An analytical model to predict the temperature in subway-tunnels by coupling thermal mass and ventilation

https://doi.org/10.1016/j.jobe.2021.102564Get rights and content

Highlights

  • An analytical model for deeply buried subway tunnels is developed.

  • The model can describe the interaction between complicated thermal processes.

  • How important factors determine tunnel temperature is analyzed.

  • Efficacious solutions to reduce tunnel-air temperature are discussed.

Abstract

There is an increasing incidence of overheating in subway tunnels in recent years especially in old subways without air-conditioning e.g., London Underground. There is still lack of a clear understanding how tunnel-air temperature is determined by complex thermal processes in subway tunnels. In this study, a mathematical model that describes the thermal processes in deeply buried subway tunnels was developed. Analytical solution was derived by separating the solution into time-averaged component and periodic component. The results show that the time-averaged component of tunnel-air temperature will approach steady state as the time tends to infinity, which has a positive linear relation with internal heat-source and average ambient temperature. Active cooling or heat-recovery systems could soon become a necessity in subway tunnels due to both global warming and increasing internal heat generation. Compared with outdoor air, the amplitude of the tunnel-air temperature shows a significant reduction in the day period but not in the year period. The surrounding soil temperature will keep changing for thousands of years. This study offers a new physical insight to analyse and mitigate overheating in subway tunnels.

Introduction

The number of subway systems increased globally in the last few decades thanks to their high passenger-capacity and low operating-cost. As of December 2019, 188 cities in 56 countries around the world use approximately 192 subway systems [1,2]. The total system-length is over 16377 km, and the number of annual passengers exceeds 65620 million [1,2]. Unfortunately, with climate warming many of these subway systems suffer from overheating in summer - especially older systems, where air-conditioning systems are not installed [[3], [4], [5], [6]]. The air temperature in the London Underground often reaches 30 °C in summer [7], with in-train temperatures of up to 41 °C [8,9]. During the 2006 European heatwave, temperatures as high as 47 °C were recorded [10]. Overheating also occurred in the subways in Tokyo, Osaka, and New York [11]. Surprisingly, a very high temperature (53 °C) was recorded in the Wuhan underground (China) [11]. Such high tunnel-air temperature has a significant impact on the environment and the energy consumption (air-conditioning) in trains and subway stations [9,12,13]. To solve the overheating problem in subway tunnels, it is essential to predict the tunnel-air temperature and understand the influential factors and their interactions.

There are many tools developed to predict tunnel-air temperature, and they can be classified into two categories: commercial tools and self-built models. The commercial tools include SES [14,15], IDA Tunnel [16], CFD [15,17,18], and STEES [9,14]. SES uses a 1-dimensional quasi-steady heat-transfer model that only outputs the maximum/minimum/average temperatures for the hottest month in the long term. The detailed temporal temperature distribution is not considered [14]. IDA Tunnel, which is based on the same basic equations and concepts as SES [16], has similar limitations. STESS could output hourly temperatures, which represents some improvement over SES [14]. However, none of the above commercial tools enable an intuitive identification of the important parameters that affect tunnel-air temperature, which limits the exploration and assessment of the methods to solve overheating problem in subway tunnels. Among self-built models, few studies focused on the mathematical models that describe the thermal processes in subway tunnels [19,20]. Related mathematical models, however, can be found in studies of tunnels used for other purposes, such as earth-to-air heat exchangers [[21], [22], [23]], underground ventilation-tunnels for underground hydro-power stations [24], and railway tunnels through hills [25]. All these models considered the unsteady heat-transfer process through surrounding soil and the Robin condition at the tunnel-wall surface. Among these studies [21], employed a 1-dimensional model to explore the effect of an earth-to-air heat exchanger on indoor thermal comfort and energy-saving effects in a typical building. A significant difference between an earth-to-air heat exchanger and a subway tunnel is that there is no internal heat source in the earth-to-air heat exchanger, which simplifies the energy-balance equation to describe the air in the tunnel. Liu [24] also proposed a 1-dimensional model, without an internal heat source, for the underground ventilation tunnel of a hydro-power station. This model was solved numerically, using the finite-difference method, to determine the variation of the tunnel-air temperature as a function of the tunnel length. Zhou [25] proposed a 2-dimensional model, which took into account the internal heat source, to study the freeze-distance at the entrance of the railway tunnel through a hill in cold regions. Using the finite difference method, a numerical solution was obtained, which can describe how the freeze-distance depends on the outdoor temperature and the wind speed in the tunnel. Another model, which also considers the internal heat source and focuses on subway tunnels, was developed by Zhang et al. [19]. The Green function was used to find analytical solution to the equations. However, a numerical solution, which uses the finite element method, was proposed later (instead of using the exact formulas for an analytical solution). The results of this study also focused on the prediction of the inner tunnel-wall temperature (instead of the factors that influence the tunnel-air temperature or the interactions of the relevant thermal processes). Additionally, Yuan et al. [26] proposed a 1-dimensional model for an underground refuge chamber. In this model, both the heat conduction equation and the Robin condition at the tunnel-wall surface are applicable for subway tunnels. However, the two assumptions (I: The inner air-temperature is independent of time and already known. II: The distance from the tunnel centre to the remote constant-temperature boundary is a finite constant and already known) are not suitable for subway tunnels. In other words, the governing equations for subway tunnels are more complex and the corresponding solution-seeking method is very different from Yuan's model [26]. However, none of the models above provided sufficient scientific insight for tunnel-air temperature prediction and overheating mitigation effectiveness in the tunnel environment.

Although few previous studies focused on the main factors that influence the tunnel-air temperature and the interdependence among the relevant thermal processes in subway tunnels [9], much research has been done to reveal the indoor-air temperature influential factors and the thermal processes in buildings [[27], [28], [29], [30], [31], [32]]. Li [[27], [28], [29], [30]] and Ma [31,32] et al. researched the effect of internal heat sources, ventilation, thermal mass, and heat transfer on the indoor-air temperature in simplified buildings. The thermal processes in buildings are similar in subway tunnels in some ways, however, the physical model, governing equations, and boundary conditions differ significantly because the surrounding soil is (assumed) infinite for deep-buried tunnels, whereas the envelope and thermal mass of a building is of finite size. Hence, the results, which were generated from buildings, cannot be used for subway tunnels directly. Zhang and Li [9] studied the relationship between the maximum tunnel-air temperature and some influencing factors. However, there is no evidence that all main factors were considered. After all, ventilation was not considered at all. Additionally, statistical methods were used in this study, which substantially weakens a study of thermal processes.

By learning from the thermal mass and ventilation study in buildings, this paper aims to apply the analytical model developed for buildings [[27], [28], [29], [30]] into the tunnel environment to provide further insight on the tunnel-air prediction and overheating mitigation. Fig. 1 shows the flowchart for the present study. An ideal physical/mathematical model for subway tunnels is firstly developed in this study. The governing equations are solved by separating the solutions to the time-averaged component from the periodic component. The influential factors of the tunnel-air temperature, tunnel-wall surface temperature, surrounding-soil temperature, and the heat flux through the tunnel-wall surface will be discussed. The model is also applied into London Underground to understand how overheating in London underground conditions is affected by increasing internal heat source and global warming. Finally, the solutions to cool down tunnel-air are discussed, which provides guidance for improved subway-tunnel design and operation to avoid overheating.

Section snippets

Physical model and assumptions

The structure of the subway tunnel is shown in Fig. 2. It consists of a tunnel tube, surrounding soil, and air shafts. Trains travel through the tunnel tube and generate waste heat, which represents the internal heat source in the analytical model. The waste heat is eliminated via ventilation through the air shafts as well as the heat transfer through the tunnel-wall surface and the surrounding soil. Based on this subway-tunnel model the following assumptions are made:

  • (1)

    The subway tunnel is

Analytical solutions

It is expected that the solutions can be expressed as Tin=Tin+ΔT˜in=Tin+ΔTincos(ωtφin), Tsur=Tsur+ΔT˜sur=Tsur+ΔTsurcos(ωtφsur), and Ts=Ts+ΔT˜s=Ts+ΔTscos(ωtφs); i.e. they comprise time-averaged (non-periodic) components and the periodic components.

Validation of the model in London Underground

To validate the above model, a comparison between the measured value and the calculated results was conducted. The month-averaged tunnel-air temperature in the Sub-surface-lines of London Underground was considered. The measured values in 2017 [7] and the predicted trend generated from the model are shown in Fig. 10. The predicted results generally agree well with the measurement. Small discrepancy occurs from July to October. This is likely due to the employment of sinusoidal form in the

Methods to control tunnel-air temperature

Only the methods to reduce tunnel-air temperature in summer are discussed here in detail. The methods to increase the tunnel-air temperature in winter can be obtained in a similarly way.

Considering the solutions for both the time-averaged and the periodic components, there are seven parameters that affect the tunnel-air temperature - see Table 1. However, ρs and Cs can be treated as one parameter because they always appear together as the product of ρsCs. Among these parameters, E affects the

Conclusion

An analytical model to predict the in-tunnel air temperature was developed that can describe the thermal processes in deeply buried subway tunnels. The following conclusions can be drawn:

  • i)

    The time-averaged component of tunnel-air temperature will approach steady state as the time tends to infinity, which has a positive linear relation with internal heat-source and average ambient temperature. Compared with outdoor air, the amplitude of the tunnel-air temperature shows a significant reduction in

Declaration of interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “An analytical model to predict the temperature in subway-tunnels by coupling thermal mass and ventilation”.

CRediT authorship contribution statement

Tingting Sun: Methodology, Formal analysis, Data curation, Validation, Software, Writing – original draft. Zhiwen Luo: Conceptualization, Project administration, Supervision, Methodology, Writing – review & editing. Tim Chay: Software.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was supported by the National Natural Science Foundation of China (No. 51408457), and the State Scholarship Fund awarded by the China Scholarship Council (No. 201807835013).

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