Experimental investigation on longitudinal and transverse temperature distribution in a horseshoe shaped tunnel fire

Abstract

The longitudinal temperature distribution in a tunnel fire has been investigated wildly as the classical problem, while the transverse temperature distribution, especially sidewall temperature, has not received adequate attention. In this article, a 1:3.7 reduced scale horseshoe shaped model tunnel constructed by concrete was established, in which a series of comparative burning experiments were carried out to investigate the longitudinal and transverse temperature distributions. The quantitative trends of smoke longitudinal and transverse temperature including sidewall temperature were observed and analyzed. The major conclusions are summarized as follows: The temperature rise under the ceiling first decreases sharply with longitudinal distance from fire source, followed by a slight decrease, which can be well predicted by Gong’s model of a sum function of two exponential equations. The transverse temperature rise in fire zone is dominated by two different heat transfer regions: convection region (angle below 45° or dimensionless angle below 0.8) and radiation region (angle beyond 45° or dimensionless angle beyond 0.8). The inclination angle is the angle between center line of tunnel and connection line of thermocouple with fire source. The transverse temperature drops with angle in convection region and rises in radiation region, which can be well described by proposed empirical exponential functions. The non-monotonic variation trend of transverse temperature distribution in fire zone is a result of competition between convection of hot smoke and radiation of fire source. All these results are significantly important for fire safety design of tunnel and fire hazard evaluation of tunnel fire.

Keywords

horseshoe shaped tunnel longitudinal temperature decay transverse temperature distribution tunnel fire

Introduction

Fires in tunnels have attracted great attention in recent years due to large fire events, such as Austria Mont-Blanc tunnel fire in 1999 and Korea Dague tunnel fire in 2003 killing 41 and 198 people, respectively (Hu et al., 2013a). The temperature distribution is a key parameter for fire safety design of tunnels, which plays a decisive role in the stability of tunnel structure. Once the steel bars are exposed to flame or hot smoke, the strength of bars in concrete is reduced, which may result in sinking or collapse of tunnel structure (Ji et al., 2012). To the best of our knowledge, the temperature distribution in a tunnel fire is not uniform, which is more likely to lead to instability or collapse of tunnel structure. Therefore, it is necessary to carry out studies on the non-uniform temperature distribution in tunnel fires including longitudinal and transverse temperature profiles.

Over the years, there has been significant progress in our understanding of longitudinal temperature distribution in tunnel fires. Delichatsios (1981) put forward an exponential correlation for temperature variation along the longitudinal direction for fully developed one-dimensional smoke flow. Evers and Waterhouse (1981) conducted experimental studies on temperature distribution of hot smoke under the ceiling and established an empirical expression for longitudinal temperature attenuation. Hu et al. (2005) experimentally and theoretically studied the temperature profiles along the longitudinal direction in a rectangular shaped tunnel and proposed a modified model for longitudinal temperature decay. Gong et al. (2016) provided a theoretical model for longitudinal temperature distribution by taking air entrainment effects into account. Tang et al. (2017) conducted a series of experiments in a reduced scale model tunnel with rectangular cross section to investigate the longitudinal temperature decay with different transverse fire source locations and put forward a modified model considering the fire source location effects to predict the smoke temperature. Liu et al. (2017) carried out burning experiments to explore the ceiling temperature profile in node area of a tunnel and proposed a normalized expression of longitudinal temperature decay by taking heat release rate and fire locations into account. Chow et al. (2016) performed burning tests in a titled rectangular tunnel and derived an empirical expression for longitudinal temperature decay taking slop effects into account. Hu et al. (2014) carried out burning experiments in a rectangular shaped tunnel model and proposed a global model to describe the longitudinal temperature profiles with combined effects of ceiling extraction and longitudinal forced air flow. Hu et al. (2007a) also experimentally investigated the effects of fire size, fire height above the floor, and longitudinal velocity on temperature distribution along the tunnel ceiling in large-scale and full-scale tunnels. Moreover, a series of simulations were performed by fire dynamics simulator (FDS) to investigate the ceiling temperature distributions upstream and downstream in a tunnel fire (Hu et al., 2007b). Furthermore, the effects of smoke screen (Meng et al., 2014), natural ventilation (Yuan et al., 2013), aspect ratio (Li et al., 2012), and blockage-fire distance (Hu et al., 2013b) on longitudinal temperature decay have been addressed in previous researches using burning tests in a reduced scale model tunnel. However, most of experiments were conducted in scale model tunnels constructed by fireproof board, stainless steel, or fireproof glass, which differed from concrete in thermal properties. These discrepancies may lead to different behaviors of smoke temperature distribution. Therefore, it is necessary to revisit the longitudinal temperature distribution in tunnel fires.

For the transverse temperature distribution, Gao et al. (2016, 2017) experimentally investigated the transverse temperature distribution under the ceiling in a sidewall confined tunnel fire and established different correlations for continuous flame region, intermittent flame region, and buoyant plume region to predict the transverse ceiling temperature distribution. Burning experiments in a scale model tunnel by Fan et al. (2013) found that the decay rate of transverse ceiling temperature was larger than that of longitudinal one. Moreover, an empirical correlation was proposed to determine the transverse ceiling temperature profile by taking the fire location into account. Liu et al. (2017) experimentally observed the transverse ceiling temperature in node area of a full-scale tunnel and proposed a dimensionless expression for predicting transverse ceiling temperature distribution. However, the previous work only put emphasis on transverse temperature under the ceiling, rather than the entire transverse temperature distribution including sidewall temperature. Compared with smoke temperature under the ceiling, the gas phase temperature near sidewall below the smoke layer would be affected by additional radiation of fire source. The mechanism of gas phase temperature rise below the hot smoke layer may differ from that above the hot smoke layer, which may lead to a non-uniform temperature distribution of the transverse cross section. Nevertheless, the non-uniform transverse temperature distribution may have a significant effect on the structural stability of the tunnel. Therefore, it is important to explore the entire transverse temperature distribution including sidewall temperature to protect the tunnel surface structure.

Therefore, a 1:3.7 reduced scale horseshoe shaped model tunnel was established, which was constructed by concrete. A series of comparative experiments with different fire sources varying from 12 to 120 kW were conducted to investigate the longitudinal and transverse temperature distribution. The results of this study have implications concerning tunnel design for fire safety and may help advance understanding of entire temperature profiles in tunnel fires.

Experimental setup

A reduced scale model tunnel with dimensions of 1.37 m (height) × 1.5 m (maximum width of cross section) × 20.0 m (length) was established to conduct comparative experiments, with its ceiling, sidewall, and floor constructed by concrete, which was schematically illustrated in Figure 1. The Froude modeling was applied in the current model, which was most widespread scaling technique to build up a bridge between reduced scale and realistic scale experiments (Gong et al., 2016; Khattri, 2017; Meng et al., 2014; Tang et al., 2017; Yuan et al., 2013). The relationship between model tunnels and real tunnels can be determined by the following equations according to Froude law

\frac{T_{m}}{T_{r}} = 1

(1)

\frac{Q_{m}}{Q_{r}} = ϕ^{5 / 2}

(2)

\frac{t_{m}}{t_{r}} = ϕ^{1 / 2}

(3)

where $ϕ$ represents the scaling coefficient, which is a constant value of 1:3.7 in this article, subscript m and r represent model and real tunnels, respectively. Therefore, the temperature T, heat release rate Q, and burning time t of model tunnels can be converted into corresponding values of real tunnels.

Figure 1.

Cross section of model tunnel: (a) view of cross section and (b) longitudinal cross section.

The pool fire burned with gasoline #90 was used as fire source for all experiments, which was set centrally on the tunnel floor. Five circular pools with different diameters of 15, 18, 20, 22, and 28 cm were used as burning objects. To the best of our knowledge, the heat release rate (HRR) can be determined by following equation

Q = χ m Δ H

(4)

where Q represents the HRR, $χ$ combustion efficiency, m the mass loss rate, and $Δ H$ , combustion heat, is 45 kJ/g for gasoline #90. The combustion efficiency of pool fires was necessary for the present experiments, which could be measured and deduced in laboratory by oxygen consumption method. Generally, five circular pools with different diameters of 15–28 cm were tested in laboratory. During the tests, the combustion products were collected by an exhaust hood above the fire, which could be used to calculate the rate of heat release. Simultaneously, the mass loss rate was measured by the weighting system placed below the burning objects. Compared the two methods with each other, the combustion efficiency of five different pool fires was measured to be about 0.78, which was similar to that in Hu’s pioneering work (Hu et al., 2007a). In tunnel fire tests, the fuel thickness in each experiment was kept about 5 cm before ignition. An electronic balance set under the pool objects was used to measure the mass loss rate of the fuels. The mass loss rates measured in steady stage were 0.34, 0.68, 1.17, 1.65, and 3.42 g/s, respectively, corresponding to HRRs of 12, 24, 41, 58, and 120 kW. If corresponding to a real tunnel, the HRRs were 316, 632, 1080, 1527, and 3160 kW, respectively. The calculation methods of HRR have been described in detail in the literature (Gao et al., 2018).

In order to obtain the transverse temperature profile in fire zone, a sequence of 13K-type thermocouples #14–26 were distributed along the cross section, except for the tunnel floor, as shown in Figure 1(a). The thermocouple angle $α$ was the angle between center line of tunnel and connection line of thermocouple with fire source. Since all the experiments were conducted in a relatively static environment, the smoke temperature distributions of upstream and downstream were similar. Therefore, a sequence of 13K-type thermocouples #1–13 were placed at about 5 cm beneath the axis of the ceiling to obtain the longitudinal temperature distribution of upstream, spanning from 0 to 7.25 m from the fire source, as shown Figure 1(b). All the thermocouples have a diameter of 0.5 mm and a response time of 0.03 s, with a data acquisition frequency of two times per second. Its measure range was 0°C–1200°C, with an accuracy of ±2.2°C. Before each experiment, all the thermocouples were calibrated in boiling water to minimize experimental errors. Each test at same condition was repeated at least three times to reduce the experimental errors. All the experiments were performed under similar conditions of ambient temperature and relative humidity at 20°C ± 2°C and 37% ± 5%.

Results and discussion

Longitudinal temperature decay

Figure 2 presents the temperature rise $Δ T$ of thermocouple #1 right above the fire source as a function of time under different HRRs. Actually, similar phenomenon can be observed for other thermocouples. As shown in Figure 2, the temperature development trends of thermocouple #1 under different HRRs are similar, exhibiting three clear stages of growing stage, steady stage, and decaying stage. In the present paper, the characteristic temperature for each thermocouple discussed in next sections is the average temperature of steady stage.

Figure 2.

Temperature rise of thermocouple #1 as a function of time under different pool fires.

Figure 3 shows the dependence of the temperature rise $Δ T$ on longitudinal distance from fire source under different HRRs. It could be obviously observed that the temperature development along the longitudinal direction exhibited similar shape. For a fixed HRR, the temperature rise $Δ T$ shows a largest value right above the fire source, followed by a sharp decrease near the fire source, and finally a slight decrease at distance of 3–7.25 m. This trend demonstrates that the temperature rise $Δ T$ on longitudinal distance from fire source is not uniform. Note that the current trend of longitudinal temperature rise is similar to pioneering work (Gong et al., 2016; Hu et al., 2005; Liu et al., 2017; Tang et al., 2017). Moreover, the temperature rise $Δ T$ at the same distance from fire source exhibits an increase as HRR increases. The error bars represent the average standard deviations of repeated tests ranging from 3.7% to 9.6%.

Figure 3.

Temperature rise as a function of longitudinal distance from fire source under different pool fires.

To the best of our knowledge, the dimensionless smoke temperature rise under the ceiling with dimensionless longitudinal distance from fire source falls into an exponential function (Fan et al., 2013; Hu et al., 2013a; Ji et al., 2012; Liu et al., 2017; Zhong et al., 2016). Therefore, the temperature rise and longitudinal distance are processed dimensionless by $Δ T_{(x)} / Δ T_{max}$ and x/H (where $Δ T_{(x)}$ and $Δ T_{max}$ are temperature rise at distance x from fire source and maximum temperature rise right above the fire source, respectively; x and H are longitudinal distance from fire source and the height of tunnel, respectively), as shown in Figure 4. It is clear that the dimensionless temperature rise $Δ T_{(x)} / Δ T_{max}$ is primarily dependent on dimensionless longitudinal distance from fire source x/H and not on HRR. Moreover, as x/H increases, the dimensionless temperature rise $Δ T_{(x)} / Δ T_{max}$ initially decreases sharply gradually evolving into a slight decrease.

Figure 4.

Dimensionless longitudinal temperature rise $Δ T_{(x)} / Δ T_{max}$ as a function of dimensionless longitudinal distance from fire source x/H.

The prediction model of Evers et al. for longitudinal temperature distribution under the ceiling can be calculated using following equation (Evers and Waterhouse, 1981)

\frac{Δ T_{(x)}}{Δ T_{max}} = k_{1} e^{- k_{2} x / H}

(5)

where k₁ and k₂ are constant, which can be obtained by experiments. However, he did not take the air entrainment into account and assumed that it was considerably small and could be neglected. Moreover, the theoretical model of Gong et al. considering air entrainment effects can be described by the following equation (Gong et al., 2016)

\frac{Δ T_{(x)}}{Δ T_{max}} = A_{1} e^{B_{1} x / H} + A_{2} e^{B_{2} x / H}

(6)

where A₁, A₂, B₁, and B₂ are constant parameters. In order to provide a general quantitative understanding of longitudinal temperature decay, the prediction models of Evers and Waterhouse (1981) and Gong et al. (2016) were used to fit the data of $Δ T_{(x)} / Δ T_{max}$ and x/H, which can well describe the longitudinal temperature distribution under the ceiling. The fitted results are summarized in Table 1. It can be seen that the R² value of Evers’s model is only 0.85, which is smaller than that of Gong’s model. It could be deduced that Gong’s model taking air entrainment effects into account is more appropriate to predict the temperature distribution along the longitudinal direction. Note that the values of fitting parameters in present paper are different from that of experiments conducted by Gong et al. due to discrepancies in thermal properties of tunnel structure. Figure 5 shows the comparison of longitudinal temperature rise between experimental values and predictions by Gong’s model. The average difference between the predictions by Gong’s model and experimental values is not exceeding 5.2%, which demonstrates that Gong’s model provides fairly good predictions to the longitudinal temperature distribution.

Table 1.

Fitted curves for longitudinal dimensionless temperature rise.

Cases	Fitted curve
Cases	Evers’s model	R ²	Gong’s model	R ²
Experimental	$\frac{Δ T_{(x)}}{Δ T_{max}} = 0.89 e^{0.24 x / H}$	0.85	$\frac{Δ T_{(x)}}{Δ T_{max}} = 0.536 e^{- 1.203 x / H} + 0.466 e^{- 0.048 x / H}$	0.98

Figure 5.

Comparison of longitudinal temperature rise measured experimentally and predicted by Gong’s model.

Transverse temperature distribution

The transverse temperature distribution is significantly important to fire safety design for tunnels, which should be deserved increasing attention in fire research. Figure 6 describes the transverse temperature distribution in fire zone as a function of thermocouple angle a under different pool fires. Note that the transverse temperature distribution as a function of thermocouple angle a is not uniform. It can be seen that as a increases, the temperature rise first decreases and then increases with its value being lowest at around 45° under different pool fires. It should be noted that the current trend of transverse temperature profile is different from results of reference (Fan et al., 2013), in which the ceiling transverse temperature keeps going decrease. This is due to the fact that reference (Fan et al., 2013) only measured the transverse temperature of ceiling, not the entire transverse temperature distribution including sidewall temperature. To the best of our knowledge, the smoke spreads longitudinally and ultimately reaches a fully developed one-dimensional smoke flow form (Ji et al., 2012). Above the hot smoke layer, the temperature rise is determined by the convection heat flux of hot smoke. On the contrary, below the hot smoke layer, the temperature rise is mainly controlled by combined effects of hot smoke and fire source. This suggests that the temperature rise at different angles in fire zone is dominated by two different heat transfer regimes: convection regime and radiation regime. During the pool fire tests, a developed one-dimensional smoke flow form is fully generated and the height of smoke layer is almost located at the position of thermocouple of angle $a = 45^{°}$ . Based on the analysis mentioned, above the hot smoke layer (below thermocouple angle a of 45°), the convection heat flux of hot smoke is mainly dominant and the temperature rise decreases with a. Below the hot smoke layer (as a increases beyond 45°), the radiation heat flux of fire source gradually becomes dominant and temperature rise shows an increase with a. Therefore, the transverse temperature distribution as a function of thermocouple angle a can be divided into two different regimes: convection regime and radiation regime. Moreover, the variation trend of transverse temperature distribution in fire zone is a result of combined effects between convection of hot smoke and radiation of fire source. Note that there is a significant increase in temperature rise at the same angle a with increasing HRR. The error bars indicate the standard deviations of repeated tests, which are lower than 10.4%.

Figure 6.

Transverse temperature distribution as a function of thermocouple angle a under different pool fires.

To provide the quantitative dependence of transverse temperature distribution on angle a, the transverse temperature rise and angle a are processed dimensionless by $Δ T_{(α)} / Δ T_{max}$ and $θ = π a / 180^{°}$ , as shown in Figure 7. It is noted that as HRR increases, the change in dimensionless transverse temperature rise $Δ T_{(α)} / Δ T_{max}$ is not significant, which demonstrates that the dimensionless transverse temperature rise $Δ T_{(α)} / Δ T_{max}$ mainly depends on dimensionless angle $θ$ rather than HRR of fire source. Below dimensionless angle $θ$ of 0.8, the convection of hot smoke is dominant and dimensionless transverse temperature rise $Δ T_{(α)} / Δ T_{max}$ decreases with $θ$ . In contrast, in the radiation dominant region, the dimensionless transverse temperature rise $Δ T_{(α)} / Δ T_{max}$ should increase as $θ$ increases.

Figure 7.

Dimensionless transverse temperature rise $Δ T_{(α)} / Δ T_{max}$ as a function of dimensionless angle $θ$ under different pool fires.

To quantitatively estimate the transverse temperature distribution in fire zone, exponential functions were applied to fit the data of $Δ T_{(α)} / Δ T_{max}$ and $θ$ in convection and radiation regions, respectively, as summarized in Table 2. It is apparent that the R² values of fitted curves are more than 0.98, which indicates exponential functions can well predict the transverse temperature distribution in fire zone. In previous work of Fan et al. (2013), an exponential decay function was proposed to describe the relationship between smoke temperature rise at a certain transverse location and transverse distance away from fire

Δ T_{max, d_{f}} / Δ T_{max, D} = a e^{- b d_{f} / w} + c

(7)

where d_f and w represent transverse distance away from fire and width of tunnel, respectively, and a, b, and c are constants. The form of transverse temperature distribution in convection region is similar to the results of Fan et al., but the values of fitting parameters are different due to discrepancies in thermal properties of tunnel structure. This result indicates that the exponential decay function can well predict the transverse temperature distribution in convection region. On the contrary, the transverse temperature distribution in radiation region follows an exponential growth function. But in reference of Fan et al. (2013), the increase trend of transverse temperature distribution was not observed, which was due to the fact that Fan et al. only measured the transverse temperature of ceiling above the hot smoke layer. Figure 8 presents the comparison of predictions by exponential functions with experimental measured values of transverse temperature rise in fire zone. Their differences are within 11.2% with an average of 4.5%, which indicates that the prediction values proposed by exponential functions can agree well with the experimental measured data.

Table 2.

Fitted curves for transverse dimensionless temperature rise.

Cases	Fitted curve
Cases	Convection region	R ²	Radiation region	R ²
Experimental	$\frac{Δ T_{(α)}}{Δ T_{max}} = - 0.432 e^{1.232 θ} + 1.423$	0.985	$\frac{Δ T_{(α)}}{Δ T_{max}} = 0.0069 e^{2.612 θ} + 0.1725$	0.994

Figure 8.

Comparison of transverse temperature rise measured experimentally and predicted by functions.

In summary, Gong’s model $Δ T_{(x)} / Δ T_{max} = A_{1} e^{B_{1} x / H} + A_{2} e^{B_{2} x / H}$ can well predict the longitudinal temperature distribution under the ceiling, by which the smoke temperature under the ceiling at any longitudinal distance away from the fire source can be obtained. To the best of our knowledge, the maximum smoke temperature rise right above the fire source $Δ T_{max}$ can be predicted by Li et al. (2011) model, and the coefficient values of A₁, A₂, B₁, B₂ are constant for a certain tunnel, which can be obtained by experiments. Moreover, the exponential function $Δ T_{(x, θ)} / Δ T_{(x)} = A_{x} e^{B_{x} θ} + C_{x}$ can be used to describe the transverse temperature profiles including sidewall temperature. As we know, coefficient values of A_x, B_x, and C_x are different for different cross sections from fire source. More experiments should be conducted to obtain more values of A_x, B_x, and C_x for different cross sections and eventually proposed empirical equations for A_x, B_x, and C_x. Therefore, if we obtain (1) the maximum smoke temperature under the ceiling right above the fire source $Δ T_{max}$ , (2) the longitudinal temperature decay coefficients of A₁, A₂, B₁, and B₂, and (3) the transverse temperature coefficients of A_x, B_x, and C_x, the temperature rise at any longitudinal distance and angle can be predicted by $Δ T_{(x, θ)} = (A_{x} e^{B_{x} θ} + C_{x}) (A_{1} e^{B_{1} x / H} + A_{2} e^{B_{2} x / H})$ . At present, the first two key issues have been addressed in literatures (Gao et al., 2014; Gong et al., 2016; Hu et al., 2005, 2006; Li et al., 2011; Liu et al., 2017; Zhong et al., 2016). For the third one, empirical exponential functions have been proposed for the transverse temperature profiles in fire zone.

Conclusion

In this article, a series of comparative burning experiments were carried out in a reduced scale horseshoe shaped model tunnel to investigate the longitudinal and transverse temperature distributions. The quantitative trends of smoke longitudinal and transverse temperature including sidewall temperature were observed and analyzed. The major findings from this article are summarized as follows.

The temperature rise under the ceiling first decreases sharply with longitudinal distance from fire source, followed by a slight decrease, which can be well predicted by Gong’s model of a sum function of two exponential equations. The transverse temperature rise in fire zone is dominated by two different heat transfer regions: convection region ( $a < 45^{°}$ or $θ < 0.8$ ) and radiation region ( $a \geq 45^{°}$ or $θ \geq 0.8$ ). The transverse temperature drops with angle a in convection region and rises in radiation region, which can be well described by proposed exponential functions. The non-monotonicity in transverse temperature in fire zone is the result of combined effects of convection by hot smoke and radiation by fire source.

In this article, the longitudinal and transverse temperature distributions including sidewall temperature were evaluated in a model tunnel constructed by concrete, which was of important significance for fire protection to the tunnel structure. When the whole temperature distribution profiles are obtained and then loaded into the structural analysis software, the regularity of sinking or collapse of tunnel structure can be predicted during the fire. However, only five reduced scale pool fire tests were carried out in this article, which corresponding to fires with HRR from 316 to 3160 kW in real tunnel. Therefore, the present results are only capable of predicting the temperature distributions in full-scale tunnel fires with HRR from 316 to 3160 kW. Based on the analysis, a further study is in progress to investigate the transverse temperature distribution for different cross sections from fire source and propose an empirical function for transverse temperature profile.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by National Key Research and Development Plan (project no. 2016YFC0802900), Fire Fighting and Rescue Technology Key Laboratory of MPS Open Project (no. KF201802), the Fundamental Research Funds for the Central Universities (no. 2018BSCXC02), Postgraduate Research & Practice Innovation Program of Jiangsu Province (no. KYCX18_1914), Sichuan Science and Technology Project (no. 2018JY0429), National Natural Science Foundation of China (no. 51606215), Natural Science Foundation of Jiangsu Province (no. SBK2016041452), and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

ORCID iD

Guoqing Zhu

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