4.1. Establishment of Full-Size Tunnel Model
During a visit to a mining enterprise in Shanxi Province, a scaled-down model of a tunnel section measuring 4 m × 3 m was established. The model was created based on the principles of power similarity and motion similarity in hydrodynamics, ensuring that it was isometrically scaled with the actual mode. The scaling relationship can be described by Equation (8):
where
λ is the scaling relationship between the scaled model and the full-size model,
l is the feature length, m.
m is the scaled model corner scale, and
p is the full-size model corner scale.
A scaled model with a geometrically similar scale relationship of about 7.2 is utilized for fire experiments. A tunnel model measuring 300 m in length, 4 m in width, and 3 m in height was created using Pyrosim. A smoke exhaust tunnel measuring 4 m in width and 3 m in height was established at 250 m along the tunnel. An ignition source was placed at 110 m from the air inlet of the tunnel, with a surface area of 1 m
2. The upwind fire source served as the reference source. Another ignition source was placed at a distance ‘D’ from the first source. Temperature sensors were strategically placed at the top of the tunnel and at a height of 1.6 m to monitor various fire characteristics during fire incidents. These sensors were spaced 5 m apart, with the first sensor positioned at the center of the reference fire source. Additionally, six sensors of the same type were placed on the upwind side at the same vertical height, followed by 19 sensors downstream of the fire and 26 sensors at the same vertical height. Refer to
Figure 10 for the lane model diagram.
4.2. Mesh Irrelevance Test
It has been shown that the simulation accuracy of Pyrosim is higher when the mesh size is 1/16 to 1/4 times the diameter of the surface of the fire source. Its calculation, Equation (9) [
27], is:
where
D* is the characteristic diameter of the fire source, m;
ρ0 is the ambient air density, taking the value of 1.293 kg/m
3;
cp is the specific heat capacity of air, taking the value of 1.005 KJ/(kg·K);
T0 is the temperature, taking the value of 293 K.
The sparsity of the grid not only significantly affects the accuracy of the simulation but also influences the computational runtime. The Pyrosim manual suggests that the value of D*/x should be maintained between 4 and 16 to achieve higher calculation accuracy. According to the Formula (9), D* is calculated to be 2.627 m, indicating that a grid size between 0.16 m and 0.65 m yields optimal accuracy. To verify this, grid sizes of 0.1 m, 0.25 m, 0.35 m, and 0.5 m were tested under windless conditions, with a fire source spacing of 15 m, focusing on the midpoint temperature of the double fire source to assess grid independence.
As illustrated in
Figure 11, when the grid sizes are set to 0.1 m, 0.25 m, and 0.35 m, the results demonstrate a high degree of fit. Considering the computational time, a grid size of 0.1 m × 0.1 m was selected for areas near the fire source, while a grid size of 0.25 m × 0.25 m was chosen for the other tunnel areas. In total, four mesh regions were established, encompassing 1,984,256 mesh. Additionally, the parallel computing mode of Pyrosim is employed, significantly reducing the overall computation time.
4.4. Determination of Critical Wind Speed for Twin Source Fires
The critical wind speed problem for the nine conditions and the single fire source was initially determined by simulating the nine conditions. Its simulation flowchart is shown in
Figure 12.
The criterion for determining the critical wind speed for a two-fire source fire was based on ensuring that the backflow of smoke and temperature did not exceed that of the upstream fire source. The critical wind speed of a single fire source for this tunnel condition was calculated using Wu and Bakar’s critical wind speed prediction model. It is modeled as in Equation (10) [
27].
In the formula, Q* for the dimensionless heat release rate; Q for the heat release rate of the fire source, kW; ρ0 for the air density, kg/m3; T0 for the ambient temperature of the air, K; g for the acceleration of gravity, m/s2; H for the hydraulic diameter, m. The expression of the hydraulic diameter is: H = 4S/P, S for the cross-sectional area of the tunnel, m2, and P for the perimeter of the tunnel cross-section, m. The hydraulic diameter of the tunnel cross-section of the tunnel cross-section of the perimeter of the tunnel cross-section of the tunnel cross-section, m.
Baker calculates the dimensionless wind speed by taking the heat release rate from the fire source, and its prediction model for the dimensionless wind speed is Equation (11) [
27].
By calculating the dimensionless wind speed, the critical wind speed can be calculated using the critical wind speed prediction model, which is shown in Equation (12) [
28]:
where
v is the critical wind speed, m/s, which is approximately 1.76 m/s as determined by an empirical formula.
Taking into account various factors such as section and wall characteristics, a wind speed of 1.7 m/s is chosen as the central value, with incremental and decremental variations of 0.1 m/s for ten simulations on either side. Through simulation studies, it was observed that the critical wind speed for a single fire source is 1.8 m/s.
Table 5 presents the critical wind speeds under different conditions.
The critical wind speed calculated is 1.68 m/s, whereas the critical wind speed in the simulation is 1.8 m/s. This discrepancy can be attributed to the fact that the prediction of the critical wind speed does not consider the wall friction of the tunnel, resulting in a slight deviation between the modeling and simulation outcomes. Some scholars have investigated the impact of using a large nest model on the critical wind speed in numerical simulations of turbulence models. They found that the critical wind speed for a double fire source is slightly higher than that for a single fire source. The primary reason for this is that dual-source fires exhibit higher thermal resistance compared to single-source fires, which in turn increases the local ventilation resistance within the fire zone. Consequently, this necessitates higher critical air velocities. Analysis of nine different conditions revealed a negative correlation between the critical wind speed for a double fire source and the distance between the fire sources. Specifically, the greater the distance between the fire sources, the lower the required critical wind speed. At the same time, when the distance between fire sources reaches 20 m, its critical wind speed is close to the critical wind speed of a single fire source. This phenomenon can primarily be attributed to the increased distance between fire sources, which has weakened the local thermal resistance. Additionally, the heating of the upstream fire source affects the downwind side, leading to a reduction in fluid density. As the temperature rises, a certain amount of energy is acquired, resulting in an increased flow rate downstream of the upstream fire source. Consequently, for fire sources that are significantly spaced apart, the critical wind speed required for fire propagation will be lower compared to that of fire sources that are positioned closer together.
The simulation revealed that when the power of two fire sources in a tunnel is equal, the fire characteristics align closely with scaled model experiments. The horizontal temperature distribution in the tunnel resembles a ‘concave’ shape after the fire under these conditions. However, the influence of wind speed on the two fire sources differs, with the upstream source being more affected. This results in a lower peak temperature for the upstream source compared to the downstream source, due to the thermal resistance effect cutting the wind speed impact on the downstream fire source. The thermal resistance effect of the upstream fire source mitigates the wind speed influence on the downstream fire source temperature, leading to a lower temperature peak for the upstream source. The temperature rise between the two fire sources is primarily driven by the fire plumes of both sources. As high-temperature smoke accumulates between the two sources, the thermal resistance effect of both sources limits smoke propagation, creating an anti-buoyancy wall jet. The vertical temperature rise between the two fire sources relies on convective heat transfer, while the high-temperature smoke on the roof of the sources exchanges heat with the surroundings, causing the middle region’s temperature to rise from top to bottom. The vertical temperature gradient in this middle area becomes more pronounced as the temperature decreases from top to bottom.
Simulation experiments were conducted under four identical dual-fire source conditions 1, 4, and 7, where wind velocity surpassed the critical threshold. The study focused on analyzing temperature field variations at a vertical height of 1.6 m, corresponding to the characteristic height of the human eye. The findings are illustrated in
Figure 13,
Figure 14 and
Figure 15.
The analysis of
Figure 13,
Figure 14 and
Figure 15 indicates that all three scenarios follow the same temperature decay pattern, with temperature decreasing as wind speed increases. However, when considering fires at different distances from each other but with the same heat release rate and wind speed, it is observed that greater spacing between fires leads to higher average temperatures along the tunnel due to the temperature differences between the fires. Specifically, temperatures between closely spaced fires are significantly higher than those downstream, with temperatures evening out at points after the downstream fire source. Regardless of wind speed, the temperature distribution between the fire sources maintains a ‘concave’ shape, with the lowest temperature occurring at the midpoint between the two fires.
The influence of wind speed on the maximum temperature within the tunnel is more pronounced, particularly regarding the upstream fire source in comparison to the downstream fire source. This phenomenon can be attributed to the fact that as wind speed increases, the thermal resistance effect of the upstream fire source on the wind flow diminishes, while the cooling effect of the wind flow on the downstream fire source intensifies. At a wind speed of 3.5 m/s, the temperatures above both sources are nearly identical, indicating a negative correlation between the maximum temperature and wind speed.
4.5. Fire Characterization of Different Ignition Powers
By simulating equal fire growth factors under different fire powers in a two-ignition fire, a developmental relationship between the two ignition sources was observed. Specifically, when one ignition source develops rapidly, it suppresses the development of the other ignition source. This relationship is illustrated in the temperature cloud shown in
Figure 16.
Under critical wind speed conditions, the power of the upstream fire source remains constant while the downstream fire source has a power of 4 MW, resulting in a more intense flame compared to the 3 MW source. However, the combustion of the upstream fire source is relatively suppressed, leading to a noticeable decrease in temperature and flame height. This phenomenon occurs due to the rapid influx of fresh air towards the downstream fire source, causing a reduction in oxygen available for the upstream source. As a result, the combustion of the upstream source is hindered, leading to a decrease in flame height and a change in temperature. This relationship is illustrated in
Figure 17.
As illustrated in
Figure 18, working condition 3 exhibits the lowest average temperature. However, the temperature above its upstream fire source is the highest due to the relatively high heat release rate. Despite having the same power as the downstream fire source in working condition 1, the downstream fire source in working condition 3 is inhibited by the upstream fire source, resulting in a significantly lower temperature compared to working condition 1. The temperature difference between the two cases is approximately 70 °C.
For the other two types of conditions, a consistent regularity is maintained, and the temperature schematics for conditions 4, 5, 6, 7, 8, and 9 are shown in
Figure 18 and
Figure 19.
Comparison of the three working conditions reveals that the upstream fire source power is larger when the average temperature and temperature peak in the starting tunnel are lower. On the other hand, the downstream fire source power is larger when the average temperature and temperature peak are higher. Therefore, in cases of dual fire sources, it is crucial to focus on treating the fire source on the downwind side. When the wind speed is greater than the critical wind speed, the fire source upstream is less affected by the escape environment. Conversely, the fire source power on the downwind side has a more significant impact on the escape route. It is essential to optimize firefighting strategies based on this pattern.