Performance optimisation and predictive modeling of smoke control in asymmetrical V-shaped tunnels: Synergistic effects of air curtains and side-wall extraction on temperature and smoke propagation

Abstract

Controlling smoke propagation in asymmetrical V-shaped tunnels remains a formidable challenge, particularly at slope transitions where buoyancy-driven stack effects often compromise traditional ventilation strategies. This study proposes and optimizes a synergistic smoke control system that integrates side-wall extraction with an active air curtain barrier. Using Fire Dynamics Simulator (FDS), a comprehensive parametric analysis was conducted under varying fire loads (5–15 MW) and geometric configurations, specifically targeting the critical scenario of a 1% fire-side and 3% non-fire-side gradient. The results demonstrate that the proposed system significantly outperforms standalone extraction, effectively confining smoke to the fire source side and reducing peak ceiling temperatures. Through sensitivity analysis, jet velocity and injection angle were identified as the dominant control parameters, with an optimized configuration (2 m/s at 15°) achieving maximum confinement efficiency. Crucially, based on dimensionless analysis, predictive correlations are proposed for the ceiling-level temperature rise as functions of the lateral extraction velocity and air-curtain parameters, showing good agreement with simulations. These predictive models provide a robust theoretical tool for fire safety engineering, offering practical guidance for designing resilient smoke control systems in complex V-shaped underground infrastructures.

Practical application

This study provides building services engineers and fire safety consultants with a validated smoke control strategy for complex asymmetrical V-shaped tunnels. By integrating side-wall extraction with optimized air curtains, professionals can effectively prevent smoke backlayering at critical slope transitions. The research defines optimal design parameters—specifically identifying jet velocity and angle as primary control factors—offering a more space-efficient and cost-effective alternative to traditional oversized longitudinal ventilation. The proposed dimensionless correlations serve as a direct technical reference for sizing extraction systems, ensuring enhanced life safety and structural protection in modern underground infrastructure design.

Keywords

V-shaped tunnel lateral smoke extraction air curtain smoke extraction effectiveness maximum temperature

Introduction

The rapid expansion of road tunnel networks in both China and the United Kingdom has brought the critical issue of fire safety to the forefront of infrastructure management. In China, the scale of construction is unprecedented; as shown in Figure 1, the cumulative total length of highway tunnels reached 32,596.7 km by the end of 2024, representing a year-on-year increase of 2364.9 km compared to 2023. Road tunnels currently dominate the national network, accounting for 54.93% of the total mileage.^1,2 Similarly, the UK maintains a vital tunnel infrastructure supporting high-density traffic. While the growth in the UK is more focused on the refurbishment of existing tunnels, both regions face a corresponding boost in the frequency of fire incidents, a trend that is further illustrated by the data in Figure 1.

Figure 1.

Total number and length of highway tunnels in China from 2012 to 2022.

As the scale of tunnel operations expands, the risk profile associated with vehicle-related fires becomes more pronounced. As presented in Table 1, recent statistics on typical tunnel fire incidents reveal that the vast majority of these accidents are directly linked to vehicle dynamics, such as fuel leaks or mechanical failures. This mirrors safety concerns in the UK, where modern fire loads necessitate robust smoke control. The historical data summarized in Table 1 underscores the urgency for advanced prevention and control measures, particularly for complex geometries.

Table 1.

Fire smoke characteristics of complex structure tunnels.

Year	Description of the event	Cause	Tunnel type/length
2022	Engine spontaneous combustion in the Maoliling Tunnel, Ningbo-Yantai-Wenzhou Expressway	Mechanical breakdown	Motorway tunnel
2023	Vehicle spontaneous combustion in the Nanjing Xuanwu Lake Tunnel (near the V-shaped structure)	Circuit fault	City Tunnel
2023	G15 Shenhai Expressway Maoliling Tunnel lorry head on fire	Cargo friction	Motorway tunnel
2024	A truck rear-ended and caught fire in the Yunding Mountain No.1 Tunnel of Sichuan’s S2 Chengba Expressway	Traffic accident	Highway tunnel (long tunnel)
2024	G60 Shanghai-Kunming Expressway Wutong Tunnel vehicle fire	Traffic accident	Motorway tunnel
2024	Fire in a truck at the Yunzhongshan Tunnel, Cangyu Expressway	Vehicle fault	Motorway tunnel

Complex vertical alignments in urban and mountainous corridors often create asymmetric V-shaped profiles where buoyancy-driven flow interacts with slope-induced pressure differences. Prior work has examined back-layering length under natural ventilation, effects of slope composition on point extraction, and critical velocities in branched and T-shaped tunnels,^1–14 with research focusing on how key parameters—such as tunnel configuration (e.g., slope combinations in V-shaped tunnels, branching angles in T-shaped tunnels), smoke extraction methods (natural ventilation or mechanical extraction), and fire source power—influence smoke propagation pathways, temperature distribution, and backflow length. However, for asymmetric V-shaped tunnels with a gentle fire-side slope and a steeper non-fire-side slope, lateral extraction on the fire-side alone may not prevent smoke from crossing the slope-transition point, particularly when the chimney effect favours upslope spread on the non-ignition side.

The objective of this research is to establish a theoretical foundation for fire safety design and risk reduction in specialized tunnel configurations. To clearly present the current state of research and core findings in this field, Table 2 systematically summarises representative studies on fire smoke characteristics in complex-structure tunnels (primarily focusing on V-shaped tunnels, while incorporating T-shaped tunnel research for comparative reference) from relevant literature. Organised by tunnel type and research content, this study provides a foundation for subsequent in-depth analysis of smoke propagation mechanisms in V-shaped tunnel fires.

Table 2.

Fire smoke characteristics of complex structure tunnels.

Tunnel type	Research contents	Author and year
V-shaped tunnel	(Force characteristics of flue gas in double-slope coupled V-shaped tunnel)Under natural ventilation and chimney effect, the influence of slope (5%–15%), fire source and distance to the variable slope point on fire wind pressure was analyzed. It was found that when the slope is>7%, the length of smoke reflux is not sensitive to the change of fire source position; the parallel movement law of the upstream smoke layer and roof plate was revealed.	Chen et al. (2022).⁴
V-shaped tunnel	(Smoke return length prediction)The concept of equivalent longitudinal wind speed under natural ventilation is proposed, and it is found that the length of smoke reflux decreases with the increase of heat release rate, and a semi-empirical prediction formula based on the sine difference of slope on both sides is established.	Jiang et al. (2022).⁵
T-shaped and curved tunnel group	(Temperature and smoke diffusion in large underground space under natural ventilation)Analyze the influence of large space such as plant and transformer room on airflow, and evaluate the smoke hazard and evacuation path optimization under different fire source locations.	Huang et al.(2022).⁸

In accordance with British Standard CD 109 (a core industry standard within the Design Manual for Roads and Bridges, DMRB, published by National Highways), the longitudinal gradient of motorway tunnels should be kept as low as practicable and must not exceed 3%, so as to ensure road safety and the reliability of the ventilation system. While steeper gradients up to 5% or 6% may only be permitted in exceptional topographical circumstances under a rigorous safety risk assessment, research indicates that even within the recommended 3% limit, gradient significantly dictates smoke propagation patterns in V-shaped configurations. Specifically, in asymmetrical V-shaped tunnels, smoke tends to traverse the slope transition point toward the non-fire side when the fire-side gradient is low (e.g., 1%), as the buoyancy-driven stack effect is insufficient to counteract the expansion of smoke.¹⁵ Conversely, a steeper gradient on the non-fire side facilitates smoke spread due to the enhanced chimney effect.^3,16 Therefore, configurations with a gentle fire-side slope and a steep non-fire-side slope represent the most critical fire safety scenarios, requiring integrated smoke control measures to effectively manage propagation across the transition point. In order to investigate the most unfavourable conditions for smoke extraction in V-shaped tunnels, the slope on the fire side in this study has been set to the gentle gradient most commonly found in urban and mountain road tunnels, namely 1%. The slope on the non-fire side is steeper and has been set at the upper limit of the standard design range, namely 3%.

Air-curtains form a high-momentum planar jet that can deflect and dilute hot gases, and have been studied for tunnel smoke confinement and aerodynamic sealing.¹⁷ Their operating principle involves creating a high-velocity airflow wall to block smoke and heat. According to studies on the smoke control mechanisms of air curtains in tunnel fires, the air curtain jet angle, curtain thickness, and jet velocity influence their effectiveness.^18,19

This study investigates the impact of integrating lateral smoke extraction with air curtain technology in the crown region of V-shaped tunnels on smoke dispersion and peak temperature reduction. Fire smoke behaviour and peak temperature variations within an asymmetrical V-shaped tunnel were assessed through FDS simulations. Based on these findings, a model was developed to predict peak temperatures within asymmetrical V-shaped tunnels under the coupling operation of lateral smoke extraction systems and air curtains. This study evaluates the synergistic effects of lateral wall smoke extraction and gradient transition zone air curtains, quantifies parameter sensitivity, and establishes a predictive model for roof temperatures under extreme fire conditions.

As can be seen from the findings in Table 2, most existing studies on fires in V-shaped tunnels have focused on the patterns of smoke propagation under natural or longitudinal ventilation. They have only analysed the effect of gradient on the length of smoke backflow and have not addressed the optimisation of active smoke control systems. A few studies have investigated lateral smoke extraction in V-shaped tunnels, but none have considered the synergistic smoke control effect of air curtains and lateral wall exhaust. The research explores the combined efficacy of air curtain systems and lateral smoke extraction in controlling gas diffusion beneath the roof of V-shaped tunnels and reducing peak temperatures. Through FDS simulation analysis of fire dynamics in asymmetric V-shaped tunnels, a comprehensive roof temperature prediction model was developed for integrated system coordination. The study focused on quantifying the synergistic effects and parameter sensitivity of sidewall smoke extraction and gradient transition zone air curtains under extreme fire conditions. This study also established a dimensionless prediction model for the maximum temperature rise in asymmetric V-shaped tunnels, incorporating the synergistic effects of air curtains, which fills the gap in existing models that neglect the coupling interaction between air curtains and lateral smoke exhaust systems.

Numerical modelling

Setup of the physical model

Figure 2 depicts the asymmetrical V-shaped tunnel model established for this study. The specific dimensions and other details of the asymmetric tunnel are shown in Table 3, consistent with the typical geometry derived from tunnel surveys in China. The slope φ on the fire side was set at 1% over a length of 100 m, while the slope α on the non-fire side was set at 3% over a length of 100 m. An air curtain was positioned midway along the tunnel at the transition point (x = 100 m). Smoke extraction vents were installed along the sidewalls of the tunnel. The coordinated action of smoke containment via the air curtain and smoke extraction through the side vents was employed to prevent smoke propagation to the non-fire side of the tunnel.

Figure 2.

Tunnel model with the layout of measurement points.

Table 3.

Dimensions and other details of the asymmetric tunnel.

Tunnel geometry	Ambient temperature(°C)	Tunnel material	Density(kg/m³)	Specific heat(kJ/(kg·K))	Thermal conductivity(W/(m·K))
200m(L)×8m(W)×5m(H)	20	Concrete	2280	1.04	1.8

Multiple measurement points were deployed throughout the simulation experiment to monitor temperature and the velocity vector. Measurement points for temperature were placed along the centreline of the tunnel at 5-m intervals. A temperature measurement point was installed directly above the fire source at a height of 4.8 m to collect important data on peak temperatures at the top of the tunnel and temperature distribution, while also monitoring temperature variations on either side of the fire origin. Furthermore, thermocouple strings were positioned 10 m from the fire source and spaced 0.5 m apart across the height range of 0–5 m from ground level, in order to evaluate mesh density. Temperature and visibility slices were configured at Y = 4 m to enhance the analysis of the results. The configuration of the measurement points and slices is illustrated in Figure 2.

To replicate natural ventilation, both ends of the tunnel were modeled with open boundary conditions. The smoke duct and air curtain were defined as ‘vent’ boundaries to simulate variable-speed fan operation, specifically set to ‘exhaust’ and ‘supply’, respectively. A 1 m × 1 m square fire source was centred between the two extraction fans on the left ramp.

The gravity decomposition method was used to construct the tunnel gradient, enhancing the ventilation and natural airflow at both ends. This method decomposes the force of gravity into horizontal and perpendicular components based on gradient variations, enabling the slope to be modelled more precisely. This approach reduces the number of mesh elements required, improves computational efficiency, and significantly mitigates the impact of sudden angle changes at gradient transitions, all while maintaining simulation accuracy.

Fire scenario setting

Under the operating conditions, the space between the smoke exhaust outlets is set to 40 m. Five distinct smoke extraction rates are considered: 43,200, 64,800, 75,600, 86,400, and 108,000 m³/h. The dimensions of each smoke exhaust outlet are set at 3 m × 1 m. Consequently, five smoke extraction velocities were established: 4, 6, 7, 8, and 10 m/s. This velocity range covers the critical threshold for effective smoke confinement in tunnel fire scenarios, which has been widely verified in existing tunnel fire smoke control research.

The air curtain was positioned at the gradient change point midway along the tunnel, and the air curtain jet velocity was set to one of four parameters ranging from 1 m/s to 4 m/s. The air curtain jet angle was adjusted to four parameters: 0°, 15°, 30°, and 45°. This range is the most widely applied parameter interval in tunnel fire air curtain smoke control research, covering full scenarios from vertical downward to inclined jets, with its rationality fully verified by classical studies in the field.²⁰The air curtain length was set to 8 m, and the thickness was adjusted to three parameters: 0.5, 1, and 1.5 m. This thickness range refers to the 0.2–2 m general scope widely adopted in published research and practical tunnel engineering,¹⁶ comprehensively balancing conventional tunnel fan air supply capacity, on-site construction space constraints and long-term system operating energy consumption.The HRR was set to three scenarios: 5, 10, and 15 MW. This setting covers over 90% of common vehicle fire types in highway tunnels, follows the conservative design principle for tunnel fire safety, and the established dimensionless analysis framework is extendable to ultra-high HRR scenarios such as heavy goods vehicle fires.²¹

The total simulation duration for all working conditions is set to 300 s, consistent with the conventional setting in mainstream tunnel fire numerical simulation research, covering the critical time window for personnel evacuation and initial fire rescue. Time-domain analysis of all operating conditions indicates that the fire flow field reaches a quasi-steady state between 120 and 200 s after ignition. All simulation results presented in this paper are calculated based on average temperature values over the 150–200-s period, which corresponds to a stable quasi-steady-state condition.

The following experiments were conducted to investigate the coupled effects between lateral smoke exhaust ventilation and the air curtain. The variables included the HRR, lateral smoke exhaust vent velocity, air curtain jet angle, thickness and jet velocity. Table 4 presents the detailed experimental conditions.

Table 4.

Operating conditions and settings.

Operating mode	Heat release rate (MW)	Tunnel slope (%)	Exhaust port size (m)	Side ventilation airflow speed (m/s)	Jet speed from the air curtain (m/s)	Jet angle of air curtain (°)	Air curtain thickness (m)
A-1∼48	5,10,15	−1%(fire side)/3%(Non-fire side)	3 $\times$ 1	4,6,8,10	1,2,3,4	0	1.0
A-49∼96					1	0,15,30,45	1.0
A-97∼132					1	15	0.5,1.0,1.5
B-1∼20	15			4,6,7,8,10	1,2,3,4	0	1.0
B-21∼40	15			4,6,7,8,10	3	0,15,30,45	1.0

Grid independence assessment

When conducting simulations using FDS fire numerical simulation software, determining the number of grid cells is a critical step that directly impacts the accuracy of the results. An insufficient number of grid cells will lead to inaccurate simulation outcomes, whereas an excessive number not only increases simulation time but also yields only marginal improvements in precision. We calculate the characteristic fire diameter D^* using the following equation.

D^{*} = {(\frac{Q}{ρ_{0} \sqrt{g} T_{0} C_{p}})}^{2 / 5}

(1)

The symbols are defined as follows: D^* is the characteristic fire source diameter (in meters);Q denotes the fire heat release rate (in kW); ρ₀ is the density of ambient air (in kg/m³), typically assumed to be 1.204 kg/m³; T₀ indicates the ambient air temperature (in K), commonly approximated as 293 K, C_p refers to the specific heat capacity of ambient air (in kJ/(kg·K)), which is generally taken as 1.005 kJ/(kg·K), and g signifies gravitational acceleration (in m/s²), typically accepted as 9.8 m/s².

The equation indicates that a larger Q yields a greater characteristic diameter D^*, consequently increasing the required number of computational grids. Based on this relationship, selecting a 5 MW HRR and Technology (NIST), which recommend a grid size between 0.06D^* and 0.25D^* for accurate simulations, the corresponding valid range is 0.114 m to 0.457 m.

Therefore, mesh sizes ranging from 0.1 m to 0.5 m were tested at a slope of −1/3% and a lateral extraction velocity of 10 m/s (parameters in Table 5). Figure 3 displays the temperature distribution 20 m downstream. As the mesh size decreased, the temperature curves gradually converged, with the 0.1 m and 0.2 m meshes exhibiting identical trends. Following a trade-off between computational efficiency and accuracy, the 0.2 m mesh was selected.

Table 5.

Operating conditions for the grid independence analysis.

Order number	Tunnel geometry and gradient (%, m)	Grid size (m)	Side smoke extraction volume (m³/s)	Fire source heat release power (MW)
1	200 m(L) × 8 m(W) × 5 m(H) −1%(fire side)/3%(Non-fire side)	0.1 × 0.1	30	5
2		0.2 × 0.2
3		0.3 × 0.3
4		0.5 × 0.5

Figure 3.

Effect of mesh size on vertical temperature distribution.

Results and discussion

Optimal parameters of the air curtain for gas control

In scenarios involving fires within asymmetrical V-shaped tunnels, where the fire source on the burning side exhibits high power output and the slope is gentle, a standalone lateral smoke extraction system on the burning side often proves insufficient to prevent smoke from traversing the gradient change point and spreading towards the non-burning slope. The deployment of the air curtain at the apex of the gradient change point can effectively suppress smoke propagation and produce a significant cooling effect at the tunnel roof impacted by the fire.^22,23 This method is particularly effective in lowering temperatures on the non-fire slope side, thereby enhancing tunnel fire safety.^20,24,25 The experiment positioned the air curtain at the mid-slope transition point of an asymmetrical V-shaped tunnel. The influence of key air curtain parameters on the maximum controlled gas temperature was investigated under varying fire source power levels and lateral smoke extraction velocities. Through a comprehensive comparison, the optimal parameter combination was identified.

Optimal air curtain jet velocity

Figures 4–6 illustrate the smoke propagation control diagrams for tunnel environments under three fire source power levels (5, 10, and 15 MW), a gradient of 1/3%, and varying lateral smoke extraction velocities. Figure 7 shows the temperature distribution of the tunnel roof during a stable quasi-steady-state phase under the same operating conditions. By comparing smoke propagation diagrams under varying air curtain jet velocities, the optimal operating conditions for air curtain jet velocity when different fire source powers and lateral smoke extraction velocities interact within the tunnel are identified.

Figure 4.

Smoke spread diagram for a 5 MW fire source with the combined effects of air curtain and side ventilation.

Figure 5.

Smoke spread diagram for a 10 MW fire source with the combined effects of air curtain and side ventilation.

Figure 6.

Smoke spread diagram for a 15 MW fire source with the combined effects of air curtain and side ventilation.

Figure 7.

Temperature distribution map at the tunnel ceiling at different jet velocities of the air curtain.

Overall, for given fire power and lateral extraction settings, a lower air curtain velocity attenuates its capacity to restrict smoke spread toward the non-fire slope. Enhancing the jet velocity intensifies this suppressing effect until a critical threshold is reached, beyond which smoke is successfully confined to the burned slope. Similarly, within a range, raising the jet velocity improves cooling on the fire slope side; however, beyond a certain point, the thermal benefits plateau. The detailed analysis is presented below.

At Q = 5 MW and v = 4 m/s, an v_air of 1 m/s suffices to suppress smoke on the fire slope. Increasing v_air from 1 to 4 m/s does not significantly alter the ceiling temperature distribution, indicating that v_air = 1 m/s already provides adequate cooling.

Under a 10 MW fire scenario, the system configuration presented in Figure 4 (v = 4 m/s and v_air = 1 m/s) did not succeed in containing smoke propagation to the unignited side slope. Effective control is achieved either by increasing the extraction velocity to 6 m/s while maintaining v_air at 1 m/s, or by raising v_air to 2 m/s at a constant extraction rate. Regarding cooling, lower extraction rates see a significant temperature drop when v_air increases from 1 to 2 m/s, but further increase to 4 m/s yields minimal change. Under high extraction (6 m/s), overall temperatures are lower, but varying v_air from 1 to 4 m/s has no discernible thermal impact. This suggests the optimal cooling velocity has reached its minimum. Consequently, for a 10 MW fire, the effective v_air decreases as the v increases.

When the fire source power increases to 15 MW, the optimal operating condition is shown in Figure 5 (v = 6 m/s and v_air = 1 m/s) failed to suppress smoke propagation towards the non-fire slope side. However, increasing the v to 8 m/s reduces v_air to 1 m/s while controlling smoke spread towards the unignited side. However, at the minimum lateral smoke extraction velocity of v = 4 m/s, increasing the v_air to 2 m/s effectively suppresses smoke propagation towards the non-fire slope. This phenomenon mirrors that observed at a 10 MW HRR. Regarding cooling efficacy, when v is low, the cooling effect diminishes significantly when v_air exceeds 2 m/s. Notably, under these conditions, the minimum optimal cooling v_air is obtained by increasing v to 8 m/s.

Furthermore, examining the smoke extraction effectiveness in Figures 4–6, it is evident that under the same smoke extraction volume, an increase in the air curtain jet velocity weakens the extraction of smoke from the tunnel. This phenomenon is likely driven by the entrainment effect: a higher jet velocity increases the amount of ambient air entrained by the rising fire plume, which in turn increases the theoretical smoke exhaust volume required. Consequently, maintaining the air curtain jet velocity within a reasonable threshold is critical. If the velocity is too high, it not only compromises lateral extraction but also induces turbulence and the “smoke logging” phenomenon, reducing visibility for evacuees even if temperatures fall. According to relevant safety standards, the critical visibility for safe evacuation during a tunnel fire is 10 m. As illustrated by the visibility profiles at a human breathing height of 1.6 m under the most unfavourable 15 MW fire scenario (Figure 8), visibility gradually decreases as the air curtain jet velocity increases. When v_air is ≤ 2 m/s, visibility in the affected areas on the fire side remains around 10 m. However, when v_air increases to 3–4 m/s, the high-velocity jet intensifies turbulent mixing and causes the smoke layer to settle. This causes visibility in localised areas to drop completely below the 10 m safety threshold.

Figure 8.

Visibility slices at different air curtain jet velocities(z = 1.6 m).

In summary, while the optimal is positively correlated with fire source power Q and negatively correlated with lateral smoke exhaust velocity, it must be strictly capped to prevent adverse entrainment and smoke settling. Under extreme fire conditions in the 1/3% gradient V-shaped tunnel (extremely high Q, extremely low v), a v_air of 2 m/s is sufficient to control smoke propagation. This parameter achieves optimal smoke containment and ceiling temperature reduction while preserving lateral extraction efficiency and avoiding dangerously low visibility at the 1.6 m human breathing height. Therefore, 2 m/s is identified as the optimal threshold velocity for the air curtain to effectively suppress smoke spread to the non-fire side of the V-shaped tunnel.

Optimal jet angle of the air curtains

Figure 9 illustrates the impact of different air curtain flow velocities on visibility and velocity fields, while Figure 10 schematically presents the resultant airflow patterns. The air curtain modifies the flow direction at the slope transition, thereby affecting smoke dynamics and thermal distribution. Enhancing the jet angle improves its synergy with lateral extraction, accelerating airflow near the fire to remove heat and reduce temperatures. To this end, the study focused on the jet angle α (angle from vertical; α = 0° is vertically downward). Comparisons of smoke propagation and ceiling temperatures at t = 200 s across angles identified the optimal α for smoke control and cooling (Figures 11, 12 and 13).

Figure 9.

Visibility and velocity slices at different air-curtain flow velocities.

Figure 10.

Streamline diagram.

Figure 11.

Schematic of the effect of jet angle variation on smoke spread under different fire source power levels and side-wall exhaust air velocities(t = 200 s).

Figure 12.

Schematic of the effect of air curtain jet angle variation on smoke spread.

Figure 13.

Map of the temperature distribution on the tunnel ceiling at different air curtain jet angles.

Increasing the air curtain jet angle significantly suppresses smoke crossing the slope transition point under various fire source power and side smoke extraction combinations. Furthermore, as the α increases, the deflection of smoke towards the α direction at the slope transition point progressively intensifies. As illustrated in Figure 12, increasing α (α₀ < α₁ < α₂) progressively amplifies the shape deflection of the smoke plume. As illustrated in Figure 13, when the lateral smoke extraction velocity is set to its minimum value v = 4 m/s, the maximum temperature within the zone between the tunnel fire source and the air curtain (50–100 m) exhibits a cooling trend as α increases. The effect of α on temperature diminishes with increasing fire source power but intensifies with higher air curtain jet velocities. The specific findings are as follows:

The influence of the air curtain jet angle varies with fire power. For a 5 MW Q at v_air = 1 m/s, the tunnel’s maximum temperature decreases significantly as the jet angle increases. Conversely, for a 10 MW fire with 6 m/s lateral extraction and v_air = 1 m/s, smoke control is angle-dependent: it fails at 0° but succeeds at 15°. Regarding cooling under these 10 MW conditions, the maximum temperature is insensitive to the angle at v_air = 1 m/s, yet shows a marked decrease with increasing angle at v_air = 2 m/s.

For a 15 MW fire, the smoke containment outcome mirrors the 10 MW case. With either 6 m/s or 4 m/s lateral extraction (and v_air = 1 m/s), smoke spreads at a 0° angle but is effectively contained at 15°. Notably, regarding ceiling cooling for the 15 MW fire, the angle’s influence on the maximum temperature becomes progressively stronger as v_air rises from 1 to 3 m/s. While increasing the angle from 0° to 15° enhances peak temperature reduction, the cooling benefit diminishes when the angle is further increased to 45°.

In summary, altering the air curtain jet angle exerts a pronounced effect on smoke propagation, whereas its influence on peak temperatures is moderate. This impact diminishes as the fire source power increases and intensifies with higher air curtain jet velocities. Under extreme V-shaped tunnel conditions, where Q reaches its maximum of 15 MW and v is at its minimum of 4 m/s, the v_air is at its minimum of 1 m/s, setting α to 15° is sufficient to control smoke propagation towards the unburned side. Consequently, variations in the air curtain jet angle have a negligible effect on the maximum temperature within the tunnel due to the relatively low v_air.

Therefore, if only smoke control effectiveness and cost control are considered, the α can be set to 15° when the air curtain velocity is set to v_air = 1 m/s in actual engineering applications. If both cooling and smoke control effects are comprehensively considered, α can be set to 15° when v_air is set to 2 m/s in actual engineering applications.

Optimal air curtain thickness

The analysis in the “Optimal jet angle of the air curtains” section indicates that altering the jet angle can further enhance the coupling effect between the air curtain and lateral smoke extraction, with the air curtain jet angle exerting a significant influence on smoke propagation within the tunnel. The air curtain thickness d was varied as a variable to refine the investigation. The lateral smoke extraction velocity was set at 4 m/s, the v_air at 1 m/s, and the air curtain jet angle was fixed at 15° under different fire source power levels. Under these extreme conditions, three distinct air curtain thicknesses d (0.5, 1.0, and 1.5 m) were employed, thereby altering the effective area of the air curtain jet. By comparing local smoke cross-section diagrams (tunnel sections 0–130 m) and temperature distribution map, the optimal air curtain thickness was identified.

As shown in Figures 14 and 15, under varying fire source powers, with constant v, v_air, and α, increasing air curtain thickness yielded no discernible difference in smoke propagation behaviour or ceiling temperature variation. Consequently, the air curtain thickness may be disregarded in terms of its impact on tunnel temperatures. For practical engineering applications, the air curtain thickness may be set to a default value that aligns with project conditions and cost considerations. This finding holds practical value for real-world engineering projects.

Figure 14.

Temperature distribution at the tunnel roof under different air curtain thicknesses(t = 200 s).

Figure 15.

Comparison of the influence of air curtain thickness on smoke spread under different fire source power(t = 200 s).

In summary, the optimal air curtain configuration for extremely hazardous asymmetric V-shaped tunnels (fire-side slope 1%, non-fire side 3%) is a v_air of 2 m/s, a deflection angle of 15°, and a thickness of 1 m. This configuration not only effectively confines fire and gas to the combustion slope but also markedly lowers the peak temperature rise at the crown of the tunnel, thereby significantly improving structural safety. Consequently, these operational parameters provide a key reference for designing integrated smoke and temperature control systems in V-shaped slope tunnels.

Safety performance analysis of system failure

To address the issue of side-mounted smoke extraction fan failure, we selected the most unfavourable operating conditions: under fire conditions with a heat release rate of 15 MW, we simulated scenarios where a single side-mounted smoke extraction fan failed and where two adjacent smoke extraction fans failed simultaneously, resulting in a 25% and 50% reduction in total smoke extraction capacity, respectively. These represent the most common single-point failure scenarios in engineering practice. The performance comparison results are shown in the Figures 16 and 17, with the dashed box indicating the location of the failed fan. The results demonstrate that in the coordinated system proposed in this study, when the air curtain operates at the optimal configuration (2 m/s, 15°), even if a single smoke extraction fan fails, smoke can still be confined to the fire side, with the peak ceiling temperature rising by only approximately 5%; in the event of simultaneous failure of two adjacent smoke extraction fans, only a negligible amount of smoke crosses the transition point to spread to the non-fire side, with virtually no impact on visibility or ceiling temperature on the non-fire side. Consequently, the addition of the air curtain system significantly enhances the fault-tolerance of the smoke control system, providing redundant safety assurance against smoke extraction system failures, and fully meets the risk assessment requirements for tunnel fire safety design set by the Authority Having Jurisdiction.

Figure 16.

Temperature distribution map of the tunnel roof under different scenarios of failed smoke extraction on the side walls.

Figure 17.

Smoke spread diagram under different lateral exhaust fan Failures(t = 200 s).

Influence factor of air curtain on the cooling effect of the tunnel roof

The maximum temperature rise in a side-ventilated tunnel, T_max (K), is governed by the combined effects of fire heat release rate,Q (kW), the lateral ventilation velocity v (m/s), the ambient air density ρ₀ (kg/m³),the ambient temperature T₀ (K),the specific heat of air at constant pressure C_p (kJ/kg·K), the gravity constant g (m/s²), the tunnel height H_d (m), and the tunnel gradient ω.^3,26–29 Based on Zhang’s research,³⁰ the temperature can be represented as follows:

T_{\max} = f (Q, C_{p}, g, v, ρ_{0}, T_{0}, H_{d}, ω),

(2)

\frac{{Δ T}_{\max}}{T_{0}} = f (\frac{Q}{ρ_{0} C_{p} T_{0} g^{1 / 2} H_{d}^{5 / 2}}, \frac{V}{\sqrt{g H_{d}}}, ω),

(3)

In the formula: g is the gravity constant (m/s²), taken as g = 9.8 m/s²,H_d is the height of tunnel (m); C_p is the specific heat capacity of the environment at constant pressure (kJ/kg·K), taken as C_p = 1.02 kJ/kg·K, ρ₀ is the ambient air density (kg/m³), taken as ρ₀ = 1.2 kg/m³,v is the lateral smoke exhaust velocity (m/s), ω is the slope angle of the V-shaped tunnel.

Through the dimensionless transformation, the following equation is obtained:

\frac{{Δ T}_{\max}}{T_{0}} = f (Q^{*}, V^{*}, ω),

(4)

Here, Q^* denotes the fire source’s dimensionless heat release rate, V^* represents the dimensionless wind speed at the side smoke exhaust outlet, and ω is the dimensionless slope of the V-shaped tunnel.

Deriving from previous studies,^24,28–35 wherein vehicle fires in tunnels can generate heat release rates (HRR) up to 15 MW, this investigation adopted a 15 MW HRR to examine the impact of lateral smoke extraction and air curtains on ceiling temperatures under a severe fire scenario. The gradient of the V-shaped tunnel was not a variable within this research; hence, the dimensionless gradient ω was held constant. With both the dimensionless heat release rate Q^* and ω constant under these defined conditions, equation (5) simplifies to the following form:

\frac{{Δ T}_{\max}}{T_{0}} \sim V^{*},

(5)

This simplified expression demonstrates that, for the prescribed extreme fire scenario and fixed tunnel geometry, the non-dimensional rise in ceiling temperature is principally determined by the non-dimensional lateral ventilation velocity.

Effect of the air curtain jet velocity on the maximum temperature rise

Figure 18 shows the correlation between dimensionless lateral exhaust smoke velocity V^* and dimensionless maximum top temperature ΔT_max/T₀ at various air curtain jet velocities. For varying air curtain jet velocities, the relationship between the maximum thermal gradient in a V-shaped tunnel and the longitudinal ventilation rate can be derived, as presented in equation (6).

\frac{{Δ T}_{\max}}{T_{0}} = A_{1} \cdot \exp (‐ V^{*} / t_{1}) + y_{0},

(6)

In the equations, y₀, A₁, and t₁ are the coefficients.

Figure 18.

Relationship between V^* $[v / {(g H)}^{0.5}$ ] and ΔT_max/T₀.

Based on experimental data fitting, the relationships between the coefficients y₀, A₁, and t₁ and the dimensionless air curtain jet velocity V_air^* can be obtained, as shown in equations (7), (8), and (9). Figure 19 provides a detailed description of the relevant fitting.

y_{0} = 79.64 ‐ 36.79 {V_{a i r}}^{*},

(7)

A_{1} = ‐ 19.54 + 37.25 {V_{a i r}}^{*},

(8)

t_{1} = ‐ 3.34 + 4.36 {V_{a i r}}^{*},

(9)

Figure 19.

Relationship between coefficients y₀, A₁, t₁ and V^*_air.

Substituting the coefficients y₀, A₁, and t₁ into equation (6) yields the theoretical model for the peak temperature rise at the ceiling zone of a V-shaped tunnel governed by the synergistic effect of the air curtain and lateral smoke exhaust facilities when Q = 15 MW and α = 0°, as shown in equation (10).

\frac{{Δ T}_{\max}}{T_{0}} = (‐ 19.54 + 37.25 {V_{a i r}}^{*}) \cdot \exp (‐ \frac{V^{*}}{‐ 3.34 + 4.36 {V_{a i r}}^{*}}) + 79.64 ‐ 36.79 {V_{a i r}}^{*},

(10)

A close correspondence is observed in Figure 20 between the experimentally measured peak temperature rise beneath the roof of the tunnel under various operating conditions and the values predicted by the theoretical model (10).

Figure 20.

Comparison of the predicted and simulated maximum temperature rises.

Role of air curtain jet angle in determining maximum temperature rise

Figure 18 indicates that under the four tested longitudinal ventilation conditions, the effect of the air curtain jet velocity on the main tunnel’s maximum temperature plateaus once it reaches 3.0 m/s, signifying a dynamic equilibrium between the air curtain and longitudinal ventilation flows. Given this plateau, the v_air was fixed at 3.0 m/s to isolate and investigate the specific effect of the α on the temperature distribution. The resulting relationship between the normalized lateral exhaust velocity V^*and the ceiling temperature rise ΔT_max/T₀ across different jet angles is presented in Figure 21. This figure, alongside equation (11), characterizes the connection between the maximum temperature increase in a V-shaped tunnel and the lateral exhaust ventilation for varying air curtain orientations.

\frac{{Δ T}_{\max}}{T_{0}} = B \cdot V^{*} + A_{2},

(11)

In the equation, A₂ and B are the coefficients.

Figure 21.

Correlation between V^*and ΔT_max/T₀.

Based on experimental data fitting, the relationship between coefficients A₂, B and the sine value of the air curtain jet angle sin α can be obtained, as shown in equations (12) and (13). A detailed description of the relevant fitting is provided in Figure 22.

A_{2} = 41.74 \sin^{2} α ‐ 38.41 \sin α + 57.31,

(12)

B = ‐ 39.67 \sin^{2} α + 27.63 \sin α ‐ 7.87,

(13)

Figure 22.

The correlation between coefficients A₂, B and Sin α.

For a fire with a Q of 15 MW and a v_air of 3.0 m/s, a theoretical model for the maximum temperature rise in a V-shaped tunnel under combined lateral ventilation and air curtain action is obtained by incorporating coefficients A₂ and B into equation (13). This model, given in equation (14), quantifies the influence of the air curtain jet angle on the temperature increase.

\frac{{Δ T}_{\max}}{T_{0}} = (‐ 39.67 \sin^{2} α + 27.63 \sin α ‐ 7.87) V^{*} + (41.74 \sin^{2} α ‐ 38.41 \sin α + 57.31),

(14)

Figure 23 demonstrates close alignment between the experimental results and the theoretical formula, which was derived by fitting the maximum temperature rise against various air curtain jet angles under the conditions of a 15 MW fire source and a fixed air curtain velocity of 3.0 m/s.

Figure 23.

Comparison of the predicted and simulated maximum temperature rises.

Conclusion

This research utilized Fire Dynamics Simulator to investigate the combined efficacy of side-wall smoke extraction and an air curtain at the slope transition point in an asymmetric V-shaped gradient tunnel (fire-side slope 1%, non-fire-side slope 3%; combined gradient 1/3%). The simulations aimed to analyze their coupled effects on smoke control and ceiling temperature distribution. Building upon the findings, a predictive model was formulated for the peak ceiling temperature rise under the joint operation of these systems in such tunnel geometries. The main findings are:

(1) Parameter influence and optimal configuration.

The differential impact and optimal values of key air-curtain parameters for fire control in asymmetric V-shaped gradient tunnels were clarified. Under extreme conditions (1% fire-side slope; 3% non-fire-side slope), the configuration that best suppresses cross-slope smoke spread toward the non-fire-side and maximizes roof cooling is a jet velocity of 2 m/s, a jet angle of 15°, and a thickness of 1 m. Among the parameters, jet velocity most strongly affects both smoke propagation and the maximum roof temperature, jet angle primarily affects propagation across the transition point, and thickness exerts a minor influence on both.

(2) Non-monotonic synergy and threshold behaviour.

The synergy between lateral smoke extraction and the air curtain does not follow a simple “more-is-better” rule. For fixed combinations of fire source power and extraction velocity, the smoke-blocking and cooling benefits increase with jet velocity and angle up to a threshold, after which improvements stabilize. Thus, parameter thresholds—rather than maxima—should be matched to realistic operating conditions to balance performance and cost.

(3) Predictive, dimensionless correlations.

A model for predicting the dimensionless maximum temperature rise in asymmetric V-slope tunnels was established from simulations, considering the coupled effects of lateral exhaust and air curtain systems. The model captures the dependence of the maximum temperature on longitudinal/lateral ventilation (via a dimensionless velocity) and air-curtain jet velocity at a fixed heat-release rate (HRR) of 15 MW, as well as on lateral extraction and air-curtain jet angle (with jet velocity held at 3 m/s and HRR = 15 MW). The predicted results show high consistency with the simulation outcomes, indicating a good fit between the maximum temperature and the governing parameters.

In summary, this study elucidates the application methodology and intensity of synergistic smoke and heat control through air curtains and sidewall smoke extraction systems in asymmetrical V-shaped tunnels. It provides validated thresholds and rapid estimation prediction models, while outlining implementation pathways and establishing a practical framework for future validation and dissemination.

The limitation of this study is that the proposed correlations and parameter thresholds originate from numerical simulations conducted under controlled conditions. However, real-world tunnels may exhibit additional complexities, such as variable traffic loads, multi-point fires, dynamic ventilation scenarios, and extreme fire accidents with ultra-high heat release rates from heavy goods vehicles. Furthermore, this study assumes fixed tunnel geometry and material properties; variations in these factors could alter flow patterns and thermal behaviour. It is worth noting that the dimensionless analysis framework and parameter design logic of the synergistic system proposed in this study can be extended to scenarios with higher HRR, and a special study focusing on heavy goods vehicle fires will be carried out in our subsequent work. To validate applicability and refine predictive models for broader engineering scenarios, experimental verification and extended parameter studies are essential—including analyses of transient fire development and multi-hazard interactions in the future study.

Footnotes

ORCID iDs

Bochen Li

Yanfeng Li

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Beijing Natural Science Foundation (Grant No: 8222002).

Declaration of conflicting interests

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

Appendix

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