https://orcid.org/0000-0002-5076-6421
Figures
Abstract
The tracer gas wind measurement method must measure the average concentration based on the known mixing distance of the tracer gas in order to accurately calculate the air volume. we established a T-shaped cross-ventilation duct with a square cross-sectional side of 0.3 m to simulate mine tunnels experimentally, and created the above duct model in Fluent software. Using the renormalization group (RNG k-ε) and detached eddy simulation (DES) models in Fluent to calculate the concentration and mixing distance of sulfur hexafluoride (SF6) tracer gas in air collection duct, and conducted SF6 blending experiments. In the first 7m stage of air collection duct, the SF6 mixing rate in the experiment was the fastest, while the RNG k-ε model was the slowest. However, after 7 meters, the mixing rate in the experiment rapidly slowed down, while there was no significant change in the RNG k-ε model. The rate of change of the DES model was between the above two results, but the concentration change was the most unstable. And the mixed distance results of the three were highly consistent. The results of this study provide a reference for selecting appropriate numerical simulation models for future calibration work of mine ventilation systems.
Citation: Xu F, Liu J, Wang D (2024) Comparing and analyzing the accuracy and stability of calculating SF6 tracer gas mixing results in mine tunnels using RNG model and DES model through experiments. PLoS ONE 19(12): e0314142. https://doi.org/10.1371/journal.pone.0314142
Editor: Dave Mangindaan, Bina Nusantara University, INDONESIA
Received: July 6, 2024; Accepted: November 6, 2024; Published: December 23, 2024
Copyright: © 2024 Xu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the paper and its Supporting Information files.
Funding: The paper is financially supported by the National Natural Science Foundation of China (No. 51574142 and No.51774169).
Competing interests: The authors have declared that no competing interests exist.
1 Introduction
Ventilation is key to ensuring the safety and health of underground production environments and personnel [1, 2]. Owing to their complex underground engineering, mines require proper ventilation to maintain a sustainable environment and avoid accidents. It is necessary to regularly measure the air volume of each main tunnel to ensure the normal operation of the mine ventilation system [3]. As production work in a mine progresses, the number and size of tunnels, and hence, the air volume within, change constantly, requiring the air dampers to be adjusted accordingly. For continued normal and orderly wind measurements once per day, when the ventilation system changes, the air volume of each tunnel must be first recalibrated [4]. At this point, no tunnel/ventilation parameters are calibrated, and hence, more accurate methods are needed for air volume measurement. Once calibration is completed, if the ventilation system remains unchanged in the future, a simpler wind measurement method with lower accuracy can be employed.
In the tracer gas wind measurement method, the tracer gas concentration is used to calculate the air volume with better accuracy compared to traditional wind measurement methods. This method does not require measuring the cross-sectional area and average wind speed of the tunnel, but only the stable release of a tracer gas in the tunnel [5]. Once the tracer gas diffuses evenly, its concentration is measured and the tunnel air volume is calculated according to the volume fraction law. This solves the problem of large errors due to the difficulty of measuring the tunnel cross-sectional area and the uneven wind speed distribution inside tunnels.
Sulfur hexafluoride (SF6) exhibits properties such as chemical stability, non-flammability, and non-toxicity. Moreover, its concentration can be accurately measured, making it an excellent tracer gas candidate [5, 6]. When using SF6 to test the overall mine air volume, multiple gas release points need to be arranged within the mine. For this purpose, the airflow entering the intake tunnel at an intersection must be mixed with the tracer gas.
As the SF6 concentration is measured at one or several points within the tunnel, uneven gas mixing SF6 can result in inaccurate average concentration, and hence, air volume measurements. The distance from the air inlet position of the tunnel to the point where SF6 and air are just evenly mixed (i.e., the mixing distance) is then determined. The area where air inlet distance ≥ mixing distance is the point where SF6 concentration becomes uniform. The SF6 concentration measured only at the mixing distance can be used to accurately calculate the air volume. Most intersecting tunnels in mines exist in the form of triple intersections [7, 8] and are divided into two forms, diverging and converging. In the converging form, the airflow from two tunnels converges into one tunnel. When measuring the airflow of the intersecting tunnels, one or no SF6 releasing device is needed to be installed in the inlet tunnel to calculate the combined airflow. This effectively reduces the SF6 cost and simplifies the airflow calculation.
Adel et al. used CO2 as a tracer to calculate the ventilation rate in the classroom, and conducted uncertainty analysis on the gas using three calculation methods: steady state, deck rate, and build up. They found that the uncertainty of steady state was the lowest [9]. Chen et al. discussed the tracer gas wind measurement method and proposed a formula for calculating the mixing distance [10]. Gao et al. studied the effects of tracer gas density and release rate on concentration distribution and ventilation effectiveness using computational fluid dynamics (CFD) method. When tracer gases with smaller release rates and density differences are released into stronger indoor airflow, their impact on indoor ventilation airflow is relatively small [11]. Widodo et al. studied the influence of the ratio of tunnel length and characteristic length on the SF6 concentration curve with time at a certain location in a tunnel [12]. Xu et al. established an experimental model of a mine tunnel and developed a proportional CFD model for the experimental model. We compared the concentrations of SF6 tracer gas at five points in the CFD model and experimental model, and proposed a method for detecting faults in mine ventilation systems using tracer gas [13, 14]. CFD method was used to optimize the release and sampling position of tracer gas, and the influence of release rate and time on the measured concentration was studied. And CFD methods can reduce the number of trial and error in engineering applications [15, 16]. However, most of these works focus on singular non-cross tunnels, and there is currently no research on the mixing distance of tracer gases in cross tunnels. When measuring cross tunnels, only SF6 needs to be released in one of the intake tunnels, and the air volume of the three tunnels can be calculated by knowing the release flow rate of SF6 and its mixing distance in the collection tunnel. This method can save SF6 release points and simplify the calculation process. When measuring the air volume of the entire mine air network, the study of the mixing distance of tracer gases in cross tunnels can simplify the calculation of air volume. Therefore, in this study, we compared the SF6 mixing process in cross tunnel models experimentally; obtained the mixing distance; and verified numerical simulation accuracy. The effect of wind speed and SF6 flow rate and amount at the release point on the mixing distance were also analyzed. In this T-shaped model, we constructed two intake ducts and one collection duct that intersect at a point, where one intake duct has a 90°angle with the collection duct, and the other intake duct has a 180° angle with the collection duct. The cross-section was a square with a side length of 0.3 m. Based on the gas lateral diffusion relation [10] and the Nikuradse experimental relation [17], a similarity relationship between the mixing distance, tunnel size, and wall roughness was derived. The measured mixing distance was compared to that computed by the numerical simulation of the mine tunnel to verify the accuracy. During practical applications of this mine wind measurement method, our numerical simulations and experimental results can provide data reference for the placement of SF6 concentration sensors, saving calculation time. We chose the renormalization group (RNG) k-ε and detached Eddy simulation (DES) models for this study. In the application of mine wind measurement and air volume calibration, the CFD method can calculate the mixing distance. In practical applications, the placement of concentration sensors can be roughly determined based on the CFD calculation results, saving the process and time of determining sensor positions on site, and also saving the use of tracer gases. This study has established an accurate, fast, and stable CFD model, providing a basis for determining the placement of sensors during air volume calibration.
2 Wind tunnel model numerical simulation setup
The method for calculating the air volume for tunnel intersections is detailed as follows: In one of intake tunnel, 100% volume fraction SF6 is continuously released at a constant flow rate using a release device and mixed uniformly with the air within. The SF6 concentration reaches the standard of mixes uniformly with the airflow at the air intake tunnel 2, and collection tunnel 3, concentration measurements are taken at the minimum and maximum concentration points at that location, and the average concentration is obtained by taking the average of the two maximum and minimum concentrations. Subsequently, based on the SF6 average concentration in the mine and in a single air intake tunnel, the tunnel air volume is calculated using the volume fraction law.
To visually compare with experimental data, an intersecting duct model of the same size and angles was constructed using the ICEM CFD software. The duct cross-section was set to a square with a side length of 0.3 m, with two intake air ducts measuring 2.5 m in length and a collection air duct measuring 40.0 m in length, used to simulate and calculate the SF6 mixing process and mixing distance. The grid adopted a highly accurate and fast hexahedral structure grid with a maximum grid edge length of 0.012 m, i.e., 1/25 times the cross-sectional edge length of the wind duct. We have conducted research on grid independence. When the maximum grid size is 0.012, at least 25 grids can be divided into the edges of the cross-section of the wind duct. When the maximum grid size is set to 0.0085, the edges of the cross-section can be divided into 36 parts. The concentration distribution and mixing distance calculated by the two grid sizes are almost indistinguishable. When the grid size has a minimal impact on the calculation results, a grid size of 0.012 was chosen to save computation time and space. Then determine the y+ (non-dimensional distance from the wall) of the grid close to the wall of the air duct. After verification, this grid size ensured both accurate calculation and fast operation. The grid near the duct wall needs to increase density, and the grid close to the duct wall should be in the log-law region, which is 30≤y+≤300 [18, 19]. The height of the first layer grid of the model was set to ensure 30 ≤ y+ ≤ 300 for wind speeds ranging from 6–12 m/s (the upper limit of the wind speed was set by the limitations of the fan and mixing blade speeds). The wall roughness was set to 0.5 mm, similar to the inner wall roughness of the experimental model. The Re for the model can be defined as [20]
(1)
where ρ is the gas density, kg/m3; v is the wind speed, m/s; L is the characteristic length, m; and μ is the gas dynamic viscosity, Pa·s.
The tunnel airflow is known to be in a completely turbulent state during actual mine ventilation. To similarly design the airflow state of the experimental air duct, we must introduce complete turbulence during the gas mixing experiments. In the experimental model, if Re ≥ 105, a fully turbulent state can be achieved [21]. Using Eq (1), we found that this value for Re could be obtained by setting ν ≥ 5.159 m/s inside the experimental duct. The wind speed was fixed to a range of 6–12 m/s for the collection duct and the height of the first grid layer near the wall set to 0.012 ensuring 30 ≤ y+ ≤ 300, meeting the conditions for using the wall function [18].
The Navier Stokes (RNS) method is a low-cost approach, and the ke turbulence model also has the advantage of low computational cost in the RNS method. The RNG k-ε model takes into account the rotation and rotational flow conditions of the average flow based on the standard k-ε model, enabling the model to better predict the effects of transient flow and streamline bending. Additionally, it takes into account the low Reynolds number (Re) effects due to the wall roughness and gas viscosity in the near-wall region, improving accuracy for a wider range of flow and near-wall regions [22].
The transport equation of turbulent kinetic energy k in RNG k -ε model [23]:
(2)
The transport equation of turbulent dissipation rate for RNG k-ε model:
(3)
Gk represents the turbulent kinetic energy generated by the average velocity gradient, Gb represents the turbulent kinetic energy generated by buoyancy, and YM represents the contribution of wave expansion to the total dissipation rate in compressible turbulence.
u is velocity, m/s; ρ is density, kg/m3; αk and αε are the reciprocal of the effective Prandtl numbers of k and e, respectively. C1ε and C2ε are model constants, where C1ε = 1.42, C2ε = 1.68.
The DES version of the Wray-Agarwal model is presented below [24].
Among them, FDES is the characteristic length scale, and a new constant CDES is introduced.
If eddy currents are considered in the calculation, the DES model can be used. The DES model adopts the large Eddy simulation (LES) algorithm in the turbulent core region, taking vortices into account, while the RANS (Reynolds-Averaged Navier-Stokes) algorithm was still used for the near-wall region [25]. Compared to the LES model, it could increase the grid size near the wall and reduce computational overhead. By comparing the results of these two algorithms with the experimental results, we analyzed their pros and cons and practical applicability. The constructed model and grid are shown in Figs 1 and 2.
We labeled the two intake air ducts as 1 and 2, and the collection air duct as 3, where duct 1 was parallel to duct 3 and duct 2 was perpendicular to duct 3.
At 25°C and standard atmospheric pressure, the densities of air and SF6 are 5.97 and 1.185 kg/m3, respectively [26], and the dynamic viscosities are 1.834 × 10−5 and 1.526 × 10−6 Pa·s [27].
The diffusion coefficient caused by molecular thermal motion is referred to here as the self-diffusion coefficient (D). The self-diffusion coefficient D of two different gases is calculated using FSG semi-empirical formulas [28]:
(8)
where P is the total air pressure (kPa), T is temperature (K), MA and MB are the molar masses of gases A and B (g/mol), respectively, and ∑VA and ∑VB are the diffusion volumes of gases A and B (cm3/mol), respectively.
The molar masses of air and SF6 are 28.959 and 146.06 g/mol, respectively, and previous studies have shown that the diffusion volumes of air and SF6 are 19.7 and 71.3 cm3/mol [29]. Therefore, when the temperature is 298.15 K and the pressure is 101.325 kPa, the diffusion coefficient of air–SF6 is approximately 9.281 × 10−6 m2/s. The parameter settings are shown in Table 1.
After calculating the simulation parameters (Table 1), for the convenience of comparison with experimental results, the concentration data was kept accurate to 0.1 ppm. As a result, the mixing distance was calculated using the RNG k-ε model to be 32.8 m. Due to eddy current effects, the mixing distance calculated by the DES model fluctuated in the range of 27–30 m and was not stable; a value of 28.8 m was obtained once the calculation stopped at a certain timestep. The volume fractions in Figs 2–4 are dimensionless, and range from 0 to 1. cE−05 is c×10−5.
The SF6 concentration calculated by the (i) RNG k-ε model had a regularly layered distribution (Fig 3), and (ii) DES model showed an irregular wavy pattern (Fig 4). Under the influence of obstacles, turbulence, and flow velocity gradients, the fluid formed vortex-like flow states (vortices). Due to the DES model considering both turbulence and eddy currents, the effect of the latter caused SF6 to rotate alongside, forming an irregular distribution. The RNG k-ε model did not consider vortices due to turbulence, but only the natural and turbulence-related gas diffusion, resulting in a regular SF6 diffusion.
The equidistant SF6 concentration measurements in duct 3 calculated by the RNG k-ε model were relatively regular (Fig 5). The areas with higher SF6 concentrations were always distributed on the side with higher incoming SF6 concentration, with a concentration gradient in the negative x-axis direction. Under the DES model, SF6 exhibited a vortex-like pattern due to the influence of eddy currents (Fig 6). Although the areas with high SF6 concentrations at most stages were still roughly on the positive x-axis direction, the results of the DES model were more irregular and the positions of the maximum and minimum SF6 concentrations were not fixed.
SF6 concentration distribution cross-sections taken every 1 m within the upstream of duct 3 in the DES model.
Due to the cross-sectional area of duct 3 being much smaller than that of the mine tunnel, the influence of gravity on the small-scale pipeline tracer gas turbulence was minimal. Therefore, at the point of uniform mixing, the calculated SF6 concentration using the RNG k-ε model tended to have a regular left-right symmetric relationship with the region of high concentration (Fig 7). On the other hand, the DES model concentration distribution was relatively chaotic due to the effect of eddy currents, with the minimum and maximum concentrations located in the upper left and lower right corners, respectively (Fig 8).
3 Experimental and simulation results comparison
The experimental setup (Figs 9 and 10) included a T-shaped cross air duct to simulate a mine tunnel, with two intake air ducts (1 and 2) measuring 3.0 m in length and a collection air duct 3 measuring 35.0 m in length. The air ducts were composed of several smaller ducts (each measuring 2.5 m in length), connected using sealing rubber rings and bolts. The SF6 gas flow controller was connected to the gas cylinder through a pipeline. The gas flow control valve was connected to the SF6 gas flow controller and a computer which input the flow data to control the gas release flow rate. The release port of the gas flow controller was connected to the air supply pipe, entering the intake duct with stirring fan blades to mix SF6 for an even distribution before flowing to the intersection point; this setup vastly increased the experiment accuracy. An SF6 concentration sensor was used to observe and record the concentration data with an accuracy of 0.1 ppm. The inlet of the sensor was connected to the gas supply pipe to sample the gas at the test position in the collection duct and measure the SF6 concentration. The air outlet of the collection duct was connected to the fan to provide wind power. The two intake ducts were connected to louvers. The wind speed adjustment range of duct 3 in this experimental system is 6-12m/s. The maximum release flow rate of the gas flow controller was 500 mL/min.
The relationship between the release flow rate, Q, of the gas flow controller and the average SF6 concentration in duct 2 can be expressed as
(9)
where S is the cross-sectional area of the air duct, m2; v2 is the wind speed in inlet duct 2, m/s; and
is the average SF6 concentration in duct 2, ppm.
3.1 Experimental process
Firstly, all equipment was switched on and the wind speed of the two intake air ducts, with a cross-sectional area of 0.09 m2, was adjusted to 3 m/s. For an SF6 concentration of 10 ppm in duct 2, the release flow rate was calculated to be 162 mL/min using Eq (9). After inspection, the overall leakage rate of the experimental air duct was found to be ~ 3%. To ensure a uniform SF6 concentration of 5 ppm in the collection air duct, the release flow rate was set to 168 mL/min.
We obtained SF6 concentration measurements at the midpoints of four edges, 4 corners, and the center of the cross-sections taken at 1-m intervals in duct 3. The concentration at a certain location was recorded only if the value displayed by the sensor remained stable for 10 s. We determined the maximum and minimum SF6 concentrations for each cross-section. After measurement, the airflow started at a distance of 16 m from the intake duct 3. The experimental measurement results are shown in Table 2.
3.2 Comparative analysis of experimental and simulation results
As the minimum and maximum SF6 concentrations were almost stably distributed in the corners, only these values of each cross-section were recorded to determine the mixing distance. Draw a concentration curve graph (Fig 11).
The results of Table 2 and Fig 6 are shown. The vertical direction of the airflow in the two intake ducts resulted in clear vortex formation upon convergence, leading to an unstable SF6 concentration distribution at the duct 3 positions closer to the intersection. However, as the distance from the intersection point increased, the size of the vortex gradually decreased and the airflow stabilized. At and beyond 16.0 m, with the y-axis as the line of sight, the maximum and minimum SF6 concentrations of each cross-section were stably distributed in the lower- and upper-right corners, respectively. At 30.5 m, the minimum-to-maximum SF6 concentration ratio reached > 90%, achieving the standard of uniform mixing.
We set the simulated concentration precision to 0.1 ppm and compared it with the experimental results to analyze the accuracy of the RNG k-ε and DES models (Table 3).
In the 1–7 m range of duct 3, the minimum-to-maximum SF6 concentration ratio in the experiment changed significantly faster than in the simulations, indicating that the SF6 mixing rate in the experiment was much faster (Figs 12 and 13; Table 3). However, as the concentration ratio crossed 60% of its maximum value at the 7-m mark, the mixing rate reduced in comparison to the simulations due to the weakening of eddy currents. After the 26-m mark, the concentration ratio between simulated and experimental data tended to be consistent, both crossing 80%. The mixing distances for the RNG k-ε model, DES model, and experiment were 32.8, 28.8, and 30.5 m, respectively, with a < 10% error rate for the two models compared to the experimental results. Due to the inevitable presence of slight air leakage in the setup, the external air entering from the air duct gap also facilitates gas mixing. Therefore, the ideal mixing distance is speculated to be slightly longer than our experimental data, i.e., slightly closer to that of the RNG k-ε model. In the real environment, the SF6 concentration distribution is influenced by both large- and small-sized eddies. Smaller eddies can make the mixing process more stable and rapid. However, as the DES model neglects eddies smaller than the grid size, its SF6 concentration is relatively unstable, with a strongly fluctuating concentration ratio. The average SF6 concentration at the uniform mixing point calculated by the DES model is 4.85 ppm, which has the largest error compared to the experimental results. The RNG k-ε model computed an average SF6 concentration of 4.95 ppm at the point of uniform mixing. Under the influence of large-sized eddies, the concentration distribution and average concentration fluctuations throughout the SF6 flow were more pronounced in this case. However, the presence of small-sized eddies in this experiment assisted gas mixing and reduced the SF6 concentration fluctuation amplitude compared to the DES model. The RNG k-ε model ignored all vortices, resulting in the smallest concentration ratio fluctuation amplitude.
3.3 Error analysis of simulation and experimental results
We analyzed the relative errors between the two numerical simulation models and the minimum and maximum concentrations at various positions in the experiment (Figs 14 and 15). We observed that as the distance increased, the errors of both models decreased. The error variation between the RNG k-ε model and experimental results was regular, stable, and decreasing with increasing distance; the minimum (maximum) concentration error was always negative (positive) above 1 m. The error variation between the DES model and the experimental results was, however, quite chaotic. This difference was observed due to the relatively stable concentration variations in the RNG k-ε model and experimental results compared to the large fluctuations in the DES model due to ignoring the instability caused by small-scale eddies. Up to a distance of 20 m, the large eddy current effect led to a small error between the DES model and experimental results, beyond which it destabilized and led to strong fluctuations. No decreasing pattern was observed in this case, and the error rate occasionally exceeded 10%. However, the error between the RNG k-ε model and experimental results maintained stability for all distances and gradually decreased (the error of the minimum and maximum concentrations remained within 10%). At this stage, the overall error of the DES model was greater than that of the RNG k-ε model; comprehensive comparison revealed the latter to be superior in determining the mixing distance.
In the experiment, under different wind speeds and SF6 release rates, the mixing distance always fluctuated in the range of 29.5–30.5 m. Therefore, we confirmed that in a small-sized air duct with completely turbulent airflow, the mixing distance is minimally affected by the wind speed and SF6 release rate.
4 Comparison of mixing distances between air ducts and real mine tunnels
There exists a roadway with a rectangular cross-section and a characteristic length of about 4 meters in reality [30]. Based on the actual size of the mine tunnel, we established a cross tunnel model with a cross-sectional area of 4 m × 4 m with the same shape as the air duct model in Section 2. The dimensions of the tunnel and air duct models were proportional to the grid, and the tunnels were labeled 1, 2, and 3 in the corresponding order. The wind speed for tunnels 1 and 2 was set to 2 m/s; the SF6 concentration in tunnel 2 was set to 80 ppm; and the wall roughness was set to 0.05 m; other parameter settings remained the same as in Table 1. According to the Coal Mine Safety Regulations [31], the wind speed in tunnels should be within the exact range of 0.25–8.00 m/s. To ensure this, along with 30 ≤ y+ ≤ 300 for tunnel 3, the first grid height of the tunnel model was set to 0.012. Using the RNG k-ε method, the SF6 mixing distance in the tunnel was computed to be 335 m.
The analytical solution for the three-dimensional turbulent diffusion at point (x, z) of the cross-section at y during the continuous and constant release of tracer gas can be expressed as [10, 32]
(10)
(11)
(12)
where Er is the lateral diffusion coefficient, m2/s; m is the mass of the gas released per unit time, kg/s; x and z are the horizontal and vertical coordinates in the inner diameter direction of duct 3, respectively, m; and y is the longitudinal coordinate within duct 3, m; α is the friction resistance coefficient of the tunnel or air duct, kg/m3.
Based on the work of Nikuradse et al. [12], in a fully turbulent state, we have
(13)
where λ is the friction coefficient of the tunnel or air duct; and Δ is the absolute roughness of the tunnel or air duct, m.
According to Eq (12), the similarity relationship between the mixing distance and the size of the air duct and tunnel, as well as the roughness of the wall, can be derived as
(14)
In the experimental air duct, we fixed the mixing distance to y1 = 30.5 m, the characteristic length to L1 = 0.3 m, and the roughness to Δ1 = 0.0005 m. The characteristic length and roughness of the tunnel were L2 = 4 m and Δ2 = 0.05 m, respectively. The calculated mixing distance of the tunnel was 333.1 m, which was consistent with the RNG k- ε simulation result of 335.0 m. For intake tunnel wind speeds of 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m/s, the mixing distances were 350.0, 343.0, 335.0, 330.0, 327.0, 325.0, and 324.0 m, respectively, with errors within 5%.
5 Conclusion
This study compared and analyzed the SF6 concentration data and mixing distance calculated and experimentally measured by RNG and DES models. The results showed that in a 0.3×0.3m cross duct, the blending distances calculated by RNG k-ε model and DES model were 32.8m and 28.8m, respectively. The blending distance in the experiment was 30.5m, which was basically consistent. And the mixing distance remained almost unchanged under different wind speeds and SF6 release amounts in the experiment. The RNG k-ε model revealed the longest mixing distance, while demonstrating a higher accuracy and stability. It also offers a low computational overhead. Therefore, the RNG model is deemed far superior to the DES model. Although both models are unable to accurately calculate the SF6 concentration distribution before uniform gas mixing, in practical application, only the mixing distance needs to be computed. Concentration sensors can be installed at or beyond the mixing distance from the inlet of the tunnel to accurately measure the airflow. Therefore, the RNG k-ε model already meets the needs of practical wind measurements. After similarity verification, the mixing distance computed for the experimental model and the RNG k-ε mine tunnel model essentially conforms to the similarity relationship, indicating that the RNG k-ε numerical simulations can accurately calculate the mixing distance. For the practical installation of SF6 concentration sensors for tunnel wind measurement in the future, the proposed numerical simulation method can be used to determine the approximate sensor placement positions, making the process time-efficient.
SF6 has several advantages as a tracer gas. However, as it is also a greenhouse gas, in practical applications, it is necessary to maintain a low release amount. The average SF6 concentration range in a tunnel during the release process must be maintained in the range of 5–100 ppm, ensuring accurate measurement, while minimizing environmental impact. Future works must attempt to discover a tracer gas that does not adversely affect the environment and has a density closer to air in order to employ the proposed numerical simulation method to determine the mixing distance.
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