Study on the Fire Temperature Pattern of Tunnels with Beams Under the Longitudinal Smoke Exhaust Mode

Abstract

Previous studies on tunnel fires have primarily focused on tunnels with flat ceilings and lacked studies on tunnels with beams. The present study is predicated on a reduced-scale tunnel model with a beam structure. Through meticulous analysis of the effects of factors such as longitudinal ventilation velocity and beam dimensions, the study unveils the distribution pattern of ceiling temperatures under the longitudinal smoke exhaust mode. The findings suggest that the presence of beams can induce turbulence in the longitudinal ventilation airflow. It has been demonstrated that the magnitude of this phenomenon is directly proportional to the spacing of the beams. This results in fluctuations in the ceiling temperature rise close to the combustion zone. The smoke storage capacity of the open cavities formed between adjacent beams is significantly affected by the beam height, thereby influencing the overall temperature rise beneath the ceiling. The greater the beam height, the higher the overall ceiling temperature rise near the combustion zone, but the lower the ceiling temperature rise downstream of the fire source. A prediction model for the longitudinal decay of ceiling temperature downstream of the fire source in tunnels with beams has been obtained. This model is related to the dimensionless beam dimension.

1. Introduction

The advent of accelerated urbanization and the concomitant development of three-dimensional transportation networks within China has rendered tunnel engineering an integral component of the subterranean transportation infrastructure. By the conclusion of 2024, China had 28,724 highway tunnels, with a total length of 32,596,600 linear meters, marking an increase of 1427 tunnels and 2,364,800 linear meters compared to the previous year. It is evident that China is currently the leading global contributor to highway tunnel construction, with the most extensive network, the highest number of tunnels, and the most rapid development pace.

During the development of highway tunnels, various structurally complex tunnels have emerged to ensure operational safety and facilitate travel, such as bifurcated tunnels, tunnels with top openings, and tunnels with beams [1,2,3]. In such structures as tunnels with beams, the presence of top beams can significantly change the flow path of the smoke, thereby affecting the temperature field inside the tunnel. A substantial corpus of research has been amassed on the impact of the top beam structure on tunnel smoke characteristics. Huang et al. [4] analyzed gas flow in confined spaces with beam structures. Their research focuses on the impact of altered beam heights on gas flow rate, the depth of the smoke layer, and its mean temperature. The results showed that as the beam height increased, there was less air entrainment and a shallower smoke layer. Concurrently, the mean temperature of the smoke layer rose. Chaabat et al. [5] studied the effect of small and large beams on smoke spread in ventilation tunnels. They found that beams can suppress smoke backflow, thereby reducing critical velocity, and that large beams can do so even at very low velocities. Halawa and Safwat [6] studied how beams in a tunnel affect smoke propagation under a centralized smoke exhaust mode. They found that smoke traveled 66.5% further when beams were 1 m high and 5 m apart, compared to the case without beams. Wei et al. [7] studied temperature and visibility changes at a height of 2 m in a complex tunnel. They found that when beam spacing was greater than 3.6 m, the open cavities formed between adjacent beams exhibited a significant smoke storage effect. Smoke spread was shortened, and stability was disrupted. Compared to tunnels without top beams, high temperature/low visibility hazards, which are bad for personnel evacuation, expanded. It has been demonstrated in prior studies that the configuration of the beam structure at the tunnel’s summit can effectively mitigate smoke backflow, curtail the extent of smoke propagation, and diminish the critical velocity of the tunnel. However, it may also destabilize the smoke layer and expand the scope of dangerous areas with high temperatures and low visibility.

The maximum ceiling temperature rise is defined as the maximum increase in the temperature of the gas beneath the ceiling of the tunnel relative to the ambient temperature under certain conditions, and the maximum ceiling temperature rise constitutes a critical indicator for evaluating the fire hazard in tunnels [8,9]. Concurrently, previous researchers have conducted in-depth investigations into the temperature distribution patterns under the ceiling in beamless tunnels. Tang et al. [10] studied ceiling temperature under mechanical exhaust and ventilation. They found that when a fire is downstream of a ceiling vent, airflow velocity decreases with ceiling extraction speed. Without ventilation, ceiling temperature decreases linearly with extraction speed. Qiu et al. [11] investigated the impact of heat release rate and separation between the two sources of ignition on the distribution of ceiling temperature under conditions involving double fire sources. The investigation revealed that placing the fire sources near the wall resulted in the highest temperature being recorded at the center of the tunnel ceiling. Li et al. [12] studied how blockage and source location affect ceiling temperature. With low ventilation, the peak increase in ceiling temperature within the tunnel remained nearly constant. In scenarios of high ventilation, the maximum temperature rise under the ceiling is inversely proportional to the distance between the blockage and the fire source. Chen et al. [13] analyzed how the burner size and burner shape affect the peak increase in ceiling temperature and the critical velocity. They found that as the area of the burner expanded, the ceiling temperature rise diminished, and it exhibited an initial sharp increase, followed by a subsequent gradual decrease with the burner’s aspect ratio, reaching its peak when the burner was square. Zhang et al. [14] studied the maximum temperature beneath the tunnel ceiling of double fire sources. They found that the two-flame merging phenomenon gradually disappeared as the increase in fire source pitch in the absence of wind. A larger fire source pitch resulted in less impact on the maximum temperature beneath the tunnel ceiling. A prediction model for maximum temperature beneath the tunnel ceiling of double fire sources was developed. Pan et al. [15] revealed the two-dimensional evolution patterns of ceiling jet temperature characteristics beneath curved ceilings through experimental and theoretical studies. Based on conservation equations, they established engineering models for the longitudinal decay of gas temperature in the impact zone for different fire plume types.

In summary, previous studies on tunnel ceiling temperature beneath the ceiling have primarily focused on tunnels without beam structures, with limited research on fire temperature patterns in tunnels with beams. Under normal circumstances, the forms of tunnel smoke evacuation are natural smoke evacuation, longitudinal smoke evacuation and centralized smoke evacuation [16,17,18], and longitudinal smoke exhaust is widely used in tunnels due to its simple structure, low cost and effective smoke extraction [19,20,21]. When studying longitudinal smoke exhaust mode, most previous studies have provided tunnels with stable, full-section longitudinal ventilation [22,23,24]. However, in actual engineering practice, when a tunnel fire occurs, in addition to overall longitudinal ventilation, there is also local ventilation provided by jet fans. Furthermore, Yu et al. [25] found that the presence of beams can cause turbulence in the airflow generated by jet fans, leading to local velocity turbulence. The present study is predicated on a reduced-scale tunnel model with beam structures, incorporating the concurrent existence of full-section longitudinal ventilation and local ventilation from jet fans. By altering parameters such as the fire source’s heat release rate (HRR), longitudinal ventilation velocity, beam height and beam spacing, this study investigates the distribution patterns of maximum temperature rises beneath the ceiling and longitudinal temperature decay patterns in tunnel fire scenarios involving beam structures. This research holds significant implications for minimizing casualties and property losses if a fire breaks out in tunnels that are reinforced with beams.

2. Materials and Methods

2.1. Experimental Tunnel

One of the necessary conditions for maintaining flow similarity between model tunnels and physical tunnels is that the gas flow should be turbulent. Generally, when the Reynolds number (Re) of the gas flow within the tunnel exceeds 5000, the flow can be maintained in the turbulent regime, as shown in Equations (1) and (2). Nowadays, the Froude similarity criterion has been widely applied in the establishment of tunnel models [26,27,28], according to the Froude similarity criterion [29], as shown in Equation (3). Through calculation, it can be determined that $d_m$/$d_p$ is greater than 1/20.12. Taking into account factors such as the minimum scale dimension and experimental facilities, the present study constructed a tunnel model at a reduced scale, using a 1:20 scale ratio, comprising a substantial number of beams, as illustrated in Figure 1.

$$Re={\displaystyle \frac{u_p{d}_p}{v}}>5000$$

(1)

$$Re={\displaystyle \frac{u_m{d}_m}{v}}>5000$$

(2)

where $R_e$ is Reynolds number; $u_p$ is characteristic velocity in the physical tunnel, m/s; $d_p$ is equivalent diameter of the physical tunnel, m; $\nu$ is fluid kinematic viscosity, taken as 0.000019 m²/s; $u_m$ is characteristic velocity in the model tunnel, m/s; $d_m$ is equivalent diameter of the model tunnel, m.

$${\displaystyle \frac{u_m}{u_p}}=\sqrt{{\displaystyle \frac{d_m}{d_p}}}$$

(3)

The tunnel model has a length of 11 m, a width of 0.75 m, and a height of 0.3 m, and the main material is acrylic, but the fire source section of the tunnel is made of steel. Beam heights (H_b) are set at 0.05 m and 0.1 m, with corresponding beam spacings (L_b) of 0.075 m, 0.175 m, and 0.375 m. As demonstrated in the experiments, the tunnel’s longitudinal ventilation velocity is determined by two major factors: the environmental velocity and the jet fan velocity. An axial fan is arranged at the anterior portion of the tunnel, with a flow straightener installed at the outlet of the axial fan, to simulate natural wind, traffic wind, or other mechanical ventilation, providing the tunnel with a stable environmental velocity across the entire cross-section. Three small jet fans are arranged side by side inside the tunnel, to simulate the jet fans closest to the fire, providing local jet fan velocity to the tunnel. According to the theoretical pressure increase calculation for a single jet fan [25], as shown in Equation (4), v_r represents the environmental velocity inside the tunnel, and v_j represents the outlet velocity of jet fan, as illustrated in Figure 2. Using an oil pool fire formed by filling an oil pan with alcohol as the fire source. All oil pans are square-shaped, with side lengths of 8 cm, 11 cm, 14 cm, and 16 cm. The oil pans are positioned on top of an electronic balance, which is utilized to accurately record the quality loss that occurs during combustion. Through measurement and calculation, it can be determined that the heat release rates corresponding to oil pan sizes from smallest to largest are 1.88 kW, 4.33 kW, 7.83 kW, and 10.18 kW.

$$\Delta p_j=\eta \cdot \rho \cdot v_j^2\cdot {\displaystyle \frac{A_j}{A_r}}\cdot (1-{\displaystyle \frac{v_r}{v_j}})$$

(4)

where $\eta$ is positional friction loss reduction coefficient; $\rho$ is air density, kg/m³; v_j is jet fan velocity, m/s; v_r is environmental velocity, m/s; A_j is jet fan outlet area, m²; A_r is cross-sectional area of a tunnel, m².

2.2. Detector Layout

The experiment used thermocouples as temperature measurement instruments, with 46 measurements distributed along the length of the tunnel, spaced 0.25 m apart. In consideration of the effects of longitudinal ventilation, it can be posited that the flame would be displaced in the direction of the airflow. Three additional measurement points were added in close to fire source, specifically at 0.15 m to the left of the oil pan center, 0.1 m and 0.15 m to the right. Each measurement point was equipped with four thermocouples vertically, with the first one located 0.05 m from the ceiling and each subsequent one spaced 0.05 m apart, as shown in Figure 3a. Pitot tubes were used as instruments to measure velocity. A total of 22 Pitot tubes were installed, with 11 measurement points along the longitudinal axis, each spaced 1 m apart, and two measurement points were arranged vertically, at distances of 0.1 m, 0.2 m from the ceiling, as depicted in Figure 3b. The cross-section illustrating the overall configuration of the tunnel is presented in Figure 4.

2.3. Fan Calibration

This study utilized fans with adjustable velocities for experimentation. Prior to the experiment, a hot-wire anemometer was used to calibrate the average environmental velocity within the tunnel and the average outlet velocity of the jet fan, both measured without ignition. The specific measurement points are shown in Figure 5, and the calibration results are presented in Figure 6. A positive linear correlation is evident between the frequency of the axial flow fan and average environmental velocity within the tunnel. The adjustment of the axial flow fan’s frequency enables the precise regulation of tunnel environmental velocity, thereby meeting the experimental requirements. Within the velocity range necessitated by the experiment, the voltage of the jet fan exhibited a predominant linear correlation with the average outlet velocity. The required velocity for the experiment can be obtained by altering the voltage of the jet fan.

2.4. Experimental Conditions

An exhaustive list of the experimental conditions can be found in

Table 1. Experimental conditions.

Test No.	Heat Release Rate Q (kW)	Beam Height Hb (m)	Beam Spacing Lb (m)	Jet Fan Velocity vj (m)	Environmental Velocity vr (m/s)
1–20	1.88, 4.33, 7.83, 10.18	-	-	7.27	0, 0.22, 0.45, 0.67, 0.89
21–140	1.88, 4.33, 7.83, 10.18	0.05	0.075, 0.175, 0.375	0, 7.27	0, 0.22, 0.45, 0.67, 0.89
141–220	1.88, 4.33, 7.83, 10.18	0.1	0.075, 0.175	0, 7.27	0, 0.22, 0.45, 0.67, 0.89

, which includes 220 distinct experimental conditions, inclusive of the control group. Based on the control group and five different beam structures, this research analyzes the consequences of varying heat release rates, longitudinal ventilation velocities, and beam dimensions on temperature distribution inside the tunnel, considering whether jet fans are turned on.

3. Results and Discussion

3.1. The Impact of Different Factors on the Maximum Ceiling Temperature Rise

As demonstrated in Figure 7, the maximum ceiling temperature rise is dependent on both the heat release rate and the velocity of the surrounding environment. Under equivalent velocities, it is evident that an elevated heat release rate results in a corresponding increase in the maximum ceiling temperature rise. At a constant heat release rate, the maximum ceiling temperature rise is observed to decrease with increasing tunnel environmental velocity. However, an increase in velocity, from 0.22 m/s to 0.45 m/s, leads to an essentially constant rise in the maximum ceiling temperature, suggesting that within the velocity range of 0.45 m/s or less, the overall velocity in the tunnel remains relatively low and the impact of environmental velocity remains restricted. When the environmental velocity exceeds 0.45 m/s, the overall velocity is high, resulting in a greater flame inclination angle, leading to a continuous decline in the maximum ceiling temperature rise.

Figure 8 compares the velocities at different heights close to the fire source and presents a comparative analysis of the maximum ceiling temperature rise, both with and without the operation of jet fans. It can be observed that without jet fans, due to the influence of the beams, the velocity at the bottom of the tunnel close to the fire source exhibits a marginal increase in comparison to that of the upper segment, but overall velocity is relatively uniform. The presence of the beams causes turbulence in the airflow; upon activation of the jet fans, an increase in velocity is observed at the upper part near the fire source. In contrast, the velocity at the lower part exhibits minimal change, resulting in the velocity at the upper part being higher than that at the lower part. Compared to when only environmental velocity is present, the incorporation of jet fans has been demonstrated to enhance the longitudinal ventilation velocity. Through meticulous observation of the maximum ceiling temperature rise change curve, it was determined that during the operation of the jet fan, the maximum ceiling temperature rise was lower, exhibiting a faster rate of decline, which was evidently attributable to the increase in longitudinal ventilation velocity. It is evident that irrespective of the method employed to increase the longitudinal ventilation velocity, the maximum temperature rise will decrease accordingly. This assertion is substantiated by the empirical evidence provided by the velocity curve, thereby enhancing the confidence in the conclusion drawn.

Figure 9 shows the maximum ceiling temperature rise as a variable of beam height for different tunnel environmental velocities when the beam spacing is 0.175 m. At an equivalent environmental velocity, the greater the beam height, the more pronounced the maximum ceiling temperature rise. This is primarily because the increased beam height enhances the smoke storage capacity of the open cavities formed between adjacent beams, while simultaneously making smoke propagation more difficult, thereby increasing the temperature rise. The increase in beam height from 0.05 m to 0.1 m results in a significant increase in temperature rise compared to the rise from 0 m to 0.05 m. This indicates that beam height significantly affects smoke storage capacity, when the beam height is low, the smoke storage capacity is weak, and it only slightly increases the maximum temperature rise. The capacity for smoke storage is enhanced when the beam height is sufficiently elevated, resulting in a significant increase in the maximum temperature rise.

The maximum ceiling temperature rise as a function of tunnel environmental velocity for different beam spacings when the beam height is 0.05 m is compared in Figure 10. As the environmental velocity within the tunnel increases, the maximum rise in ceiling temperature consistently decreases when the beam spacing is set at 0.075 m. This observed trend remains independent of variations in the heat release rate. As the environmental velocity increases, the maximum ceiling temperature typically diminishes when the beam spacing is set at 0.175 m. However, the maximum ceiling temperature increase stays relatively the same when the environmental velocity increases from 0.22 to 0.45 m per second. This indicates that increasing the beam spacing reduces the impact of low velocities on maximum temperature rise. As the environmental velocity escalates, the maximum ceiling temperature rise diminishes once the velocity surpasses a certain threshold. As the beam spacing is adjusted to 0.375 m, the maximum ceiling temperature rise initially fluctuates before decreasing as the environmental velocity increases. This pattern is also unaffected by the heat release rate. In general, the alteration in maximum ceiling temperature rise with changes in environmental velocity is influenced by the beam spacing. Increasing the beam spacing can weaken the impact of longitudinal ventilation on high-temperature smoke spread in some measure, resulting in fluctuations in the maximum ceiling temperature rise at lower velocities.

3.2. The Impact of Different Factors on Ceiling Temperature Decay Pattern

The distribution of temperatures in the tunnel at varying tunnel environmental velocities is shown in Figure 11. The combined influence of the jet fan and environmental wind causes smoke to spread downstream from the location of the oil pan. The high-temperature areas exceeding 60 °C also shift downstream. Increasing the environmental velocity in the tunnel accelerates the spread of smoke. At low velocities, the smoke backflow occurs. When the velocity reaches 0.67 m/s, the high-temperature area is only present above and downstream of the fire source. This indicates that the velocity has reached its critical point and that the smoke will no longer flow back, and the smoke flow in the experiment is shown in Figure 12. Increasing the tunnel environmental velocity (for example, from 0.45 m/s to 0.89 m/s) when the longitudinal ventilation velocity reaches a sufficiently elevated level causes the high-temperature areas exceeding 60 °C within the tunnel to continuously decrease. This indicates that when the longitudinal velocity of the airflow is sufficiently elevated, it can inhibit the combustion of the fire source, facilitate the dispersion of smoke, and improve the efficiency of convective heat transfer. Consequently, it exerts a positive influence lowering the aggregate temperature within the confined space of the tunnel.

As illustrated in Figure 13, the distribution of ceiling temperature rise is contingent upon the surrounding environmental velocity and the heat release rate of the fire source. It is evident that the heat release rate exerts a substantial influence on the overall ceiling temperature. When the heat release rate is relatively low, the maximum ceiling temperature rise does not exceed 250 °C. However, upon elevating the heat release rate to 7.83 kW, the maximum ceiling temperature rise reaches 550 °C. Research indicates a positive correlation between the increase in the heat release rate and the increase in the overall ceiling temperature. Through the implementation of longitudinal ventilation, a shift in the flame’s trajectory occurs, moving downstream from the center of the oil pan, as shown in Figure 14. It has been demonstrated that an increase in longitudinal ventilation velocity correlates with a more pronounced shift in the flame, subsequently resulting in a greater displacement of the maximum temperature rise downstream from the fire source. At a constant heat release rate, an increase in velocity is associated with a decrease in overall ceiling temperature.

Figure 15 compares the ceiling longitudinal temperature rise at different beam heights. As the beam height is increased from 0 to 0.1 m under constant longitudinal ventilation velocity, the overall temperature near the fire source experiences an increase, and the maximum ceiling temperature rise also increases. This is because the higher the beam, the more smoke can be stored in the open cavities formed between adjacent beams, the stronger its ability to block smoke spread, and the stronger its thermal feedback on the fire source. Consequently, this leads to an elevated temperature in the area surrounding the fire source. In the upstream area of the burner, due to the influence of longitudinal wind, the temperature remains relatively stable irrespective of the presence of the beam. In the downstream area of the burner, an augmentation in beam height from 0 to 0.1 m leads to a decline in the overall temperature downstream. This phenomenon occurs because of the increased capacity of beams to prevent smoke spread with the height of the beam, making it more difficult for smoke to spread downstream, leading to a reduction in the overall temperature downstream.

Figure 16 compares the distribution of ceiling longitudinal temperature with and without jet fans at different beam spacings. In circumstances where longitudinal ventilation is established through the interplay of environmental wind and jet fan airflow, a conspicuous decline in near-fire source ceiling temperature is observed when compared to the condition without jet fan operation. As beam spacing increases, the longitudinal ventilation airflow within the tunnel becomes more turbulent. When the beam spacing is 0.075 m or 0.175 m, the smaller beam spacing results in less influence on longitudinal ventilation by the beams, with normal airflow. The ceiling temperature displays an initial rise, followed by a subsequent decline, reaching a maximum value in proximity to the source of combustion. As the beam spacing increases to 0.375 m, the longitudinal ventilation airflow becomes turbulent, causing disordered smoke flow beneath the ceiling. Despite the overall longitudinal temperature distribution continuing to exhibit an initial rise and subsequently decrease, temperature fluctuations have been observed close to the combustion zone.

Because of the influence of longitudinal ventilation, fire smoke is concentrated primarily in the downstream area of the tunnel. Gong et al. [30] posited that the decay of ceiling temperature can be expressed as the aggregation of two exponential functions. Therefore, this paper adopts a universal double exponential decay model to indicate the ceiling longitudinal temperature decay along the longitudinal axis downstream of the fire source, as shown in Equation (5).

$${\displaystyle \frac{\Delta T_x}{\Delta T_{max}}}=A{e}^{B{\displaystyle \frac{x}{H}}}+C{e}^{D{\displaystyle \frac{x}{H}}}$$

(5)

where ${∆T}_x$ is ceiling longitudinal temperature rise, K; ${∆T}_{max}$ is temperature rise at the reference point, K; $x$ is the distance from the fire source, m; H is the distance from the fire source surface to the ceiling, m; A, B, C, D is coefficients to be fitted.

Figure 17 shows a comparison of longitudinal temperature decay with and without beams. It is evident that in the presence of beams, the longitudinal temperature decay downstream of the fire source within the tunnel occurs more rapidly. Furthermore, the greater the beam height, the more pronounced the longitudinal temperature decay becomes.

As demonstrated in Figure 18, the findings of the fitting demonstrate the variation in ceiling temperature decay downstream at varying heat release rates in the absence of a beam. When the velocity rises from 0.22 m/s to 0.89 m/s, the rate of temperature decay downstream of the fire source remains essentially unchanged, indicating that the influence of longitudinal ventilation on temperature decay can be neglected. The utilization of Equation (6) to dimensionless the heat release rate facilitates the extraction of the alterations in each coefficient with respect to the dimensionless heat release rate Q* [31], as shown in Figure 19.

$$Q^{*}={\displaystyle \frac{Q}{{\rho }_a{c}_p{T}_a{g}^{1/2}{H}^{5/2}}}$$

(6)

where Q* is dimensionless heat release rate; Q is heat release rate, kW; ${\rho }_a$ is environmental air density, kg/m³; c_p is specific heat capacity of the environmental air, kJ/(kg·k); T_a is environmental temperature, K; g is gravitational acceleration, taken as 9.81 m/s²; H is tunnel height, m.

From Figure 19, the coefficients A, B and C remain constant under variations in Q*, while coefficient D shows a weak linear relationship with the change in Q*, which indicates that the heat release rate also exerts a minimal impact on the temperature decay. The dimensionless longitudinal temperature decay relationship can be obtained in the case of the no-beam scenario, as depicted in Equation (7).

$${\displaystyle \frac{\Delta T_x}{\Delta T_{max}}}=0.28e^{-0.05{\displaystyle \frac{x}{H}}}+0.72e^{(3.97Q^{*}-2.29){\displaystyle \frac{x}{H}}}$$

(7)

As demonstrated in Figure 20, the fitting results demonstrate the variation in ceiling temperature decay downstream of the fire source at different longitudinal ventilation velocities when there are beams. It can be found that, in the case of the presence of beams, with the increase in tunnel environmental velocity, the coefficients also remain basically stable. Additionally, the heat release rate exerts a negligible influence on the decline of temperature. Employing Equation (8) to dimensionless the longitudinal ventilation velocity, the alterations in each coefficient with respect to the dimensionless velocity V* are obtained, as illustrated in Figure 21.

$$V^{*}={\displaystyle \frac{v_r}{v_j}}$$

(8)

where V* is dimensionless longitudinal ventilation velocity.

As evidenced in Figure 21, the coefficients A, B, C, and D remain constant when V* is altered. This indicates that, when beams are present, longitudinal ventilation within the tunnel has a negligible effect on temperature decay and can be disregarded.

Figure 22 shows the fitting results of ceiling temperature decay downstream of the fire source vary according to various beam dimensions. It has been demonstrated that as beam dimension changes, coefficients A, B, and C fluctuate slightly, while coefficient D changes significantly. By using H_b/L_b to dimensionless the beam dimension, the variation in the temperature decay coefficients with H_b/L_b is obtained, as shown in Figure 23.

As demonstrated in Figure 23, coefficient B exhibits negligible variation in relation to H_b/L_b, taking the mean value of −0.10. Coefficients A and C exhibit minor fluctuations and are also averaged, yielding values of 0.22 and 0.78. The coefficient D exhibits a linear distribution with respect to changes in H_b/L_b. By fitting the data, the dimensionless relationship of ceiling longitudinal temperature decay in the downstream direction in the presence of beams, can be obtained, as shown in Equation (9).

$${\displaystyle \frac{\Delta T_x}{\Delta T_{max}}}=0.22e^{-0.10{\displaystyle \frac{x}{H}}}+0.78e^{(-0.49H_b/L_b-1.09){\displaystyle \frac{x}{H}}}$$

(9)

A comparison was made between the longitudinal temperature decay model with beams and that without beams. Research indicates that in the absence of beams, the heat release rate of the fire source is the primary factor influencing longitudinal temperature decay. When beams are present in the tunnel, they become a primary factor affecting longitudinal temperature decay, particularly due to the influence of beam dimensions.

Substituting the variables into Equations (7) and (9), the predicted values of the ceiling temperature decay downstream of the fire source for the absence and presence of beams were obtained. A comparison of these results with the outcomes of reduced-scale experiments, as illustrated in Figure 24, is warranted.

As shown in Figure 24, regardless of the presence or absence of beams, the predictive model for the decline in ceiling temperature, established in this paper based on the scenario of longitudinal ventilation in the region downstream of the fire source, exhibits a general alignment with experimental results. The error in most regions is within 20%, with only a limited number of data points exceeding the 20% error range in areas that are distant from the combustion zone. Consequently, the ceiling temperature decay prediction model developed in this study for the area downstream of the fire source under the longitudinal smoke exhaust mode proposed in this paper exhibits satisfactory predictive performance and can adequately describe the ceiling temperature decay conditions within tunnels with beams.

4. Conclusions

This investigation employs a modified reduced-scale tunnel model, incorporating beam structures, to examine the distribution of ceiling longitudinal temperature. This study incorporates a range of parameters, including heat release rate, beam heights, beam spacings and longitudinal ventilation velocity. The primary conclusions that can be drawn from this analysis are as follows:

• The distribution of interior tunnel ceiling temperatures is influenced by two factors: the heat release rate and the longitudinal ventilation velocity. During the operation of jet fans, a notable increase in velocity at the top of the tunnel is observed, resulting in a considerable reduction in the maximum ceiling temperature rise.
• The presence of longitudinal ventilation will cause the flame to shift downstream from the fire source. An increase in the longitudinal ventilation velocity has been shown to accelerate the spread of smoke. When the velocity exceeds the critical velocity, the smoke ceases to flow back, and high-temperature areas exceeding 60 °C are only present above and downstream of the fire source.
• The presence of beams has been shown to induce turbulence in the longitudinal ventilation airflow beneath the tunnel ceiling. The magnitude of this phenomenon is directly proportional to the beam spacing; the greater the beam spacing, the more pronounced the phenomenon. This results in fluctuations in the ceiling temperature rise near the fire source.
• The beam height exerts a substantial influence on the smoke storage capacity within the open cavities formed between adjacent beams, consequently affecting the overall ceiling temperature rise. It is evident that the greater the beam height, the more pronounced the overall ceiling temperature rise in the vicinity of the fire source, while concurrently exhibiting a decrease in ceiling temperature downstream of the fire source.
• Through the application of data fitting techniques, a prediction model for the ceiling longitudinal temperature decay downstream of the fire source, related to the dimensionless heat release rate Q*, was obtained for the absence of beams. In the context of beams, a predictive model has been derived for the longitudinal decay in ceiling temperature downstream of a fire source. This model is related to the dimensionless beam dimension H_b/L_b.

This paper focuses on investigating the temperature characteristics within a reduced-scale rectangular cross-section tunnel model incorporating beam structures. It remains to be verified whether different tunnel geometries and different scale ratios affect the research results. Further research is still needed to obtain more reliable conclusions. For full-scale experiments, more realistic fire sources should be employed while accounting for variations in carbon monoxide concentration and visibility within the tunnel. Additionally, a more detailed investigation is required into the entrainment and settling processes of smoke within the open cavities formed between adjacent beams.