Impact of Dual Fire Sources on Temperature Distribution and Smoke Ventilation in Road Tunnels with Shafts

2.1 Model establishment

FDS, developed by the United States' National Institute of Standards and Technology (NIST), serves as a computational tool for simulating fire scenarios [14]. Its widespread application by researchers in simulating real-life fire incidents [15-17] has been noted for producing results that closely mirror the actual dynamics of smoke movement in fire events. For the purpose of this study, the PyroSim software was utilized to construct a model of a highway tunnel incorporating a shaft. This tunnel model is characterized by dimensions of 120 meters in length, 10 meters in width, and 5 meters in height. The shaft, designed with a cross-sectional area measuring 2 meters by 2 meters and a height of 5 meters, is strategically located directly above the tunnel's central longitudinal axis, 50 meters from the right entrance of the tunnel. The fire source placement within the tunnel model is specified at 70 meters from the right entrance and 20 meters from the shaft entrance, aligned along the tunnel's longitudinal centerline. In this context, the distance 'D' between dual fire sources is defined as the span from the right extremity of the first fire source to the left boundary of the subsequent fire source, maintaining a constant relative position of the latter fire source to the shaft. Figure 1 presents a schematic representation of the tunnel's geometric model.

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Figure 1. Geometric model of the tunnel

2.2 Computational conditions and measurement point arrangement

This study's tunnel model, reflective of an actual highway tunnel project, predominantly accommodates cars, small trucks, and buses. Adhering to the National Fire Protection Association (NFPA) 502 guidelines for highway tunnel fire scales [18], fire source powers were designated as 5 MW, 10 MW, and 20 MW for cars, small trucks, and buses, respectively. In scenarios involving dual fire sources, each source was assigned a power of 10 MW, simulating challenging conditions like the burning of small trucks or buses in highway tunnels. The fire sources were fueled by n-heptane, characterized by a carbon monoxide yield rate of 0.006 and a soot mass yield rate of 0.015. The tunnel's right side and the shaft opening were configured as “open”, establishing a connection with the external environment, while the left side opening was set as “supply”, indicative of the presence of longitudinal wind ranging from 0m/s to 3m/s. The tunnel's initial temperature and atmospheric pressure were set at 20℃ and the standard 101.325 kPa, respectively, with “concrete” as the material for both the tunnel and shaft, mirroring real-world constructions.

Temperature slices were methodically arranged along the tunnel's longitudinal centerline. This arrangement included 120 thermocouples and carbon monoxide concentration measurement points placed every meter along the length, 0.1 meters below the tunnel's ceiling. On a plane at Z=2m, temperature and carbon monoxide measurement points were uniformly distributed at 1-meter intervals along the centerline. To monitor temperature and carbon monoxide concentration changes within the tunnel and shaft, slices were positioned on the Y=5m plane. Moreover, five carbon monoxide concentration measurement points, situated 0.1 meters from the shaft's top opening for averaging purposes, along with gas mass flow points, were established to assess the shaft's smoke exhaust performance. Recognizing the impracticality of a fire source achieving its maximum heat release rate instantly in actual incidents, the study treated tunnel combustion as unsteady. The unsteady heat release rate's growth function predominantly utilized a t² growth function, expressed as:

Table 1. Fire growth coefficient

$Q=\alpha t^2$     (1)

where, Q denotes the fire power (kW); $\alpha$ symbolizes the combustion growth coefficient (kW/s²), with reference values [19] presented in Table 1; and t represents the combustion time (s). The fire source was modeled as an ultra-fast unsteady fire. For a fire source power of 10 MW, the calculated time t approximated 231s, enabling smoke flow to reach a stable state. Similarly, for a 20 MW power, t was around 327s, thus the simulation runtime was set to 600s to ensure smoke flow stability.

2.3 Grid independence analysis

In the realm of FDS fire simulations, the selection of an appropriate grid size is pivotal for ensuring the precision of results. A smaller grid size, while enhancing experimental accuracy, imposes substantial demands on computational resources and escalates the complexity of the experiment. In contrast, opting for a larger grid size might compromise both the accuracy and scientific integrity of the results. Drawing from independent grid size experiments conducted by McGrattan et al. [20], the ratio between the fire characteristic diameter D* and the tunnel grid size d_x is typically within the range of 4 to 16. The formula for calculating D* is as follows:

$D^*=\left(\frac{Q}{\rho_0 c_\rho T_0 g^{1 / 2}}\right)^{2 / 5}$     (2)

where, Q denotes the heat release rate of the fire source (kW); r₀ is the air density (kg/m³), with a value of 1.205kg/m³; c_p represents the specific heat capacity of air (kJ/(kg·K)), set at 1.003kJ/(kg·K); T₀ is the ambient temperature, measured in Kelvin, and assigned a value of 293K(20℃); g stands for the acceleration due to gravity (m/s²), which is 9.81m/s².

For a fire source with a power of 10 MW in this study, the grid size was calculated to be within the range of 0.150m to 0.599m, based on the fire characteristic diameter formula and the grid size ratio. Simulations were executed with grid sizes of 0.167m, 0.2m, 0.333m, and 0.5m to determine an optimal size. Figure 2 depicts the temporal temperature variation at the tunnel roof directly above the fire source. Given the unsteady nature of the fire source in the experiment, significant temperature fluctuations were observed. It was noted that the temperature range for a grid size of 0.5m was substantially lower than that of the other sizes. As the grid size decreased, the differences in temperature range became negligible. Consequently, considering the balance between computational efficiency and experimental time, a grid size of 0.333m was selected for the simulations.

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Figure 2. Roof temperature variations in the tunnel under different grid sizes

2.4 Scheme design and simulation of working conditions

For the experimental simulations conducted in this study, scenarios involving dual fire sources were established, with each source having a power of 10 MW. Comparative analyses were also carried out with a single fire source scenario, where the fire source was assigned a power of 20 MW. Figures 3-5 illustrate the variations in smoke dispersion within a shaft ventilated tunnel under different longitudinal wind speeds for a single fire source of 20 MW.

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Figure 3. Longitudinal wind speed at 0m/s

It was observed that in the absence of longitudinal ventilation, smoke initially reached the tunnel's ceiling and subsequently dispersed in both directions. By 200s, the smoke had extended to both ends of the tunnel, starting to disperse downwards, with a notably thinner smoke layer beneath the shaft compared to the sides. At 400s, as the fire source attained its maximum heat release rate and stabilized, a considerable amount of smoke accumulated within the tunnel, exhibiting clear stratification with similar distribution patterns both upstream and downstream.

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Figure 4. Longitudinal wind speed at 1m/s

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Figure 5. Longitudinal wind speed at 2.8m/s

With a longitudinal wind speed of 1m/s, the smoke dispersion was slower compared to the scenario without longitudinal wind, and backflow of smoke was still evident. By 200s, the smoke had predominantly dispersed to the left end of the tunnel. Due to the influence of the longitudinal wind, the thickness of the smoke layer upstream of the fire source was significantly greater than downstream. At 400s, heavy smoke accumulation on the tunnel's left side and the chimney effect of the shaft on the right led to asymmetric smoke distribution and thinner smoke layers near the ventilation shaft. At a longitudinal wind speed of 2.8m/s, no smoke propagation was observed upstream of the fire source at various intervals, indicating a backflow distance of zero. Thus, the critical wind speed for a single fire source scenario with a power of 20 MW was determined to be 2.8m/s.

Previous studies [21-23] have demonstrated that as the distance between two fire sources increases to a certain threshold, the critical wind speed converges to a limit value. At this juncture, the critical wind speed is equivalent to that necessary for a single fire source. When the distance between two fire sources is zero, they effectively merge into a single source, and the critical wind speed corresponds to the combined power of both sources. Consequently, in the dual fire source scenarios of this study, distances between fire sources were set at 3m, 6m, and 9m. Simulations were then performed combining these distances with varying longitudinal wind speeds and were compared with a single fire source scenario of 20 MW, as detailed in Table 2.

4.1 Analysis of shaft temperature variations

In the context of this study, the establishment of shafts above the tunnel exploits the chimney effect, arising from the density differential between internal and external environments. This phenomenon facilitates the outward flow of high-temperature smoke from the tunnel through the shaft, utilizing the thermal pressure effect. Not only does this process maintain smoke stratification, but it also efficiently expels a portion of the smoke generated during a fire incident. Moreover, it substantially reduces the temperature at the shaft's entrance, thereby aiding in the evacuation process and enabling swift escape from hazardous areas. Figure 12 depicts temperature variations within the shaft under different wind speeds, 360s into the fire (a state of stability with parameters such as thermal radiation and heat release rate being relatively stable). In dual fire source scenarios, D=6m is taken as an example, since the cloud diagram captures the tunnel length between 65~80m, precisely downstream of the fire source. Analysis from the previous section suggests that temperature curves beyond 10m downstream of the roof in different scenarios with varying distances and wind speeds in dual fire source cases are essentially similar.

From Figures 12(a) and (b), it is evident that during natural ventilation in the tunnel, the temperature inside the shaft under both scenarios does not differ significantly, remaining around 100℃, with minimal thermal stratification inside the tunnel. A low-temperature zone is observed at the shaft entrance, and the temperature below is almost the same as the ambient, due to the ingress of cold air from below the tunnel. Figures 12(c) and (d) indicate that at a longitudinal wind speed of 1m/s, the temperature inside the shaft is higher than in scenarios without longitudinal wind. The chimney effect of the shaft is relatively stronger here, with smoke primarily being exhausted through the shaft. Influenced by the longitudinal wind, a low-temperature zone still exists below the shaft on the side. The higher temperature below the shaft compared to the no-wind scenario could be due to smoke partially dispersing downstream of the fire source under the influence of the longitudinal wind. When the smoke reaches the shaft entrance, the strong vertical inertial force created by the chimney effect surpasses the horizontal inertial force of the smoke, causing partial smoke and cold air to be directly drawn into the shaft, resulting in a breakthrough phenomenon. The temperature inside the shaft in dual fire source scenarios is higher than in single fire source scenarios, correlating with the analyzed smoke dispersion, as the influence of longitudinal wind and shaft ventilation causes smoke accumulation at the downstream shaft entrance, increasing shaft exhaust and elevating shaft temperature. When longitudinal wind speed increases, the horizontal inertial force of the smoke inside the tunnel also increases, weakening the chimney effect and making the breakthrough phenomenon less likely.

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Figure 12. Temperature distribution cloud diagram of shaft and downstream tunnel under different longitudinal winds

Figures 12(e) and (f) show the temperature distribution in the shaft and tunnel at critical wind speed, with no low-temperature zone at the shaft entrance and distinct smoke stratification inside the tunnel. In dual fire source scenarios, the smoke layer thickness is around 4.5m, greater than in single fire source scenarios. The temperature inside the shaft in single fire source scenarios is around 200℃, 50℃ higher than in dual fire source scenarios. Due to the higher wind speed, the fire smoke disperses entirely downstream, and the single fire source scenario, with greater power, releases more heat radiation than the dual fire source scenarios. At critical wind speed, the smoke exhaust efficiency in the single fire source scenario is better than in dual fire source scenarios, leading to a higher temperature and thinner smoke layer inside the shaft in the former.

4.2 Shaft gas mass flow and carbon monoxide concentration analysis

Figure 13 presents the variations in gas mass flow expelled from the shaft under different fire scenarios and longitudinal wind speeds. It was observed that the mass flow of gas discharged from the shaft exhibited an initial increase with wind speed, followed by a subsequent decrease. In dual fire source scenarios, the trend of gas mass flow remained largely consistent across different conditions, surpassing that of single fire source scenarios at equivalent wind speeds. From a longitudinal wind of 0m/s to 0.5m/s, there was a rapid increase in gas mass flow, which then plateaued with further increases in wind speed. The disruption of smoke stratification by longitudinal ventilation enhanced the smoke’s ability to entrain surrounding air, thereby escalating the mass flow. The peak of gas mass flow inside the shaft was reached at a wind speed of 2m/s, beyond which it demonstrated a declining trend. This finding underscores that higher wind speeds do not necessarily improve the shaft's smoke exhaust efficiency, and optimal exhaust efficiency is not guaranteed at critical wind speed. An ideal wind speed is necessary for maximal smoke exhaust efficiency in the shaft, aligning with findings from previous research [24, 25]. When the longitudinal wind speed surpassed the critical value, gas mass flow across all scenarios tended to converge due to the increased horizontal inertial force of the smoke, which diminished the chimney effect and reduced the smoke’s entrainment into the shaft.

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Figure 13. Variation in gas mass flow under different longitudinal winds

Figure 14 illustrates the carbon monoxide concentration within the shaft and downstream tunnel at various longitudinal wind speeds. Upon the occurrence of a tunnel fire, combustion from vehicles produces copious smoke and toxic gases, which disperse and diminish visibility over time, complicating evacuation efforts. Individuals trapped within the fire zone are continually exposed to toxic gases, including carbon monoxide, carbon dioxide, hydrogen chloride, and hydrogen cyanide, among others. Carbon monoxide and carbon dioxide are notably responsible for causing unconsciousness or death [26]. Study [27] indicate that the maximum tolerable carbon monoxide concentration for adults is 50ppm (5×10^-5mol/mol), with prolonged exposure at this level causing symptoms such as dizziness and nausea, and higher concentrations posing lethal risks.

The figure shows the carbon monoxide concentration 360s post-fire outbreak in both fire source scenarios, at which point the fire sources have reached and stabilized at their peak heat release rates. Generally, the concentration of carbon monoxide inside the shaft initially increased and then decreased with rising longitudinal wind, mirroring the pattern observed in gas mass flow. In the absence of longitudinal wind, the concentration of carbon monoxide below the shaft entrance was lower than that at the sides, indicating effective smoke expulsion from the downstream area of the tunnel shaft in fire scenarios. In single fire source scenarios, the carbon monoxide concentration inside the shaft was measured at 1.5×10^-5mol/mol, with relatively sparse carbon monoxide content in the tunnel, not extending to human height. Conversely, in dual fire source scenarios, both carbon monoxide stratification in the shaft and tunnel exceeded those in single fire source scenarios, with the highest concentration in the shaft reaching 2.2×10^-5mol/mol. In the tunnel downstream, carbon monoxide dispersed to a human height of 2m, albeit at concentrations posing no harm. At a wind speed of 1m/s, the carbon monoxide concentration in the shaft escalated, improving smoke exhaust efficiency. Influenced by longitudinal wind, the concentration of carbon monoxide in the smoke beneath the diagonal side of the shaft remained lower than the sides.

In dual fire source scenarios, the highest concentration in the shaft was 4×10^-5 mol/mol, showcasing superior exhaust efficiency compared to single fire source scenarios. The smoke propagation analysis reveals that while the upstream area of the tunnel becomes fully saturated with smoke, the downstream area beneath the shaft remains comparatively safer, facilitating evacuation. At critical wind speed, the carbon monoxide content in the smoke inside the shaft decreases while increasing in the tunnel. In single fire source scenarios at this wind speed, the carbon monoxide content inside the shaft is higher than in dual fire source scenarios, but the carbon monoxide content and stratification in the tunnel are lower than in dual fire source scenarios. This suggests that in dual fire source scenarios, the generated smoke is more abundant, causing its horizontal inertial force to exceed the chimney effect's smoke entrainment capability, leading to a decrease in carbon monoxide content inside the shaft and an increase and clear stratification of carbon monoxide in the tunnel. Overall, in the downstream area of the tunnel with shaft ventilation, the carbon monoxide concentration at human height under different longitudinal wind speeds remains within safe limits, but this does not imply that individuals can remain there for extended periods. Prompt evacuation from the tunnel is recommended.