Study on the Effect of Natural Wind on the Smoke Spread Law of Extra-Long Tunnel Fires with Inclined Shafts for Air Supply and Exhaust

Abstract

High-temperature smoke generated by tunnel fires is the most important factor causing casualties. To explore the influence of natural wind on fire smoke movement in an extra-long highway tunnel based on the Taihang Mountain Tunnel, the distribution law of natural wind in the tunnel was obtained by on-site monitoring of the meteorological conditions at the tunnel site. A three-dimensional fire dynamics tunnel model considering an inclined shaft smoke exhaust was established, and the influence of natural wind on tunnel temperature distribution, smoke spread and smoke exhaust efficiency was studied. The results show that the natural wind speed of the Taihang Mountain Tunnel is mainly concentrated at 0~3 m/s. The main wind direction of the natural wind on the left tunnel is opposite to the driving direction, and the distribution probability of the main wind direction in each section is 81.27% and 72.15%, respectively. The main wind direction of the right tunnel is the same as the driving direction, and the distribution probability of the main wind direction in each section is 56.78%, 69.73%, 67.32% and 64.65%, respectively. The negative natural wind can inhibit the smoke spread downstream of the smoke exhaust port, but it is not conducive to the smoke exhaust. The positive natural wind promotes the smoke spread to the downstream of the smoke exhaust port, and the larger the natural wind speed, the longer the spread length. Natural wind reduces the smoke exhaust efficiency. For positive or negative natural wind with a guaranteed rate of 70%, the smoke exhaust efficiency is reduced by 27.76% and 15.59%, respectively, compared with the condition without natural wind. The research results can provide a useful reference for the design of fire smoke exhausts and smoke control schemes in extra-long highway tunnels.

1. Introduction

With the development and progress of tunnel construction technology, the number of traffic tunnels is increasing, the length of tunnels is also increasing, and the frequency of tunnel fires is also rising [1,2]. Due to the narrow and closed structural characteristics of tunnels, the fire develops rapidly, which is not conducive to personnel evacuation, disaster prevention and rescue work, often causing significant casualties and huge economic losses [3,4,5,6,7]. Therefore, tunnel fires have always been the focus of discussion and attention among experts and scholars.

In tunnel fire scenarios, more attention has been paid to the characteristics of temperature change in the tunnel vault. Qiu et al. [8] conducted full-scale tunnel fire tests and found that the temperature of the tunnel vault exhibited an exponential decay along the longitudinal direction. Lee et al. [9] found that the temperature at the top of the tunnel near the fire source decreases with an increase in aspect ratio, and the reduction rate decreases with a decrease in heat loss. Based on the longitudinal temperature distribution characteristics below the ceiling of different size experimental models, Ingason et al. [10] established a temperature prediction model. Li et al. [11,12,13] analyzed the effect of blockage ratio on the maximum temperature of the tunnel vault under different fire scales by combining scaled and full-scale tests. Han et al. [14] studied the effects of longitudinal wind speed and blockage ratio on the fuel combustion rate, maximum temperature, critical wind speed and smoke back-layering length in a longitudinal ventilation tunnel. Hu et al. [15], Ji et al. [16] and Oka et al. [17] studied the effect of tunnel slope on vault temperature. In addition, the high-temperature toxic smoke generated by tunnel fires is the most important factor causing casualties [7]. In order to grasp the process of smoke propagation in tunnel fires, Hu et al. [1] analyzed the basic flow characteristics of ceiling smoke diffusion based on full-scale experiments and numerical simulations. Meng et al. [18] studied the characteristics of tunnel fires and the variation in smoke back-layering length through model experiments, considering different heat release rates, combustion interval distances and ventilation speeds. Yao et al. [19,20] investigated the characteristics of smoke movement and control in a longitudinal ventilation tunnel fire by considering different heat release rates, fire locations, longitudinal wind speeds and transverse channel intervals. Chow et al. [21] studied the smoke movement law of inclined tunnel fires under longitudinal ventilation conditions and proposed a modified empirical formula for the critical velocity of inclined tunnels. Based on the full-scale tunnel experiments, Zhou et al. [22] studied the smoke movement characteristics with forced ventilation by a movable fan and discussed the smoke back-layering phenomenon under different fan inclination angles and fan—fire distance.

Due to the existence of natural wind in the tunnel, some tunnels with small lengths can meet the ventilation demand only through natural ventilation, and natural ventilation tunnel fire has attracted the attention of scholars. Wang et al. [23] studied the influence of vehicle blockage ratio on the smoke exhaust efficiency of natural ventilation tunnels with shafts through model tests and found that the smoke extraction efficiency decreased first, then increased and finally dropped with increasing blockage ratio. Kashef et al. [24] studied the vault temperature distribution and smoke diffusion of natural ventilation tunnel fire through a model test and derived formulas for predicting the temperature distribution and smoke diffusion degree. Wan et al. [25] carried out numerical simulations of fire scenarios in inclined tunnels with shafts under natural ventilation conditions and investigated the effects of tunnel slope on temperature distribution, smoke back-layering length and inlet air velocity in shafts and tunnels. Du et al. [26] studied the smoke back-layering length of inclined tunnel fires under natural ventilation conditions and found that the smoke back-layering length decreases with the increasing tunnel inclination angles, and the influence of HRR on smoke back-layering length can be ignored. However, for extra-long road tunnels with large burial depths or crossing different climatic zones, the natural wind inside the tunnel can reach more than 3 m/s, and the natural wind will have a greater impact on the ventilation speed of the tunnel [27]. Although many scholars have studied the smoke diffusion characteristics of tunnel fires under natural ventilation conditions, the natural wind intensity in extra-long highway tunnels is significantly higher than that in general tunnels, and its research conclusions are not fully applicable to extra-long highway tunnel fires. Therefore, it is necessary to study the characteristics of fire smoke spread in extra-long highway tunnels under the influence of natural wind.

A series of studies were conducted to reveal the fire smoke spread law in extra-long highway tunnels under the influence of natural winds, without considering vehicle blockage and vehicle movement. In this study, the meteorological conditions of the extra-long highway tunnel were monitored on-site, and the natural wind speed in the Taihang Mountain tunnel was calculated based on the natural wind pressure theory to study the annual distribution of natural wind in the tunnel. Through numerical simulation technology, the temperature field, smoke field and smoke exhaust efficiency of tunnels under the influence of natural wind were studied. The smoke spread characteristics in extra-long highway tunnel fires under the influence of natural wind are revealed, and the research results can provide a useful reference for the design of fire smoke exhaust and smoke control schemes in extra-long highway tunnels.

2. Project Background

2.1. Project Overview

This study is based on the Taihang Mountain Tunnel, located near the border of Xiyang County, Shanxi Province and Zanhuang County, Hebei Province, crossing the northern section of the Taihang Mountains from east to west. As shown in Figure 1, the tunnel entrance is located 500 m west of Wangjiaping Village, Zanhuang County, and the tunnel exit is situated 700 m south of Chayewa Village, Xiyang County. The left tunnel is 13,915 m long, and the right tunnel is 14,108 m long, both of which are extra-long highway tunnels. The designated driving speed is 100 km/h. It is a separated bidirectional four-lane tunnel with a clear width of 11.40 m, a clear height of 7.10 m and a clear cross-sectional area of 67.77 m². The transverse slope of the Taihang Mountain Tunnel is 2.0%. The horizontal alignment of the tunnel is mainly a straight line, due to the limitation of the terrain, and a circular curve is used locally. The horizontal and vertical indexes of the tunnel are shown in

Table 1. Horizontal and vertical indexes of tunnel.

Tunnel Name		Design Elevation (m)		Plane Curve	Longitudinal Slope (%)
		Entrance	Exit
Taihang Mountain Tunnel	Left tunnel	526.529	778.414	R3200 m/R−∞	−1.9
	Right tunnel	526.85	777.96	R−∞/R6000 m	+1.9

.

2.2. Ventilation Scheme

The longitudinal sectional ventilation method is applied to the Taihang Mountain Tunnel, and the ventilation scheme is shown in Figure 2. There are three inclined shafts along the tunnel. The left tunnel is divided into two ventilation sections by the 2# inclined shaft (left tunnel). The right tunnel is divided into four ventilation sections by 1# inclined shaft, 2# inclined shaft (right tunnel) and 3# inclined shaft.

3. Calculation Method of Natural Wind Pressure in the Tunnel

3.1. Theory of Natural Wind Pressure

Natural wind pressure is the driving force for the formation of natural wind, referring to the pressure difference between two regions. Factors influencing natural wind pressure include environmental temperature, atmospheric pressure, wind speed and wind direction. Static pressure difference and thermal gradient are the main components of natural wind pressure [28].

3.1.1. Super-Static Pressure Difference

In a static atmosphere, the difference between the pressure P₁ of the low tunnel portal and the pressure P₂ of the high tunnel portal is called the static pressure difference.

$$P_1-P_2=\rho gh$$

(1)

When there is air flow caused by the natural wind outside the tunnel, the following expression must be true:

$$P_1-P_2\ne \rho gh$$

(2)

The difference in airflow pressure between the two portals of the tunnel is referred to as the super-static pressure difference ΔP.

Taking a single-shaft tunnel as an example, the calculation method of the natural wind volume (velocity) in each section and shaft of the tunnel under the sole effect of the super-static pressure difference is depicted in Figure 3 [27,28,29].

As shown in Figure 3, with node 3 as a reference, the static pressure differences at each portal are denoted as ΔP₁, ΔP₂, ΔP₃ and ΔP₄, where ΔP₃ = 0. Upon the establishment of stable airflow, the full pressure at node 4 is ΔP₄′ (ΔP₄′ ≠ ΔP₄). The full pressures at sections 1-1′, 2-2′ and 3-3′ are equal to ΔP₄′, if pressure losses associated with flow convergence or diversion are not considered. Simultaneously, it is stipulated that airflow Q_m flowing toward node 4 is positive; otherwise, it is negative, and the following applies:

$$\Delta P_m-\Delta {P_4}^{\prime }=(R_m+{R_m}^{\prime })\times Q_m\times \left|Q_m\right|$$

(3)

As shown in Figure 3, if the inflow air volume at any position is equal to the outflow air volume, then node 4 satisfies Equation (4).

$$Q_1+Q_2+Q_3=0$$

(4)

where m = 1, 2, 3; $R_m$ is frictional resistance of tunnel air duct, $R_m=\frac{{\lambda }_m\rho }{8}\times \frac{L_m{C}_m}{S_m^3}$; ${R_m}^{\prime }$ is local resistance of the airflow at the inlet of air duct, when m is an inlet, ${R_m}^{\prime }=\frac{\rho }{2}\times \frac{{\xi }_e}{S_m^2}$, when m is an outlet, ${R_m}^{\prime }=0$.

Combined with Equations (3) and (4), the air volume of each section can be solved by trial calculation. Setting ΔP₄′ = Min(ΔP₁, ΔP₂, ΔP₃) and substituting it into Equation (3), Q₁, Q₂ and Q₃ are calculated, respectively. When Q₁ + Q₂ + Q₃ < q (q is the precision of the control solution, e.g., 0.1), the obtained Q₁, Q₂ and Q₃ are considered as the solutions to the equation set. The same principle applies to tunnels with multiple ventilation shafts, where cyclic calculation can be performed through programming.

3.1.2. Thermal Potential Difference

The airflow pressure difference caused by the temperature difference between the inside and outside of the tunnel is the thermal potential difference. As shown in Figure 4, assume that the temperature in the tunnel is T₀, the tunnel entrance and ventilation shaft outlet are T₁, T₂ and T₃, respectively, the air density at the corresponding positions is ρ₀, ρ₁, ρ₂ and ρ₃, and the elevations of each portal and the shaft bottom are H₁, H₂, H₃ and H₄, respectively. The thermal potential difference in each segment is shown in Equations (5) and (6) [27,28,29]:

$$\Delta h_{\mathrm{I}}={\rho }_{\mathrm{I}}g{H}_{1-3}-{\rho }_{0}g{H}_{1-4}-{\rho }_{0}g{H}_{4-3}$$

(5)

$$\Delta h_{\mathrm{II}}={\rho }_{\mathrm{II}}g{H}_{2-3}-{\rho }_{0}g{H}_{2-4}-{\rho }_{0}g{H}_{4-3}$$

(6)

Among them, Δh_I and Δh_II are the thermal potential differences between the lower portal (node 1)/higher portal (node 2) and the shaft outlet (node 3). It is specified that the direction of such a difference is positive from the tunnel portal to the inclined shaft outlet; otherwise, the difference is negative. Hn-m is the relative height difference between nodes, namely, H_m− − H_n. ${\rho }_{\mathrm{I}}$ and ${\rho }_{\mathrm{II}}$ are the average density of external air between the lower portal (node 1)/higher portal (node 2) and the inclined shaft outlet (node 3), with values according to ${\rho }_{\mathrm{I}}=({\rho }_1+{\rho }_3)/2$ and ${\rho }_{\mathrm{II}}=({\rho }_2+{\rho }_3)/2$.

In a still atmosphere, the super-static pressure difference between two points is zero. When the air densities inside and outside the tunnel are unequal, the thermal potential difference facilitates the driving force for airflow formation inside the tunnel. Therefore, it can be assumed that the thermal potential difference between the lower portal (node 1)/higher portal (node 2) and shaft outlet (node 3) is the ultra-static pressure difference in each portal relative to the inclined shaft outlet, namely, $\Delta P_{\mathrm{I}}=\Delta h_{\mathrm{I}}$ and $\Delta P_{\mathrm{II}}=\Delta h_{\mathrm{II}}$. Then, based on the theoretical calculation method for super-static pressure difference, the airflow velocity and volume at various cross-sections under the influence of the thermal potential difference can be obtained. Thus, the calculation of thermal potential difference ultimately translates into the calculation of super-static pressure difference.

3.2. Determination Method of Natural Wind

According to the method for natural wind calculation, a nonlinear equation system is established to solve the airflow in various ventilation sections of the tunnel. To efficiently and rapidly complete the calculation tasks, a computer programming approach is utilized to solve the nonlinear equation system, enabling continuous batch solving under multiple operating conditions. Before calculating the natural wind speed within the tunnel, a simplified model is established based on the ventilation segmentation of the tunnel, as shown in Figure 5.

Combining the simplified model, MATLAB programs for solving equations and batch calculations are developed, and the calculations are performed using MATLAB R2018b software. Firstly, the monitoring data are preprocessed into MATLAB-readable file types and formats. Secondly, based on the tunnel route and the corresponding simplified model, programs for solving equation systems and batch calculations are written. Finally, the calculation results are outputted in a unified format. By completing the calculations using the method mentioned above, the natural wind speed within the Taihang Mountain Tunnel can be obtained.

4. On-Site Monitoring

4.1. Monitoring Scheme

The meteorological conditions of the Taihang Mountain Tunnel are monitored by the multi-functional automatic weather station. The monitoring contents include ambient temperature, humidity, atmospheric pressure, wind speed and wind direction. According to the monitoring content, the weather station is equipped with an environmental data acquisition instrument, a temperature, humidity and atmospheric pressure sensor, a wind speed sensor and a wind direction sensor; the detailed parameters of various sensors are shown in

Table 2. Technical parameters of various sensors.

Item Category	Temperature	Humidity	Atmospheric Pressure	Wind Speed Sensor	Wind Direction Sensor
Measuring range	−50–100 °C	0–100% RH	500–1100 hPa	0–70 m/s	0–360°
Accuracy	±0.5 °C	±5% RH	±1.5 hPa	±(0.3 + 0.03 V) m/s (V: wind speed)	±3°
Resolution	0.1 °C	0.1% RH	0.1 hPa	0.1 m/s	-
Start-up wind speed	-	-	-	≤0.5 m/s
Working environment	-	-	-	Temperature: −40 °C–80 °C, Humidity: ≤100% RH

. The monitoring period is 380 days, with data collected every 30 min. The monitoring equipment and on-site layout are shown in Figure 6.

4.2. Natural Wind Distribution Pattern

A total of 91,200 sets of meteorological data were obtained through on-site monitoring. According to the calculation method in Section 3, the natural wind speed of each ventilation section of the Taihang Mountain Tunnel was calculated. As shown in Figure 2, the driving direction in the left tunnel is from Yuci to Hebei, and that in the right tunnel is from Hebei to Yuci. It is stipulated that when the natural wind direction inside the tunnel is the same as the driving direction, it is positive (+), and when it is opposite, it is negative (−).

4.2.1. Natural Wind Speed Magnitude

The natural wind speed values (absolute value) of each ventilation section were counted according to the interval of 0.5 m/s, as shown in Figure 7.

As shown in Figure 7, the natural wind speed of each ventilation section is mainly concentrated in 0~3 m/s, with a cumulative percentage of over 80%. As shown in Figure 7a,b, the distribution frequency of natural wind speed in the first section of the left tunnel is relatively high in the range of 0~1.5 m/s, where the natural wind speed of 0.5~1 m/s is dominant; the distribution frequency of natural wind speed in the second section of the left tunnel is relatively high in the range of 0.5~2.0 m/s, where the natural wind speed of 1.0~1.5 m/s is dominant. As shown in Figure 7c–f, the natural wind speeds in the right tunnel are generally greater than those in the left tunnel. The natural wind speeds in the first section of the right tunnel are mainly distributed in the range of 1.5~3.0 m/s, and the natural wind speeds in the second and third sections of the right tunnel are mainly distributed in the range of 1.0~2.5 m/s, and the natural wind speeds in the fourth section of the right tunnel are mainly distributed in the range of 1.0~2.0 m/s. In extreme conditions of sudden changes in temperature and atmospheric pressure, a larger natural wind speed will form inside the tunnel, but the probability of extreme weather occurring is small, so natural wind speeds above 5 m/s account for less than 2% of the total.

4.2.2. Main Wind Direction and Distribution Probability

The main wind direction and its distribution probability in each ventilation section of the Taihang Mountain Tunnel are shown in Figure 8. The main wind direction is from Hebei to Yuci, and the distribution probability of the main wind direction in the left tunnel is higher than that in the right tunnel. However, the main wind direction in the left tunnel is opposite to the driving direction, while the main wind direction of the right tunnel is the same as the driving direction. Among them, the distribution probabilities of the main wind direction in the first and second sections of the left tunnel are 81.27% and 72.15%, respectively, while the distribution probabilities of the main wind direction in the first to fourth sections of the right tunnel are 56.78%, 69.73%, 67.32% and 64.65%, respectively.

4.2.3. Assurance Rate of Natural Wind Speed

Assurance rate is the reliability level of a meteorological element value less than or greater than a certain value, usually expressed as the cumulative frequency of a meteorological element less than or greater than a certain value in a long period of time [28]. The higher the assurance rate, the greater the cumulative probability of being less than or greater than a certain value, and conversely, the smaller. Assurance rate wind speed refers to the natural wind speed value that meets a certain assurance rate during the whole year.

Table 3. Natural wind speed with different assurance rates.

Ventilation Section		95%		90%		85%		80%		75%		70%
		+	−	+	−	+	−	+	−	+	−	+	−
Left tunnel	Section 1	1.42	1.83	1.67	2.17	1.93	2.35	2.26	2.65	2.54	2.98	2.92	3.38
	Section 2	1.08	1.51	1.34	1.81	1.65	2.04	1.97	2.33	2.32	2.59	2.64	3.02
Right tunnel	Section 1	1.72	1.63	1.97	1.91	2.23	2.17	2.55	2.46	2.78	2.73	3.06	2.96
	Section 2	1.95	1.56	2.17	1.84	2.45	2.07	2.88	2.39	3.12	2.61	3.38	2.78
	Section 3	2.04	1.48	2.28	1.73	2.56	1.95	2.97	2.22	3.22	2.48	3.47	2.65
	Section 4	1.84	1.35	2.08	1.62	2.34	1.86	2.66	2.12	2.95	2.36	3.24	2.53

shows the natural wind speed under the assurance rate of 95%, 90%, 85%, 80%, 75% and 70%.

5. Numerical Simulation

In numerical simulations of tunnel fires, the smoke spread must satisfy the fundamental conservation equations of fluid flow, including the equations of mass conservation, momentum conservation, species conservation and energy conservation [30].

5.1. Numerical Model

The difficulty of smoke exhaust and the risk of personnel evacuation are relatively higher when the fire occurs in the middle of the tunnel. Therefore, the area near the 2# inclined shaft of Taihang Mountain Tunnel was selected as the research object, and combined with the natural wind speeds of different assurance rates, FLUENT was used to simulate the tunnel fire scenarios considering the smoke exhaust of the inclined shaft and to study the influence of natural wind on the smoke spread.

Fluent 2020 R2 software is based on the basic principles of fluid dynamics to make a variety of assumptions, and the solution settings and parameter values are closely related to the experience of researchers, which makes the stability of the calculation results difficult to control. However, many studies have shown that Fluent software has the advantages of high efficiency, high precision and good stability in the numerical simulation of fluid flow characteristics and heat transfer characteristics and has been widely used [30].

After the tunnel fire occurs, the longitudinal wind can be provided by adjusting the ventilation system to control the smoke flow. The upstream of the smoke exhaust port is mainly affected by the longitudinal wind, and the downstream ventilation section of the smoke exhaust port is mainly affected by the natural wind after the ventilation system is closed, so the smoke exhaust effect and smoke spread characteristics are mainly affected by the downstream natural wind. Therefore, the influence of natural wind in the downstream area of the smoke exhaust port was mainly considered in the numerical calculation.

Figure 9 shows the numerical model and its local grids. The main tunnel is 307.4 m long, and the inclined shaft is 1777.8 m long. The smoke exhaust port is 7.4 m wide and 15 m long, and the connecting air duct is 5.4 m wide and 35 m long. The inclination angle of the inclined shaft is 6°. In fact, the inclined shaft is divided into the exhaust shaft and air supply shaft, and only the exhaust shaft was considered here, with an area of 22.9 m². The fire source is located 50 m upstream of the smoke exhaust port, 50 m away from the model entrance, and the downstream length of the smoke exhaust port is 200 m. A mixed mesh with tetrahedral and hexahedral as the main meshes was used for mesh delineation.

According to the current specification [31], the fire source power was set at 30 MW, the longitudinal wind speed was 3.0 m/s, and the smoke exhaust wind speed in the inclined shaft was set to 15.0 m/s. The natural wind speed downstream of the smoke exhaust port in the numerical simulation was set with reference to Table 3, and the reference group was the condition without natural wind. A total of 13 calculation cases were set, as shown in

Table 4. Calculation condition table.

Case	HRR (MW)	Longitudinal Wind Speed (m/s)	Smoke Exhaust Speed (m/s)	Natural Wind Speed Assurance Rate	Natural Wind Speed (m/s)
1	30	3.0	15	95%	1.95
2	30	3.0	15		−1.56
3	30	3.0	15	90%	2.17
4	30	3.0	15		−1.84
5	30	3.0	15	85%	2.45
6	30	3.0	15		−2.07
7	30	3.0	15	80%	2.88
8	30	3.0	15		−2.39
9	30	3.0	15	75%	3.12
10	30	3.0	15		−2.61
11	30	3.0	15	70%	3.38
12	30	3.0	15		−2.78
13	30	3.0	15	/	0.0

.

The standard $k-\epsilon$ turbulence model was used for steady-state simulation; meanwhile, the energy equation was turned on, the working temperature was set to 20 °C, and the operating pressure was standard atmospheric pressure. The model entrance was set as a velocity boundary to simulate longitudinal wind speed, with a wind speed of 3.0 m/s. The model exit was set as a velocity boundary to simulate natural wind speed, and the wind speed was set according to Table 4. The inclined shaft exit was also set as a velocity boundary to simulate the fire smoke exhaust wind speed, with a wind speed of 15.0 m/s. The tunnel wall is a non-slip wall with a roughness constant of 0.5 and a roughness height of 5 mm. A volumetric heat source was used to simulate the fire source, without considering the actual combustion process, characterizing the fire smoke by setting the CO source term.

5.2. Grid Sensitivity Analysis

To ensure the accuracy of the calculation results and high computational efficiency, it is necessary to analyze the grid sensitivity before conducting a large number of numerical simulations.

The mixed mesh with tetrahedral and hexahedral elements is used to mesh the numerical model. The cross structure and irregular parts of the numerical model are divided by tetrahedral elements, and the regular part of the numerical model is divided by hexahedral elements to reduce the number of grids. Three grid size schemes are set up for grid sensitivity analysis. Scheme A: the maximum size of the hexahedron is 0.5 m, and the size of the tetrahedron is 0.4 m; scheme B: the maximum size of the hexahedron is 1.0 m, and the size of the tetrahedron is 0.6 m; scheme C: The maximum size of the hexahedron is 1.5 m, and the size of the tetrahedron is 0.8 m. The CO mass fraction concentration of the tunnel vault in the calculation results is extracted and analyzed, as shown in Figure 10.

It can be seen from Figure 10 that the calculation results of Scheme C are significantly smaller than those of Scheme A and Scheme B, and the accuracy of the calculation results needs to be improved. The calculation results of scheme A and scheme B are similar, and the calculation accuracy of the two schemes is acceptable. However, due to the smallest grid size of scheme A, the calculation time required is significantly larger than that of scheme B, and the advantage of scheme B is more obvious. Therefore, the grid size of scheme B is finally selected for subsequent numerical calculation.

5.3. Calculation Results

5.3.1. Temperature Distribution Characteristics

(1)

Negative natural wind

The longitudinal temperature cloud diagram is intercepted along the axis of the tunnel. Figure 11 shows the longitudinal temperature distribution for each case under the influence of negative natural wind. Due to the smoke exhaust effect of the inclined shaft, the smoke enters the inclined shaft from the smoke exhaust port and exits the tunnel, resulting in a significant decrease in the longitudinal section temperature near the smoke exhaust port. The temperature rise range downstream of the smoke exhaust port is mainly distributed in the tunnel arch area, and the temperature rise length along the longitudinal direction does not exceed 20 m.

According to Figure 11, the range of temperature rise downstream of the smoke exhaust port under the influence of negative natural wind is smaller than that without natural wind. With the increase in negative natural wind, the range of temperature downstream of the smoke exhaust port remains almost unchanged, which indicates that negative natural wind can shorten the range of temperature rise downstream of the smoke exhaust port to a certain extent, but the effect is not obvious.

(2)

Positive natural wind

When the natural wind direction is the same as the driving direction, the longitudinal temperature distribution under each case is shown in Figure 12.

According to Figure 12, under the influence of positive natural wind, the temperature distribution of each case is basically the same between the fire source and the smoke exhaust port. The range of temperature rise downstream of the smoke exhaust port is significantly larger than that without natural wind; with the increase in natural wind speed, the range of temperature rise gradually expands, mainly because the positive natural wind is equivalent to providing negative pressure, which promotes the flow of high-temperature airflow to the downstream of the smoke exhaust port, and the greater the natural wind speed, the greater the range of temperature rise. Compared with Figure 10, the longitudinal temperature between the fire source and the smoke exhaust port is smaller under the influence of positive natural wind.

5.3.2. Smoke Spread Characteristics

(1)

Negative natural wind

The cloud diagram of longitudinal smoke distribution for each case under negative natural wind conditions is shown in Figure 13.

According to Figure 13, the longitudinal distribution pattern of fire smoke is similar to that of temperature, and the longitudinal wind limits the fire smoke spread upstream of the fire source. Under the combined effect of smoke exhaust and negative natural wind, the length of smoke diffusion downstream of the smoke exhaust port is small, and the fire smoke is well controlled. The smoke near and downstream of the smoke exhaust port is mainly distributed in the tunnel arch, and there is almost no smoke at the bottom of the tunnel, and the closer to the vault, the higher the smoke concentration. The length of smoke spread downstream of the smoke exhaust port is the largest in the case of no natural wind; with the increase in natural wind, the length of smoke spread gradually decreases until it tends to be constant.

Figure 14 shows the smoke concentration curve of the tunnel vault under negative natural wind cases. The smoke concentration decreases rapidly after reaching the peak value, and the smoke concentration of the tunnel vault decreases sharply at the smoke exhaust port due to the influence of the smoke exhaust from the inclined shaft. Between the fire source and the smoke exhaust port, the attenuation trend of smoke concentration for each case is close; however, the greater the negative natural wind speed, the greater the smoke concentration in the tunnel vault, because a large amount of smoke accumulates in the tunnel under the influence of negative natural wind, and the greater the natural wind speed, the more smoke accumulates, resulting in a higher smoke concentration in the tunnel vault. In the downstream of the exhaust port, the smoke concentration attenuation rate is the smallest for the condition without natural wind, and its spread length is the largest, about 11 m, while the spread length of the other cases is very close, about 3 m. Therefore, on the one hand, negative natural wind can shorten the spread length of fire smoke; on the other hand, it is not conducive to tunnel smoke exhaust.

(2)

Positive natural wind

Figure 15 shows the longitudinal smoke distribution for the positive natural wind case. With the increase in positive natural wind, the spread length of smoke increases significantly. This is because as the natural wind speed increases, the negative pressure downstream of the smoke exhaust port also increases, and more smoke enters the downstream of the smoke exhaust port. When the positive natural wind speed does not exceed 2.45 m/s, the smoke downstream of the smoke exhaust port is mainly distributed in the tunnel arch, and the bottom of the tunnel remains at ordinary temperature. When the positive natural wind speed reaches 2.88 m/s, the laminar structure of the smoke is destroyed due to the intensification of turbulence in the flow field inside the tunnel, resulting in the downstream of the smoke exhaust port being full of smoke, and the smoke is evenly distributed along the longitudinal section of the tunnel.

Figure 16 shows the smoke concentration curve of the tunnel vault for the positive natural wind condition. Between the fire source and the smoke exhaust port, the smoke concentration of the tunnel vault without natural wind conditions is the largest; the smoke concentration between the fire source and the smoke outlet decreases with the increase in the positive natural wind speed, because a large amount of smoke spreads downstream of the smoke exhaust port due to the influence of the positive natural wind. In the smoke exhaust port and its downstream area, due to the smoke exhaust effect of the inclined shaft, the smoke concentration of each case decreases to different degrees. When the natural wind speed does not exceed 2.45 m/s, the higher the wind speed, the slower the attenuation of the smoke concentration in the tunnel vault, and the greater the corresponding spread length, with a maximum spreading length of 103 m. After the natural wind speed reaches 3.12 m/s, the smoke concentration of the tunnel vault at the smoke exhaust port does not decrease significantly, and the smoke concentration of the vault under each case is similar and almost constant, because the smoke exhaust effect is further weakened by the influence of the positive natural wind; more smoke enters the downstream area of the smoke exhaust port.

5.3.3. Smoke Exhaust Efficiency of the Inclined Shaft

The smoke extraction efficiency can be expressed as the ratio of the amount of smoke discharged from the inclined shaft to the amount of smoke generated by the fire source per unit time [23]. In this paper, the smoke exhaust efficiency is expressed as the ratio of the total amount of CO discharged from the inclined shaft to the total amount of CO generated by the fire source per unit time.

Figure 17a shows the smoke exhaust efficiency of each case under the influence of negative natural wind. The smoke exhaust efficiency of the inclined shaft decreases with the increase in natural wind speed. The greater the negative natural wind speed, the greater the pressure downstream of the smoke exhaust port, which is not conducive to the flow of fire smoke to the smoke exhaust port; hence, a large amount of smoke accumulates between the fire source and the smoke exhaust port, resulting in a decrease in smoke exhaust efficiency with the increase in natural wind speed, compared to the condition without natural wind, where the natural wind speed increases to 2.78 m/s, and the exhaust efficiency decreases by 15.59%.

Figure 17b shows the smoke exhaust efficiency of each case under the influence of positive natural wind. The smoke exhaust efficiency under the condition without natural wind is the highest, which is 98.86%; when the natural wind increases from 0 m/s to 3.38 m/s, the smoke exhaust efficiency decreases by 27.76%. As the natural wind speed increases but does not exceed 2.45 m/s, the smoke exhaust efficiency of the inclined shaft can still remain above 90%, and when the natural wind speed reaches 2.88 m/s, the smoke exhaust efficiency of the inclined shaft decreases significantly, with a reduction of more than 15%. Under the influence of natural wind speed with an assurance rate of 70%, the smoke exhaust efficiency of the inclined shaft can be maintained above 70%. Therefore, the positive natural wind promotes the smoke to flow downstream of the smoke exhaust port, which reduces the smoke exhaust efficiency of the inclined shaft and is not conducive to fire smoke exhaust.

Based on the above analysis, for tunnel fire scenarios under the influence of natural wind, the recommendations are as follows:

(1)

When there is a positive natural wind in the ventilation section where the fire occurs: if the natural wind is small, the natural wind can be used to assist the smoke extraction and reduce the number of jet fans turned on; if the natural wind is large, the ventilation system is required to provide pressure to suppress the natural wind pressure, so that the wind speed in the tunnel can meet the needs of the smoke exhaust.

(2)

When there is a negative natural wind in the ventilation section where the fire occurs: it is necessary to increase the opening power of the jet fan to overcome the influence of the negative natural wind so that the wind speed in the tunnel can meet the needs of the smoke exhaust.

(3)

When there is natural wind in the downstream ventilation section of the smoke exhaust port, whether the natural wind downstream of the smoke exhaust port is positive or negative, the pressure opposite to the natural wind pressure should be generated through the ventilation system of the downstream ventilation section to overcome the influence of the natural wind.

6. Conclusions

In this paper, on-site monitoring of meteorological conditions was carried out, and the natural wind distribution law was obtained by combining the natural wind pressure theory. Based on natural wind data, the influence of natural wind on the temperature, smoke distribution characteristics and smoke exhaust efficiency of extra-long highway tunnel fires was investigated by the numerical simulation method. The research conclusions are as follows:

(1)

The temperature and atmospheric pressure of the environment are the main factors affecting the formation of natural wind. The natural wind speed is mainly distributed in 0~3 m/s, accounting for more than 80% of the natural wind speed in each ventilation section. The main direction of the natural wind is from Hebei to Yuci, the main wind direction of the left tunnel is opposite to the driving direction, and the distribution probabilities of the main wind direction in each section are 81.27% and 72.15%, respectively. The main wind direction of the right tunnel is the same as the driving direction, and the distribution probabilities of the main wind direction in each section are 56.78%, 69.73%, 67.32% and 64.65%, respectively.

(2)

Under the influence of positive natural wind, the temperature rise range downstream of the smoke exhaust port increases with the increase in natural wind speed. Under the influence of negative natural wind, the temperature between the fire source and the smoke exhaust port increases with the increase in wind speed, the temperature of tunnel vault downstream of the smoke exhaust port decreases sharply, and the length of temperature rise decreases with the increase in natural wind until it tends to be constant.

(3)

Positive natural wind promotes the smoke to spread downstream of the smoke exhaust port, and the greater the wind speed, the greater the smoke spread length; when the natural wind speed reaches 2.88 m/s, the smoke uniformly fills the tunnel space. Negative natural wind is not conducive to the smoke exhaust but can shorten the length of the smoke spread; with the increase in natural wind speed, the length of smoke spread to the downstream of the smoke exhaust port gradually decreases and tends to be constant.

(4)

The smoke exhaust efficiency of tunnel fire is the highest under conditions without natural wind, and natural wind reduces the smoke exhaust efficiency. Compared with the condition with no natural wind, under the influence of the same direction or reverse direction natural wind speed with a guaranteed rate of 70%, the smoke exhaust efficiency of the inclined shaft is reduced by 27.76% and 15.59%, respectively.