Abstract
Previous studies have shown that there is a large difference in the temperature of smoke in the upstream and downstream of a vertical shaft, but no quantitative study on the subject has been conducted. In this paper, a model experimental test was conducted to study the effect of a natural vertical shaft on the distribution of smoke temperature in tunnel fires. A laser sheet was used as an assisting tool to show the smoke flow field. A series of tests were conducted with shaft heights varying from 0.2 m to 1.2 m and a heat release rate (HRR) of 9 kW, 17 kW, 29 kW, and 65 kW. The entrainment phenomenon around the vertical shaft was analyzed, and the results showed that the amount of fresh air entrainment is the main reason for the temperature decrease in upstream and downstream smoke temperatures. Based on the experimental results, an empirical model for predicting the amount of fresh air entrainment and a prediction model of the downstream smoke temperature were proposed, and the predicted values are in good agreement with the experimental values.
1. Introduction
As the process of urbanization in China continues to accelerate, increasingly more traffic tunnels have been built across the country. By the end of 2021, China established 23268 tunnels, 24698.9 km, including 1599 special long tunnels, 7170.8 km, and 6211 long tunnels, 10844.3 km [1]. Tunnels have improved crowded traffic conditions and the environmental landscape in cities.
However, the spatial structure of tunnels is long and narrow, posing challenges to safety, particularly as fire dynamics differ significantly from unconstrained spaces, and the conditions for heat dissipation and smoke exhaustion are also poor [2–5]. Smoke and other toxic gases from a fire can easily accumulate in the tunnel, reducing the visibility inside the tunnel and threatening the life safety of the trapped people [6–8]. The tunnel fire accident average annual frequency (times/108 vehicles•km) in China increased rapidly from less than 3 in 2001 to approximately 15 in 2016. Compared with other countries, the Chinese tunnel fire accidents are more likely to cause serious losses [9]. Tunnel fire safety has therefore attracted increasing attention from the public [10, 11].
The tunnel ventilation system is an important component of tunnel fire protection design [12]. Reasonable smoke exhaust system design can effectively control the spread of fire and ensure the trapped person’s safety. It can also avoid heat accumulation inside the tunnel which may cause damage to the structure of the tunnel [13]. Most of the ventilation systems of China’s special long tunnels are longitudinal ventilation. However, in western countries, the proportion of smoke extraction systems, such as multipoint exhaustion systems and vertical shaft exhaustion systems, is relatively high [14]. The natural smoke exhaustion system is a type of tunnel ventilation system that uses natural vertical shafts within a certain distance of the tunnel to exhaust smoke. Smoke can be discharged through the vertical shaft by the stack effect. The heat carried by the smoke released from the fire can be exhausted from the tunnel through the vertical shaft. With the optimal exhaust flow rate of the vertical shaft, smoke will be confined within a smaller field [15–18].
The exhaust vent, however, also affects the smoke movement field in the tunnel [19]. Wang et al. [20, 21] conducted a series of small-scale experiments and proposed a modified model of Li et al. [22], taking into account the heat exhaust carried by discharged smoke from the shaft. The predicted values of the newly modified model accord well with experimental values. Tang et al. found that the max ceiling temperature increased first and then decreased with an increase in the exhaust velocity [23]. Yuan et al. [24] found through experiments that exhaustion has a great impact on the smoke movement, such as disturbing the stratification of smoke, causing the smoke temperature to decrease flow through the exhaust vent. Therefore, they divided the tunnel into fire sections and nonfire sections by vertical shafts to analyze the temperature distribution. A prediction model of the longitudinal distribution in these two sections and the smoke spreading area has also been proposed. Takeuchi et al. [25] provided a simple calculation model for the temperature decrease between the upstream and downstream of vertical shafts. Moreover, Fan et al. [26] found that a strong mixing area is formed under the exhaust vent and that the hot and cold interfaces are disturbed and no longer maintain stability. A large amount of fresh air and smoke is mixed in this area and is then discharged through the exhaust vent, and the other part continues to spread downstream, which caused the downstream smoke temperature to decrease. Many studies [16, 27–30] have noted that plug-holing has a great impact on the performance of smoke exhaust systems, and severe plug-holing will lead to a decrease in the efficiency of smoke exhaust [31, 32].
In summary, the previous research studies about the longitudinal temperature distribution have not considered the influence of the exhaust vent. In a previous study [33], the authors found that there is also a decrease in temperature between the upstream and downstream of the tunnel mechanical exhaust vent due to fresh air entrainment induced by the mechanical smoke exhaust vent. However, the natural vertical shaft extraction system is different from the mechanical extraction system due to different driving forces. The performance of the natural extraction system is influenced by the shaft height, HRR, smoke temperature, etc. However, the mechanical extraction system depends on the exhaust velocity. These are huge differences between these two systems.
In this paper, a subscale experiment is conducted to investigate the temperature decrease between upstream and downstream smoke under the effect of the HRR and the shaft height. The innovation of this study lies in two aspects: (1) a new dimensionless number is proposed to describe the degree of entrainment near the axis; (2) a downstream gas temperature prediction model is developed for tunnel fires with natural vertical shafts to illustrate the entrainment effect. However, the proposed model neglects the heat losses around exhaust vents, which leads to certain errors in calculations. The experimental results indicate that the entrainment of fresh air by exhaustion results in a temperature decrease. A prediction model of the tunnel smoke temperature distribution considering natural vertical shafts is proposed. The conclusions of this paper improve the longitudinal temperature prediction model of tunnel fires and provide reference for the design of tunnel natural smoke exhaust ventilation systems.
2. Theoretical Analysis
When a fire occurs in a tunnel, the fire source heats the air above it, thus raising the temperature and decreasing the density. The heated air moves upward with the effect of buoyancy and continuously entrains the fresh air around it to form a fire plume. The fire plume rises to a certain height, hits the ceiling, and then spreads in the longitudinal direction of the tunnel. This stage is called the one-dimensional horizontal spreading stage [34]. This paper mainly studies the influence of the shaft in this stage on the flow field of smoke.
The exhaust process accelerates the smoke flow velocity in the smoke layer. The smoke movement is first controlled by the horizontal inertial force and then by both the horizontal inertial force and the vertical discharge force. As shown in Figure 1, the interface of the smoke layer below the exhaust vent becomes disturbed due to the exhaust process, the smoke flow field begins to be chaotic, and a large amount of cold air and hot smoke is mixed intensely. The mixed cold air and smoke continue to spread through the vertical shaft and downstream. The amount of mixed cold air in the downstream smoke layer determines the downstream smoke temperature.

The mass flow of the smoke in the vertical shaft and the downstream of the shaft are shown in equations (1) and (2). In order to simplify the calculation, the heat loss and the radiative effect are ignored. The fresh air mass fraction in the smoke can be calculated by temperatures in equations (3) and (4) [25, 33]:
The heat exhaust coefficient is defined as the ratio of the vertical shaft exhaust rate of heat to the flow rate of heat of upstream smoke, which is as follows:
The main methods to determine the thickness of the smoke layer are the N-percentage rule [35] method, integral ratio method [36], least-squares method [37], and buoyancy frequency method [38]. Among them, the N-percentage rule is more subjective in selecting NL values. Especially when the temperature gradient at the interface does not change much, the small change in the NL value may bring an error of smoke layer thickness. The calculation values of the smoke layer thickness by the integral ratio method and the least squares method are lower than the experimental value [38]. Compared with the former two methods, the buoyancy frequency method has clear physical meaning and does not depend on other empirical parameters. The calculated value and the experimental value are in good agreement. Therefore, this method is used to calculate the thickness of the smoke layer in this paper.
We take the test condition of a 0.6 m shaft as an example. First, nonlinear fitting of the vertical smoke temperature distribution of different HRRs is shown in Figure 2. The parameters of each curve after Boltzmann fitting are presented in Table 1. Then, we substitute the fitting formulas into equation (9). The interface height refers to the height of the smoke layer determined by the buoyancy frequency method. When a fire occurs, hot smoke rises under the action of buoyancy, while the cold air remains in the lower region, gradually forming increasing layers of smoke. There exists a significant density difference between the upper smoke layer and the lower air layer interface. The buoyancy frequency method assumes that the smoke layer has a sharp density gradient, and its goal is to determine the position of the maximum density difference [38]. As shown in Figure 3, the interface of the smoke layer is located at a maximum value of NL:


Combining equations (6)–(8), the downstream smoke temperature can be calculated in the following equation [33]:
3. Experimental Design
3.1. Model Design
The experiments were conducted in a small-scale model tunnel at a scale ratio of 1 : 10, as shown in Figure 4. Froude modeling was applied to build up the physical scale model. The model is 6 m long, 1 m wide, and 0.7 m high, which corresponds to a 60 m long, 10 m wide, and 7 m high tunnel on a real scale. The length, width, and height of the full-scale tunnel before scaling were based on those of a real tunnel in a certain location in China. The other parameters should be geometrically scaled according to Froude’s law, as shown in Table 2.

The tunnel was made of a 30 mm thick fireproof board, and one side wall was made of 8 mm thick fireproof glass convenient to observe smoke movement behaviors. As shown in Figure 4, the fuel pan was placed 1.4 m from the left end of the tunnel, and ethanol was selected as a fuel. The utilization of ethanol as a fuel source presents several advantages: (1) It is easy to handle, (2) it emits minimal smoke, facilitating the observation of experimental phenomena, and (3) it maintains a stable fire heat release rate over a prolonged combustion period, enabling us to study the changes in smoke parameters. Four different sizes of oil pans (15 cm, 20 cm, 25 cm, and 40 cm) were used in the experiment, corresponding to reduced-size fire sources of 9 kW, 17 kW, 29 kW, and 65 kW and full-size fire sources of 2.84 MW, 5.37 MW, 9.17 MW, and 20.55 MW, respectively. Urban tunnel fires are mostly caused by burning vehicles, primarily small cars and buses. Referring to PLARC [39], the values used in this experiment correspond to the fire release rates of a small car, a large bus, 2-3 small cars, and a large truck in a real scenario.
The vertical shaft is placed 2 m from the fire source and 1.3 m from the right end of the tunnel, with a cross-sectional area of 20 × 20 cm. Six different shafts were used in the experiment with heights of 0.2, 0.4, 0.6, 0.8, 1.0, and 1.2 m. Two sides of the shaft were made of fireproof boards, and the others were made of fireproof glass to observe the smoke flow field inside the shaft.
3.2. Measurement System
Temperatures were measured by using K-type thermocouples, as shown in Figure 4. Three thermocouple trees each comprising 15 thermocouples were installed at the center axis with an interval of 0.06 m within the tunnel to measure the vertical temperature distribution.
The flow velocity measuring points were arranged inside the shaft as well as under the ceiling, and the flow velocity measuring points were composed of pitot tubes and microdifferential pressure sensors. The smoke velocity can be calculated by the measured dynamic pressure. The measurement range was −50–50 Pa. The accuracy was 1%, and the uncertainty pressure measurement was less than 7% by the repeated test in the same condition. Therefore, the total uncertainty was 7% using the methods described in [40].
The HRR was calculated by the mass loss rate. A laser sheet was used as a visualization assistant tool to observe smoke movement behaviors, and a particle generator was placed near the fire source.
For the temperature measurement system in this paper, the error can be divided into 3 types based on the occurrence reason: (1) The measurement error of the K-type thermocouple was ±1°C, (2) the uncertainty caused by the radiation of the environment and thermocouple was less than 6% [41], and (3) the uncertainty temperature measurement was less than 7% by the repeated test in the same condition. Therefore, the total uncertainty was calculated as 9%.
3.3. Experimental Conditions
In this paper, a total of 24 test conditions with 6 shaft heights and 4 HRRs were used in the experiment and each case was repeated twice, to assure its reliability and repeatability. The test conditions are shown in Table 3. The maximum temperature of this experiment is in good agreement with the test of Li et al. [22, 23], as shown in Figure 5.

4. Results and Discussion
4.1. Smoke Movement Behaviors
In this experiment, the shaft is located in the one-dimensional horizontal spread stage. As the smoke flows through the exhaust port, the hot smoke layer and the cold air layer mix strongly under the exhaust vent due to the extraction of the vertical shaft. In this area, a large amount of cold air is entrained in the hot smoke layer. A portion of the mixed cold air is exhausted through the vertical shaft, and the remainder stays in the downstream smoke layer.
In Figure 6, during the process of smoke flow toward the exhaust vent, the smoke layer is continuously thinned and forms a recessed area below the exhaust vent or forms a cavity if plug-holing occurs. On the downstream side of the shaft, there is a strong mixing area and a turbulent flow field. After the strong mixing area, the flow of the smoke layer restored stability to the one-dimensional horizontal spread stage. However, the temperature of smoke is significantly decreased compared with the upstream side of the shaft.

(a)

(b)
Ji et al. [29] conducted fire testing to study the extraction performance of a natural vertical shaft. For tunnel fires, the horizontal inertia force of smoke cannot be ignored. The Richardson number (Ri) is proposed to determine the degree of plug-holing below the exhaust vent, which can be calculated in equation (11). As shown in Figure 7, critical Ri is positively correlated with the shaft height and negatively correlated with the thickness of the smoke layer. This article includes experimental conditions for both plug-holing and non-plug-holing.

The experimental results indicate that the exhaust velocity increases continuously with the increasing shaft height, as shown in Figure 8. In addition, the higher HRR produced higher temperature smoke, which means that the stack effect is more serious and that the exhaust velocity is faster. It is worth noting that when the height of the shaft is 0.4 m, the exhaust velocity increases significantly. When the height of the shaft is increased to 0.6 m, the exhaust velocity decreases slightly. This is because smoke continues to dissipate heat and decrease buoyancy as it flows through the shaft. In addition, as the height of the shaft increases, ventilation resistance increases. When the vertical shaft increases from 0.4 m to 0.6 m, the negative effects of resistance and heat loss exceed the pressure difference, resulting in a decrease in the exhaust velocity. This phenomenon has also been found in other research [29] and needs further study in the future.

As shown in Figure 9, the flow velocity and temperature of upstream smoke are insensitive to the shaft height. As shown in equations (5–8), the heat exhaust coefficient increases continuously with the increasing shaft height. The effect of different HRRs on the heat exhaust coefficient, however, is not significant. The heat exhaust coefficient in equation (8) was taken as the mean value of different experimental conditions with the same shaft height, as shown in Figure 10.


4.2. Fresh Air Entrainment
This paper proposes a new dimensionless number to describe the entrainment phenomenon under the exhaust vent. The entrainment coefficient refers to the ratio of the mass flow of cold air entrained by the downstream smoke layer to the smoke exhaust through the shaft, as shown in equation (12). As shown in Figure 11, when the vertical shaft is short, the stack effect is weak, and most of the cold air that mixes with hot smoke stays in the smoke layer and continues to spread in downstream. With an increase in the HRR, however, the thickness of the smoke layer increases, plug-holing is weaker, and less cold air is discharged through the shaft. Therefore, the entrainment coefficient increases continuously with the increasing HRR.

As the vertical shaft height increases to 0.4 m, plug-holing occurs below the exhaust vent. A large amount of fresh air is discharged through the shaft, causing a sharp decrease in the entrainment coefficient. With the same shaft height, the large HRR leads to high smoke temperatures around the exhaust vent, resulting in a larger pressure difference. The exhaust velocity is higher, and disturbance is severe, which increases the mixing of cold air and smoke below the exhaust vent, resulting in a slight increase in the entrainment coefficient:
When the vertical discharge force of the shaft is too strong, plug-holing is likely to occur. Previous studies used to determine the occurrence of plug-holing by the Fr number, as shown in equation (13) [32, 42]. The Fr number is proposed by Hinkley, and it can also be used to qualify the amount of the entrainment fresh air and the degree of plug-holing [33]:
Through the regression analysis of a total of 48 tests on 24 experimental conditions, as shown in Figure 12, a simplified prediction model for the entrainment coefficient is proposed as follows:

4.3. Prediction of the Downstream Smoke Temperature
The smoke temperature of the tunnel ceiling continuously decreases in a longitudinal direction from the fire source to both sides, and there is a significant difference between the upstream and downstream temperatures of the natural vertical shaft. On the one hand, the smoke that is discharged by the vertical shaft carries part of the heat. On the other hand, the vortex is formed below the exhaust vent due to the exhausting process, which results in the entrainment of large amounts of cold air. The mixture of large amounts of cold air and hot smoke results in a decrease in the temperature. Therefore, the prediction of the smoke temperature near the exhaust vent must consider the effect of the entrainment phenomenon induced by the exhausting process.
A portion of the incoming smoke from upstream is discharged through the shaft, and the remaining part of the smoke is mixed with the cold air and continues to spread downstream. Therefore, the temperature of downstream smoke can be written as follows:
The temperature of downstream smoke predicted by equation (16) is compared with the predicted value of the model by Takeuchi et al. [25] and the experimental values, as shown in Figure 13. Since the Takeuchi formula is only applicable to situations where the heat release rate of the fire source is relatively low, further improvements are required for predicting temperature distributions in high heat release rate fires. Therefore, as the fire source power increases, the difference between equation (16) and the Takeuchi formula becomes greater. The result indicates that the accuracy and convergence of the prediction values, which consider the entrainment effect near the shaft, are better than before and that R2 is 98%. However, it should be noted that, when the HRR is larger, the predicted values are slightly lower than the experimental values.

5. Conclusion
This paper investigates the phenomenon of entrainment around a natural exhaust shaft. A new dimensionless number was proposed to describe the degree of entrainment near the shaft. For tunnel fires with natural vertical shafts, a prediction model for the downstream smoke temperature was developed to account for the entrainment effect. The prediction results indicate that the accuracy and convergence are better than before after accounting for the entrainment fresh air. The predicted values are in good agreement with the experimental values. The main conclusions are as follows:(1)The downstream smoke temperature (ΔTcs’) decreases due to a large amount of cold air mixing with the hot smoke layer. Therefore, the prediction of the smoke temperature near the exhaust vent must consider the effect of the entrainment phenomenon induced by the exhausting process.(2)As the shaft height and HRR increase, the stack effect continues to increase and the entrainment coefficient decreases. The value rapidly decreases to approximately 1 when plug-holing occurs. The entrainment coefficient after plug-holing is no longer sensitive to the HRR.(3)As the height of the shaft increases, the heat exhaust coefficient of the shaft continuously increases. The effect of the shaft height on the heat exhaust coefficient is greater than that of the HRR.
The model proposed in this paper is based on the calculation that ignored the heat loss around the exhaust vent. The prediction accuracy is good with a low HRR but is slightly lower than the experimental value with a larger HRR.
Abbreviations
cp: | Specific heat at constant pressure (J/kg·K) |
Fr: | Froude number |
: | CO2 mass fraction (mg/kg) |
: | Velocity (m/s) |
W: | Width of the tunnel (m) |
A: | Cross-sectional area of the vertical shaft (m2) |
E: | Heat exhaust coefficient |
d: | Thickness of the smoke layer (m) |
z: | Tunnel height |
h: | Shaft height |
L: | Length |
T: | Temperature (K) |
ΔT: | Smoke temperature rise (K) |
: | Heat release rate (MW) |
: | Mass flow rate of the plume (kg/s) |
: | Gravitational acceleration (m/s2) |
NL: | Value of buoyancy frequency (s−1) |
Ri: | Richardson number |
: | Vertical discharge force |
Fh: | Horizontal inertial force |
Greek symbols
φ: | Air mass fraction of smoke exhausted from shafts |
ρ: | Density (kg/m3) |
ŋ: | Entrainment coefficient |
Δ: | Deviation property |
Subscripts
cs: | Upstream smoke flow |
cs′: | Downstream flow |
cs′, s: | Smoke mixed in downstream flow |
cs′, a: | Air mixed in downstream flow |
es: | Smoke discharged through vents |
es, a: | Air mixed in smoke discharged through vents |
m: | Model |
p: | Practical |
s: | Smoke |
a: | Fresh air |
exp: | Experiment |
pre: | Prediction. |
Data Availability
The experimental data used to support the findings of this study are currently under embargo, while the research findings are commercialized. Requests for data, 12 months after publication of this article, will be considered by the corresponding author.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the Science and Technology Plan Project of Fire Department (2022XFZD01).