Insights into turbulent airflow structures in blind headings under different ventilation duct distances | Scientific Reports

Scientific Reports volume 14, Article number: 23768 (2024) Cite this article 80 Accesses Metrics details The paper explores the 3D stationary vortex structure of turbulent airflow near the dead-end

Scientific Reports volume 14, Article number: 23768 (2024) Cite this article

80 Accesses

Metrics details

The paper explores the 3D stationary vortex structure of turbulent airflow near the dead-end face of a blind heading, ventilated via a forcing ventilation system. Despite its significance in blind heading ventilation, previous studies primarily focused on temporal dynamics of harmful impurities, overlooking flow structure details crucial for mass transfer processes. Our study delves into the ventilation flow structure across diverse parameters of the auxiliary ventilation system. Alongside standard flow visualization tools, we introduce three dimensionless indicators to comprehensively characterize flow structure, facilitating analysis of its variations with parameter changes and quantitative evaluation of system efficiency. Analysis revealed the formation of a single large-scale vortex within the entire range of considered ventilation system parameters in the heading. This vortex induces a significant increase in air circulation, approximately 2.5–3.5 times greater than airflow emerging from the ventilation duct’s end, thus intensifying mass transfer processes within the heading. We found that ventilation efficiency of the dead-end face zone in a blind heading with a 29.2 m² cross-section decreases linearly with increasing distance between the ventilation duct’s end and the dead-end face. However, compensating for this distance by increasing duct velocity is feasible, bearing significant implications for mine ventilation safety, particularly in ventilating blind headings with distant ducts from the dead-end face.

The operational efficiency and safety of blind headings in underground mines are closely related to the effectiveness of the auxiliary ventilation system. This system transforms the dead-end area into a functional part of the mine’s ventilation network, ensuring adequate air flow and contaminant removal. The most commonly used system for ventilating blind headings is the forcing system. In this system, fresh air is supplied directly to the dead-end face through a ventilation duct1,2,3. Some countries mandate the use of forcing ventilation systems in their regulatory acts and require special reasoning for any deviation from mandatory cases4,5.

The primary advantage of forcing ventilation in the drill-and-blast excavation method lies in the presence of a high-velocity jet of fresh air. This jet ensures the efficient displacement of contaminated air from the dead-end face zone. Ventilating the narrow frontal zone near the dead-end face poses the greatest challenge. Here, only an intense air jet penetrating this zone and flowing about the dead-end face proves most effective for ventilation.

In situations where toxic or explosive gases are not a significant concern, and pollution mainly comes from dust or heat during mechanized cutting, the forcing ventilation system might not work as well as should exhausting system1,4.

Practically speaking, we gauge the effectiveness of the forcing ventilation system by how long it takes for impurity levels to decrease to the maximum allowable level within the entire space of the blind heading. This time depends on the volume of air entering the dead-end face zone, which, in turn, relies on the rate of fresh air entering the face and how far it penetrates into the dead-end face zone. The latter largely hinges on the distance between the end of the ventilation duct and the dead-end face. The smaller this distance, the better the ventilation in the dead-end face zone.

However, placing the end of the ventilation duct too close to the dead-end face is impractical. In such cases, its integrity can be regularly compromised during an explosion due to shock waves and the scattering of rock fragments, leading to a loss of operational capabilities6,7. This could necessitate halting the technological process for ventilation duct repairs, significantly reducing productivity.

Hence, finding and rationalizing the best parameters for auxiliary ventilation systems in blind headings has always been crucial8. Throughout much of the twentieth century, the challenge of studying 3D flows collided with the need for theoretical solutions. Analysis of ventilation processes in blind headings largely relied on labor-intensive full-scale experiments, alongside limited analytical models and methods for calculating jet flows3.

The recent advancement of 3D numerical simulation methods for ventilation processes has offered new research possibilities, but it has also raised several methodological questions. In our view, two key areas deserve special attention: ensuring the adequacy of turbulence models (both physical and numerical) for the studied flow, and developing tools to visualize and/or comprehend how the flow structure depends on ventilation system parameters, enabling effective management in practice.

The flow in blind headings is complex, comprising streaming flow and large-scale vortex flow near the dead-end face, along with intense counterflows and low-velocity turbulence. These factors collectively influence vortex motion and require careful consideration in turbulence modeling. Primarily, the Reynolds-averaged Navier–Stokes (RANS) approach is commonly used. It divides the vortex’s motion into an averaged part influenced by velocity structure and a pulsating part describing turbulent mixing processes. This includes the displacement of specific small air volumes from the dead-end face zone, along with turbulent viscosity and diffusion at the microlevel.

A review of the literature reveals that researchers employ various turbulence models to describe aerodynamic processes in blind headings: Realizable k-epsilon model4,9,10, RNG k-epsilon model11,12, Spalart-Allmaras model13, Reynolds stress model14, among others. The most commonly used model is the relatively simple standard k-epsilon model15,16,17,18,19. However, the results of calculations using these models consistently exhibit certain deviations from experimental data17, which themselves are not perfect as a ‘comparison standard’ for validation.

The challenges in fully capturing the complex characteristics of real blind headings, such as their varying configuration, cross-sectional area, including macro-roughness, air flow pulsation, and the impact of buoyancy forces due to non-isothermal conditions, are fundamental. Moreover, inaccuracies in initial data when simulating ventilation problems can often outweigh the influence of the chosen turbulence model itself20. In this context, the choice of a specific turbulence model should prioritize the stability of the iterative computational procedure’s convergence and the simplicity of numerically implementing the nonlinear partial differential equations of the selected model.

Previously, we opted for the “Realizable k-epsilon model” and validated it through a detailed field experiment21. The work21 was the first stage of a large study that we continue in this paper, and the experimentally measured airflow parameters in a real blind heading provided validation for the model that we use in this paper.

It’s worth noting that currently, 3D numerical simulations of turbulent flows in blind headings are extensively used to analyze various physical processes and auxiliary ventilation systems. These include dust transfer18, gas dynamics22,23, DPM24, as well as ensuring adequate oxygen concentration11 and maintaining a comfortable microclimate25,26.

The flow structure in these and similar problems depends on numerous interconnected factors. For instance, a relatively straightforward issue regarding the stationary, isothermal flow of an incompressible medium (such as air) is influenced by nine parameters: the flow rate of fresh air supplied to the heading (\(\: {{Q}}_{{\text{o}}}\)), the initial velocity of the air jet leaving the ventilation duct (\(\: {{U}}_{{\text{o}}}\)), the distance from the end of the ventilation duct to the dead-end face (L), the cross-sectional area of the heading (S), the diameter of the duct (d), the location of the duct axis in the cross-sectional plane of the heading (top, bottom, side, etc.), described by two radial coordinates (\(\:r,\:\phi\:\)), as well as the air density (\(\:\rho\:\)) and dynamic viscosity (\(\:\mu\:\)). Analyzing the behavior of even the primary indicator—the air velocity field \(\:U(x,y,z)\)—is quite challenging under these conditions, especially considering that systems of nonlinear equations generate nonlinear dependencies.

As a result, in most publications, the findings of studying such multi-parameter problems are typically presented through separate illustrations showing the general distribution of air flows, utilizing standard visualization tools. These are often accompanied by qualitative conclusions regarding the influence of specific parameters9,11,12,24,27. Quantitative conclusions about the extent of influence of certain parameters of the ventilation duct and auxiliary fan on the ventilation efficiency of blind headings are relatively scarce22,25. This scarcity can be attributed at times to the complex nonlinear dependencies of the 3D flow on the problem parameters22 or a limited number of performed calculations. Additionally, a detailed analysis of the air flow distribution is often avoided15,18,25 or conducted superficially, relying solely on visual analysis of the 3D distribution of air flows in the computational domain24,27,28. Occasionally, to evaluate the ventilation efficiency of a blind heading, it is necessary to employ non-standard indicators, such as ‘mean air age’9,29. Moreover, given the practical orientation of most studies, authors usually focus solely on specific technical parameters of blind headings, dead-end tunnels, and particular ventilation scenarios, proposing targeted measures to enhance the efficiency of auxiliary ventilation systems30. Simple relationships between the parameters of the heading and the auxiliary ventilation system are derived only in a few works18.

In the current literature, there is a noticeable scarcity of studies analyzing the intricate influence of multiple parameters of the auxiliary ventilation system on the airflow dynamics within blind headings6,31,32. Feroze and Genc31 utilized 3D numerical simulations to investigate the qualitative relationship between airflow near the dead-end face and key parameters of the auxiliary ventilation system. They assessed ventilation effectiveness by considering airflow at distances of 0.3–0.5 m from the dead-end face. García-Díaz et al.32 delineated effective and stagnant (“dead”) zones within blind headings, demonstrating that the length of the effective zone can extend up to 50 m and exhibits a nonlinear dependence on airflow. Their criterion for distinguishing these zones was based on the transition of the average transverse air velocity in the cross-section of the blind heading to negative values. Kazakov et al.6 observed discrepancies among existing calculation formulas for determining the air jet penetration range. They proposed associating this range with the distance at which the air velocity in the jet decreases to 0.25 m/s. Similar conclusions were drawn by other researchers9,32.

A review of the literature highlights a lack of systematic and comprehensive understanding of the patterns governing changes in ventilation flow structures at the dead-end face zone employing the forcing ventilation systems. Key parameters, such as the distance between the ventilation duct’s end and the dead-end face, remain underexplored.

Understanding the movement patterns of air masses in blind headings, which dictate concentration fields and gas (and dust) dynamics, is vital for predictive theory and practical ventilation improvement strategies. However, this comprehension is hindered by the absence of suitable tools for visualizing the qualitative state of airflow. In 3D flows, the stream function’s ability to visually represent flow structures, as seen in 2D flows, is lost. Instead, analysis requires consideration of ‘flat’ sections capturing instantaneous flow states at local points. This abundance of options complicates analysis and necessitates the use of generalized indicators to condense information into understandable patterns.

In this study, we introduce a novel tool termed ‘vision sense’ alongside standard visualization methods. This tool consists of three main generalized indicators, providing insights into ventilation flow structures in blind headings ventilated using the forcing system. These indicators enhance understanding of airflow changes across various ventilation conditions. Further details on these indicators and their applications will be discussed as we progress through our research.

We examined airflow dynamics within the confines of a blind heading, which is ventilated via a forcing system utilizing a ventilation duct (see Fig. 1). The heading measures 80 m in length, 5.34 m in width, and 5.5 m in height, featuring an arched section with a cross-sectional area of 29.2 m². Positioned along the side wall, closer to the roof, is a ventilation duct with a circular cross-section and an area of 0.8 m². These dimensions and configurations correspond to those observed in the Kupol gold mine, as outlined by Kamenskikh et al.21.

Geometric model of a blind heading with a ventilation duct.

The airspace within the heading, characterized by a length \(\:{L}_{h}\) and an average cross-sectional area \(\:S\) is partitioned by the ventilation duct’s end, situated L units from the dead-end face. This division yields two primary zones interconnected as follows:

Dead-end face zone: Here, the bulk of harmful impurities (gases and dust) and a stream of fresh air are introduced to facilitate their removal at a flow rate of \(\:{Q}_{0}\).

Ventilation duct zone: Spanning from the end of the ventilation duct to the mouth of the heading, this area serves as the conduit for expelling contaminated air emanating from the dead-end face zone.

The most challenging and crucial aspect of ventilation lies in the narrow zone adjacent to the dead-end face. Let’s call it the frontal zone. Its thickness, as determined in our previous work21, is set at 1 m to align with the diameter of the ‘breathing zone’ of a person working directly at the dead-end face.

The airflow structure originating from the face and progressing along the heading’s length is generally straightforward and typical, with its primary significance lying in its impact on ventilation time (to achieve standard pollution values). This time depends on the initial velocity of the air jet, \(\:{U}_{0}={Q}_{0}/S\) (in accordance with the law of conservation of mass), and the total length of the heading, \(\:{L}_{h}\).

The ventilation flow pattern within the dead-end face zone is governed by its geometric characteristics and the influx of fresh air supplied to the face at an initial velocity of \(\:{U}_{0}={Q}_{0}/s\), where \(\:s\) denotes the cross-sectional area of the ventilation duct.

The geometric configuration of the air space within the dead-end face zone is defined by the ratio of the distance between the end of the ventilation duct and the dead-end face L, to the characteristic transverse dimension of the heading, which can be represented by either \(\:\sqrt{S}\) (where S is the cross-sectional area of the heading) or the equivalent diameter of the heading D, defined as D = 4S/P (where P is the perimeter of the cross-section of the heading). We referred to this geometric parameter as the form factor, denoted by \(\:f=L/\sqrt{S}\), in our previous study21.

Let us recall that according to the regulatory requirements in force in Russia, when \(\:L=10\) m, the form factor varies from 5 for a heading with \(\:S=4\) m² to 2.5 for a heading with \(\:S=16\) m². For a distance \(\:L=15\) m allowed at \(\:S\ge\:16\) m², the form factor will be 3.75 for a heading with \(\:S=16\) m², decreasing as the cross-sectional area increases. The form factor is particularly interesting since the relationship of geometric parameters significantly influences the flow structure.

Moreover, the propagation patterns of jets in the airspace of a dead-end face zone are also associated with the ratio of the cross-sectional area of the air duct \(\:{S}_{d}\) to the cross-sectional area of the workings \(\:S\), which characterizes the tightness of the jet (the influence of the limited space of a heading on the outflow of the jet), defined by us as \(\:F={S}_{d}/S\) (where \(\:F=0\) when flowing into infinite space, and \(\:F=1\:\)when the jet is completely confined by the heading walls). The dynamic characteristics of this jet determine the velocity field and the configuration of the structure of forward (in the direction of the dead-end face) and return (from the dead-end face) flows, depending on the geometry of the heading air space.

This study primarily focuses on examining the variations in the structure of air flows at various distances from the end of the ventilation duct to the dead-end face (in the range from 10 to 50 m with a fixed cross-section \(\:S=29.2\) m²). This determines the range of change in the form factor from 1.85 to 9.25 (with the most typical values for practical application being 3 to 6). Additionally, the results of a series of options with a changed velocity \(\:{U}_{0}\) of the fresh jet flowing from the end of the ventilation duct were analyzed.

The mathematical model of a stationary turbulent, isothermal, incompressible air flow is based on the continuity and RANS equations:

where is the air density, is the static pressure, is the molecular viscosity of air, is the Reynolds-averaged air velocity vector, \(\:\overrightarrow{\varvec{F}}\) is the vector of the averaged external body force, is time, ∇ is the Hamilton operator, \(\:{\Delta\:}\) is the Laplace operator, and R is the Reynolds turbulent stress tensor, determined from the concept of scalar “turbulent/eddy viscosity”:

where is the kinetic turbulent energy, \(\:{\mu\:}_{t}\) is the turbulent viscosity, and E is the unit tensor.

To close the system of Eqs. (1), (2), we used (in addition to the Boussinesq hypothesis) a two-parameter Realizable k − ε turbulence (RKE) model. According to Zhang and Che33, it performs better than other two-parameter turbulence models when simulating structurally complex turbulent air flows. It also provides better calculation convergence for flows involving rotation, boundary layers with severe adverse pressure drops, separation, and recirculation.

To determine the turbulent kinetic energy and the dissipation rate of turbulent kinetic energy , the following equations were solved within the RKE model:

where \(\:{G}_{k}\) is the generation of turbulent kinetic energy due to average velocity gradients; \(\:{\sigma\:}_{k}\) and \(\:{\sigma\:}_{\epsilon\:}\) are turbulent analogues of the Prandtl number; \(\:S\) is the invariant of the tensor \(\:\varvec{S}\) of flow deformation rates; \(\:{C}_{1}\) and \(\:{C}_{2}\) are empirical coefficients of the model.

Within the framework of the chosen turbulence model, turbulent viscosity \(\:{\mu\:}_{t}\) was determined by the formula:

where \(\:\varvec{\Omega\:}\) is the rotation rate tensor in a rotating reference frame taking into account angular velocity; \(\:{A}_{0}\) and \(\:{A}_{s}\) are model parameters.

The system of Eqs. (1), (2), (3), (4), (5), (6), (7), (8) was supplemented with boundary conditions on the walls of the heading and the ventilation duct (no velocity slip), at the flow inlet into the computational domain (velocity inlet condition at the end of the ventilation duct) and the flow exit from the computational domain (pressure outlet condition at the mouth of the heading). The turbulence intensity at the inlet zone to the domain was set to 5%. Zero static pressure was set at the outlet zone.

The numerical solution of the system of Eqs. (1), (2), (3), (4), (5), (6), (7), (8) was carried out by the finite volume method in the ANSYS Fluent software package. The computational domain was discretized using an unstructured tetrahedral mesh (see Fig. 2). The mesh was built in the Ansys Workbench Meshing module. A prismatic boundary layer was specified on the solid walls of the heading and duct to correctly display high gradients of air flow velocity down to the logarithmic sublayer. The characteristic dimensions of the cells and the number of boundary layers near the walls of the heading and the duct are determined based on the conditions of convergence of the stationary solution and independence of the solution from the mesh.

When analyzing mesh independence, we compared airflow parameters calculated on four different meshes. The coarsest mesh had a maximum tetrahedral cell size of 28 cm and consisted of 710,810 cells, while the finest had a cell size of 10 cm with 6,002,952 cells. Two intermediate meshes had cell sizes of 14 and 20 cm. As the mesh quality changed, the boundary layer detailing also varied proportionally. We quantitatively assessed how changes in the longitudinal coordinate along the heading axis affected two flow characteristics: the maximum air velocity in the section relative to the average duct velocity \(\:{V}_{0}\), and the airflow rate towards the dead-end face relative to the duct airflow \(\:{Q}_{0}\) (see Fig. 3). We concluded that the flow characteristics changed only slightly across the range of mesh sizes studied. We selected a mesh with a 14 cm tetrahedral cell size as the main option, as it provided adequate flow distribution detail in the graphical analysis. At the same time, the height of the prismatic element closest to the wall was about 1.5 cm. The average \(\:{Y}^{+}\) value for the heading and duct walls was 224.

Finite-volume mesh in a vertical section of the computational domain passing through the axis of the ventilation duct.

Verification and validation of the numerical solution: the maximum air velocity in the cross-section related to the average air velocity in the duct (a) and the air flow moving towards the dead-end face, related to the air flow in the duct (b), the case of distance L = 15 m.

The final number of cells depended on the distance from the end of the ventilation duct to the dead-end face. For the cross-section of a blind heading of 29.2 m2 considered in the work, the calculation options yielded varying numbers of cells. Specifically, the smallest number of cells (2,945,810 cells) was implemented for the calculation option with \(\:L=50\) m, while the largest number was utilized for the calculation option with \(\:L=10\) (3,103,213 cells).

The SIMPLE algorithm was employed to couple the pressure and velocity fields. To achieve a stationary distribution of air parameters, adjustments were made to under-relaxation factors. The iterative procedure continued until the residuals for all flow parameters reached a value of 10− 5.

As noted earlier, the model we developed was validated using field measurements taken in a blind heading of a gold mine in Chukotka. Figure 3 also presents a comparative analysis of the model data and the field experiment for a distance of \(\:L\) = 15 m. The figure shows that the mathematical model qualitatively predicts the pattern of air stream attenuation accurately. However, a quantitative analysis reveals some discrepancies between the theoretical predictions and the experimental results. These discrepancies can be attributed to both model errors (such as neglecting the macro-roughness of heading walls) and random factors not accounted for in the experiment (such as slight ‘sloshing’ of the duct). At the same time, we believe that our model provides a good quantitative description of the flow patterns near the end of the ventilation duct and near the dead-end face. A more detailed analysis of the experimental study is provided in21.

The primary purpose of ventilation in mining is to ensure safe operations while maintaining high productivity. In the case of the drill-and-blast method of excavation, this involves minimizing the ventilation time between the explosion and the re-entry of personnel into the work area.

It is known that this time is influenced by the volume of the ventilated zone, the amount of fresh air entering it, and the level of initial pollution relative to the maximum permissible values. The criterion for such efficiency is the exchange time of the most difficult-to-ventilate zone—the frontal zone. This exchange time should be less than the ventilation time for the entire volume of the blind heading. This requirement imposes specific demands on the flow rate of fresh air entering the frontal zone and, consequently, on the total flow rate in the blind heading.

For effective ventilation, the fresh air jet exiting the ventilation duct must reach the frontal zone with the required flow rate. This requirement can be conveniently expressed using the concept of the jet “range,” which has been discussed in various studies. Essentially, the range of the jet refers to the distance over which the jet propagates as a distinct flow structure. This range should be approximately equal to or slightly greater than the distance from the end of the ventilation duct to the dead-end face.

Although the term “jet range” is widely used in theory and practice, it is not formally defined. We associate the “jet range” with the distance between the start of the jet and the frontal zone (1 m from the face), where the airflow entering the frontal zone ensures effective ventilation.

We have chosen a minimum air velocity of 0.15 m/s as the criterion for the absolute minimum flow entering the frontal zone and flowing along the dead-end face. An additional, less stringent criterion is 0.25 m/s6. At the same time, to ensure comfortable working conditions, the maximum air velocity in the working area, approximately 2 m above the ground, should not exceed 4 m/s. This means that the fresh air flow rate entering the heading should be no less than \(\:0.15\:S\) and no more than 4S. For the base case we are considering, with \(\:S\:=\:29.2\:\)m², this gives \(\:{Q}_{0}\:=\:4.38\:\--\:116.8\) m³/s.

The complexity of the 3D turbulent vortex flow structure in the dead-end face zone requires identifying several quantitative indicators. These indicators should clearly characterize the flow structure, facilitating its understanding, and allow a quantitative description of changes in ventilation efficiency criteria based on variations in the flow’s nature when altering the basic ventilation parameters.

Our analysis showed that the most informative indicators for understanding the flow structure are the following three, which are normalized to the average initial velocity or initial flow rate of the air jet. For the base case of our study, \(\:{Q}_{0}\:=17.4\) m3/s and \(\:{U}_{0}=21.75\) m/s.

As the first indicator, we chose the value traditionally considered in the theory of “jet velocity”3. This refers to the maximum longitudinal Reynolds-averaged flow velocity directed towards the dead-end face, taken at various cross-sections along the x-axis. The behavior of this value as it approaches the frontal zone characterizes the intensity of ventilation.

Using the selected coordinate system (see Fig. 1), the corresponding dimensionless indicator is calculated using the formula:

where is the coordinate along the excavation axis, measured from the end of the ventilation duct; is the component of the velocity vector along the x-axis, in the same direction as the axis of the ventilation duct; and the function \(\:{\text{max}\left(.\right)}_{x}\) selects the maximum value of the parameter in the cross-section of the excavation characterized by the coordinate.

The second indicator is the forward flow (air flow rate directed towards the dead-end face). This indicator clearly characterizes the air masses attached to the jet and the interaction of the forward flow with the dead-end face.

The corresponding dimensionless indicator can be expressed as the ratio of the forward air flow \(\:{Q}^{+}\) directed to the dead-end face to the air flow \(\:{Q}_{0}\) supplied through the duct to ventilate the heading. In this case, the air flow in the considered section of the heading is determined by the formula:

where integration occurs over the area \(\:S\left(x\right)\) of the cross-section of the heading, characterized by the coordinate . The \(\:{I}_{Q}\) indicator characterizes the advective transport of air masses and the development of the jet, as well as the structure of a large-scale vortex circulating in the dead-end face zone. The \(\:{I}_{U}\) indicator characterizes the behavior of the jet, including its energy, dynamic “power,” and propagation range.

A priori, we can distinguish three possible typical situations for ventilating a blind heading, each determining the flow structure and ventilation efficiency.

With relatively small distances between the end of the ventilation duct and the dead-end face, and a sufficiently high initial velocity of the air jet, the forward flow hits the dead-end face, generating additional turbulence that contributes to the effective ventilation of the frontal zone.

At intermediate values, the forward flow smoothly turns due to the law of conservation of mass (continuity equation), transforming into a transverse flow that flows along the dead-end face, aiding in achieving the minimum acceptable ventilation of the frontal zone.

With a further increase in , the forward flow, limited by the range of the jet, fails to reach the dead-end face, resulting in a stagnant, difficult-to-ventilate zone. This zone includes a low-intensity vortex of reverse swirl relative to the main flow.

The first and second cases are evident from our calculations depicted in Fig. 4, illustrating the spatial distribution of turbulent kinetic energy. We did not encounter the third case within the range of values considered, extending up to 50 m. With even greater distances , the flow in the frontal zone starts to oscillate and becomes inherently unsteady. This phenomenon is likely attributed to the disruption of the vortex structure near the dead-end face, its detachment from the face, and subsequent transformation. Since our study specifically focused on stationary flow regimes, we have touched upon this issue and deferred it for future investigation.

Distribution of turbulent kinetic energy in longitudinal vertical sections of the heading passing through the duct axis.

In Fig. 4, the turbulent kinetic energy is minimal in the streamlined flow of fresh air from the duct, with the core of the jet and the Coanda effect clearly visible.

High values of turbulent kinetic energy (yellow, orange, and red zones) are typical where the return flow and the forward jet collide, or when the jet strikes a solid obstacle such as the dead-end face. This results in the formation of powerful vortices (local peaks in turbulent kinetic energy near the dead-end face).

As increases, turbulence generation decreases, and turbulent kinetic energy diminishes considerably. In the lower right corner of the figures, within the return flow zone, a vortex zone is clearly observable, characterized by stable rotation and averaged parameters, resulting in low values of turbulent energy.

Considering the aforementioned conclusions, a comprehensive analysis of the airflow dynamics in the dead-end face zone necessitates examining not only the characteristics of longitudinal airflow but also the nature of airflow in the cross-sectional plane of the heading.

To address this, we introduce the third primary dimensionless indicator—the average transverse velocity of the airflow across the heading’s cross-section, determined as follows:

where and represent the y- and z-components of the airflow velocity vector, respectively.

The significance of this indicator lies in its ability to characterize airflow perpendicular to the main (longitudinal) movement. This allows for the identification of conventional boundaries of the vortex flow—namely, the attachment of its air masses to the forward flow and the rotation of a portion of the forward flow to create a return flow. When combined with the \(\:{I}_{Q}\) indicator, which quantifies the magnitude of the forward flow, the behavior of this indicator enables monitoring of the features of the large-scale structure of the 3D flow.

The analysis of the results from the multiparametric numerical simulation of the ventilation of a blind heading was conducted using both classical methods of visualizing flow parameters in CFD-post and the dimensionless indicators proposed above.

Figure 5 provides a 3D view of the air jet entering the dead-end face zone from the end of the ventilation duct, represented by velocity magnitude distributions in various cross-sections. This figure effectively illustrates the jet’s expansion and the forward flow development due to increased additional air volume. However, it is less informative for analyzing the return flow and the overall flow structure. The Coanda effect, the nature of the ventilation in the frontal zone, and the entrainment of air from the heading’s ventilation duct zone into the air jet exiting the ventilation duct are not easily discernible to the researcher’s eye.

Contour plots of the air velocity magnitude in various cross sections of the blind heading at L = 10 m, f = 1.85, U0 = 21.75 m/s (this value corresponds to Re0 = 1,500,000).

Let us recall that the most significant factors in forming the structure of air flows in a blind heading, ventilated via a forcing system, are the law of conservation of mass and the incompressibility of the medium, as described by the continuity equation. Due to these principles, a return flow arises, with the flow rate in each cross-section of the heading equal to the forward flow rate towards the dead-end face. The values of forward and return air flows vary along the axis of the blind heading.

The high-velocity air jet leaving the ventilation duct creates a large-scale vortex structure, where the main vortex occupies not only the dead-end face zone but also part of the ventilation duct zone. Part of the air contributing to the main vortex is drawn from the ventilation duct zone.

To illustrate these principles, Fig. 6 shows streamlines and contour plots of the streamwise velocity in the longitudinal section of the computational area, passing through the axis of the ventilation duct, with three different distances (\(\:L\)) between the end of the ventilation duct and the dead-end face (10, 15, and 21 m).

Streamlines of the main vortex in the dead-end face zone with a characteristic high-velocity air jet and a return low-velocity air flow: (a) – L = 10 m, (b) – L = 15 m, (c) – L = 21 m.

For all presented distances, the Coanda effect is clearly visible, i.e., the curvature and “sticking” of the jet to the nearest solid wall. This effect in the ventilation of blind heading was also noted by Kazakov et al.6, Liang et al.34, and others. The clear evidence of the Coanda effect in our calculations indicates the good predictive power of the numerical model used.

Figure 6 clearly shows the jet flow, the presence of forward and return flows, the main airflow around the dead-end face in the frontal zone, the approximate size of the main vortex, and the spatial complexity of the vortex movements.

Analyzing individual flat sections of the general spatial structure of the flow is complicated by the tilt of the entire large-scale 3D flow structure. This tilt occurs due to the asymmetric location of the ventilation duct relative to the center of the heading’s cross-section. The slope generally depends on the transverse dimensions of the heading and the location of the ventilation duct in the cross-section.

To fully visualize the flow structure with this approach, it is necessary to compare the velocity field in many sections of the blind heading. Figures 7, 8 illustrate this comparison, showing streamwise velocity distributions in several cross-sections of a heading. This allows for a clearer analysis of the division of the cross-sectional area into forward and return flow regions.

Contour plots of the streamwise velocity in the cross section of the heading at various distances from the end of the ventilation duct, at L = 21 m: (a) – 5 m, (b) – 12 m, (c) – 17 m.

Contour plots of the streamwise velocity in the cross section of the heading at various distances from the end of the ventilation duct, at L = 50 m: (a) – 5 m, (b) – 20 m, (c) – 40 m.

Figures 7, 8 show typical features of air flow structure in several cross-sections of the heading. Near the end of the ventilation duct, the velocity field has a complex structure due to the reorganization of the vortex, which depends on the distance L. However, at a distance of 10–20 m from the end of the ventilation duct to the dead-end face, the interface between the direct and return flows acquires a stable shape that remains almost unchanged up to the dead-end face.

It is evident that near the end of the ventilation duct, the air jet emerging towards the dead-end face is much narrower than the return flow zone (see Fig. 8a). As the air jet progresses, it expands (see Fig. 8b), bends under the influence of the Coanda effect (see Fig. 8c), and begins to occupy a part of the cross-section comparable to the return flow area. This indicates that within a wide range of distances \(\:L\) in the dead-end face zone, one large-scale vortex dominates, determining the patterns of mass transfer of impurities. Within this large-scale vortex, smaller vortex structures are embedded, especially near the dead-end face.

However, the above results illustrate only a few typical cases from a large series of numerical calculations for various distances between the end of the ventilation duct and the dead-end face, different flow rates, and different sections of the heading. This limited scope does not allow for a detailed general analysis covering the entire range of studied parameters. Such an analysis is possible and more convenient in terms of invariant indicators for the slope of the flow structure relative to Cartesian coordinates and integral cross-sections of the flow structure as a whole, which we introduce in the next section.

First, let us analyze the changes in the relative maximum longitudinal air flow velocity (indicator \(\:{I}_{U}\)) with different distances L (see Fig. 9). The x-axis represents the longitudinal coordinate along the axis of the heading, measured from the end of the ventilation duct (0 m) towards the dead-end face.

Dependence of the relative maximum longitudinal velocity in the cross sections of the blind heading on the longitudinal coordinate at different distances L between the end of the ventilation duct and the dead-end face.

The attenuation of the maximum longitudinal velocity in the jet for all considered distances follows a power law with an exponent of − 1/7. This aligns well with the classical theory of the decay of a free circular turbulent jet in semi-infinite space35. However, in the last two meters before the dead-end face, the nature of the jet’s attenuation changes sharply. In this zone, the relative maximum longitudinal flow velocity rapidly drops to zero at the wall corresponding to the dead-end face, and the − 1/7 attenuation law no longer applies as the jet transitions into a transverse flow.

The calculated dependences of the \(\:{I}_{U}\) indicator on the longitudinal coordinate suggest that the 2-meter-thick zone near the dead-end face is intensively ventilated. The air stream entering this zone has a velocity ranging from 20 to 60% of the initial velocity \(\:{U}_{0}\) of the stream leaving the ventilation duct. For our calculations (\(\:{U}_{0}\:=\:21.75\) m/s), this corresponds to velocities of 4.35 to 13.05 m/s, which is sufficient for intensive ventilation of the dead-end face and significantly higher than the minimum velocity of 0.15–0.25 m/s. Notably, all these velocities exceed the maximum permitted velocity of 4 m/s.

However, the change in the \(\:{I}_{U}\left(x\right)\) indicator along the blind heading does not fully capture the nature of the transverse flows. Therefore, we consider the behavior of the relative average transverse air flow velocity (indicator \(\:{I}_{VW}\left(x\right)\)) depending on the x-coordinate. The calculation results are shown in Fig. 10.

Dependence of the relative average transverse velocity in the cross sections of the blind heading on the longitudinal coordinate at different distances L between the end of the ventilation duct and the dead-end face.

The curves shown in Fig. 10 provide additional and critical information about the structure, length, and magnitude of vortex flows in a blind heading. First, let us consider the behavior of air flows near the dead-end face, which is of greatest importance for ventilation practice. At first glance, it may seem, by analogy with boundary layers, that the velocity of the flow decreases as it approaches the solid wall of the dead-end face. However, the curves in Fig. 10 suggest that this is not entirely true. A fresh air stream, initially appearing to flow freely into the air space of the heading, is quickly influenced by the Coanda effect, turning into a wall stream and reaching the dead-end face. In these calculations, the velocity of the transverse flow is higher the closer it is to the dead-end face. The turning of the air jet begins approximately 2 m from the dead-end face for L = 10 m and extends to 6 m for L = 50 m. Typically, the turning zone starts about 4 m from the dead-end face. The maximum values of the\(\:\:{I}_{VW}\) indicator are observed at distances less than 0.25 m from the dead-end face, ensuring intensive ventilation of the frontal zone, 1 m wide, near the face. At the same time, the boundary condition of zero velocity is set on the dead-end face wall itself, which means that upon further approaching the face wall, the transverse velocity over a very short spatial segment (less than 0.25 m) rapidly drops to zero.

At the same time, the \(\:{I}_{VW}\) indicator is non-zero not only in the frontal zone near the face but throughout the entire dead-end face zone. The general behavior of \(\:{I}_{VW}\left(x\right)\) is as follows: near the end of the ventilation duct, the value of this indicator increases, reflecting the recirculation of the return flow. Then, the transverse movements decay monotonically with increasing \(\:x\). After reaching a certain minimum, the value of \(\:{I}_{VW}\left(x\right)\) begins to grow again to a certain maximum before dropping monotonically until it peaks again near the dead-end face.

In this case, the average value of the \(\:{I}_{VW}\) indicator for the dead-end face zone increases as the distance \(\:L\) decreases. Thus, the most intense transverse air movements are observed with small values of \(\:L\) (10–20 m). This indicates strong air flows between the forward and reverse flows within a large-scale vortex, which may be associated with smaller-scale vortices, both locally concentrated and spatially distributed, resembling a Möbius strip.

With small distances \(\:L\), the large-scale vortex limited by the dead-end face has a minimal length. Since in shorter vortices, the transverse air flows between the direct and return flows are confined to a smaller spatial area, they logically have higher average velocities given a constant supply \(\:{Q}_{0}\) of fresh air (as in these calculations).

Moreover, while a pronounced peak of the \(\:{I}_{VW}\) indicator is observed near the dead-end face, indicating the end of the vortex, such a peak is barely noticeable near the end of the ventilation duct. This suggests that the vortex shape in the dead-end face zone is asymmetrical. Additionally, the curves in Fig. 10 show weakly expressed local maxima at intermediate points between the end of the ventilation duct and the dead-end face. This is due to the complex 3D structure of the vortex, which twists along the axis of the heading. The intricate shape of the vortex is partly visible from the trajectories of some streamlines in Fig. 6, as well as changes in the zones of direct and return flows depending on the distance from the end of the duct to the dead-end face (Figs. 6, 7).

The indicators \(\:{I}_{U}\left(x\right)\) and \(\:{I}_{VW}\left(x\right)\:\)discussed above are based on the longitudinal and transverse components of the air velocity field and clearly show the main local features of the flow. However, for an integral assessment of ventilation, it is necessary to know the airflow reaching the dead-end face. The most convenient indicator for this task, in our opinion, is the forward flow moving towards the dead-end face, or the \(\:{I}_{Q}\) indicator.

The dependence of the \(\:{I}_{Q}\) indicator on the coordinate x is shown in Fig. 11 for various distances from the end of the duct to the dead-end face.

Dependence of the relative forward air flow in the cross sections of the blind heading on the longitudinal coordinate at different distances L between the end of the ventilation duct and the dead-end face.

The behavior of the relative forward airflow depending on the x-coordinate is highly informative. Firstly, the curves in Fig. 11 show that the airflow rate circulating in a large-scale vortex in the dead-end face zone is 2.5–3.5 times greater than the airflow rate \(\:{Q}_{0}\) supplied through the ventilation duct to ventilate the blind heading. This significant increase in the forward flow ensures intensive ventilation of the frontal zone due to advective displacement processes, despite the partial recirculation of polluted air in the return flow. Of course, we are speaking here conditionally about polluted air as the air that has flowed along the dead-end face, and we are not explicitly considering the transfer of pollutants.

Approximately 5 m before the end of the duct (towards the mouth of the heading), additional air masses are sucked into the jet flow, forming an intensive forward flow moving towards the dead-end face. This flow contains approximately one-third fresh air and two-thirds recirculated air from the return flow. The significant increase in the forward airflow was also recorded in a full-scale experiment21.

Two flow regimes are clearly visible, with the transition occurring at a distance \(\:L\) of about 25 m. For clarity, we will refer to distances \(\:L\) between the end of the ventilation duct and the face of less than 25 m as small, and distances of more than 25 m as large.

With large distances , the \(\:{I}_{Q}\) indicator becomes insensitive to the value, except in a small zone (about 5–7 m) near the dead-end face, where the forward airflow initially stops decreasing and then sharply drops to zero. The global maximum of the \(\:{I}_{Q}\left(x\right)\) dependence is observed at a distance of about 15 m from the end of the ventilation duct. This zone can be considered the core of a large-scale vortex circulating in the dead-end face space. Notably, for distances of 30 m and 40 m, the magnitude of the forward flow near the dead-end face begins to increase slightly and reaches a local maximum at a distance of 3–4 m from the face before entering the frontal zone.

For relatively small distances between the end of the ventilation duct and the dead-end face (less than 25 m), the behavior of the \(\:{I}_{Q}\) indicator along the heading changes significantly for different . The global maximum of the \(\:{I}_{Q}\left(x\right)\) dependence is now observed at a distance of 4–5 m from the dead-end face, indicating that the vortex core is located in this zone. This fact highlights a fundamental difference in the structures of the vortices formed in the dead-end face zone at large (> 25 m) and small (< 25 m) distances between the end of the ventilation duct and the dead-end face.

The restructuring of the vortex flow structure as the distance increases does not occur instantly. With small values, a local maximum of the \(\:{I}_{Q}\) indicator is formed at a distance \(\:x=\:\)5–7 m from the end of the ventilation duct. This is clearly visible in Fig. 11 for distances of 15 and 21 m. As the value increases further, at \(\:L=30\) meters this local maximum becomes global for all large values of . Meanwhile, the previous maximum of the \(\:{I}_{Q}\) indicator, which is now local, also remains at a distance \(\:x=\) 3–4 m from the dead-end face up to values of \(\:L=50\:\)meters, as noted earlier.

It is important to understand that the presence of two maxima of \(\:{I}_{Q}\left(x\right)\) does not indicate the existence of two separate vortices in the dead-end face zone. In all the situations we considered, there was only one large-scale vortex, and the structure of airflows in its center (i.e., in the zone of the smallest velocity vector magnitudes) is always quite complex. This can be inferred from the complex “twisted” shapes of individual streamlines shown in Fig. 6 and the spatial distributions of the turbulent kinetic energy shown in Fig. 4.

Kamenskikh et al.21 proposed determining the efficiency of ventilation in blind headings by examining the nature of mass transfer in the frontal zone, 1 m from the dead-end face. This value is based on the size of a person’s breathing zone, which extends 1 m around the head, as a person can be close to the dead-end face.

Following this approach, we conducted a detailed analysis of the variation in ventilation efficiency indicators in the cross-section of a heading, 1 m from the dead-end face, for different ventilation system parameters (\(\:L,\:{U}_{0}\)).

Figure 12 shows the dependencies of all three mentioned indicators on the distance L, with a constant initial velocity of the fresh air jet \(\:{U}_{0}\:=\:21.75\) m/s. For convenient comparative analysis, the curves are scaled to their value at the minimum considered distance, \(\:L=10\) m, and plotted from a common reference point.

Dependences of the dimensionless indicators in the frontal zone (1 m from the dead-end face) on the distance L.

The relative value of the forward flow \(\:{I}_{Q}\) shows an almost linear dependence on the distance over the entire studied interval. The other two indicators (\(\:{I}_{U}\) and \(\:{I}_{VW}\)) exhibit nonlinear behavior at small distances but subsequently decrease linearly with increasing . We attribute the nonlinear behavior of \(\:{I}_{U}\) in the frontal zone at small to the incomplete opening of the air jet in the blind heading when it flows toward the dead-end face. As the distance increases, the air jet opens more fully as it approaches the dead-end face. Furthermore, the dynamics of the maximum air velocity in the jet follow a power law with an exponent of –1/7.

To some extent, we can assume that over the interval from 15 to 50 m, all three indicators linearly depend on and are proportional to each other. This indicates that, despite their different physical meanings, all indicators predict the same decrease in the intensity of ventilation in the frontal zone as increases. This conclusion was reached under the assumption that the cross-section of the blind heading is constant.

It is also important to note that the linear dependence of the indicators on will obviously break down with a further increase in , as they would otherwise reach negative values at approximately \(\:L=60\) meters, which is not possible by definition. The distance around \(\:L=60\) meters, although theoretically interesting, is not practical (as rarely exceeds 40–50 m). At this critical distance, a stagnation zone with a reverse swirl vortex might appear due to the conservation of mass and momentum, suggesting the existence of a single-vortex large-scale motion.

Figure 13 illustrates the dependence of all three indicators on the initial air jet velocity at a distance \(\:L=15\) meters. The velocity varied from \(\:0.25{U}_{0}\) to \(\:1.25{U}_{0}\) in steps of 0.25, with the dimensionless velocity \(\:U/{U}_{0}\) marked on the x-axis. When varying the air velocity at the outlet of the ventilation duct, the diameter of the duct d, and consequently the jet tightness coefficient , were assumed to be constant.

It is important to note that when calculating indicators (9), (10), (11), we assumed that their denominators (Uo and Qo) remain unchanged with velocity variations and correspond to the situation where Uo = 21.75 m/s. However, the numerators of the indicators changed with variations in the velocity Uo at the end of the duct, according to the data from 3D simulations. This approach was used to analyze how the absolute values of the mass transfer characteristics in the frontal zone change. Additionally, if the denominators of indicators (9), (10), (11) were adjusted according to the changes in the velocity Uo at the duct’s end, the values of indicators (9), (10), (11 would remain practically unchanged.

Dependences of the dimensionless indicators in the frontal zone (1 m from the dead-end face) on the dimensionless initial velocity \(\:U/{U}_{0}\) of the air jet leaving the duct at a distance \(\:L=15\) m.

Figure 13 shows that all three indicators increase linearly with increasing velocity at the end of the ventilation duct. Moreover, all three indicators are proportional to the velocity . This conclusion is logical, as at \(\:U=0\) we would expect all three indicators to be zero.

Given the observed dependencies of the indicators on the ventilation system parameters and , we can draw an important conclusion: we can always compensate for an increase in the distance between the end of the ventilation duct and the dead-end face by increasing the initial velocity of the jet (in practice, by increasing the flow rate of supplied fresh air). For a blind heading with a cross-section of 29.2 m², as considered in this study, an increase in distance by every 10 m leads to a decrease in ventilation efficiency indicators by approximately 20% (relative to the indicator values at \(\:L=10\) meters). To avoid this decrease in performance, it is sufficient to increase the velocity (and consequently the flow rate) of air in the ventilation duct by about 20%, which is feasible in practice.

This study aimed to investigate the structure of airflow in a blind heading ventilated via a forced system. For a detailed analysis, we proposed three indicators to comprehensively characterize the flow structure in the heading: (1) longitudinal maximum velocity in a specific cross-section of a heading, (2) transverse average velocity in a specific cross-section of a heading, and (3) forward air flow passing through a specific cross-section towards the dead-end face. Numerical simulation of the steady-state 3D vortex structure of air flows in the dead-end face zone of a blind heading was carried out across a wide range of distances between the end of the ventilation duct and the dead-end face (from 10 m to 50 m) and a wide range of velocities of the air jet emerging from the ventilation duct. Based on the simulation results, we formulated the following main conclusions:

Analysis of the structure of air flows, conducted using the proposed indicators, revealed that within the entire considered range of ventilation system parameters in the blind heading, a large-scale vortex (the size of the dead-end face zone or larger) is formed. This vortex recirculates an amount of air 2.5–3.5 times higher than the fresh air flow rate leaving the end of the ventilation duct. Such recirculation significantly intensifies mass transfer processes in the dead-end face zone and ensures stable advective removal of impurities from it.

As the distance between the end of the ventilation duct and the dead-end face increases from 10 to 50 m, the vortex structure changes significantly. Local vortices appear, and the location of the main core of the vortex changes, moving closer to the dead-end face.

For the blind heading with a cross-section of 29.2 m² considered in the work, it was found that the ventilation efficiency of the frontal zone (1 m from the dead-end face) decreases linearly with increasing distance between the end of the ventilation duct and the dead-end face. It was shown that it is always possible to compensate for this increased distance by increasing the velocity of the air jet emerging from the duct. This conclusion is extremely important for mine ventilation practice, as it opens up prospects for justifying the safety of ventilating blind headings with ventilation ducts located far from the dead-end face.

This work does not consider the influence of the cross-section of a heading, the diameter of the duct, or the location of the duct in the cross-section of the heading on ventilation efficiency indicators. These factors will be addressed in future studies.

Additionally, future work will involve directly considering the mass transfer of harmful impurities by flow and determining the correlation between the proposed ventilation efficiency parameters and the time required to ventilate a heading from harmful impurities to permissible concentrations. The final justification of our findings regarding changes in the efficiency of blind heading ventilation should be made after conducting a study of the dynamics of harmful impurities.

All data generated or analyzed during this study are included in the manuscript.

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This research was carried out as part of a major scientific project funded by the Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075-15-2024-535 dated 23 April 2024).

Mining Institute of the Ural Branch of the Russian Academy of Sciences, Perm, Russia

Mikhail Semin, Grigoriy Faynburg, Aleksei Tatsiy, Lev Levin & Evgeniy Nakariakov

Perm National Research Polytechnic University, Perm, Russia

Grigoriy Faynburg

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Conceptualization, M.S. and G.F.; methodology, M.S. and G.F.; software, A.T and E.N.; validation, M.S. and A.T.; formal analysis, M.S., G.F. and A.T.; investigation, M.S. and A.T.; resources, M.S. and G.F.; data curation, M.S. and G.F.; writing—original draft preparation, M.S., G.F. and A.T.; writing—review and editing, M.S. and G.F.; visualization, M.S. and A.T.; supervision, G.F. and L.L.; project administration, L.L.; funding acquisition, M.S., G.F., A.T., L.L. and E.N. All au-thors have read and agreed to the published version of the manuscript.

Correspondence to Mikhail Semin.

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Semin, M., Faynburg, G., Tatsiy, A. et al. Insights into turbulent airflow structures in blind headings under different ventilation duct distances. Sci Rep 14, 23768 (2024). https://doi.org/10.1038/s41598-024-74671-3

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Received: 23 May 2024

Accepted: 27 September 2024

Published: 10 October 2024

DOI: https://doi.org/10.1038/s41598-024-74671-3

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