Numerical study on smoke temperature and exhaust efficiency in electric cable tunnel

Cable tunnels are the lifeline of cities. Once a serious fire occurs on cables, the toxic smoke generated by cable combustion spreads and escapes, causing serious harm to the surrounding environment and personnel. The heat generated can also ignite nearby combustibles, causing casualties and property damage. Based on the above issues, using fluid dynamics methods, fire dynamic simulation was used to simulate cable tunnel fire scenarios under four variables: wind speed, fire source power, smoke outlet height, and smoke exhaust airflow. The temperature distribution law of the ceiling smoke layer inside the cable tunnel, smoke generation law, tunnel smoke exhaust efficiency, and other factors were clarified, revealing the impact mechanism of the above factors on tunnel fire smoke exhaust efficiency and smoke performance improvement methods. The research results indicate that the combination mode of exhaust air volume and ventilation air speed can effectively control tunnel fire smoke, providing a reference for the fire prevention design of cables in urban cable tunnels.


Introduction
The fire simulation software FDS is widely utilized for simulating smoke layer and temperature changes in enclosed space fires.Simon [1] et al. conducted numerical simulations using CFD software to explore the combustion characteristics and fire propagation laws of cable trays, providing reference value for fire engineers to evaluate the fire hazard of cables.Kim [2] et al. set an instantaneous wind speed tunnel fire with a fire scale of 100 MW and verified the rationality of software grid division and the consistency between CFD prediction and actual results.Li [3] used FDS software for numerical simulation to explore the smoke diffusion and temperature changes of cable fires in comprehensive pipe corridors.Chow [4] used CFAST software to establish a numerical model similar to the actual tunnel and analyzed the characteristics of smoke during interval tunnel fires, verifying that CFAST is more effective in predicting smoke layer temperature increase and smoke layer interface elevation.Kunsch [5] from Switzerland developed a simplified calculation model that provides an analytical formula for the critical wind speed to prevent smoke backflow while verifying that the critical wind speed is independent of the power of the ignition source.Chow et al. [6] used a combination of model experiments and numerical simulations to study the effect of slope on critical wind speed and established a calculation model for critical wind speed using theoretical analysis methods.
Also, Gao et al. [7] developed an empirical formula for determining the maximum temperature increase of the ceiling under natural ventilation by analyzing the correlation between heat release rate and flame height, combined with experimental data.Evers and Waterhouse [8] obtained a longitudinal distribution prediction model for roof temperature rise based on data analysis by establishing a scaled model tunnel experimental study.Based on the continuity equation and energy equation, Hu et al. [9] obtained a relatively simplified temperature attenuation prediction model under the roof of a tunnel structure through theoretical analysis.Liu et al. [10] derived a model for predicting longitudinal attenuation of ceiling temperature based on one-dimensional theory, and compared the model with FDS numerical simulation results, which were highly consistent.Wang and Zhao [11] investigated the influence of the L-shaped inclined shaft on tunnel smoke dispersion properties and exhaust efficiency and found a positive correlation between the fire source and the longitudinal decay rate of CO.Wu et al. [12] observed that a higher proportion of blockage within the cable tunnel corresponded to a shorter duration for smoke to fill the tunnel, a more rapid rate of temperature reduction, and an increased concentration of CO.Wu and Bakar [13] carried out experiments in five tunnels with varying crosssections based on previous studies and found that the tunnel cross-section had a minimal impact on the critical wind speed.Zhou et al. [14] established a T-shaped cable tunnel model based on FDS numerical simulation and conducted a full-scale simulation of cable tunnel fires, obtaining the changes in smoke concentration, oxygen concentration, and longitudinal temperature.Hu et al. [15] combined experimental data from full-scale highway tunnel fires and compared it with theoretical equations, and found that the rate of decay of smoke temperature is much faster than the decay rate of CO concentration.Liang [16] conducted numerical simulations on the propagation of fire and smoke in T-shaped pipe gallery cables, revealing the influence of the factors on the temperature and smoke layer height changes at intersections.Tang [17] conducted numerical simulations on the fire and smoke spread of L-shaped pipe gallery cables and found that the CO concentration varied in a V-shape with the horizontal distance from the fire source.The rise in cable inclination angle had a considerable influence on the CO concentration near the air intake.Tao et al. [18] investigated the smoke control effectiveness in the horizontal tunnel section of the rescue station and obtained the changes in the flow field and smoke spread over time in the horizontal passage under different air supply rates and vertical shaft smoke exhaust rates through a 1:50 scale model experiment.
In summary, scholars have conducted massive simulations and experiments to study the characteristics of the fire smoke layer in narrow and long spaces of cable tunnels, including the maximum ceiling smoke temperature, longitudinal reduction of the smoke temperature of the ceiling, and lateral distribution of tunnel fire site temperature.However, there is relatively little study on the smoke exhaust efficiency of cable tunnels.Therefore, based on fire scenario simulation, this article reveals the smoke exhaust and ventilation laws in cable tunnels by simulating cable tunnel fires under the coupling of multiple factors.

Simulation system and introduction
Based on the physical objects of "Type I" urban underground the "Design Specification for Urban Power Tunnels", we established a "Type I" urban underground cable tunnel model.As shown in Figure 1, the entire "Type I" cable tunnel is 500 m long, with a section width of 2 meters and a height of 2 meters.There are four layers of cables laid inside, with an interval of 0.3 m between the top and bottom layers.The left end of the horizontal ventilation outlet is the air inlet, and the right end is the exhaust outlet.The length and width of the ventilation outlet are 2×2 meters, with smoke exhaust outlets arranged at intervals of 2×2 meters.The cable is sustained by the bridge, and the cable setup is simplified to a thin plate consisting only of outer cable material.The width of the thin plate is 0.1 m, and the distance from the tunnel wall is 0.05 m.The cables inside the tunnel are copper core rubber insulated cables, and the cable material ratio is determined according to copper: PVC=6:4.The specific material parameters are shown in Table 1, and the pertinent simulation parameters about the cable tunnel model are shown in Table 2:  In the numerical simulation, when the ratio range of   is between 4 and 16, the simulation calculation results are relatively good.According to the calculation, the calculated grid size of the fire source is 0.14~0.57.Considering the time and accuracy requirements of numerical simulation, 0.25 m is selected as the grid size.The research object of this article is the simulation of cable fires in urban underground cable tunnels.The heat level of the overhead smoke layer and CO and CO₂ smoke exhaust efficiency are studied under the effects of smoke outlet height, wind speed, fire source power, and smoke exhaust airflow.The selected cable fire simulation conditions are shown in Table 3:

Temperature distribution of ceiling smoke layer
Figure 2 shows the temperature changes at the ceiling measurement points at different times.From the temperature variation diagram of the ceiling measurement point at 200 seconds, it can be observed that when the smoke exhaust volume reaches 10   / , the maximum temperature of the smoke layer is 341℃.When the smoke exhaust volume reaches 30   /, the maximum temperature of the smoke layer is 311℃, which is slightly lower than the temperature under the 10   / working condition.When the smoke exhaust volume reaches 50   /, the maximum temperature of the smoke layer is 316℃.Although it slightly increases compared to 30   /, the overall temperature is the lowest.From the temperature change chart of the ceiling measurement point at 400 seconds, it can be seen that when the smoke exhaust volume is 10   /, the maximum temperature of the smoke layer is 382℃.At the 30   / smoke exhaust volume, the maximum temperature of the smoke layer is 354℃, which is slightly lower than the temperature under the 10   / working condition.At the 50   / smoke exhaust volume, the maximum temperature of the smoke layer is 331℃.Under this working condition, the temperature in the smoke layer is lower than in other operating conditions.From the temperature change chart of the ceiling measurement point at the time of 600 seconds, it can be seen that at the 10   / and 30   / smoke exhaust volume, the maximum temperature of the smoke layer is 372℃.However, the temperature under the smoke exhaust volume of 30   / is lower than the 10   / condition on the whole.When the low smoke exhaust volume is 50   /, the overall temperature within the smoke layer is the lowest, and the maximum temperature of the smoke layer is only 358 ℃.From the temperature change chart of the ceiling measurement point at 800 seconds, it is evident that when the smoke exhaust volume is 10   / and 30   /, the maximum temperature of the smoke layer peaks at 393℃.However, the temperature under the smoke exhaust volume of 30   / is lower than the 10   / condition on the whole.At the 50   / smoke exhaust volume, the overall temperature of the smoke layer is the lowest, and the smoke layer reaches a maximum temperature of merely 342℃.

Law of smoke generation in cable tunnels
From Figure 3, it can be seen the working condition of V=1 m/s, with the increase of ignition power Q and the overall CO₂ mass flow rate demonstrates a rising tendency.As the power Q of the ignition source increases, in addition to a substantial rise in the rate of CO₂ mass flow generation, the amount of CO₂ generation also increases significantly.Moreover, when the power Q of the ignition source is low, the amount of CO₂ generation increases more.
As the power Q of the ignition source increases, the increase in CO₂ generation is fewer.When the Q is 3 MW, the CO₂ generation rate is relatively low, and the CO₂ mass flow rate reaches around 0.02 kg/m 2 /s during the stable period.When the Q increases to 7 MW, the rate of CO₂ generation increases, and the CO₂ mass flow rate reaches around 0.045 kg/m 2 /s during the stable period.When the Q increases to 10 MW, the CO₂ generation rate continues to increase, and the CO₂ mass flow rate reaches around 0.06 kg/m 2 /s during the stable period.When the Q increases to 15 MW, the CO₂ generation rate remains almost unchanged, similar to the 10 MW conditions.The CO₂ mass flow rate reaches around 0.07 kg/m 2 /s during the stable period.From Figure 4, it can be seen the working condition of V=2 m/s, with the increase of ignition power Q, the overall CO₂ mass flow rate demonstrates a rising tendency.As the power Q of the ignition source increases, in addition to a substantial rise in the rate of CO₂ mass flow generation, the amount of CO₂ generation also increases significantly.Moreover, when the power Q of the ignition source is low, the amount of CO₂ generation increases more.As the power Q of the ignition source increases, the increase in CO₂ generation decreases.When the Q is 3 MW, the CO₂ generation rate is relatively low, and the CO₂ mass flow rate reaches around 0.02 kg/m 2 /s during the stable period.When Q increases to 7 MW, the rate of CO₂ generation increases, and the CO₂ mass flow rate reaches around 0.045 kg/m 2 /s during the stable period.When the Q increases to 10 MW, the CO₂ generation rate continues to increase, and the CO₂ mass flow rate reaches around 0.06 kg/m 2 /s during the stable period.When the Q increases to 15 MW, the CO₂ generation rate remains almost unchanged, similar to the 10 MW conditions.The CO₂ mass flow rate reaches around 0.07 kg/m 2 /s during the stable period.From Figure 5, the same power and different wind speeds have similar CO₂ generation rates, with the difference being that when the wind speed is 2 m/s, the CO₂ mass flow rate has a larger vibration amplitude.Other differences such as CO₂ generation rate and CO₂ generation amount are very small.

Law of smoke generation in cable tunnels
From Figure 3, it can be seen the working condition of V=1 m/s, with the increase of ignition power Q and the overall CO₂ mass flow rate demonstrates a rising tendency.As the power Q of the ignition source increases, in addition to a substantial rise in the rate of CO₂ mass flow generation, the amount of CO₂ generation also increases significantly.Moreover, when the power Q of the ignition source is low, the amount of CO₂ generation increases more.
As the power Q of the ignition source increases, the increase in CO₂ generation is fewer.When the Q is 3 MW, the CO₂ generation rate is relatively low, and the CO₂ mass flow rate reaches around 0.02 kg/m 2 /s during the stable period.When the Q increases to 7 MW, the rate of CO₂ generation increases, and the CO₂ mass flow rate reaches around 0.045 kg/m 2 /s during the stable period.When the Q increases to 10 MW, the CO₂ generation rate continues to increase, and the CO₂ mass flow rate reaches around 0.06 kg/m 2 /s during the stable period.When the Q increases to 15 MW, the CO₂ generation rate remains almost unchanged, similar to the 10 MW conditions.The CO₂ mass flow rate reaches around 0.07 kg/m 2 /s during the stable period.

ICEEPS-2023
Journal of Physics: Conference Series 2728 (2024) 012010 IOP Publishing doi:10.1088/1742-6596/2728/1/0120108 is similar, both reaching 86%.When the wind velocity escalates to 1 m/s, the smoke exhaust efficiency of CO and CO₂ slightly decreases, reaching 82%.When the wind velocity escalates to 2 m/s, the smoke exhaust efficiency of CO and CO₂ greatly increases, reaching 94%.When the wind velocity escalates to 3 m/s, the CO and CO₂ smoke exhaust efficiency continues to increase to the maximum value of 97%.For smoke exhaust conditions at different heights, the smoke exhaust efficiency of CO and CO₂ shows similar patterns.Except for the smoke exhaust efficiency at a height of 4 m, which is 72%, the smoke exhaust efficiency of CO and CO₂ is within the range of 86-87% under other conditions.
From Figure 6, it can be seen that the CO₂ and CO smoke exhaust efficiency show a significant increasing trend when the wind velocity escalates from 0-4 m/s.Especially under the 3 m/s wind speed condition, the smoke exhaust efficiency is the maximum value of 97%.In actual cable tunnel fire protection facilities, the efficiency of the smoke exhaust can be improved by installing fans to increase the wind speed appropriately.However, the change in smoke exhaust height has a minimal effect on smoke exhaust efficiency.Especially under the working condition of 4 m height, not only does the smoke exhaust efficiency not increase, but it also slightly decreases.Therefore, in actual cable tunnel fire protection facilities, it is not advisable to change the height of the smoke exhaust outlet.According to Table 6, it can be seen for the same wind velocity and different fire source powers, as the power of the heat source rises from 3 MW to 15 MW, the CO₂ smoke exhaust efficiency is 78.50%, 80.46%, 90.90%, and 91.08% respectively under 1 m/s conditions.Under the condition of 2 m/s, the CO₂ exhaust efficiency is 85.85%, 89.13%, 92.26%, and 93.11%, respectively.It can be concluded that when the wind speed remains constant, the CO₂ smoke exhaust efficiency increases as the power of the heat source increases.As the fire source power remains constant, the CO₂ smoke exhaust efficiency increases as the escalation of wind velocity.
According to the analysis of CO and CO₂ smoke exhaust efficiency at different heights in Table 5, it is evident that as the height of the smoke exhaust port rises from 1 m to 5 m, the CO₂ smoke exhaust efficiency is 86.123%, 86.673%, 87.263%, 72.998%, and 87.246%, respectively.The modification in smoke exhaust port altitude has a minimal influence on smoke exhaust effectiveness.When no ventilation speed and smoke exhaust volume are applied to the cable tunnel, a decrease in smoke exhaust efficiency may also occur when the elevation of the smoke exhaust port is excessively high.
According to the analysis of CO₂ smoke exhaust efficiency under different wind velocities in Table 4, it is evident that when the wind velocity is 1 m/s, the CO₂ smoke exhaust efficiency is 80.46%.When the wind speed is 2 m/s, the CO₂ smoke exhaust efficiency is 83.52%.When the wind speed is 3 m/s, the CO₂ smoke exhaust efficiency is 87.56%.The CO₂ smoke exhaust efficiency increases from 80.46% to 87.56% only by increasing the tunnel ventilation speed.Therefore, changing the wind speed condition alone is an effective method to improve the CO₂ smoke exhaust efficiency, but its CO₂ smoke exhaust efficiency is slightly lower compared to the condition of simultaneously increasing wind speed and smoke exhaust air volume.
During the analysis of CO₂ smoke exhaust efficiency under different exhaust air volumes in Table 7, when the wind speed remains constant and the exhaust air volume is varied, the difference in CO₂ smoke exhaust efficiency is very small and almost unchanged.Therefore, only changing the exhaust air volume cannot improve the smoke exhaust effect.When the exhaust air volume stands at 10  3 / and the wind velocity ranges from 1 m/s to 2 m/s, the CO₂ exhaust efficiency increases from 81.06% to 90.77%.When the exhaust air volume stands at 30  3 / and the wind velocity ranges from 1 m/s to 2 m/s, the CO₂ exhaust efficiency increases from 80.53% to 91.66%.When the exhaust air volume stands at 50  3 / and the wind velocity ranges from 1 m/s to 2 m/s, the CO₂ exhaust efficiency increases from 80.59% to 88.99%.When the exhaust air volume remains constant and the tunnel's ventilation rate accelerates, the CO₂ exhaust efficiency greatly increases.Moreover, when both exhaust air volume and ventilation speed are applied simultaneously, the CO₂ exhaust efficiency is significantly higher than the condition of only applying ventilation speed.

Conclusion
(1) The longitudinal temperature distribution of smoke gas exhibits significant variations under the influence of exhaust airflow rate and fire source distance.As the exhaust airflow rate increases, there is an overall decreasing trend in the smoke layer temperature.Specifically, under the condition of an exhaust airflow rate of 10 m 3 /s, the smoke layer temperature is at its highest.In the case of a 30 m 3 /s exhaust airflow rate, the highest temperature of the smoke layer experiences a slight reduction, although the decrease is not very pronounced.Moreover, under the condition of a 50 m 3 /s exhaust airflow rate, the smoke layer temperature exhibits the most substantial decrease, resulting in both the overall smoke layer temperature and the highest temperature being the lowest.
(2) By analyzing the parameters of CO₂ mass flow rate over time under different fire conditions, the generation mechanism of smoke from the burning cable under the influence of wind speed and firepower was elucidated, and the mechanism of CO₂ generation quality over time in cable tunnels was revealed.At the same flow velocity, an increase in the heat source power results in a general rise in carbon dioxide mass flow rate.Higher heat source power results in an augmentation of both the CO₂ generation rate and CO₂ production, particularly pronounced at lower source power levels.However, as the heat source power continues to increase, the growth rate of CO₂ production gradually diminishes.Under equivalent heat source power conditions, CO₂ generation rates exhibit a similar pattern.
(3) In the design of smoke extraction systems for cable tunnels, it is imperative to comprehensively assess the impact of various factors, including wind velocity, exhaust volume, and exhaust outlet elevation, on the efficiency of smoke extraction within cable tunnels.The variations in the exhaust outlet height have a relatively minor impact on smoke extraction efficiency, particularly under conditions where the exhaust outlets are situated at a height of 4 meters.The smoke extraction efficiency does not increase under these conditions.Instead, it exhibits a slight decrease.When wind velocity remains constant, the carbon dioxide smoke extraction efficiency increases with an escalation in the power of the fire source.Conversely, when the fire source power remains constant, the CO₂ smoke extraction efficiency rises with an increase in wind velocity.Enhancing the tunnel ventilation rate is an effective means of improving CO₂ smoke extraction efficiency, and the improvement is more pronounced when both wind velocity and smoke extraction airflow are increased.

Figure 2 .
Figure 2. Temperature changes at ceiling measurement points at different times.

Figure 3 .
Figure 3. CO₂ mass flow rate image under different ignition source powers at 1 m/s.

Figure 4 .
Figure 4. CO₂ mass flow rate image under different fire powers.

Figure 2 .
Figure 2. Temperature changes at ceiling measurement points at different times.

Figure 6 .
Figure 6.CO₂ and CO exhaust efficiency at different smoke exhaust outlet heights of 0 m/s and different wind speeds.

Table 1 .
Cable Material Parameter Settings.

Table 3 .
Parameters of cable fire simulation working conditions.

Table 6 .
CO₂ Smoke Extraction Efficiency under Different Fire Source Power.

Table 7 .
CO₂ Smoke Extraction Efficiency under Different Smoke Exhaust Airflows