Abstract
In this study, a tunnel temperature field model test bed is built according to the similarity principle to study the variation law of temperature in the tunnel in the cold season. According to the variation law of temperature in the tunnel, a new active thermal insulation measure, namely, an air curtain system, is developed. According to the principle of flow function superposition and heat balance, the governing equation of air curtain system is obtained. Taking the Zhengpantai tunnel as an example, the feasibility of the air curtain system is verified, and the jet angle of air curtain is optimized. The research results show that outside temperature and surrounding rock temperature are the main factors affecting the temperature field of tunnels in cold regions. The calculation results show that the air curtain system can effectively prevent tunnel freezing damage. The optimal jet angle of air curtain system should be 30°–40°. When the outside temperature is extremely low, multiple air curtains can be used in series to heat the temperature in the tunnel, and it is recommended that the distance between the two air curtains is not less than 20 m.
1. Introduction
As the process of global economic integration continues to accelerate, the world’s transportation network has become increasingly complete, and railways have gradually expanded to cold regions with high altitude and high latitude, such as China’s Qinghai-Tibet Railway, Harbin–Dalian high-speed railway, and Russian Moscow–Kazan high-speed railway. For tunnels in cold regions, the extremely low-temperature weather at the tunnel site in winter brings great challenges to the construction and maintenance of the tunnel. According to the existing literature, low temperature can cause freezing damage such as tunnel leakage, road icing, and lining cracking [1], once the problem of freezing injury occurs, it will not only increase the cost of tunnel maintenance but also threaten the safe operation of the tunnel. Therefore, it is of great significance to reveal the variation law of temperature field in a tunnel in the cold region and formulate reasonable thermal insulation measures.
At present, the research on tunnel temperature field in cold regions mainly focuses on three aspects: theoretical research of tunnel temperature field, actual measurement of tunnel temperature field, and thermal insulation method of tunnel in cold regions. In the theoretical research of tunnel temperature field, the representative research results are as follows: Xuefu et al. [2] and Yuanming et al. [3] studied the freezing and thawing of tunnel surrounding rock in cold regions and established the heat balance governing differential equations with phase change. Taking a tunnel on the Qinghai–Tibet Railway as an example, they obtained the variation law of surrounding rock temperature. Tan et al. [4] studied the variation law of tunnel temperature field in cold regions under the influence of wind flow, deduced a temperature field model including surrounding rock temperature and air temperature, and applied numerical analysis to calculate the temperature field of the Galongla tunnel in Tibet under ventilation conditions. The results showed that the temperature and velocity of the wind flow are two important factors affecting the temperature field of the tunnel, and the entrance and exit sections of the tunnel are most prone to frost damage. Zhou et al. [5] established a finite difference equation for unsteady heat conduction and calculated the temperature distribution when there is a train running in the tunnel in cold regions. The results showed that the train wind has an influence on the temperature field of the tunnel. Xia et al. [6] derived the analytical solution of the maximum freezing depth of tunnel surrounding rock in cold regions when the frozen surrounding rock contains unfrozen water based on quasi-steady state assumption. After calculation, it was concluded that the initial ground temperature of surrounding rock has the greatest influence on the freezing depth of surrounding rock.
In the actual measurement of the tunnel temperature field, the representative research results are as follows: Zhao et al. [7] measured the internal temperature of Xing’anling tunnel, and the results show that as the depth of the tunnel increases, the influence of the outside temperature on the temperature in the tunnel gradually decreases. Jun et al. [8] measured the temperature of 104 tunnels in South Korea in winter. The results showed that the temperature at the entrance and exit of the tunnel changed significantly due to the influence of the outside temperature. At the same time, the traffic wind caused by vehicles passing by will also affect the temperature distribution in the tunnel. Zhao et al. [9] measured the temperature field of Zuomutai tunnel in China in winter. The results showed that the temperature at the depth of the tunnel is asymmetrically distributed due to the thermal potential difference caused by the elevation difference between the inlet and outlet of the tunnel, and the temperature at the low altitude is lower. Wu et al. [10] selected three tunnels in the Wushaoling tunnel group and continuously monitored 31 temperature test points for 5 500 hours. The measurement data found that the longitudinal temperature distribution curve of the tunnel was a parabola with a low inlet and outlet and high middle, which provided a reference basis for tunnel cold protection engineering.
The most widely used insulation method for tunnels in cold regions is the thermal insulation layer method. Rigid foam polyurethane, polyphenolic, and other insulation materials with low thermal conductivity are laid on the tunnel lining or surrounding rock to prevent freezing damage of the tunnels [11–13]. However, only the traditional insulation layer method can passively respond to the changes of the natural environment and reduce the heat transmission and freezing and thawing speed. Moreover, the insulation materials are vulnerable to the erosion of groundwater in the surrounding rock. With the increase of service time, the insulation efficiency will gradually decrease. Therefore, relying solely on the insulation materials cannot prevent the freezing damage of the tunnel. Nowadays, some tunnels in cold regions are equipped with heating equipment in the lining to prevent freezing injury of the tunnel [14, 15], but if the cold natural wind can be actively blocked from entering the tunnel, thus the freezing injury can be eliminated from the root.
In 1904, Theophilus Van Kennel installed air curtains on both sides of the gate for the first time, successfully blocking the cold air entering the room. Nowadays, air curtain has been widely used in different occasions. For example, air curtains can be used for ventilation in high-rise buildings. In case of fire, the air curtain can also inhibit the diffusion of flue gas and reduce the CO2 concentration in the air [16]. Air curtain is used for thermal insulation in a station and cold storage [17]. Air curtain is used in the museum to protect newly unearthed cultural relics [18]. The installation of air curtain in the fully mechanized mining face of the mine can isolate 40% of waste gas and dust and protect the health of workers [19, 20]. From the perspective of tunnel thermal insulation, the research on air curtains is still in its infancy, but the existing research has confirmed that the high-speed and high-temperature jet sprayed by air curtain can form an air curtain wall, which can not only block and heat the cold natural wind but also flexibly set the jet parameters, erection quantity, operation time, and other data of air curtain according to different natural environments. In addition, the disassembly and replacement of air curtain are relatively simple. Compared with laying the insulation layer and building a cold proof door at tunnel entrance, the air curtain system is obviously safer and more flexible.
In the actual measurement of tunnel temperature, the complex and changeable natural environment will affect the accuracy of the measurement results and increase the difficulty of data analysis. Therefore, in order to eliminate interference and highlight the impact of a single variable on the tunnel temperature field, this study uses the tunnel temperature field model test bed in cold regions to simulate four working conditions to analyze the variation law of tunnel temperature field with different outside temperatures, different surrounding rock temperatures, different train running speeds, and different train running interval times. Based on the principle of flow function superposition and heat balance, the governing equation of air curtain system is obtained. Taking the Zhengpantai tunnel as an example, the finite element software Ansys Fluent is used to verify the accuracy of the control equation, optimize the jet angle of the air curtain, and simulate the actual insulation effect to demonstrate the feasibility of air curtain system. Finally, the economy of the air curtain system is analyzed.
2. Model Test of Tunnel in Cold Region
2.1. Composition of the Model Test Bed
When the geometric conditions, dynamic conditions, motion conditions, and boundary and initial conditions of the model and the physical object are similar, it can be guaranteed that the final test results of the model and the physical object are the same. A cold region tunnel with an equivalent diameter of 11 m and a length of 1 500 m on the Russian Moscow–Kazan high-speed Railway is selected as the design background. The railway has the characteristics of high speed (design maximum operating speed of 400 km/h) and low temperature (extreme minimum temperature of −48°C). Our research team has built a model test device for the temperature field of tunnel in the cold region based on the similarity theory. The selection of similarity criteria, the specific research and development process, and the verification of the accuracy of test data in the model test have been shown in reference [21], which will not be repeated in this study. The similarity ratios are listed in Table 1.
The model test bed is composed of six parts: the cold region, the outside temperature control system, the surrounding rock temperature control system, the tunnel model, the surrounding rock temperature control system, the test system, and the high-speed train drive system, as shown in Figure 1. The cold region and outside temperature control system simulate the natural environment outside the tunnel in the cold region; the tunnel model and the surrounding rock temperature control system simulate the initial ground temperature of the tunnel surrounding rock; the test system can collect temperature data inside the tunnel in real time; the high-speed train drive system simulates the train running.
The operation methods of the test bed are as follows:(1)The outside temperature control system is a small gas refrigerator produced by LNEYA company in Wuxi, China. The appearance size is 1.2 m × 0.8 m × 1.65 m, the required voltage is 220 V, the power is 1.8 kW, and the model is LQ-4030. The refrigerator contains a compressor and heat exchanger. The material of heat exchanger is SUS304, the heat exchange area is 1.5 m2, the inlet and outlet diameter of gas is G1/2, and the gas flow is 30 m3/h. After the dry air is cooled by the refrigerator, it can reach the external temperature required for the test, and the minimum refrigeration temperature is −40°C The insulation baffle is placed between the cold region and the tunnel model, and the refrigerated air is blown from the intake pipe into the cold region through the outside temperature control system and then flown back through the exhaust pipe. During the refrigeration period, thermal insulation materials are laid on the cold region, air inlet pipe, and air outlet pipe to reduce the convective heat transfer between the cold air and the indoor environment, and finally, the insulation baffle is removed after the temperature in the cold zone reached the temperature required for the test, as shown in Figure 2.(2)The surrounding rock temperature control system is a hot water heating system produced by LNEYA company in Wuxi, China. The appearance dimension is 0.8 m × 0.7 m × 1.65 m. The required voltage is 380 V, the power is 2.5 kW, and the model is ST-38W. The heating system uses steam as the heat source and normal temperature water as the water source to heat the normal temperature water through the heat exchanger. The steam pressure is 4–6 bar, the inlet and outlet of hot water is DN32 PN10, the flow of hot water is 200 L/min, and the maximum heating temperature is 40°C In the test, the surrounding rock temperature is set as the constant temperature boundary condition, and the circulation medium is heated to the set temperature through the surrounding rock temperature control system, continuously pushed from the inlet pipe into the insulation interlayer of the tunnel model, then flows from the return pipe to the surrounding rock temperature control system, and finally makes the temperature in the tunnel insulation interlayer reach the surrounding rock temperature required for the test, as shown in Figures 3(a)–3(d). In order to ensure that freezing does not occur when the circulation medium is close to 0°C, the mixed liquid with 3 : 7 ethylene glycol and water are used as the circulation medium. The most important link in the test is to ensure that the outside temperature and surrounding rock temperature reach the set temperature.(3)The tunnel model is sealed and connected. The tunnel model has 22 sections, each 1.155 meters long, made of plexiglass. Temperature test holes and wind speed test holes are set at 1/3 and 2/3 of each section, and the data acquisition frequency of the test system is 5 per second, as shown in Figures 4(a)–4(b).(4)CHR380A high-speed train model and acceleration slider are fixed on the high-strength belt, driven by the servo motor, and control the running speed of the train (the maximum speed is 108 km/h), and the influence law of traffic wind on the temperature field of the tunnel can be studied, as shown in Figures 5(a) and 5(b).
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2.2. Classification of Test Working Conditions
The extreme temperature of the tunnel site of Moscow–Kazan high-speed railway in winter is −47°C, the average temperature is −7–−17°C, and the surrounding rock temperature is 5–13°C. According to the measured temperature data of the tunnel site, the control variable method was adopted to divide the temperature field into four groups of working conditions to study the variation rule of tunnel temperature field in cold regions under different outside temperatures, surrounding rock temperatures, train running speeds, and train running intervals. The four groups of working conditions are shown in Figure 6.
The test duration of each group of working conditions is set to 3 days. After the test, temperature data from the entrance to the middle of the tunnel model (corresponding to the actual tunnel depth of 20–800 m) are extracted by the test system of the test bed for further analysis.
2.3. Variation Law of Tunnel Temperature Field
2.3.1. Analysis of Test Results of Working Condition 1
When there is no train running in the tunnel, that is, regardless of the influence of the train wind, the surrounding rock temperature is set to a constant temperature of 10°C, and the outside temperature is set to −5°C, −10°C, −15°C, −20°C, −25°C, and −30°C, respectively. After the test, the variation law of tunnel temperature field with outside temperature is as follows:
Generally speaking, the temperature distribution of the tunnel in the cold region conforms to the quadratic parabola shape, and the basic expression is as follows: θ = aL2 + bL + c(a ＜ 0), so the quadratic parabola was selected to fit the test data, where θ is the longitudinal temperature of the tunnel, °C; L is the longitudinal distance of the tunnel, m. The fitted curve, the obtained fitting function, and the goodness of fit R2 are shown in Figure 7. If θ = 0, the length of the negative temperature region of the tunnel at different outside temperatures can be calculated based on the fitting function.
According to Figure 7 and the fitting function obtained, under this working condition, the lower the outside temperature, the lower the temperature of the tunnel entrance section, and the longer the length of the tunnel negative temperature region.
The length of the tunnel negative temperature region under six different outside temperatures is calculated based on the fitting function, and the results are 210 m, 293 m, 376 m, 472 m, 533 m, and 605 m, respectively. It can be seen that when the outside temperature ranges from −5°C to −30°C, whenever the outside temperature decreases by 5°C, the length of the negative temperature region of the tunnel increases by about 79 m.
2.3.2. Analysis of Test Results of Working Condition 2
When there is no train running in the tunnel, that is, regardless of the influence of the train wind, the outside temperature is set to a constant temperature of −15°C, and the surrounding rock temperature is set to 5°C, 10°C, 15°C, 20°C, respectively. After the test, the variation law of tunnel temperature field with surrounding rock temperature is shown in Figure 8.
According to Figure 8 and the fitting function obtained, under this working condition, the higher the surrounding rock temperature, the higher the temperature inside the tunnel, and the temperature at the tunnel center is approximately equal to the surrounding rock temperature.
The length of tunnel negative temperature region under four different surrounding rock temperatures is calculated based on the fitting function, and the results are 480 m, 376 m, 244 m, and 180 m, respectively. It can be seen that when the surrounding rock temperature ranges from 5°C to 15°C, whenever the surrounding rock temperature increases by 5°C, the length of the negative temperature region of the tunnel decreases by about 118 m. The length of the negative temperature region decreases obviously. When the surrounding rock temperature of the deep-buried tunnel is 20°C, the length of negative temperature region decreases only 64 m compared with the surrounding rock temperature of 15°C. This shows that even if the initial temperature of tunnel surrounding rock is very high, the negative temperature region in the tunnel cannot be completely eliminated.
Existing research data show that the temperature gradient of tunnel surrounding rock is about 3°C/100 m. Therefore, the surrounding rock temperature of shallow-buried tunnel is low, and the heating effect of surrounding rock on cold air is limited, resulting in the low overall temperature of the tunnel. It is suggested that thermal insulation should be installed in all areas of shallow-buried tunnels.
The surrounding rock temperature of deep-buried tunnels is high. Although the temperature at the entrance of the tunnel is still negative, the temperature at the center of the tunnel always maintains a positive temperature under the action of convective heat transfer without freezing damage. It can be seen that the initial surrounding rock temperature plays an important role in tunnel insulation engineering.
2.3.3. Analysis of Test Results of Working Condition 3
When there is a train running in the tunnel, that is, considering the influence of the train wind, the outside temperature is set to a constant temperature of −15°C, the surrounding rock temperature is set to a constant temperature of 5°C, and the train operation interval is set to a constant cycle of 30 min/time. The train operation speed is set to 300 km/h and 400 km/h, respectively. After the test, the variation law of tunnel temperature field with train operation speed is shown in Figure 9.
According to Figure 9 and the fitting function obtained, under this working condition, the faster the train running speed, the longer the length of the tunnel negative temperature region. The length of tunnel negative temperature region is calculated based on the fitting function, and the results are 480 m, 525 m, and 549 m, respectively.
Compared with when there is no train in the tunnel, the length of the negative temperature region is increased by 45 m and 69 m, respectively, which is a small increase. The reason is that strong train wind is generated during high-speed train operation, which forms a low-pressure area around the train, which will absorb more cold air into the tunnel, as shown in Figure 10. Therefore, the temperature is lower when there is a train running in the tunnel.
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2.3.4. Analysis of Test Results of Working Condition 4
When there is a train running in the tunnel, that is, considering the influence of the train wind, the outside temperature is set to a constant temperature of −15°C, the surrounding rock temperature is set to a constant temperature of 5°C, and the train operation speed is set to a constant speed of 300 km/h. The train operation interval is set to 30 min/time, 15 min/time, 10 min/time, and 5 min/time, respectively. After the test, the variation law of tunnel temperature field with train operation interval is shown in Figure 11.
According to Figure 11 and the fitting function obtained, under this working condition, the shorter the train interval, the longer the length of the tunnel negative temperature region. The length of tunnel negative temperature region is calculated based on the fitting function, and the results are 480 m, 525 m, 547 m, 643 m, and 741 m, respectively. The increments of the length of the negative temperature region are as follows: 45 m, 22 m, 96 m, and 98 m. It can be seen that when the train operation interval is less than 15 min/time, the length of the negative temperature region in the tunnel will increase significantly.
2.3.5. Summary of Test Results
The following conclusions can be drawn from the model test results: the surrounding rock temperature of shallow-buried tunnel is low, and the heating effect of surrounding rock on cold air is limited, resulting in the low overall temperature of the tunnel. It is suggested that thermal insulation should be installed in all areas of shallow-buried tunnels; The entrance of the tunnel is connected to the outside world and is greatly affected by the natural environment. Therefore, the temperature of the entrance area is the lowest, and frost damage is most likely to occur. Controlling the temperature of the tunnel entrance section can effectively prevent the occurrence of frost damage; the influence of train wind on the temperature field of tunnels in cold regions is relatively small. When the train operation interval is greater than 15 min/time, the influence of train wind may not be considered. When the train operation interval is less than 15 min/time, the laying length of thermal insulation layer in the tunnel shall be increased appropriately.
3. Governing Equation of Air Curtain System
The entrance section of the tunnel in cold regions is most prone to frost damage. If the temperature of the tunnel entrance section can be effectively controlled, the frost damage can be prevented. In order to obtain the jet parameters of air curtain, the control equation of air curtain system is deduced based on the principle of fluid mechanics.
3.1. Flow Field Analysis of Tunnel Entrance
A rectangular shed is built in front of the tunnel opening. Considering the safety of train operation, an air curtain is installed on the top of the shed, as shown in Figure 12. The calculation model of the air curtain control equation is shown in Figure 13. The vertical direction is the x-axis; the horizontal direction is the y-axis; the origin is the point o; H is the height of tunnel entrance, m; ω is the horizontal velocity of outside natural wind, m/s; ω0 is the air curtain jet velocity, m/s; b0 is the thickness of air curtain nozzle, m; α is the air curtain injection angle, °.
Assuming that the horizontal speed of natural wind entering the shed tunnel is ω, the calculation formula of the flow function ψ1 of natural wind per unit width is as follows:
According to literature [22], the calculation formula of the flow function ψ2 of air curtain jet per unit width is as follows:Here, K is the turbulence coefficient.
According to the flow function superposition principle, the flow function ψ of the airflow at the tunnel entrance is the sum of the natural wind flow function ψ1 and the air curtain jet flow function ψ2, that is, ψ = ψ1 + ψ2. At this time, the calculation formula of ψ is as follows:
When the boundary conditions of equation (3) are x = 0 and y = 0, the flow function ψ0 of the airflow at the tunnel entrance is ψ0 = 0; when the boundary conditions are x = H and y = 0, the flow function ψH of the airflow at the entrance is as follows:
According to the principle of fluid mechanics, the volumetric flow rate per unit width between fluids in a plane flow is equal to the difference between the flow functions on the two streamlines, so the airflow rate Q at the tunnel entrance per unit width is as follows:
The expression of variable φ is given as follows:
Therefore, equation (5) can be abbreviated as follows:
3.2. Governing Equation of Air Curtain Jet Blocking Natural Wind
The flow field analysis at the tunnel entrance shows that the airflow Q per unit width is the sum of the natural wind flow Q′ and the air curtain jet Q0:Here, Q′ = ωH and Q0 = ω0b0
Combining formulas (7) and (8), when Q′ = 0, the air curtain jet can completely block the outside natural wind, namely,
From equation (9), the governing equation of air curtain jet velocity ω0 is obtained as follows:
3.3. Governing Equation of Jet Temperature of Air Curtain
When the tunnel is not equipped with an air curtain, the temperature at the entrance of the tunnel is the same as the temperature of the outside natural wind; when an air curtain is installed in the tunnel, the air curtain jet can not only block the natural wind but also generate thermal convection with the natural wind. At this time, the temperature of the airflow entering the tunnel is the temperature after the air curtain jet temperature is mixed with the natural wind temperature.
According to the principle of heat balance, the mixing temperature TA of the airflow entering the cave after heat exchange is as follows:Here, T′ is the outside natural temperature, °C and T0 is the temperature of the air curtain jet airflow, °C.
It can be seen from equation (11) that in order to prevent the occurrence of freezing damage in the tunnel, under the premise of determining the values of Q′, T′, Q0, etc., the temperature T0 of the air curtain jet should be adjusted so that the mixed temperature of the air entering the tunnel is obtained as TA ≥ 0.
4. Example Analysis
The measured data of Zhengpantai tunnel are selected to verify the accuracy of the air curtain governing equation, and the finite element model is established by using ICEM CFD software. The finite element model is composed of five parts: outside natural wind, rectangular shed tunnel, air curtain nozzle, circular tunnel with a length of 1500 m and height of 8 m, and surrounding rock, as shown in Figure 14.
Due to the large size of the model, more grids are divided and the calculation time is long. In order to improve the calculation efficiency of the software, the model shown in Figure 14 is simplified. The simplified basis is as follows: the process of air curtain jet blocking natural wind and air curtain jet heating natural wind is mainly carried out in shed tunnel; using the speed and temperature of the mixed airflow as the boundary conditions at the tunnel entrance, the radial temperature distribution of the surrounding rock at the tunnel entrance can be calculated when the tunnel is installed with an air curtain. Therefore, the finite element model of Figure 14 can be split into Figures 15(a) and 15(b).
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Figure 15(a) is composed of the outside natural wind, shed tunnel, and air curtain nozzle; Figure 15(b) is composed of the tunnel and surrounding rock.
Figure 15(a) is meshed, and the mesh at the air curtain nozzle is refined. The front of the model and the air curtain nozzle are set as the inlet boundary; the bottom of the model and the tunnel shed are set as the wall boundary; the rest of the model is set as the pressure outlet boundary, as shown in Figure 16.
Figure 15(b) is meshed and the mesh at the lining is refined. The entrance of the tunnel model is set as inlet boundary, and the exit of the tunnel model is set as the pressure outlet boundary. The rest of the model is set as the wall boundary. In the calculation, the boundary temperature of surrounding rock wall is set as 5°C. Because the tunnel model is long, the tunnel entrance is taken as an example, as shown in Figure 17. The calculation parameters of materials are listed in Table 2.
4.1. Numerical Verification of Air Curtain Governing Equation
According to the measured meteorological data, the natural wind speed in Zhangjiakou in winter is 2 m/s, the average temperature at night in December in winter is −10°C, and the air turbulence coefficient is 0.2. The thickness of the air curtain nozzle is taken as the standard size of 0.2 m, and the jet angle is 30°. Substituting the data into equations (11) and (12), the air curtain jet air velocity is calculated to be 22.66 m/s and the jet air temperature T0 is 35.30°C.
The finite element calculation results are shown in Figure 18 by using Ansys Fluent software. Because the 3D image streamline is chaotic, it is difficult to observe the airflow from inside the tunnel, as shown in Figure 18(a), so this study selects 2D images for explanation later, as shown in Figures 18(b) and 18(c).
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It can be seen from Figure 18(b) that the jet of the air curtain forms an air wall to block the natural wind, and the outer boundary of the jet facilitates the continuously convective heat exchange with the natural wind. The core area of the air curtain jet is relatively stable and finally flows into the tunnel. When the outside temperature is −10°C and the temperature of air curtain jet is 35.24°C, with the increase of tunnel depth, the temperature of mixed gas in the tunnel reaches about 0°C, which is consistent with the calculation results of the governing equation.
It can be seen from Figure 18(c) that when the outside wind passes through the entrance of the tunnel, it bends downwards and fails to enter the tunnel, indicating that the air curtain jet airflow has a better blocking effect on the outlet wind.
4.2. Optimal Selection of Air Curtain Jet Angle
According to China’s TB 10068-2010 Railway Tunnel Operation Ventilation Design Specification, the natural wind speed in the tunnel should be considered according to the most unfavorable conditions for the tunnel ventilation. The unfavorable wind speed in the single-track tunnel is 1.5 m/s, and the unfavorable wind speed in the double-track tunnel is 2.0 m/s. Therefore, in the calculation, the horizontal natural wind speed in the tunnel is 2.0 m/s. Using the parameter values in Section 4.1, the value range of air curtain jet angle is set to be 0°–50°, and each 5° is a variation interval. The relationship between jet angle and jet velocity is calculated according to formula (10), as listed in Table 3.
Nowadays, the maximum jet velocity of industrial air curtain is generally about 24 m/s, so the jet angle is optimized within the range of 20°–50°. The velocity vector diagram at the tunnel entrance is shown in Figure 19. When the jet angle α of the air curtain is small, the horizontal partial velocity ω0sinα of the jet is correspondingly small. At this time, the jet has poor ability to resist horizontal natural wind and is easy to bend into the tunnel, forming a strong wind speed in the tunnel. As the jet angle α increases, the vertical partial velocity ω0cosα of the air curtain jet decreases. The jet cannot completely penetrate the natural wind to reach the bottom of the tunnel, so that a complete wind curtain wall cannot be formed at the tunnel entrance. At this time, the natural wind can still enter the tunnel, reducing the thermal insulation efficiency of this measure.
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The velocity vector diagram of different jet angles is shown in Figure 19. In this study, Figures 19(b) and 19(f) are selected for explanation. It can be seen from Figure 19(b) that when the jet angle is 25°, the maximum wind speed formed at the tunnel entrance is 13.10 m/s. According to China’s JTG d70-2-2014 code for design of highway tunnel engineering, the design wind speed of one-way traffic tunnel should not be greater than 12 m/s, so the wind speed of 13.10 m/s is higher than the specification requirements. In addition, an obvious annular reflux area is formed at the entrance of the tunnel, and the entraining effect makes it easier to bring the cold outside air into the tunnel. Therefore, the jet angle of air curtain should be greater than 25°.
It can be seen from Figure 19(f) that when the jet angle is 45°, the vertical velocity of the jet is only 20.20 × cos45° = 14.34 m/s, and the jet cannot completely penetrate the natural wind to reach the bottom of the tunnel. At this time, the jet of the air curtain is an infinite space jet, and part of the natural wind can enter the tunnel, which reduces the insulation efficiency of this measure. Therefore, the jet angle should be less than 45°
In summary, the optimal jet angle of the air curtain should be between 30° and 40°.
4.3. Effect of Air Curtain Insulation System
When the natural wind speed is 2 m/s, the outside temperature is −10°C, the surrounding rock temperature is 5°C, and the calculation time is 30 d, and the depth of the freeze-thaw circle at the tunnel entrance without the air curtain is shown in Figure 20(a). When the air curtain is installed at the tunnel entrance and the jet angle of the air curtain is 30°, the depth of the freeze-thaw ring at the tunnel entrance is shown in Figure 20(b).
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According to Figure 20(a), after 30 days, the temperature of the tunnel without the air curtain is −8.5°C, and the freezing depth is about 2 m. According to Figure 20(b), the temperature of the tunnel with one air curtain installed is 0.53°C, which is 9.03°C higher than when the air curtain is not installed. Freezing damage is basically eliminated in the tunnel.
5. Thermal Insulation Measures of Multimachine Series Air Curtain
When the temperature of the external environment at the tunnel site is extremely low, and one air curtain cannot meet the heating demand, we can use a series connection method to increase the number of air curtains, as shown in Figure 21. This study takes two air curtains in series as an example, and the jet angle of both air curtains is 30°. D represents the distance between two air curtains, m.
5.1. D = 0 m
The two air curtains are close to each other, that is, D = 0 m. At this time, the thickness of the air curtain jet is doubled. The tunnel temperature and velocity vector are shown in Figure 22.
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It can be seen from Figure 22(a) that using this method, the temperature in the tunnel is above 0°C, which can prevent freezing damage in the tunnel. However, it can be seen from Figure 22(b) that due to the increase of jet width, the loss of air velocity in the core area of the jet is small, resulting in high wind speed in the tunnel, which is not conducive to driving safety. This method is not suitable for tunnels with higher heights.
5.2. D = 5 m and D = 10 m
It can be seen from Figures 23(a) and 23(b) that when the distance between the two air curtains is short, the second jet is blocked by the first jet and cannot reach the bottom of the tunnel, resulting in a decrease in insulation efficiency.
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Figure 23(c) shows the temperature in the tunnel when D = 10 m. It can be seen that there is still a negative temperature zone in the tunnel, so the distance between the two air curtains should be increased.
5.3. D = 20 m and D = 30 m
It can be seen from Figures 24(a) and 24(b) that when the distance between the two air curtains is far, both jets can reach the bottom of the tunnel.
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Figure 24(c) shows the temperature in the tunnel when D = 30 m. At this time, the temperature in the tunnel is above 0°C, which can prevent freezing damage in the tunnel.
6. Economic Analysis of Air Curtain System
This section takes the Zhengpantai tunnel used for 50 years as an example to compare the total cost of insulation layer method and air curtain insulation measures.
6.1. Total Cost of Insulation Layer Method
The total cost of insulation layer method mainly includes insulation material cost, labor cost, and maintenance cost. The average temperature of the coldest month at the Zhengpantai tunnel site in winter is −10°C, and the calculation formula of the laying length of insulation layer is given in reference [23], as shown in the following formula:Here, y is the laying length of thermal insulation layer at the tunnel entrance, m and x is the average temperature of the coldest month, °C.
The calculated y value is 603.93 m. Assuming that the laying length of the insulation layer at the entrance and exit of the tunnel is equal, the total length of the insulation layer required for the tunnel is 1207.86 m. Assuming that the tunnel entrance section is circular and the section radius is 4 m, the maximum circumference of the section is 25.12 m and the thickness of the thermal insulation layer is 0.05 m. The required material for the thermal insulation layer is 1517.07 m3. Rigid polyurethane is selected as the insulation layer material, and the market price of the material is about 1300 CNY/m3. According to the calculation, the cost of insulation material is 1.97 million CNY. The labor cost for laying the insulation layer is 4500 CNY/m, so the labor cost for construction is 5.44 million CNY.
The service life of rigid polyurethane insulation material is 25 years, so the insulation material needs to be replaced once during the 50 years of service in the tunnel. The cost of manually removing the insulation layer is 167 CNY/m³, so the calculated demolition cost is 0.20 million CNY.
Therefore, after the tunnel has been in service for 50 years, the total cost of insulation layer method is 15.02 million CNY, as shown in Figure 25.
6.2. Total Cost of Air Curtain System
The air curtain system mainly includes a rectangular shed, air curtain, solar panel, PLC intelligent controller, and 100 kVA box transformer.
Taking the tunnel entrance as an example, if the rectangular shed is poured with C35 concrete, the size of 5 m × 8 m × 8 m × 0.5 m is obtained as length × width ×height × wall thickness, and the calculated consumption of concrete is obtained as 60 m3, respectively, as shown in Figure 26. The market price of C35 concrete is 350 CNY/m3, and the total cost of concrete is 0.02 million CNY. The rebar needs 2 t, the market price is 4 450 CNY/t, and the total cost of rebar is 8 900 CNY. The labor cost is 0.1 million CNY. Therefore, the construction cost of rectangular shed is about 0.13 million CNY.
It costs 0.1 million CNY to customize an air curtain with a width of 8 m in Beijing Conpin company, and the installation cost is 0.04 million CNY, Therefore, the construction cost of the air curtain is 0.14 million CNY.
Laying on the top surface of the shed with a size of 1 580 mm × 808 mm solar panels, with a laying area of 40 m2, it is calculated that a total of 32 solar panels are required. The price of solar panel module with maximum output power of 180 W is 900 CNY/piece, and the total cost of solar panel is 0.03 million CNY. The installation cost of solar panels is 0.02 million CNY. The cost of a photovoltaic inverter is 0.02 million CNY. Therefore, the construction cost of the solar energy is 0.07 million CNY.
The switch of air curtain can be remotely controlled by PLC intelligent controller. The cost of a set of PLC intelligent controllers is 0.04 million CNY.
The voltage can be converted by using a 100 kVA box transformer, and the cost of one set of box transformers is 0.07 million CNY.
In addition, an HD yjy43 power cable is also required. Because the cable cost is relatively low and the required amount needs to be determined according to the actual situation, this study will not carry out a detailed calculation.
If the service life of air curtain, solar panel, PLC intelligent controller, and box transformer is 10 years, the equipment needs to be replaced four times during the 50-year service period of the tunnel, and the total cost of replacing the equipment is 1.28 million CNY.
The total power of one air curtain heater is 40 kW. The average temperature of Zhengpantai tunnel site from December to February of the next year is below 0°C, the maximum number of days below 0°C is 90 days, the annual working time of air curtain is 2 160 h, and the annual power consumption of one air curtain is 86 400 kW h. The power of PLC intelligent controller is 300 W and the annual power consumption is 1 080 kW h. The annual power consumption of the air curtain system is 87 500 kW h.
The calculation formula of solar panel output electric energy is as follows:
Here, Pf is the output electric energy of solar panel, kW⋅h; η is the conversion efficiency of solar panels; Qf is radiation, MJ/m2; Sf is the effective area of solar panel, m2.
Reference [24] has counted the annual solar radiation in North China. Considering that Zhangjiakou is a mountainous area, the annual solar radiation is taken as 2000 MJ/m2. Therefore, Qf is taken as 2000 MJ/m2, Sf is taken as 40 m2 and η is taken as 0.15. Through calculation, it can be seen that the output electric energy of solar panel is 12 000 kW⋅h. The tunnel entrance needs to supplement 75 500 kW⋅h of industrial power every year. The average price of industrial power per kW h in China is 0.875 CNY, and the annual electricity charge of tunnel entrance is 0.07 million CNY. So, the air curtain system at the tunnel entrance needs a total electricity charge of 3.5 million CNY in 50 years of operation.
Therefore, after the tunnel has been in service for 50 years, the total cost of air curtain system at the tunnel entrance is 5.23 million CNY, as shown in Figure 27.
The cost of installing the air curtain system at the tunnel exit is the same as that at the entrance. Therefore, during the 50 years of tunnel service, the total cost of air curtain system is 10.46 million CNY.
The total cost of insulation layer method is 15.02 million CNY, and the total cost of air curtain system is 10.46 million CNY. This study only roughly estimates the cost of the air curtain system, and the specific construction and power cost need to be calculated in detail in combination with the actual situation on-site. According to the cost calculated in this study, the use of air curtain system for cold prevention and thermal insulation in the tunnel has great economic benefits.
7. Conclusion
(1)The results of the model test show that when the surrounding rock temperature is 10°C and the outside temperature is −5–−30°C, the length of the negative temperature region in the tunnel increases by 79 m and the outside temperature decreases by 5°C; when the outside temperature is −15°C and the surrounding rock temperature is 5–15°C, the length of the negative temperature region decreases by 118 m for every 5°C increase in the surrounding rock temperature.(2)The surrounding rock temperature has an important influence on the initial temperature field in the tunnel. Therefore, in the construction of tunnels in cold regions, thermal insulation should be installed in all areas of shallow-buried tunnels to ensure the safe operation of the tunnel; thermal insulation must be installed in the entrance area of the deep-buried tunnels.(3)According to the principle of flow function superposition and heat balance, the governing equation of air curtain system is obtained in this study. The accuracy of the governing equation is verified by finite element numerical simulation, and the jet angle of the air curtain is optimized. The calculation results show that when the natural wind speed is 2 m/s, the optimal jet angle of the air curtain is 30°–40°.(4)According to the measured data of the Zhengpantai tunnel, when the natural wind speed is 2 m/s, the outside temperature is −10°C, the surrounding rock temperature is 5°C, the calculation time is 30 days, and the temperature of the tunnel with one air curtain installed is 0.53°C, which is 9.03°C higher than when the air curtain is not installed. It can be seen that installing an air curtain at the entrance of a tunnel in the cold region can achieve a better thermal insulation effect.(5)When the outside temperature is extremely low, multiple air curtains can be used in series to heat the temperature in the tunnel. It is recommended that the distance between the two air curtains is not less than 20 m.(6)The total cost of insulation layer method and air curtain system is compared, which proves that the air curtain insulation system has great economic benefits.Nomenclature
| θ: | The longitudinal temperature of the tunnel (°C) |
| L: | The longitudinal distance of the tunnel (m) |
| o: | The origin is the point |
| x: | The average temperature of the coldest month (°C) |
| y: | The laying length of thermal insulation layer at the tunnel entrance (m) |
| H: | The height of tunnel entrance (m) |
| ω: | The horizontal velocity of outside natural wind (m/s) |
| ω0: | The air curtain jet velocity (m/s) |
| b0: | The thickness of air curtain nozzle (m) |
| α: | The air curtain injection angle (°) |
| K: | The turbulence coefficient |
| ψ1: | The flow function of natural wind per unit width |
| ψ2: | The flow function of air curtain jet per unit width |
| ψ: | The flow function of airflow at tunnel entrance per unit width |
| Q′: | The airflow of natural wind per unit width (m3/s) |
| Q0: | The airflow of air curtain jet per unit width (m3/s) |
| Q: | The airflow per unit width at tunnel entrance (m3/s) |
| T′: | The natural temperature (°C) |
| T0: | The temperature of the air curtain jet airflow (°C) |
| TA: | The mixing temperature (°C) |
| D: | The distance between two air curtains (m) |
| Pf : | The output electric energy of solar panel (kW⋅h) |
| η: | The conversion efficiency of solar panels |
| Qf : | The radiation (MJ/m2) |
| Sf : | The effective area of solar panel (m2). |
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This research was supported by the National Science Foundation of China (grant nos. 51778380 and 51808248); Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX21_0549).