Experimental Study on Critical Ventilation Speed in Asymmetric V-Shaped Tunnel Fires

Abstract

Asymmetric V-shaped tunnels are commonly found in newly built urban underground road tunnels. In such kinds of tunnels, the flow of smoke becomes very complicated in the event of a fire, and effective smoke control under longitudinal ventilation is challenging. The critical ventilation speed under different slope combinations and heat release rates (HRRs) of fire in asymmetric V-shaped tunnels with the fire sources located at the slope change point were investigated by experiments through a 1:20 small-scale V-shaped model tunnel. The research results indicate that the critical ventilation speed increases with the increasing of fire HRR. If the fire source power remains constant, when longitudinal ventilation is implemented on the side with small slope, the critical ventilation speed decreases as the slope difference between the two sides of the slope change point increases. Conversely, when longitudinal ventilation is implemented from the large slope side, the critical ventilation speed increases as the slope difference increases. For practical engineering applications, based on the critical ventilation speed of single-slope tunnels, and incorporating the experimental results from model tests, calculation models for the critical ventilation velocity were developed, respectively, for longitudinal ventilation implemented from large or small slope sides with slope corrections taken into account. The research findings can provide technical support for effective smoke control in V-shaped tunnels during fire incidents.

1. Introduction

With the rapid development of China’s economy, urban transportation land has become increasingly tight. Constructing more underground roads is undoubtedly an effective measure to alleviate urban traffic pressure. Urban underground roads are mostly located in the city center. Due to the influence of the existing underground buildings, such as the existing subways and underground utility tunnels, the longitudinal profiles of urban underground roads are becoming increasingly complex, no longer limited to simple horizontal or single-slope tunnels but instead featuring combinations of multiple continuous V-shaped sections. The complex longitudinal structure increases the probability of traffic accidents and fires caused by vehicles.

Based on whether the slopes on either side of the slope change point are identical, V-shaped tunnels can be classified into symmetrical V-shaped tunnels and asymmetrical V-shaped tunnels [1]. For a fire occurring at the slope change point in symmetric V-shaped tunnels, smoke generally spreads symmetrically on both sides, centered on the slope change point. However, in asymmetric V-shaped tunnels, due to the different slopes on both sides of the slope change point, smoke initially spreads symmetrically from the fire source in the early stages of the fire. With the continuous development of the fire, the thermal pressure difference generated by the hot smoke within the tunnel on either side of the slope change point gradually increases. Smoke on the side with the small slope gradually flows towards the slope change point, eventually causing the smoke to flow from the small slope side towards the large slope side. A schematic diagram of smoke spread in a V-shaped tunnel is shown in Figure 1, where α_s and α_l are the tilt angle of the small slope side tunnel and large slope side tunnel respectively. When the slope difference between the two sides of the slope change point is significant, the smoke may spread entirely within the large slope section. This smoke spread is noticeably different from that in horizontal tunnels or those with a single slope [1,2].

During tunnel fires, smoke is the main cause of casualties. The commonly used smoke control system in tunnels mainly includes a longitudinal ventilation system, transverse exhaust system, or semi-transverse exhaust system [3,4,5,6,7]. Due to the low investment and operation costs, longitudinal ventilation systems have been widely applied in some unidirectional traffic tunnels where traffic congestion is less likely to occur. For longitudinal ventilation smoke control, the critical velocity is one of the key factors to determine whether the smoke can be effectively controlled. Previous studies have shown that the critical velocity is mainly affected by the tunnel’s cross-sectional dimensions and the fire size [8,9,10,11,12]. For single-slope tunnels, the chimney effect induced by the slope has a significant impact on the critical ventilation speed. When the traffic direction is uphill, the critical ventilation speed can be determined using the critical velocity for longitudinal ventilation in a straight and level tunnel under the same fire power. If the traffic direction is downhill, the critical ventilation speed value is corrected by slope on the basis of the critical ventilation speed in a straight tunnel. The determination of the slope correction coefficient is the key for calculating the critical ventilation speed in slope tunnels. Regarding the slope correction coefficient, much research has been conducted, and some empirical equations for the slope correction coefficient have been obtained [10,13,14,15,16].

Regarding the critical ventilation speed in tunnels, although there are many available calculation models, most of the current design codes commonly recommend Kennedy’s model as the calculation model for the critical speed in the longitudinal ventilation smoke control system design [3,4,5,6,7,10]. It can be calculated by the following:

$$\begin{array}{c}{v}_c=k_l{k}_g{\left[{\displaystyle \frac{ghQ}{{\rho }_0{c}_{p}A{T}_f}}\right]}^{1/3}\end{array}$$

(1)

$$\begin{array}{c}{T}_f={\displaystyle \frac{hQ}{\rho c_{p}A{v}_c}}\end{array}+T$$

(2)

where v_c is the critical ventilation speed, m/s; k₁ is a constant, k₁ = 0.606; k_g is the slope correction factor, k_g = 1 + 0.0374i^0.8, i is the slope of the tunnel, %; h is the height of the tunnel, m; g is the acceleration due to gravity, m/s²; Q is the fire heat release rate, kW; ρ₀ is the average density of the approach air, kg/m³; c_p is the specific heat of the air, kJ/(kg·K); A is the area perpendicular to the flow, m²; T_f is the average temperature of the air close to the fire site, K; T is the temperature of the approach air, K.

However, in asymmetric V-shaped tunnels, due to the existence of the slope change point and the different gradient structures on both sides, the critical speed during longitudinal ventilation smoke control is significantly different from that in the single-slope tunnel. For the different traffic directions, longitudinal ventilation may be implemented on the small slope side, or on the large slope side for controlling the smoke backflow, as shown in Figure 2. In such scenarios, the critical ventilation speed is not only related to the fire HRR and the tunnel cross-sectional size, but also to the ventilation position and the slope composition of the tunnel on both sides of the slope change point. Current research on asymmetric V-shaped tunnels predominantly focuses on internal temperature distributions and the back-layering length of smoke [1,2,16,17,18], with limited studies addressing the critical ventilation velocity under longitudinal ventilation smoke control. Based on this, this study will conduct small-scale model experiments to investigate the critical ventilation speed when the fire occurs at the gradient change point, considering various slope combinations on both sides and different heat release rates. The calculation model for the critical ventilation speed in the V-shaped tunnel would be obtained, thereby providing technical support for effectively controlling smoke during a fire in the V-shaped tunnel.

2. Theoretical Analysis of Smoke Flow in V-Shaped Tunnels

Assuming the smoke flow on both sides of the slope change point is one-dimensional and the temperature distribution is uniform, the smoke movement in a V-shaped tunnel is primarily influenced by the thermal pressure difference and flow resistance across the slope change point. Through control volume analysis, the thermal pressure difference between the two sides of the slope change point can be expressed as follows:

$$\begin{array}{cc}\hfill \Delta P& =P_l-P_s\hfill \\ & ={\displaystyle {\int }_0^{L_l}({\rho }_0-{\rho }_l)g\sin {\alpha }_{l}dl}-{\displaystyle {\int }_0^{L_s}({\rho }_0-{\rho }_s)g\sin {\alpha }_{s}dl}\hfill \\ & ={\displaystyle {\int }_0^{L_l}\Delta {\rho }_{l}g\sin {\alpha }_{l}dl}-{\displaystyle {\int }_0^{L_s}\Delta {\rho }_{s}g\sin {\alpha }_{s}dl}\hfill \end{array}$$

(3)

Following the idea gas law,

$${\rho }_0{T}_0={\rho }_s{T}_s={\rho }_l{T}_l$$

(4)

We have the following:

$$\Delta {\rho }_l={\displaystyle \frac{{\rho }_l\Delta T_l}{T_0}}$$

(5)

$$\Delta {\rho }_s={\displaystyle \frac{{\rho }_s\Delta T_s}{T_0}}$$

(6)

Substituting Equations (5) and (6) into Equation (3), we get the following:

$$\Delta P={\displaystyle {\int }_0^{L_l}\frac{{\rho }_l\Delta T_l}{T_0}g\sin {\alpha }_{l}dl}-{\displaystyle {\int }_0^{L_s}\frac{{\rho }_s\Delta T_s}{T_0}g\sin {\alpha }_{s}dl}$$

(7)

where P_l and P_s are the thermal pressures on the large slope side and the small slope side, respectively, Pa; L_l and L_s represent the smoke spread lengths on the large slope side and the small slope side, respectively, m; T_l and T_s denote the smoke temperatures on the large slope side and the small slope side, K; ρ_l and ρ_s are the smoke densities on the large slope side and the small slope side, kg/m³; T₀ is the ambient temperature, K; ρ₀ is the density of ambient air, kg/m³; α_l and α_s are the tilt angles of the large slope side and the small slope side, °.

As shown in Equation (7), the thermal pressure difference across the slope change point is affected by the temperature rise on both sides of the tunnel, the smoke spread distance, and the slope angles. For a given tunnel, the temperature rise on the large slope side and the small slope side depends primarily on the fire heat release rate and the cross-sectional dimensions. When longitudinal ventilation is implemented—whether from the large or the small slope side, the critical velocity must be sufficient to overcome the thermal pressure difference, frictional resistance, and local resistance, so as to prevent smoke backflow upstream of the fire source. That is also the reason why we mainly study the influence of slope composition and fire HRR on critical speed in this study.

3. Experimental Studies

3.1. Small-Scale Model Tunnel

To investigate the smoke flow and the critical velocity under longitudinal ventilation in V-shaped tunnels during a fire, based on the Froude similarity criterion [19], taking a real urban underground road tunnel in Beijing as the prototype, a V-shaped tunnel model with a scale of 1:20 was built. The schematic diagram of the model tunnel and the physical model tunnel are shown in Figure 3 and Figure 4, respectively. According to the Froude criterion, the scaling relationships of various physical parameters between the model tunnel and the full-scale tunnel are as follows:

Temperature:

$$T_m/T_f=1$$

Velocity:

$$v_m/v_f={\left(L_m/L_f\right)}^{1/2}$$

Heat release rate:

$$Q_m/Q_f={\left(L_m/L_f\right)}^{5/2}$$

Volumetric flow rate:

$$V_m/V_f={\left(L_m/L_f\right)}^{5/2}$$

where subscripts f = full-scale and m = small-scale model.

The model tunnel is 20.5 m long, 0.675 m wide, and 0.5 m high. The main body of the model tunnel consists of a 0.5 m long fire source section in the middle and two adjustable slope sections on both sides, each with a length of 10 m. For observing the smoke spread during experiments and arranging the thermocouples, three sides of the tunnel are covered with galvanized steel plates, and the inner side is lined with 2 mm thick asbestos fireproof boards. The front of the model tunnel is equipped with fireproof glass doors. To achieve slope adjustments on both sides of the tunnel, manual chain hoists are suspended at intervals above the tunnel on both sides, allowing the slope of the two sides to be adjusted by lifting or lowering the double chain wheels, with an adjustment range of 0~10°.

The fuel used for the experiment is liquefied petroleum gas (LPG). Changes in HRRs during the experiments are achieved by altering the flow rate of the liquefied petroleum gas. The density of the liquefied petroleum gas used in the experiments is 2.35 kg/m³, with a combustion heat value of 43.7 MJ/kg. The dimensions of the fire burner are 0.15 m × 0.10 m × 0.06 m (length × width × height). When longitudinal ventilation is implemented in the tunnel, the fan is positioned at the portal of the tunnel with a large slope or a small slope as needed. A rectification device is installed at the front of the fan. Longitudinal ventilation speed change is achieved through changing the frequency of the fan.

In the experiment, the critical ventilation speed was determined as the speed when the smoke back-layering distance upstream of the fire source reduced to zero. The arrangement of the ventilation speed measurement points is shown in Figure 3. Ventilation speed was measured using a TES-1340 Hot-Wire Anemometer (TES Electrical Electronic Corp., Shenzhen, China); the accuracy of the anemometer was ±3% of reading ±1% of full scale; and its resolution was 0.01 m/s.

3.2. Experimental Scenarios

With reference to the provisions on tunnel slopes in tunnel design guides, based on investigations of actual tunnel roads, the slopes of the tunnels currently in operation in China are mainly concentrated between 1% and 5%. A small number of tunnels may have local gradients exceeding 7% due to terrain constraints and the influence of existing structures. To further study the effectiveness of smoke control in longitudinal ventilation systems under different slope combinations, several slope combinations such as 1%, 3%, 5%, and 7% were selected on both sides of the V-shaped tunnel slope change point in the experiments. Since heavy goods vehicles (HGVs) are mostly prohibited in urban tunnels, the maximum designed fire heat release rate under fire conditions generally does not exceed 30 MW [3,4,5]. To study the influence of HRR on critical ventilation speed, fire powers of 5 MW, 20 MW, and 30 MW were selected, and the corresponding HRRs in the model experiments were 2.8 kW, 11.18 kW, and 16.67 kW, respectively. Depending on the direction of traffic flow, the implementation of longitudinal ventilation in the asymmetric V-shaped tunnel may be carried out on the side with a small slope or on the side with a large slope. The experimental scenarios are shown in

Table 1. Experimental scenarios.

Longitudinal Ventilation on the Small Slope Side			Longitudinal Ventilation on the Large Slope Side
Scenario Number	Fire HRR	Slope Combination	Scenario Number	Fire HRR	Slope Combination
S-1	2.8 kW	1–3%	L-1	2.8 kW	1–3%
S-2		1–5%	L-2		1–5%
S-3		1–7%	L-3		1–7%
S-4		3–5%	L-4		3–5%
S-5		3–6%	L-5		3–6%
S-6		3–7%	L-6		3–7%
S-7	11.18 kW	1–3%	L-7	11.18 kW	1–3%
S-8		1–5%	L-8		1–5%
S-9		1–7%	L-9		1–7%
S-10		3–5%	L-10		3–5%
S-11		3–6%	L-11		3–6%
S-12		3–7%	L-12		3–7%
S-13	16.77 kW	1–3%	L-13	16.77 kW	1–3%
S-14		1–5%	L-14		1–5%
S-15		1–7%	L-15		1–7%
S-16		3–5%	L-16		3–5%
S-17		3–6%	L-17		3–6%
S-18		3–7%	L-18		3–7%

. “S” refers to the scenarios where longitudinal ventilation is applied on the small slope side, and “L” means that the longitudinal ventilation is implemented on the side with a large slope.

4. Results and Discussions

Figure 5 shows the smoke flow at the fire source when longitudinal ventilation is applied on a small slope side at the critical ventilation velocity. As can be seen from the figure, the smoke backflow upstream of the fire source is successfully prevented.

Figure 6a,b present the changes in critical ventilation velocity under different slope combinations and fire HRRs when longitudinal ventilation is applied from the side with a large slope and from the side with a small slope, respectively. It can be found from the figure that regardless of whether longitudinal ventilation is implemented from the large slope side or the small slope side, the critical ventilation speed increases with the increase in the fire heat release rate. For the same fire size and slope configuration, the critical ventilation speed for longitudinal ventilation implemented from the large slope side is much larger than that for longitudinal ventilation implemented from the small slope side. This is because when longitudinal ventilation is implemented from the side with the large slope, greater thermal pressure must be overcome in order to effectively control the smoke backflow.

Figure 7 shows the effects of the slope of the large slope side on the critical ventilation speed under different fire HRRs. It can be observed that when longitudinal ventilation is implemented from the side with the small slope, the critical ventilation speed decreases with the increase in the slope on the large slope side. When longitudinal ventilation is implemented from the large slope side, the critical ventilation speed increases as the slope of the large slope side increases. This is because when longitudinal ventilation is implemented from the small slope side, the thermal pressure difference on both sides of the slope change point promotes smoke backflow toward the fire source. Moreover, as the slope difference increases, the thermal pressure difference gradually increases, causing the critical ventilation speed to gradually decrease. On the other hand, when ventilation is applied from the large gradient side, the direction of the thermal pressure difference between the large and small slope sides opposes the longitudinal airflow, requiring a higher airflow velocity to contain the smoke at the fire source and prevent backflow.

Figure 8 presents a comparison of the critical ventilation speed when longitudinal ventilation is implemented from the large slope side at a slope of 5% and the critical ventilation speed in a single-slope tunnel with a 5% gradient when vehicles are moving downhill. As shown in the figure, due to the presence of the slope on the small gradient side and the influence of local resistance at the slope change point, the critical ventilation speed for longitudinal ventilation implemented on the large slope side of the asymmetric V-shaped tunnel is greater than that of the single-slope tunnel. Figure 9 shows a comparison of the critical ventilation velocity when longitudinal ventilation is implemented on the small slope side with a slope of 1% and the critical ventilation speed in a single-slope tunnel with a 1% gradient when vehicles are moving downhill. The results indicate that when the slope difference on both sides of the slope change point is about 4%, the critical ventilation speed for ventilation for implementing longitudinal ventilation on the small slope side is equivalent to that of a single-slope tunnel with a slope of 1%. When the slope difference on both sides of the slope change point is greater than 4%, the critical ventilation speed when longitudinal ventilation is implemented on the small slope side is less than that of a single-slope tunnel with the same slope. When the slope difference is less than 4%, the critical ventilation speed for implementing longitudinal ventilation on the small slope side is greater than that of a single-slope tunnel with the same slope. This is mainly because when the slope difference on both sides of the slope change point is large, the thermal pressure difference between the two sides plays a dominant role. This pressure difference causes more smoke to flow toward the large slope side, thereby reducing the critical ventilation velocity required on the small slope side compared to that of a single-slope tunnel. When the slope difference is less than 4%, the local resistance at the slope change point becomes the primary factor. In this case, a higher airflow velocity is required to prevent smoke backflow compared to that in a single-slope tunnel, resulting in a higher critical ventilation velocity.

Let k_l denote the ratio of the critical ventilation velocity under longitudinal ventilation from the large slope side to that of a single-slope tunnel with the same gradient, and let k_s be the corresponding ratio for ventilation from the small slope side. Then, the critical ventilation speed for a V-shaped tunnel—denoted as v_cVl when ventilated from the large slope side and v_cVs when ventilated from the small slope side—can be expressed, respectively, as follows:

$$v_{cVl}=k_l{v}_{cl}$$

(8)

$$v_{cVs}=k_l{v}_{cs}$$

(9)

where v_cl is the critical ventilation speed of a single slope tunnel with the slope the same as that of the large slope in a V-shaped tunnel, m/s; v_cs is the critical ventilation speed of a single-slope tunnel with the slope the same as that of the small slope in a V-shaped tunnel, m/s.

Figure 10 shows the variation of the correction coefficient k_l for the large slope side with the slope difference on both sides of the slope change point. It can be seen from the figure that k_l increases with the increase in the slope difference. Through data fitting, k_l can be expressed as follows:

$$k_l=0.045\Delta i+1.189\hspace{1em}{\mathrm{R}}^2=0.982$$

(10)

Figure 11 shows the variation of the correction coefficient k_s for the small slope side with the slope difference on both sides of the slope change point. It can be seen from the figure that k_s decreases with the increase in the slope difference. Through data fitting, k_s can be expressed as follows:

$$k_s=-0.1\Delta i+1.339\hspace{1em}{\mathrm{R}}^2=0.995$$

(11)

Based on the above correction coefficients, the critical ventilation speed in an asymmetric V-shaped tunnel can be calculated by the following equations.

(1)

For critical ventilation speed from the small slope side, v_cVs can be calculated as follows:

$$v_{cVs}=(-0.061\Delta i+0.811)(1+0.037{i_s}^{0.8}){[{\displaystyle \frac{ghQ}{{\rho }_0{c}_{p}A{T}_f}}]}^{1/3}$$

(12)

(2)

For critical ventilation speed from the large slope side, v_cVl can be calculated as follows:

$$v_{cVl}=(0.028\Delta i+0.72)(1+0.037{i_l}^{0.8}){[{\displaystyle \frac{ghQ}{{\rho }_0{c}_{p}A{T}_f}}]}^{1/3}$$

(13)

The relative errors obtained by comparing the critical ventilation speed calculated by Equations (12) and (13) with the experimental values are shown in

Table 2. Relative errors between the calculated critical ventilation speed and the experimental results.

Fire HRR	Slope Composition	Relative Error of the Critical Ventilation Speed from Small Slope Side	Relative Error of the Critical Ventilation Speed from Large Slope Side
2.28 kW	1–3%	−0.13%	2.85%
	1–5%	−9.83%	4.07%
	1–7%	−4.56%	−4.85%
	3–5%	−8.51%	−5.03%
	3–7%	−5.25%	−9.02%
11.18 kW	1–3%	1.63%	4.05%
	1–5%	1.17%	7.15%
	1–7%	6.75%	4.05%
	3–5%	4.77%	−2.94%
	3–7%	6.31%	−8.59%
16.67 kW	1–3%	1.54%	5.63%
	1–5%	−3.30%	9.66%
	1–7%	1.91%	2.69%
	3–5%	6.69%	−0.38%
	5–7%	1.61%	−5.90%

, where $\gamma =(v_{cp}-v_{ce})/v_{ce}$. As can be seen from the table, all errors are within 10%, meeting the requirements for engineering application.

5. Conclusions

The critical ventilation speed when longitudinal ventilation is implemented in an asymmetric V-shaped tunnel under the influence of different fire HRRs and slope compositions when the fire source is located at the slope change point were investigated through small-scale model experiments. The following conclusions can be obtained:

(1)

The critical ventilation speed in the V-shaped tunnels increases with the rise in the heat release rate of fire.

(2)

For the same fire power and slope composition, the critical ventilation speed when longitudinal ventilation is implemented from the large slope side is much larger than that when longitudinal ventilation is implemented from the small slope side. When longitudinal ventilation is implemented from the side with the small slope, the critical ventilation speed decreases as the slope on the side with large slope increases. When critical ventilation speed is implemented on the large slope side, the critical ventilation speed increases as the slope of the large slope side increases.

(3)

Due to the influence of local resistance at the slope change point and the thermal pressure difference caused by the asymmetric slopes on both sides, when longitudinal ventilation is applied from the small slope side, there is a critical slope difference compared with the critical ventilation speed of the single-slope tunnel. Greater than this slope difference, the critical ventilation speed on the small slope side is less than that in the single-slope tunnel with same slope; conversely, the critical ventilation speed on the small slope side is greater than that in the single-slope tunnel. When longitudinal ventilation is applied from the side with a large slope, the critical ventilation speed is greater than that of a single-slope tunnel with the same slope.

(4)

Based on theoretical analysis and small-scale experimental results, the empirical equations of the critical ventilation speed in V-shaped tunnels were obtained as follows:

(a)

For critical ventilation speed from the small slope side:

$$v_{cVs}=(-0.061\Delta i+0.811)(1+0.037{i_s}^{0.8}){[{\displaystyle \frac{ghQ}{{\rho }_0{c}_{p}A{T}_f}}]}^{1/3}$$

(b)

For critical ventilation speed from the large slope side:

$$v_{cVl}=(0.028\Delta i+0.72)(1+0.037{i_l}^{0.8}){[{\displaystyle \frac{ghQ}{{\rho }_0{c}_{p}A{T}_f}}]}^{1/3}$$

The findings of this study are applicable to asymmetrical V-shaped tunnels with slope combinations ranging from 1% to 7% on both sides of the slope change point. There are many factors influencing the critical ventilation speed in V-shaped tunnels. Besides the composition of the slope and the fire HRR, the location of the fire source and the length of the tunnel also have a significant impact. Further theoretical analysis and related experimental research on the critical ventilation velocity and smoke flow characteristics within V-shaped tunnels will be continued in subsequent studies.