Keywords

1 Introduction

As a mountainous and densely populated country, China has made significant progress in constructing mountain tunnels [1], including numerous lengthy ones. However, due to their unique narrow and elongated structure, tunnels often pose a high risk of causing substantial casualties and economic losses in the event of a fire [2]. Smoke caused by tunnel fires poses the greatest threat to individuals trapped inside [3,4,5]. How to scientifically design the smoke exhaust system to reduce casualties and property losses is a key issue in tunnel construction and operation. According to relevant norms [6], the longitudinal smoke exhaust distance of mountain tunnels is not more than 5 km, and the longitudinal smoke exhaust distance of municipal tunnels is not more than 3 km. Therefore, the integration of longitudinal ventilation system and top exhaust system can be considered for the evacuation of smoke in lengthy tunnel. Extensive research has been conducted by numerous researchers and scholars on this combined smoke exhaust method. Ingason and Li [7] conducted small-scale experiments to investigate the smoke control effects of single and two vents in a top exhaust system in the presence and absence of longitudinal air velocity, respectively. Chen et al. [8] modified the dimensionless return smoke length model developed by Li [9], and developed a predictive model of return smoke lengths for a top exhaust system with vents above the fire source and a longitudinal ventilating system in concert. Tang et al. [10] found that compared with other locations, the mechanical smoke exhaust system has the most significant effect on the velocity of the smoke front when the fire source is directly below the ceiling exhaust vent. Wang et al. [11] built a full-size numerical simulation with FDS to investigate the effect of different smoke exhaust strategies (varying longitudinal and exhaust air velocities) on a coupled system of longitudinal and shaft ventilation. It can be seen that the coupling of longitudinal and top exhaust systems has received much attention in recent years, but the focus is still on the prediction of returning smoke [12,13,14]. In fact, the smoke returns to the upstream of the fire and spreads downstream across the vent, still posing a threat to the escape route of personnel. The actual project is more concerned about the setting of the exhaust volumetric flow rate so that the smoke can be completely eliminated to create a good escape environment. However, the relevant norms [6] states that there's no recognized value for smoke volume in centralized smoke exhaust tunnels. In this paper, the study focuses on the complete exhaust volumetric flow rate. The critical longitudinal ventilation velocity is set as the velocity of longitudinal ventilation, and the minimum volume flow rate of the exhaust vent required for effective containment of smoke between the fire source and the exhaust vent is defined as the critical complete volume flow rate. Furthermore, this study investigates various factors such as heat release rate (HRR), fire source location, and ventilation vent size to determine their influence on the critical exhaust rate. This research aims to provide scientific and rational foundations for determining the combined smoke exhaust system volume in engineering design.

2 Model Building

In this paper, a full-size tunnel model of a mountain tunnel is established using FDS, as shown in Fig. 1. The tunnel section consists of a semicircle with a radius of 6 m and a rectangle with a height of 1.4 m. The tunnel is 2500 m long and 12 m wide. The smoke vent is located in the central axis of the tunnel ceiling, with its inner edge is 320 m away from the entrance of the tunnel, and the width of the vent is fixed at 5 m. The vent is set in seven different lengths: 1, 3, 5, 7, 10, 13, and 15 m. N-heptane is used to simulate the fire source with heat release rate of 5 MW, 10 MW and 30 MW respectively. The fire source is located at the bottom of the tunnel along its longitudinal axis as shown in Fig. 2. The temperature probes were positioned at intervals of 0.5 m along the longitudinal direction, specifically 20 cm below the tunnel ceiling. There are four different locations for the fire source. The tunnel wall material is set as “concrete” with a thickness of 0.5 m. The boundary between the tunnel exit and the calculation area is set as “open”. At the entrance of the tunnel, “supply” is used to introduce wind into it while “exhaust” at the vent facilitates smoke evacuation. The initial ambient temperature is set at 25℃ with an ambient pressure of 101325 Pa, and a simulation time of 600 s.

Fig. 1
A schematic diagram of the front view and the left and top views of a model building. In the front view, the longitudinal wind blows from left to right toward the extraction vent on the right. In the left and top view, there are 2 extraction vents on either side. The length and width are 12 and 14 meters approximately.

Schematic of the model

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Fig. 2
A schematic diagram depicts the fire source location along the tunnel axis. The intervals between the temperature probes are 500 meters. The total height is 12 meters.

Schematic of fire source location

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Fig. 3
A photograph of a partially transparent cylindrical model tunnel with visible internal structures, wires, and equipment, placed indoors.

Grid-independent verification

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The prerequisite for conducting numerical simulation calculations is an in-depth analysis of the impact of grid size on the resulting outcomes. As specified in the FDS User’s Guide [15], the grid size is intricately linked to the characteristic diameter of the fire source. The term “characteristic flame diameter D*” is defined as follows:

$$D^{*} { = }\left( {\frac{{{\dot{\text{Q}}}}}{{\rho_{\infty } c_{p} T_{\infty } \sqrt g }}} \right)^{\frac{2}{5}}$$
(1)

where \(\dot{Q}\) is the rate of heat release from the ignition source, kW; \({\rho }_{\infty }\) is the density of ambient air, 1.2 kg/m3; cp is the specific heat of air, 1 kJ/(kg·K); \({T}_{\infty }\) is the ambient air temperature, 293 K; \(g\) is the acceleration of gravity, 9.81 m/s2.

Taking the heat release rate of the fire source as an example of 10 MW, as illustrated in Fig. 3, which presents the simulation results of the longitudinal temperature distribution of the smoke under varying grid sizes of the model, it can be observed that, as the grid size decreases from 0.088 D* to 0.072 D*, the accuracy is incrementally improved. Moreover, the calculated results for the grid sizes of 0.072 D* and 0.062 D* remain virtually unchanged. To balance the accuracy of the results and the computational cost, it is more rational to select the grid size of 0.072 D* for the subsequent three-dimensional simulation of the tunnel fire.

Fig. 4
A multi-line graph depicts delta T versus distance from the fire source. It includes four plots of 0.12 D, 0.088 D, 0.072 D, and 0.062 D. The ranges of 0.88, 0.72, and 0.062 have similar trends that begin from 160 degrees and gradually decrease to 80 degrees Celsius and between 0.0 and 3.5 meters.

Model tunnel table view

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The 1:10 scaled-down model tunnel test was conducted to validate the numerical model. Figure 4 shows the actual view of the model tunnel platform. The dimensions of the model tunnel are 5 m in width, 12 m in height, and 12 m in length. The selected fire source had a heat release rate of 5.68 kW and was positioned in the longitudinal center of the tunnel. The smoke vent measured 0.1 m in length and 0.5 m in width, located 3 m away from the source of fire, while the longitudinal wind speed was 0.62 m/s. The exhaust volumetric flow rate was set at 180m3/h. Thermocouples were used to measure the temperature and were placed at 0.2 m intervals along the tunnel, with measurement points located 2 cm below the tunnel ceiling. The ambient temperature during testing was maintained at 35 °C. It can be observed from Fig. 5 that the longitudinal temperature distribution obtained from numerical simulation results closely aligns with the experimental data, with a maximum error within 20%. This demonstrates that the proposed model is capable of accurately simulating and calculating tunnel fires.

Fig. 5
A graph depicts the changes in the results of the experiment and a simulation versus distance from the fire source. They both have approximately similar rises and falls. They begin at (negative 4, 20), gradually rise to (0, 90), and then sharply fall to (0, 0), and remain constant up to (4, 0) approximately.

Comparison of numerical simulation results with model test results

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The study investigates the critical complete exhaust volumetric flow rate in tunnel fires under the synergistic effect of longitudinal ventilation and top smoke exhaust, considering factors such as fire source heat release rate, fire source location, length of the smoke exhaust vent, and specific simulation conditions shown in Table 1.

Table 1 Simulation conditions
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3 Results and Discussion

The critical complete exhaust volumetric flow rate, as defined in this paper, refers to the volumetric flow rate of smoke exhaust that allows for complete discharge from the smoke vent without any downstream spreading through the vent when there is no smoke return. The simulation results are summarized in Table 2.

Table 2 Summary of simulation results
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3.1 Influence of the Heat Release Rate on the Critical Complete Exhaust Volumetric Flow Rate

The impact of the heat release rate of the fire source on the critical complete exhaust volumetric flow rate is illustrated in Fig. 6. From the diagram, it can be observed that an increase in the heat release rate corresponds to a rise in the critical complete exhaust volumetric flow rate. This can be explained by the force exerted on the smoke vent. As shown in Fig. 7, the smoke below the vent is mainly subject to the vertical inertia force generated by the smoke exhaust and the horizontal inertia force caused by the superposition of the longitudinal forced airflow and smoke heat pressure. On the one hand, when increasing the heat release rate of the fire source, it leads to an elevation in the temperature of the smoke below the vent. Consequently, this results in an augmented thermal buoyancy of the smoke near the exhaust vent. On the other hand, as indicated in Table 2, an increase in heat release rate corresponds to a higher critical wind speed for longitudinal ventilation. This leads to an escalation in the horizontal inertia force induced by longitudinal wind. Therefore, both the horizontal inertia force caused by longitudinal wind and smoke thermal buoyancy intensify with higher heat release rates. To counterbalance this surge in horizontal inertial force, a larger exhaust inertial force is required to prevent smoke from crossing over the vent. This can only be achieved by increasing the volume of exhaust. Therefore, the critical volume of smoke exhaust at the critical wind speed increases with an increase in the heat release rate. Furthermore, in the actual tunnel project, once the vent setting is established, the critical exhaust volumetric flow rate for complete smoke extraction under varying heat release rates can be determined. As a result, a corresponding decrease in the critical exhaust volumetric flow rate can be achieved when the heat release rate is reduced, thereby avoiding unnecessary waste caused by excessive volume.

Fig. 6
Two bar graphs depict the critical exhaust rate versus H R R. a. The values for 7 meters in length of the vent are (5, 245), (10, 321), and (30, 527). b. The values for the 15 meters in length of the vent are (5, 235), (10, 318), and (30, 519).

Effect of HRR on critical complete exhaust volumetric flow rate

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Fig. 7
A schematic of the fire source location on the critical complete exhaust volumetric flow rate. The inertial force of smoke extraction is labeled as F i and the horizontal inertial force is labeled as F h. The formulae for F i and F h are provided.

Schematic diagram of smoke force analysis underneath the smoke vent

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Note: ρs is the density of smoke, kg/m3; Vs is the exhaust volumetric flow rate at the vent, m3/s; l is the length of the vent, m; w is the width of the vent, m; uh is the average velocity of smoke when there is no smoke exhaust, m/s; A is the cross-sectional area of smoke, m2.

3.2 Influence of the Location of Fire Source on the Critical Complete Exhaust Volumetric Flow Rate

Figure 8 illustrates the critical exhaust volumetric flow rate for complete smoke exhaust under four fire source positions (A, B, C, and D) with a heat release rate of 5 MW, longitudinal wind speed at its critical velocity, and vent lengths of 7 m and 15 m. It can be observed from the figure that as the longitudinal position of the fire source increases from the vent distance, the critical complete exhaust volumetric flow rate also increases. This can be attributed to the fact that an increased distance results in a longer smoke flow path towards the vent, causing a decrease in temperature below it As indicated by Fig. 7, this reduction leads to a decrease in horizontal inertial force due to hot smoke buoyancy, thereby the inertial forces required for critical smoke evacuation can be reduced accordingly. Consequently, the critical complete exhaust volumetric flow rate is also reduced. Through the above analysis, it becomes evident that the critical complete exhaust volumetric flow rate increases proportionally with the longitudinal fire source location moving away from the vent. It is important to note that while the critical complete exhaust volumetric flow rate decreases as the vent spacing increases, excessively large spacing results in an elongated fire source section, which hinders safe personnel evacuation. Therefore, careful consideration should be given to determining the optimal smoke exhaust vent spacing, which will be further studied in future work.

Fig. 8
A dual-line graph depicts the critical exhaust rate versus the location of the fire source. It includes two plots of vent length 7 and 15 meters. The vent length of 7 meters begins at (A, 245) and decreases to (D, 205) while the 15 meter vent begins at (A, 235) and reaches (D, 200).

Influence of fire source location on critical complete exhaust volumetric flow rate

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3.3 Influence of Smoke Vent Length on the Critical Complete Exhaust Volumetric Flow Rate

Taking the case where the heat release rate of the fire source is 5 MW and the longitudinal wind speed is at its critical level as an example, Fig. 9 illustrates the impact of smoke vent length on the critical complete exhaust volumetric flow rate in tunnel fires under the combined influence of longitudinal wind and top smoke venting. It can be observed that, for a fixed heat release rate, increasing the length of the vent initially leads to an increase in critical complete exhaust volumetric flow rate, followed by a decrease. This occurs because as the length of the smoke vent gradually increases, it results in an increased area at its mouth and a reduced wind speed for smoke exhaust; consequently weakening inertia force during smoke exhaust. Although increasing the length of the vent does not significantly affect horizontal inertia force, it becomes necessary to increase smoke exhaust capacity in order to ensure complete discharge. When the length of the vent exceeds 10 m, due to its larger size, smoke can directly enter and exit through the vent without easily overflowing. This facilitates effective smoke exhaust and reduces requirements for critical exhaust volumetric flow rate. Therefore, we observe an increasing trend followed by a decreasing trend in critical complete exhaust volumetric flow rate with longer lengths of vent. This suggests that during actual tunnel operation, the exhaust volumetric flow rate can be suitably diminished in accordance with the vent length without necessitating waste. Furthermore, when adjusting the exhaust volumetric flow rate based on specific vent dimensions is infeasible, it can be set to the maximum value corresponding to the pertinent firepower (e.g., the exhaust volumetric flow rate corresponding to a 10-m-long vent under this working condition). This ensures comprehensive smoke discharge from any vent within the 1–15 m range.

Fig. 9
A graph depicts the critical exhaust rate versus the length of the vent. It includes a plot that begins at (1, 235), sharply rises to (10, 248), and then falls to (15, 235) approximately.

Effect of different vent lengths on complete exhaust volumetric flow rate

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4 Conclusions

In this paper, a full-size tunnel model is established using FDS and three-dimensional numerical calculation methods are employed to investigate and analyze the variations in the critical complete exhaust volumetric flow rate at the exhaust vent of a tunnel fire under the combined influence of longitudinal ventilation and top smoke extraction, considering various factors. The key findings obtained from this study are as follows:

  1. (1)

    When the vent size and fire source location are fixed, an increase in heat release rate leads to a corresponding increase in the critical exhaust volumetric flow rate required for complete ventilation. Therefore, the critical complete exhaust volume flow rate at varying heat release rates can be determined accurately in actual tunneling projects, ensuring both efficient smoke evacuation and the prevention of unnecessary waste resulting from excessive exhaust volume flow rates.

  2. (2)

    In cases where the vent size and the power of the fire source remain constant, as the distance between the fire source and vent location increases, there is a decrease in the critical complete exhaust volumetric flow rate. It should be noted that although increasing vent spacing leads to a reduction in the critical complete exhaust volumetric flow rate, excessively large spacing can elongate the fire source section, impeding safe personnel evacuation. Therefore, careful consideration must be given to determining optimal smoke exhaust vent spacing.

  3. (3)

    The critical complete exhaust volumetric flow rate increases when the length of the vent is less than 10 m and decreases when it exceeds 10 m, while keeping the heat release rate and location of the fire source unchanged. The findings indicate that during the tunnel operation, the exhaust volumetric flow rate can be appropriately reduced in accordance with the vent length, thereby eliminating the need for waste. Moreover, when it is impracticable to adjust the exhaust volumetric flow rate based on specific vent dimensions, it can be set to the maximum value corresponding to the relevant fire power (the exhaust volumetric flow rate corresponding to a 10-m-long vent under these working conditions). This approach ensures complete smoke discharge from any vent within the 1–15 m range.

The present study primarily focuses on a specific vent width for research and analysis, neglecting factors associated with it. These aspects will be further explored in future research, enhancing the practicality of the findings. Additionally, an investigation is being conducted to integrate theoretical concepts and derive a predictive formula for the critical complete smoke exhaust volume. This aims to develop a universally applicable equation that offers direction for tunnel smoke exhaust.