**1. Introduction**

The construction of urban tunnels in metropolitan areas provides an effective solution for traffic congestion [1]. Curved tunnels are commonly used [2] as parts of urban tunnel systems (for example, large underground interconnected infrastructure, urban traffic link tunnels, etc.). Depending on the tunnel length, parts of the urban tunnels can be operated under natural ventilation. However, it appears that little research has been conducted on the temperatures below curved tunnel ceilings induced by fires under a natural ventilation scenario.

Maximum temperature rise and longitudinal temperature attenuation properties are two aspects of concern in a tunnel fire [3–5] and can serve as references for tunnel fire protection. In 1972, Alpert [6] presented a model for the prediction of maximum temperature rise induced by fires, given as:

$$
\Delta T\_m = 16.9 \frac{\dot{Q}^{2/3}}{H\_{\varepsilon f}^{5/3}} \tag{1}
$$

where ∆*T<sup>m</sup>* is the maximum temperature rise below the ceiling (K), *He f* is the distance between the fire surface and the ceiling in the vertical direction (m), and . *Q* is the fire heat release rate (kW).

In addition, in 1979 Heskestad and Delichatsios proposed the following equation for maximum temperature rise prediction in dimensionless form [7]:

$$\frac{\Delta T\_m}{T\_{\infty}} = 6.3 \dot{\mathcal{Q}}^{\*2/3} \tag{2}$$

**Citation:** Tao, H.; Xu, Z.; Zhou, D. Investigation of the Temperature Beneath Curved Tunnel Ceilings Induced by Fires with Natural Ventilation. *Fire* **2022**, *5*, 90. https://doi.org/10.3390/fire5040090

Academic Editors: Chuangang Fan and Dahai Qi

Received: 26 May 2022 Accepted: 22 June 2022 Published: 27 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). *fire*

where . *Q* ∗ can be calculated as:

$$\dot{\boldsymbol{Q}}^{\*} = \frac{\dot{\boldsymbol{Q}}}{\rho\_{\infty} T\_{\infty} c\_{p} \sqrt{\overline{g}} H\_{ef}^{5/2}{}'} \,\tag{3}$$

where *T*∞, *ρ*∞, and *c<sup>p</sup>* are the temperature (K), density (kg/m<sup>3</sup> ), and specific heat at a constant pressure (kJ/(kg·K)) of ambient air, respectively, and *g* is the acceleration of gravity (m/s<sup>2</sup> ).

It should be noted that for a specified scenario where *T*∞, *ρ*∞, and *c<sup>p</sup>* are constants expressions of Equations (1) and (2) will be similar.

As for the longitudinal temperature attenuation, Delichatsios [8] investigated the phenomenon of smoke spreading along a beamed ceiling in building fires, and proposed a correlation for the longitudinal temperature attenuation, given as:

$$\frac{\Delta T\_{\chi}}{\Delta T\_{0}} \left(\frac{l}{H}\right)^{1/3} = 0.49e^{-6.67St\left[\frac{\chi}{H}\cdot \left(\frac{l}{H}\right)^{1/3}\right]},\tag{4}$$

where ∆*T<sup>x</sup>* is the temperature rise for a certain position denoted *x* (K), *l* is the half width between the beams (m), *x* is the distance between the fire source and the position *x* in the horizontal direction (m), *H* is the height of the ceiling (m), and *St* represents the Stanton number.

It is noted that both the models of the maximum temperature and the temperature attenuation were originally used for building fires. It was then proven by other scholars that the predicted model for tunnel fires was similar. Li et al. [9] proposed a correlation for the maximum temperature in tunnel fires. For scenarios with natural ventilation, the correlation is similar to Equation (1), and is given as:

$$
\Delta T\_m = 17.5 \frac{\dot{Q}^{2/3}}{H\_{\text{ef}}^{5/3}}.\tag{5}
$$

Meanwhilem Hu et al. [10] indicated that the temperature attenuation along the tunnel can be expressed using an exponential function, which is given as:

$$\frac{\Delta T\_{\chi}}{\Delta T\_{0}} = e^{-\mathbf{K}\mathbf{x}}\tag{6}$$

where ∆*T*<sup>0</sup> is the temperature rise at the point of reference (K), and *K* is a coefficient.

In addition, it has been shown in previous studies that the temperature in a tunnel fire can be affected by various aspects, such as the tunnel geometry, inclination, location of fires, ventilation conditions, vehicle blockage, etc. [11–16].

Zhang et al. [13] revealed that the maximum temperature below the tunnel ceiling varies with the tunnel slope. Their results showed that an increase in the tunnel slope decreases the maximum temperature. Based on these findings, a correlation of maximum temperature induced by fires for a sloping tunnel was proposed. Tang et al. [15] indicated that the maximum temperature below tunnel ceilings is influenced by the variation of fire locations in the transverse direction through experimental studies. A dimensionless coefficient *k* was introduced to modify the effect of different fire-source locations. The effect of mechanical smoke extraction was also discussed [16], in which the characteristic smoke attenuation in the transverse direction was presented. Ingason [17] conducted a small-scale fire test to reveal the tunnel fire behaviors under longitudinal ventilation. It was shown that the ventilation velocity has little effect on the maximum temperature for a fire source with a full-scale heat release rate larger than 100 MW. Chen [18] conducted a small-scale experiment to study the temperature attenuation in longitudinally ventilated tunnels, in which the modified characteristic length was introduced to develop a predictive correlation. Tao et al. [19] experimentally investigated the temperature profile induced

by fires in a tunnel with the centralized smoke exhaust on a single side. The influence of vehicle blockage on maximum temperature under longitudinal ventilation was investigated by Tang et al. [20], in which different distances between the fire source and the blockage were taken into account. vehicle blockage on maximum temperature under longitudinal ventilation was investigated by Tang et al. [20], in which different distances between the fire source and the blockage were taken into account. However, the former models of temperature distribution beneath the ceilings of tunnel fires were established based on straight tunnels. When fire occurs in a curved tunnel,

scale fire test to reveal the tunnel fire behaviors under longitudinal ventilation. It was shown that the ventilation velocity has little effect on the maximum temperature for a fire source with a full-scale heat release rate larger than 100 MW. Chen [18] conducted a smallscale experiment to study the temperature attenuation in longitudinally ventilated tunnels, in which the modified characteristic length was introduced to develop a predictive correlation. Tao et al. [19] experimentally investigated the temperature profile induced by fires in a tunnel with the centralized smoke exhaust on a single side. The influence of

Fire 2022, 5, x FOR PEER REVIEW 3 of 13

However, the former models of temperature distribution beneath the ceilings of tunnel fires were established based on straight tunnels. When fire occurs in a curved tunnel, the resistance of smoke flow spreading differs from that in a straight tunnel [21]. The results of former studies show that the curve of a tunnel leads to a different characteristic of smoke spread under longitudinally forced ventilation [22,23]. However, the effect of tunnel turning radius on the spread of fire smoke and temperature distribution in a naturally ventilated tunnel has not been considered. the resistance of smoke flow spreading differs from that in a straight tunnel [21]. The results of former studies show that the curve of a tunnel leads to a different characteristic of smoke spread under longitudinally forced ventilation [22,23]. However, the effect of tunnel turning radius on the spread of fire smoke and temperature distribution in a naturally ventilated tunnel has not been considered. In this study, an investigation is conducted via a small-scale curved tunnel experi-

In this study, an investigation is conducted via a small-scale curved tunnel experiment to disclose the temperature profiles induced by fires (both maximum temperature rise and longitudinal temperature attenuation) below tunnel ceilings. Improved correlations are provided that may be helpful for understanding smoke spreading characteristics in a curved tunnel. ment to disclose the temperature profiles induced by fires (both maximum temperature rise and longitudinal temperature attenuation) below tunnel ceilings. Improved correlations are provided that may be helpful for understanding smoke spreading characteristics in a curved tunnel.

### **2. Experimental Setup** 2. Experimental Setup

### *2.1. Small-Scale Curved Tunnel* 2.1. Small-Scale Curved Tunnel

A small-scale curved tunnel is constructed based on the Froude scaling law [24,25], whose dimensions are 3 m in length, 0.22 m in height, and 0.32 m in width. Figure 1 shows the apparatus of the small-scale curved tunnel. Fire-proof glass with a thickness of 6 mm is adopted for the tunnel sidewalls and a fire-proof plate with a thickness of 3 mm is used for the tunnel ceiling. A small-scale curved tunnel is constructed based on the Froude scaling law [24,25], whose dimensions are 3 m in length, 0.22 m in height, and 0.32 m in width. Figure 1 shows the apparatus of the small-scale curved tunnel. Fire-proof glass with a thickness of 6 mm is adopted for the tunnel sidewalls and a fire-proof plate with a thickness of 3 mm is used for the tunnel ceiling.

Figure 1. Apparatus of small-scale curved tunnel. **Figure 1.** Apparatus of small-scale curved tunnel.

Figure 2 shows the thermocouple arrangement in the small-scale curved tunnel. The tunnel longitudinal length and tunnel turning radius are also shown in Figure 2. The longitudinal length of the tunnel is defined as the length of the tunnel centerline. Thermocouples of K type are used for temperature measuring, which are placed 0.01 m below the tunnel ceiling. The thermocouple intervals in the longitudinal direction are set to be 0.2 m. To accurately measure the maximum temperature, a smaller longitudinal interval of Figure 2 shows the thermocouple arrangement in the small-scale curved tunnel. The tunnel longitudinal length and tunnel turning radius are also shown in Figure 2. The longitudinal length of the tunnel is defined as the length of the tunnel centerline. Thermocouples of K type are used for temperature measuring, which are placed 0.01 m below the tunnel ceiling. The thermocouple intervals in the longitudinal direction are set to be 0.2 m. To accurately measure the maximum temperature, a smaller longitudinal interval of 0.066 m and 0.033 m is adopted near the fire source.

0.066 m and 0.033 m is adopted near the fire source. As shown in Figure 2, the tunnel section between the entrance and the fire source is defined as being upstream of the fire source. The tunnel section between the exit and the fire source is defined as being downstream of the fire source. The artificial fire source system consists of a propane cylinder, a fuel pipeline, a mass flow controller, and a steel burner. The outlet size of the steel burner is 0.03 m × 0.03 m. During the experiment, the fire source is placed on the centerline of the tunnel at a distance of 1.4 m from the tunnel

entrance. High-purity propane is adopted to produce artificial fire, whose supply rate is monitored by a digital mass flow controller. Fire 2022, 5, x FOR PEER REVIEW 4 of 13

> Figure 2. Thermocouple arrangement in a small-scale curved tunnel. **Figure 2.** Thermocouple arrangement in a small-scale curved tunnel.

### As shown in Figure 2, the tunnel section between the entrance and the fire source is *2.2. Experimental Scenarios*

defined as being upstream of the fire source. The tunnel section between the exit and the fire source is defined as being downstream of the fire source. The artificial fire source system consists of a propane cylinder, a fuel pipeline, a mass flow controller, and a steel burner. The outlet size of the steel burner is 0.03 m × 0.03 m. During the experiment, the Table 1 summarizes the scenarios enacted in the small-scale experiments. A total of 28 scenarios were enacted, in which four different turning radiuses and seven different heat release rates are taken into account. The tunnel turning radius *R* = ∞ denotes a straight tunnel.

fire source is placed on the centerline of the tunnel at a distance of 1.4 m from the tunnel


entrance. High-purity propane is adopted to produce artificial fire, whose supply rate is **Table 1.** The experimental scenarios conducted in the small-scale curved tunnel.

Table 1. The experimental scenarios conducted in the small-scale curved tunnel.
