 13

Relative error distribution diagram

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Conclusions

The multi-field coupling mechanism between the airflow, gas, and dust in an excavation tunnel was investigated. The properties and motion characteristics of the gas and dust fields changed the original stable state of the airflow field. In addition, the change in the airflow field in terms of the structure and velocity affected the diffusion characteristics of the gas and dust. The three fields reached a coupled stable state. During the coupling process, the diffusion distance of the gas in the tunnel and diffusion time can be described with the following equation: Lg = 0.005t3 − 0.2764t2 + 7.8249t + 1.8842. The diffusion distance of the dust in the tunnel and diffusion time can be expressed with the following equation: Ld = 0.0047t3 − 0.2583t2 + 7.8433t − 3.1899.

  1. (1)

    The gas and dust preferentially accumulated in the top region of the tunnel near the cutting face and intersection angle between the cutting face and tunnel wall. When Lp = 5–8 m, a low gas concentration of below 0.50% accumulated in the tunnel; Lp = 6 m led to the least dust accumulation; the minimal dust concentration was 287.5 mg/m3. Therefore, Lp = 6 m is the optimal pollution-controlling distance of the air duct in the excavation tunnel. Under optimal conditions, dust pollution can be minimized, and a safe level of gas concentration was maintained to ensure the safety and health of workers.