# The influence of vehicles on smoke propagation in transversely ventilated tunnels

Stefano Lanzini, Cosimo Peruzzi, Massimo Marro, Livia Grandoni, Thierry Kubwimana, Antoine Mos, Pietro Salizzoni

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Stefano Lanzini, Cosimo Peruzzi, Massimo Marro, Livia Grandoni, Thierry Kubwimana, et al. The influence of vehicles on smoke propagation in transversely ventilated tunnels. Fire Safety Journal, 2025, 153, pp.104377. 10.1016/j.firesaf.2025.104377. hal-05017448

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# The influence of vehicles on smoke propagation in transversely ventilated tunnels

Stefano Lanzini<sup>a,1,*</sup>, Cosimo Peruzzi<sup>a,1,2</sup>, Massimo Marro<sup>a,1</sup>, Livia Grandoni<sup>a,1</sup>, Thierry Kubwimana<sup>b</sup>, Antoine Mos<sup>b</sup>, Pietro Salizzoni<sup>a,c,1</sup>

## ARTICLE INFO

### Keywords:

- Buoyant release

- Stratification flow

- Flow visualization

- Tunnel ventilation

- Confinement velocity

- Vehicles

## ABSTRACT

We present an experimental study to assess the influence of realistic traffic conditions on the ventilation required to confine the smoke produced by a tunnel fire. The experiments are performed on a reduced-scale tunnel, with hot smoke modeled by a buoyant helium-air release. The tunnel is ventilated by two extraction vents placed on both sides of the source to confine the smoke, and a longitudinal flow is induced by a longitudinal pressure gradient. The traffic condition is simulated by arranging cubic blocks, representing vehicles, of two different sizes inside the tunnel. For each block size and various tunnel configurations (different damper geometries and positions, and the presence or absence of vertical barriers downstream of the vents), experiments are performed with and without longitudinal flow. The presence of vehicles can lead to outcomes that differ from the well-established results in the literature obtained in their absence, i.e., in an empty tunnel. Specifically, the performance of rectangular dampers becomes equivalent to that of squared-centered dampers unless vertical barriers are used. Furthermore, when barriers are employed, the geometry and position of the dampers become irrelevant to ventilation efficiency. Obstacles primarily affect ventilation efficiency when they interact with the buoyant smoke and change its stratification regime.

## 1. Introduction

In recent decades, tunnel fires have received significant attention from engineers and scientists worldwide due to the critical importance of driver safety and protection. Particular focus has been placed on controlling buoyant smoke using different types of ventilation systems, such as longitudinal, transverse, and combined systems [1,2]. As a result, considerable knowledge has been acquired on key aspects including the critical longitudinal velocity required to confine the smoke [3,4], the evolution of the back-layering (i.e. the motion of the smoke upstream the fire) [5-7] and the heat release rate produced by a tunnel fire [8].

The majority of the scientific literature, both experimental and theoretical, has primarily examined ‘empty’ tunnels — without vehicles — because the system can be described using a reduced set of geometric parameters. While this idealized approach simplifies the problem, it

also makes the direct application of the results to real road tunnels questionable. The seminal work of Oka and Atkinson [9] was among the first to systematically address the issue of flow obstruction by a vehicle on fire smoke propagation and control with a longitudinal ventilation system. Subsequent studies have simulated the presence of vehicles by using varying numbers of blocks with different sizes, shapes, and arrangements, through both experiments [e.g.,10-13] and numerical models [e.g.,14,15].

In a longitudinal ventilation system (mainly suitable for tunnels with unidirectional traffic), the presence of vehicles can reduce the critical velocity needed to suppress back-layering when the airflow directly impacts the fire source. Conversely, if a vehicle obstructs the airflow in a manner that shields the fire source, the critical velocity increases [11,13,16-19]. Furthermore, only the obstacles close to the fire source play a role in affecting the critical velocity, while the effect of the other vehicles is negligible [20-22]. In general, the shape, size,

<footnote><sup>a</sup> Laboratoire de Mécanique des Fluides et d'Acoustique (LMFA), UMR5509, Université de Lyon, Ecole Centrale de Lyon, CNRS, Université Claude Bernard Lyon 1, INSA Lyon, 36 Avenue Guy de Collonge, 69130 Ecully, France</footnote>

<footnote><sup>b</sup> Centre d'Études des Tunnels (CETU), 25 Avenue Francois Mitterrand, 69500 Bron, France</footnote>

<footnote><sup>c</sup> Department of Environmental, Land and Infrastructure Engineering (DIATI), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin (TO), Italy</footnote>

<footnote>* Correspondence to: Laboratoire de Mécanique des Fluides et d'Acoustique (LMFA), UMR5509, Université de Lyon, Ecole Centrale de Lyon, CNRS, Université Claude Bernard Lyon 1, INSA Lyon, 36 Avenue Guy de Collonge, 69130 Ecully, France.
E-mail address: stefano.lanzini@doctorant.ec-lyon.fr (S. Lanzini).</footnote>

<footnote n="1">¹ These authors contributed equally to this work.</footnote>

<footnote n="2">² Present address: Italian Institute for Environmental Protection and Research (ISPRA), Via Vitalino Brancati 48, 00144 Rome (RM), Italy.</footnote>
and relative positions of the vehicles within the tunnel significantly influence the critical ventilation velocity during a fire [23–26].

The study of the influence of vehicles on tunnel fire safety is, instead, still at the beginning for transverse or combined ventilation systems. In transverse ventilation systems, suitable for long tunnels with bidirectional traffic or congested unidirectional traffic, the smoke is extracted through dampers located at the tunnel ceiling [27,28] while, in a combined ventilation system, a longitudinal flow is present together with the transverse aspiration [29,30]. Waman and Harish [31] were the first to address the vehicle effects on transverse ventilation by considering a tunnel with three naturally ventilated roof openings and longitudinal ventilation achieved by forcing ambient air through the tunnel inlet port. Using Large Eddy Simulation (LES), they showed that, in the case of fire, trapped vehicles significantly alter the flow features and temperature gradient, compared to an empty tunnel scenario. Another study [32], employing a large-scale Reynolds-averaged Navier–Stokes (RANS) numerical model, provided general operational procedures considering a real tunnel equipped with a semi-transverse ventilation system. Finally, Wang et al. [33] studied experimentally the natural ventilation induced by ceiling shafts, noting a variability of the smoke extraction efficiency for increasing blockage ratio of the vehicles.

Here, we aim to experimentally address the effect of vehicles on the performance of transverse and combined ventilation systems. Through a reduced-scale tunnel facility where the fire plume is modeled by an air–helium release [28,30], we investigate the effect of vehicles for: (i) different shapes and positions of the dampers (rectangular, square centered and square off-centered), (ii) presence and absence of solid vertical barriers at the tunnel ceiling. The deployment of barriers in an emergency is a strategy that can be adopted to reduce the spreading of smoke [21,28,30,34–37].

For each tunnel configuration, the experiments are conducted both with a null initial (i.e. before the fire generation) longitudinal flow (this condition will be hereafter referred to as ‘pure transverse ventilation’) and for different values of initial longitudinal velocity (hereafter referred to as ‘combined ventilation’ experiments).

The article is structured as follows. Section 2 presents our methodology: the buoyant isothermal model of the fire plume and its limitations, the similarity parameters and the conditions that must be met to up-scale the results to real-world situations, the facility set-up, and the experimental procedure. Section 3 shows the main results considering the pure transverse ventilation (Section 3.1) and the combined ventilation (Section 3.2); finally, Section 4 summarizes the main outcomes.

## 2. Methodology

### 2.1. The buoyant isothermal model

The results shown in this study are obtained considering an isothermal, reduced-scale model of the tunnel fire. In particular, the fire-induced smoke plume is simulated by a buoyant release (a gas mixture of air and helium at ambient temperature) emitted from a circular source on the tunnel floor. This method, originally proposed by Vauquelin and Megret [27], reproduces the mixed convection process — namely, the interplay between inertial and buoyancy effects — and has been adopted in different studies to gain insights into tunnel ventilation in emergency scenarios [6,16,21,27,28,30,38,39]. The primary assumption underlying the isothermal model is that, for evaluating smoke ventilation, the heat source can be fully characterized by the buoyancy flux alone and that this flux is proportional to the heat release rate HRR. Notably, when considering velocities much lower than the speed of sound and a constant heat capacity $C_p$, the fire heat release ratio HRR can be univocally linked to the buoyancy flux at the source of the isothermal plume, $B_s$, by the relation [40]:

$$B_s = \frac{g \text{ HRR}}{C_p T_0 \rho_0}, \quad (1)$$

where $T_0$ and $\rho_0$ are the ambient temperature and density, respectively, and g is the gravitational acceleration. The buoyancy flux of the isothermal plume is defined as:

$$B_s = \frac{W_s A_s g (\rho_0 - \rho_s)}{\rho_0}, \quad (2)$$

where $W_s$, $A_s$, and $\rho_s$ are the source velocity, area, and density, respectively. The same buoyancy flux can be obtained for several combinations of the source parameters $W_s$, $A_s$, $\rho_s$. In order to correctly reproduce the dynamics of the fire plume, the values of $W_s$, $A_s$, and $\rho_s$ must satisfy specific conditions, detailed in Section 2.2, so that the effects of buoyancy overwhelms that of inertia. Further, note that the isothermal (or densimetric) model cannot reproduce certain physical phenomena associated with fire. These are the radiative effects, the heat losses from conduction at the tunnel walls, and, most of all, the presence of flames. Approximately, the 30% of the fire HRR is actually transferred as a radiative flux [41–43], therefore not contributing to the buoyancy flux. The energy exchanged by radiation should be subtracted from the total HRR when switching from a fire to its equivalent densimetric plume. Regarding the effect of heat losses due to wall conduction, in the case of longitudinal ventilation, Salizzoni et al. [6] and Jiang et al. [44] showed that neglecting these effects leads to a slight overestimation of the critical velocity. However, this difference is small, exceeding the experimental uncertainty only slightly.

To evaluate the overall reliability of the isothermal model, Jiang et al. [44] and Klein [45] conducted a systematic comparison of the longitudinal tunnel ventilation in the case of densimetric and fire plumes. Jiang et al. [44] found that the same critical velocity is obtained with both approaches for non-dimensional heat release $HRR^* = HRR/(\rho_0 T_0 C_p R^{1/2} H^{5/2}) < 0.3$, where H is the tunnel height. The discrepancies observed for higher $HRR^*$ arise because, at high heat release ratios, the flames become ‘large’, i.e. exceeding half the tunnel height. In this scenario, the buoyancy flux in the fire case is emitted from a volumetrically distributed source extending across nearly the entire tunnel height, rather than from a localized ground-level source, as in the isothermal plume case. For a tunnel with a height of 5 m, considering $\rho_0 = 1.204 \text{ Kg/m}^3$, $T_0 = 293.15 \text{ K}$, and $C_p = 1006 \text{ J/kg K}$, the limit value of $HRR^* = 0.3$ corresponds to a heat release rate of approximately 20 MW. Therefore, the results obtained using the helium-plume approach can be considered scalable to real road applications for modeling small/medium-scale fires (with respect to the tunnel height), such as those involving cars or small vans. However, this approach may not be reliable in representing large fires, such as those involving heavy goods vehicles, which can exceed 100 MW. An analogous result was obtained by Klein [45], who showed that the isothermal approach could be unreliable when simulating fire with high HRRs.

Despite this limitation, we adopted this method for its numerous experimental advantages, including simplicity, precise control over source conditions, and the ability to achieve detailed and insightful plume visualizations by adding a tracer at the source—an option not feasible with a fire plume.

### 2.2. Similarity parameters

After outlining the limitations and advantages of the isothermal plume model, we now introduce the dimensionless parameters that govern the flow and are needed to up-scale our results to a real tunnel, as well as their functional relationships that will be explored in this work. Salizzoni et al. [30] conducted a dimensional analysis to identify the governing parameters in a scenario similar to the one analyzed here, that is, a tunnel equipped with both longitudinal and transverse ventilation systems. In the following, the analysis is completed considering also the effect of the obstacles representing vehicles, consisting of cubic blocks.
We analyze the flow within an infinitely long tunnel with a fixed rectangular cross-section, equipped with both longitudinal and transverse ventilation systems. A circular source on the tunnel floor releases a buoyant fluid at a steady rate. Our focus is on determining the conditions that confine this release between two extraction fans located at the tunnel ceiling, preventing the formation of a back-layering flow, whose extent is denoted as L in Fig. 1a. We assume that the same flow rate is extracted by the two ceiling vents. A confinement condition is defined by a back-layering length L equal to zero. The minimum extraction velocity required to achieve this, called $U_{e,c}$, is the lowest value of the ratio between the vent extracted flow rate ensuring L = 0 and the cross-sectional area of the vent ($A_d$). The confinement velocity $U_{e,c}$ is influenced by several parameters, including tunnel geometry (height H and width W), the buoyant source characteristics (density $\rho_s$, velocity $W_s$ and diameter $D_s$), the longitudinal velocity $U_t$ (equal to the longitudinal flow rate upstream the release and the dampers, i.e. $Q_{in}$ in Fig. 1a divided by tunnel cross-sectional area $\Omega$), the dimensions of the vents ($l_x, l_z$) and their span-wise distance $z_c$ from the tunnel center-line, the obstacles size (represented here by a single geometric quantity, l, the side of the cube), as well as the ambient fluid properties (density $\rho_0$, kinematic viscosity $\nu$, molecular diffusivity $D_m$) and gravitational acceleration $g$. For simplicity, we assume negligible differences in the kinematic viscosity and molecular diffusivity between the ambient air and the buoyant release. This allows us to establish the following functional dependence:

$$U_{e,c} = f(W_s, U_t, \rho_s, \rho_0, \nu, D_m, H, W, D_s, l_x, l_z, z_c, l, g), \quad (3)$$

With fourteen-dimensional quantities involving three independent dimensions (time, length, and mass), the Vaschy-Buckingham theorem is applied to express Eq. (3) in a non-dimensional form, illustrating the dependence of the normalized confinement velocity $U_{e,c}/U_t$ on eleven non-dimensional controlling parameters:

$$\frac{U_{e,c}}{U_t} = f \left( \Gamma_s, Re_s, S_c, \frac{\rho_s}{\rho_0}, \frac{W_s}{U_t}, \frac{D_s}{H}, \frac{W}{H}, \frac{A_d}{H^2}, S_d, P_d, O_s \right), \quad (4)$$

where $Re_s = W_s D_s / \nu$ is the source Reynolds number, $S_c = D_m / \nu$ is the Schmidt number, $A_d = l_x l_z$ is the damper opening area, $S_d = l_x / l_z$ is the damper aspect ratio, $P_d = z_c / H$ is the spanwise damper position, $O_s = l / H$ is the obstacle size, and $\Gamma_s$ is the plume Richardson number at the source, defined as Lanzini et al. [46]:

$$\Gamma_s = \frac{5}{16\alpha} \frac{g(\rho_0 - \rho_s)}{\rho_0} \frac{D_s}{W_s^2} = \frac{5}{4\pi\alpha} \frac{B_s}{W_s^3 D_s}, \quad (5)$$

where $\alpha = 0.127$ is a reference entrainment coefficient [47,48] and $B_s$ is the buoyancy flux at the source. As established by Hunt and Kaye [47], the plume Richardson number enables the classification of buoyant releases. Specifically, $\Gamma_s = 1$ corresponds to a pure plume, where momentum and buoyancy flux are in dynamic equilibrium. When $\Gamma_s < 1$, the plume is classified as forced, characterized by an excess of momentum relative to buoyancy flux. Conversely, $\Gamma_s > 1$ defines a lazy plume, where the buoyancy flux surpasses the momentum flux. Finally, $\Gamma_s = 0$ indicates a jet.

The functional dependence expressed in Eq. (4) can be simplified [30,44,49] if certain conditions are met. We consider a constant Schmidt number $S_c$, a constant diameter of the source $D_s$ (being $A_s = \pi D_s^2 / 4$ the circular area of the source, Fig. 1a), a constant tunnel aspect ratio $W/H$, and a constant damper opening area $A_d$. The flow can be considered independent of the Reynolds number $Re_s$ once it exceeds a critical threshold, typically $Re_c = 600$ [50]. For buoyancy-dominated releases ($\Gamma_s > 1$), Le Clanche et al. [39] and Jiang et al. [49] have shown that the influence of both $\Gamma_s$ and $\rho_s / \rho_0$ vanishes. Under these conditions, the confinement velocity $U_{e,c}$ is expected to become independent of individual source parameters ($\rho_s, W_s$, and $D_s$), which instead contribute only by determining the buoyancy flux $B_s$. This conclusion is consistent with the densimetric model of the fire, which implies that the heat source can be fully characterized by the

buoyancy flux alone (Section 2.1). The formulation of the problem can then be significantly simplified, as follows:

$$U_{e,c} = f(B_s, U_t, H, S_d, P_d, O_s), \quad (6)$$

or, in non-dimensional form, as:

$$Fr_{e,c} = f(Fr_t, S_d, P_d, O_s), \quad (7)$$

where

$$Fr_t = \frac{U_t}{(B_s/H)^{1/3}}, \quad (8)$$

$$Fr_{e,c} = \frac{U_{e,c}}{(B_s/H)^{1/3}}, \quad (9)$$

are the tunnel Froude number and the extraction Froude number, respectively, quantifying the ratio between inertia forces (induced by the longitudinal and transverse ventilation system) and the buoyancy forces (induced by the source). Scaling the longitudinal and extraction velocities using relations (8) and (9) enables the definition of quantities — $Fr_t$ and $Fr_{e,c}$ — that are independent of the source buoyancy flux [28] and, consequently, the fire's heat release rate HRR. The strength of this approach lies in its ability to use the $Fr_t$ and $Fr_{e,c}$ values obtained in isothermal reduced-scale experiments with a fixed $B_s$ to infer $U_t$ and $U_{e,c}$ in a full-scale tunnel with a real fire [38]. For this scaling method to be valid, the following conditions must be met:

* The geometrical similarity holds between the full-scale and the reduced-scale tunnels;

* A sufficiently high Reynolds number $Re_s$ is considered in the reduced-scale tunnel;

* A buoyancy-dominated release is produced by the experiments, i.e. $\Gamma > 1$ [6,28,49];

* The full-scale fire exhibits limited vertical flame extension (roughly up to tunnel half-height), allowing it to be reliably modeled as a steady buoyancy source on the tunnel floor (see Section 2.1). For a 5-meter-high tunnel, this corresponds to a maximum replicable HRR of approximately 20 MW;

* The heat losses from conduction at the tunnel walls do not affect $U_{e,c}$ and $U_t$;

* The real-fire buoyancy flux $B_s$ is estimated through Eq. (1), without considering the fraction of heat exchanged via radiation in the fire's HRR.

If all these conditions are verified, substituting in Eqs. (8) and (9) the $Fr_t$ and $Fr_{e,c}$ obtained experimentally, and the $B_s$ and $H$ of the real-fire scenario, allows the estimate of $U_t$ and $U_{e,c}$ in the real tunnel. The goal of the experiments is then to determine the non-dimensional functional dependencies embedded in Eq. (7).

### 2.3. Facility set-up and instrumentation

The experimental setup used in this measurement campaign is almost identical to that described by Salizzoni et al. [30], with minor modifications. We, therefore, provide here only a brief overview of the facility's configuration, instrumentation, and measurement procedures. For further details, the reader is referred to Salizzoni et al. [30]. The experiments were conducted in a 1/25 scale model tunnel at the Fluid Mechanics and Acoustics Laboratory (LMFA) of Ecole Centrale de Lyon, France (Fig. 1a). Recently renovated, the tunnel now measures 6.8 m in length with a rectangular cross-section of 0.18 m in height ($H$) and 0.36 m in width ($W = 2H$). Although shortened by 1.6 m from its previous version [28,30], these modifications have not affected its experimental performance. The interior of the tunnel allows for easy optical inspection, featuring transparent Plexiglas panels on one side wall, while the other side wall, floor, and ceiling are constructed of black fiberboard panels.
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** (a) Sketch of the whole tunnel facility along with the instrumentation. Panels (b–d) show the shape and disposition of the different dampers used in the experiments. Panel (e) reports the placement of the barriers. Finally, the arrangement of the small and large blocks is illustrated in panels (f) and (g), respectively.
Source: Modified from [30].</figcaption></figure>

Oil droplets are nebulized into the air-helium mixture, allowing for visualization when illuminated by a green laser plane. The light gas source has a circular shape with a diameter $D_s = 0.1$ m, positioned on the longitudinal center-line of the tunnel floor. The air-helium mixture and the oil droplets are regulated by three flow meters (accuracy ±3% of the measured flow rate; [51]), guaranteeing a constant source flow rate $Q_s$ during the experimental tests.

The flow in the tunnel is controlled by three extraction fans, two positioned on the tunnel ceiling (symmetrically displaced from the source center by a distance of $5H$, Fig. 1a), and one installed on the tunnel outlet. The airflow rates of two vertical fans (fans no. 1 and no. 2), denoted as $Q_1$ and $Q_2$, are measured using two separate rotameters placed in the extraction ducts. Since the rotameters are designed for

pure air, we conducted a calibration procedure to establish transfer functions that correlate the flow rates indicated by the rotameters with the actual values of the mixture flow rates $Q_1$ and $Q_2$ [28]. For this purpose, an oxygen sensor is installed downstream of each rotameter, along with a honeycomb cylinder to prevent oil droplets from reaching the oxygen sensor. This setup allows for the assessment of air and helium concentrations in the extracted flow. The longitudinal fan (fan no. 3) is employed to generate longitudinal flow within the tunnel, although this flow is also influenced by the vertical fans. In fact, the vertical fans induce a current in both the upstream and downstream stretches of the tunnel that superposes to the flow generated by fan no. 3, drawing air towards them and causing what we refer to as the ‘suction effect’. As documented in Salizzoni et al. [30], when the
buoyant release is confined between the two vertical fans (i.e. whenever the back-layering length L is null, Fig. 1a), the outlet flow rate $Q_{out}$ is always directed towards the interior of the tunnel (i.e. negative $Q_{out}$ considering the coordinate system in Fig. 1a).

At the tunnel entrance, the presence of an airflow cone equipped with a Pitot tube allows for measuring the inlet flow rate $Q_{in}$, while the related longitudinal mean velocity can be estimated as $U_t = Q_{in}/\Omega$ (where $\Omega = WH$ is the tunnel cross-sectional area). This longitudinal flow was characterized by Chaabat [52] using PIV measurements, which indicated that the longitudinal mean velocity profiles exhibit the classical shape typical for turbulent channel flows. Furthermore, Zanoun et al. [53] indicate that in turbulent channel flows, a development length of $\approx 20\delta$, where $\delta$ is the channel half height, is required to achieve self-similarity in the mean velocity profiles. In our set-up, the buoyancy source is positioned at $47\delta$ from the inlet, while the downstream extraction fan is located at $37\delta$ from the inlet.

During the experiments, three different vent (or damper) shapes were used, all having the same opening area $A_d = 0.011 \text{ m}^2$ (Fig. 1b-d). The dampers are identical to those previously employed by Chaabat et al. [28] and Salizzoni et al. [30], specifically:

* A damper with a transverse rectangular shape ($0.32 \times 0.034 \text{ m}$) which occupies almost the entire width of the tunnel, hereinafter called RSD (Fig. 1b);

* A damper with a square shape ($0.104 \times 0.104 \text{ m}$) centered with respect to the tunnel center-line, hereinafter called SSD-PC (Fig. 1c);

* A damper with a square shape ($0.104 \times 0.104 \text{ m}$) positioned on a side concerning the tunnel center-line, hereinafter called SSD-PS (Fig. 1d).

Additionally, we explored the impact of vertical barriers to enhance the capture efficiency of the vents (Fig. 1e). Two planar barriers were suspended from the tunnel ceiling near the vents' extremities, with height ($h$) and width of $H/3$ and $2H$, respectively, hence spanning the entire tunnel width. Barriers of this size are intended to be retracted in normal conditions and deployed only in emergency situations in the event of a fire.

To simulate the effect of vehicles on the propagation of buoyant-release flow, we positioned two types of cubic blocks (side $l$): cubic blocks with dimensions $l = 0.05 \text{ m}$ (small blocks arrangement SB), and cubic blocks with dimensions $l = 0.12 \text{ m}$ (large blocks arrangement LB). Cubic blocks of these dimensions well approximate the presence of cars and heavy goods vehicles (HGVs) in real tunnels [21]. Fig. 1(f-g) displays the top view of the SB and LB arrangements. The initial block was positioned precisely at the border of the source, with subsequent blocks spaced at intervals of $2H$, resulting in lines of seven blocks in both directions. This arrangement simulated a bidirectional tunnel road with congested traffic. According to Lee and Tsai [11], the tunnel blockage ratio (in percentage) is given by:

$$ \phi = 100 \left( 1 - \frac{\Omega - A_o}{\Omega} \right), \qquad (10) $$

where $A_o$ is the frontal area of the obstacles in a tunnel cross-section. In this study, $\phi = 3.85\%$ and $\phi = 22.22\%$, respectively, when SB and LB arrangements are involved. If we also consider the presence of barriers on the tunnel ceiling, the obstacle frontal area $A_o$ increases by the simultaneous presence of block and barrier in the same tunnel cross-section, yielding $\phi = 37.19\%$ and $\phi = 55.55\%$, respectively. On the other hand, the empty tunnel condition, i.e. absence of blocks ($\phi = 0\%$), is indicated in the following with the acronym NoB.

## 2.4. Experimental procedure

A total of eighteen tests were carried out, and each of them included 1 to 18 measurements (Table 1). For each test, we measured the mean vertical extraction velocity guaranteeing confinement conditions,

denoted as $U_{e,c}$, depending on a varying intensity of the longitudinal velocity $U_t$, vent configurations (i.e. vent shape, position, and presence of barriers), and obstacle dimension. The source conditions are characterized by the density ratio $\rho_s/\rho_0$ and by the plume Richardson number at the source $\Gamma_s$. Both $\rho_s/\rho_0$ and $\Gamma_s$ were kept constant in all experiments (i.e. $\rho_s/\rho_0 = 0.72$ and $\Gamma_s = 3.7$) since, as highlighted in previous works [28,30,49], for buoyancy-dominated releases (i.e. for $\Gamma_s > 1$), the flow dynamic within the tunnel is insensitive of varying values to $\rho_s/\rho_0$ or $\Gamma_s$.

The Reynolds number at the source $Re_s = W_s D_s / \nu$, where $\nu$ is the mixture kinematic viscosity at the source [54], is 2120. This value is above the critical $Re_c = 600$, indicated by Arya and Lape [50] as the threshold above which diffusive effects can be neglected. For all the experiments, the buoyancy flux at the source is $B_s = 0.01 \text{ m}^4 \text{ s}^{-3}$. The values of the governing parameters for each experimental test are listed in Table 1.

Tests 1–12 were started by activating all three fans at the minimum setting. Once the longitudinal velocity at the tunnel inlet was stabilized, the flowmeters controlling the buoyant release were activated. At this initial stage, the extraction velocity was kept low, allowing the released buoyant fluid to disperse throughout the entire tunnel. Subsequently, the power of the vertical fans was progressively raised, consistently imposing the same flow extracted by both fans, i.e. $Q_1 = Q_2$ (Fig. 1a). In all experiments, the maximum accepted difference between $Q_1$ and $Q_2$ is the 5%. When achieved the confinement condition, namely when the buoyant release was confined between the two vertical vents, we recorded the values of the two extraction velocities, i.e. $U_{e,c1}$ and $U_{e,c2}$, and the value of $U_t$. The extraction velocity in confinement conditions $U_{e,c}$ was then calculated as the average between the values recorded at fan no. 1 and fan no. 2 (Fig. 1a), specifically $U_{e,c} = (U_{e,c1} + U_{e,c2})/2$, where $U_{e,c1} = Q_1/A_d$ and $U_{e,c2} = Q_2/A_d$. To further explore the relation between $U_t$ and $U_{e,c}$, the experiment was repeated for different values of initial longitudinal velocity (i.e. the horizontal velocity in the tunnel before the activation of the extraction fans). Furthermore, an additional measurement was also performed with the longitudinal fan switched off, to investigate the pure transverse ventilation condition. Note that in Test 5 and Test 11 (i.e. SSD-PS dampers with SB and LB blocks, respectively), the confinement condition was attained only in this circumstance. It is important to emphasize that, although the longitudinal fan is switched off, $U_t$ is not zero due to the suction effect induced by the vertical fans.

Finally, Tests 13–18 were conducted without the cubic blocks (NoB) and with the longitudinal fan turned off. These tests were conducted to compare the performance of a pure transverse ventilation system in the presence and absence of vehicles in the tunnel.

## 3. Results and discussions

Below, we present the outcomes of the experimental campaign. All data are displayed along with their corresponding measurement uncertainty, calculated as a Type B uncertainty [55]. This uncertainty takes into account the manufacturer's specifications for each instrument and is represented as an error bar. In cases where data are depicted without an error bar, it indicates that the associated uncertainty is smaller than the size of the markers employed in the plots.

Initially, our attention is on experiments conducted with the longitudinal fan turned off (Section 3.1). After that, the results coming from the activation of the combined ventilation system are analyzed (Section 3.2).

### 3.1. Pure transverse ventilation

Since the source is placed at the same longitudinal distance from the two extraction vents (i.e. $5H$) and the power given to the extraction fans is the same, we assume that, under pure transverse ventilation, the flow is symmetric with respect to the source (Fig. 2a).
<caption>**Table 1**</caption>

Summary of experiments and associated fluid dynamic conditions. The columns indicate: the Reynolds number at the source $Re_i$; the plume Richardson number at the source $Γ_i$; the density ratio $ρ_s/ρ_0$; the tunnel Froude number $Fr_t$ (see Section 2.2); the extraction Froude number in confinement condition $Fr_{e,c}$ (see Section 2.2). The last four columns report the shape of the vents, the type of blocks, the presence of the barriers, and the tunnel blockage ratio $φ$, respectively.

<table><thead><tr><th>Run</th><th>Re<sub>i</sub> [-]</th><th>Γ<sub>s</sub> [-]</th><th>ρ<sub>s</sub>/ρ<sub>0</sub> [-]</th><th>Fr<sub>t</sub> [-]</th><th>Fr<sub>e,c</sub> [-]</th><th>Vent shape</th><th>Blocks type</th><th>Barriers</th><th>φ [%]</th></tr></thead><tbody><tr><td>Test 1</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.37–2.32</td><td>3.13–10.13</td><td>RSD</td><td>SB</td><td>×</td><td>3.85</td></tr><tr><td>Test 2</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.37–2.55</td><td>2.45–10.32</td><td>RSD</td><td>SB</td><td>✓</td><td>37.18</td></tr><tr><td>Test 3</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.81–2.33</td><td>4.68–9.93</td><td>SSD-PC</td><td>SB</td><td>×</td><td>3.85</td></tr><tr><td>Test 4</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.60–2.60</td><td>3.65–9.94</td><td>SSD-PC</td><td>SB</td><td>✓</td><td>37.18</td></tr><tr><td>Test 5</td><td>2120</td><td>3.7</td><td>0.72</td><td>1.92</td><td>10.21</td><td>SSD-PS</td><td>SB</td><td>×</td><td>3.85</td></tr><tr><td>Test 6</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.59–2.09</td><td>3.65–9.59</td><td>SSD-PS</td><td>SB</td><td>✓</td><td>37.18</td></tr><tr><td>Test 7</td><td>2120</td><td>3.7</td><td>0.72</td><td>1.02–1.95</td><td>5.73–10.21</td><td>RSD</td><td>LB</td><td>×</td><td>22.22</td></tr><tr><td>Test 8</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.24–2.23</td><td>2.23–10.11</td><td>RSD</td><td>LB</td><td>✓</td><td>55.55</td></tr><tr><td>Test 9</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.98–2.03</td><td>5.89–10.36</td><td>SSD-PC</td><td>LB</td><td>×</td><td>22.22</td></tr><tr><td>Test 10</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.24–2.14</td><td>2.24–9.68</td><td>SSD-PC</td><td>LB</td><td>✓</td><td>55.55</td></tr><tr><td>Test 11</td><td>2120</td><td>3.7</td><td>0.72</td><td>1.84</td><td>10.25</td><td>SSD-PS</td><td>LB</td><td>×</td><td>22.22</td></tr><tr><td>Test 12</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.55–2.24</td><td>3.62–10.04</td><td>SSD-PS</td><td>LB</td><td>✓</td><td>55.55</td></tr><tr><td>Test 13</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.25</td><td>1.95</td><td>RSD</td><td>NoB</td><td>×</td><td>0</td></tr><tr><td>Test 14</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.31</td><td>2.86</td><td>RSD</td><td>NoB</td><td>✓</td><td>33.33</td></tr><tr><td>Test 15</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.91</td><td>5.90</td><td>SSD-PC</td><td>NoB</td><td>×</td><td>0</td></tr><tr><td>Test 16</td><td>2120</td><td>3.7</td><td>0.72</td><td>0.46</td><td>3.58</td><td>SSD-PC</td><td>NoB</td><td>✓</td><td>33.33</td></tr><tr><td>Test 17</td><td>2120</td><td>3.7</td><td>0.72</td><td>1.49</td><td>10.67</td><td>SSD-PS</td><td>NoB</td><td>×</td><td>0</td></tr><tr><td>Test 18</td><td>2120</td><td>3.7</td><td>0.72</td><td>1.15</td><td>6.85</td><td>SSD-PS</td><td>NoB</td><td>✓</td><td>33.33</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** (a) Sketch of the buoyant flow in confined conditions and (b–c) possible flow regimes in pure transversely ventilated tunnels, i.e. stratified and unstratified.</figcaption></figure>

In this framework, two criteria are considered to evaluate the ventilation efficiency in different experimental configurations [28].

The first one is the value of extracted flow rate $Q_{e,c}$ that guarantees the confinement of the buoyant flow (i.e. a null back-layering length $L = 0$, Fig. 1a). The smaller is $Q_{e,c}$, the more efficient is the ventilation. Since the source condition is fixed in all our experiments (implying a constant mass flow $Q_s ρ_s$), the value $Q_{e,c}$ uniquely determines the value of $Fr_{e,c}$. We can therefore use $Q_{e,c}$ or $Fr_{e,c}$ arbitrarily to compare the different experimental configurations with each other.

The second criterion is the stratification condition of the confined buoyant smoke. Two flow regimes (Fig. 2b–c), referred to as stratified and unstratified, may potentially occur. When the flow is stratified, the role of the stabilizing density gradients prevails over turbulent mixing. A light gas layer is established below the ceiling, and the buoyant smoke does not fill the lower part of the tunnel. Instead, in the unstratified condition, there is intense mixing between the buoyant smoke and the ambient air, which are therefore well mixed over the entire tunnel height [56].

Assuming symmetric flow implies that: (i) the extracted flow rate and the density of the extracted air–helium mixture are equal at the two vents ($Q_1 = Q_2 = Q_{e,c}$ and $ρ_1 = ρ_2 = ρ_{e,c}$), and (ii) the longitudinal flow rate $Q_t$ induced in the tunnel by the vertical fans is the same on both sides of the release (Fig. 2a). For fixed source condition, we are therefore left with three unknowns, only: $Q_{e,c}$, $ρ_{e,c}$, and $Q_t$. Once the buoyant flow is confined, the mass conservation implies:

$$Q_s \rho_s + 2Q_t \rho_0 = 2Q_{e,c} \rho_{e,c}, \quad (11)$$

whereas, scalar (helium) conservation yields:

$$Q_s \chi_s = 2Q_{e,c} \chi_{e,c}, \quad (12)$$

where $χ_s = (ρ_s - ρ_0)/(ρ_{He} - ρ_0)$ is the helium volume fraction at the source, and $χ_{e,c} = (ρ_{e,c} - ρ_0)/(ρ_{He} - ρ_0)$ is the fraction in the mixture extracted at the vents, being $ρ_{He}$ the helium density.

By manipulating Eqs. (11)–(12), we can obtain the values of the longitudinal flow rate $Q_t$ induced within the tunnel and the ratio $ρ_{e,c}/ρ_0$ of the extracted air–helium mixture as a function of $Q_{e,c}$:

$$Q_t = Q_{e,c} - \frac{Q_s}{2}, \quad (13)$$

$$\frac{\rho_{e,c}}{\rho_0} = 1 - \frac{Q_s}{Q_{e,c}} \frac{\rho_0 - \rho_s}{2\rho_0}. \quad (14)$$

Eq. (13) is a volume conservation equation that shows how $Q_t$ and $Q_{e,c}$ are uniquely linearly linked. Thus, to evaluate the extraction efficiency of a symmetric configuration, measuring only one of the two flow rates, i.e. the extracted flow rate $Q_{e,c}$ or the horizontal flow rate $Q_t$ induced by the extraction (Fig. 2a), is sufficient. Eq. (14) shows that the ratio $ρ_{e,c}/ρ_0$ increases with $Q_{e,c}$, hence, for a given source condition, the more efficient is the ventilation (i.e. the smaller are values of $Q_{e,c}$ and $Q_t$ required for confinement) the lighter is the extracted mixture. This last relation can also be retrieved using the Vauquelin and Megret [27] formalism by imposing that the efficiency of the exhaust duct $ε$ is equal to 1. Eq. (14) shows that the two criteria considered to define the performance of a given configuration (i.e. the $Q_{e,c}$ value and the flow stratification) are strongly linked. When the buoyant smoke is confined, a strongly stratified regime implies that mixing and ambient air entrainment are minimal [57–59], indicating that the extracted density will be smaller compared to the ambient one. Therefore, Eq. (14) shows that this condition is possible only if $Q_{e,c}$ is small. Conversely, when the regime is unstratified, strong mixing occurs between the plume and the ambient air, leading to $ρ_{e,c}/ρ_0 \to 1$. This corresponds to a higher value of $Q_{e,c}$ with respect to the stratified
<figure><img src="image_5.png" /><figcaption>Fig. 3. (a) $Q_i$ and (b) $\rho_{e,c}/\rho_0$ as a function of $Q_{e,c}$. The experimental measurements are compared to the theoretical Eqs. (13)–(14). The gray bars correspond to the transition zone between the stratified and unstratified regimes, evaluated from flow visualizations. The acronyms denoting the different experimental configurations are defined in Section 2.3. The vertical barriers are employed in the configurations labeled with 'Bar'.</figcaption></figure>

case [60]. Note that Eq. (14) analytically completes and justifies the experimental observations of Chaabat et al. [28] regarding flow stratification and the plug-holing phenomenon (i.e. fresh air drawn directly into the vents from the lower layer in a stratified flow; [61]) within a pure transversely ventilated tunnel. Eqs. (13)–(14) can be written in terms of the dimensionless parameters that govern the problem, defined in Section 2.2, as:

$$Fr_t = Fr_{e,c} \frac{A_d}{\Omega} - \Gamma_s^{-\frac{1}{3}} \frac{1}{2} \frac{A_s}{\Omega} \left(\frac{H}{D_s}\right)^{1/3} \left(\frac{4\pi\alpha}{5}\right)^{-1/3}, \quad (15)$$

$$\frac{\rho_{e,c}}{\rho_0} = 1 - \Gamma_s^{-\frac{1}{3}} Fr_{e,c}^{-1} \left(1 - \frac{\rho_s}{\rho_0}\right) \frac{1}{2} \frac{A_s}{A_d} \left(\frac{H}{D_s}\right)^{1/3} \left(\frac{4\pi\alpha}{5}\right)^{-1/3}, \quad (16)$$

in which all symbols are defined in Section 2.

Fig. 3 reports the experimental measurements of the extraction flow rate at the ceiling $Q_{e,c}$ versus $Q_i$ (panel a) and $\rho_{e,c}/\rho_0$ (panel b) for a fixed source condition (Table 1), along with the theoretical relations expressed by Eqs. (13)–(14). Fig. 3a shows that the measurement data of $Q_i$ and $Q_{e,c}$ follow the theoretical relationship, with a small deviation for large values of $Q_{e,c}$. This discrepancy between theoretical predictions and experiments probably arises because, when the longitudinal flow increases, the influence of non-perfect symmetry relative to the source becomes non-negligible and the assumptions adopted in Eqs. (11)–(12) are not fully verified. From flow visualization, we identify a transition zone when $Q_{e,c} \approx 0.0135 - 0.0205 \text{ m}^3/\text{s}$ (that corresponds to $Fr_{e,c} \approx 3.3 - 4.8$ and $Fr_t \approx 0.5 - 0.8$) that sets a shift between stratified and unstratified flow regime. This shift zone is identified by a gray bar in Fig. 3a,b. Visualizations illustrating the transition are shown in Section 3.1.1. The transition zone extends from the point where the stratified smoke layer beneath the ceiling begins to thicken, and turbulent structures reach halfway up the tunnel height, to the point where the air-helium mixture fully occupies the entire tunnel.

This range of $Q_{e,c}$ values corresponds to a range of $\rho_{e,c}/\rho_0 \approx 0.95 - 0.97$, which delineates the distinction between stratification regimes (Fig. 3b). Despite the presence of error bars with amplitude around ±7%, our experimental results follow the trend described by Eq. (14), showing that the extracted density ratio decreases as $Q_{e,c}$ increases. As expected, for the unstratified regime, the extracted density is very close to that of the ambient air.

### 3.1.1. Effects of blocks with and without barriers

Based on the theoretical analysis reported in Section 3.1, we can now investigate the effects induced by the presence of blocks on transverse ventilation efficiency, i.e. showing their influence on $Fr_{e,c}$ and on the stratification regime.

Concerning the cases without barriers, Fig. 4a shows the values of $Fr_{e,c}$ for three damper configurations and different obstacle sizes placed in the tunnel floor (see Fig. 1). Consistently with literature results [27,

28,62], in the absence of blocks (NoB), the rectangular geometry (RSD) is the most efficient and the only one guaranteeing a stratified regime, once the buoyant smoke is confined. On the contrary, the SSD-PS is the worst configuration. Interestingly, once small blocks (SB) are placed in the tunnel, the difference in $Fr_{e,c}$ between RSD and SSD-PC is reduced and, finally, canceled out when large blocks (LB) are considered. This is mainly due to a degradation of RSD performance that passes from $Fr_{e,c} = 1.95$, when the tunnel is empty, to $Fr_{e,c} = 5.6$, when large blocks are present. Notably, in the LB case, $Fr_{e,c} > 4.8$, therefore, the confined buoyant flow is unstratified. In contrast, with SSD-PC and SSD-PS, no evident changes in $Fr_{e,c}$ are detected for different obstacle sizes, and the flow regime is always unstratified. The physics underlying the behavior of $Fr_{e,c}$ can be investigated with visualizations of the confined smoke (Fig. 4b–j). When the tunnel is empty and rectangular dampers are installed (Fig. 4b), the flow is strongly stratified, and a thin layer of the light mixture is created beneath the ceiling. With the presence of small blocks (Fig. 4c), the light fluid layer thickens but does not reach the lower part of the tunnel where the blocks are located. However, when the large blocks are placed on the tunnel floor (Fig. 4d), they penetrate the light mixture layer, leading to its disruption: the smoke disperses throughout the height of the tunnel and mixes with the surrounding air. The enhanced mixing and entrainment with respect to the RSD-NoB and RSD-SB cases implies necessarily a higher value of $\rho_{e,c}/\rho_0$ and, from Eq. (14), a higher $Q_{e,c}$ (or $Fr_{e,c}$) required for the smoke confinement.

The situation is different when considering square dampers. When the tunnel is empty, both for SSD-PC and SSD-PS (Fig. 4e,h), the confined smoke extends throughout the entire height of the tunnel, and, due to the strong turbulent mixing with the ambient air, the extracted density ratio $\rho_{e,c}/\rho_0$ is already close to 1. The mixing within the empty tunnel is so intense that the addition of obstacles of different sizes does not have an impact on it. Therefore, the obstacles do not affect the stratification regime, and the value of $Fr_{e,c}$. With square dampers, the performance of tunnel ventilation for smoke confinement is not influenced by the presence of vehicles. This reasoning is not entirely valid for the SSD-PC SB case (Fig. 4f), where the addition of the small obstacles appears to slightly enhance the performance of the fans, allowing confinement to be achieved at a lower $Fr_{e,c}$ value compared to SSD-PC NoB case. This may be attributed to the fact that the presence of small blocks hamper the turbulent vortices, thereby leading to less unstratified conditions for the buoyant flow, or to experimental uncertainties.

In Fig. 5a we investigate how the presence of small and large blocks in the tunnel influences the performance of different dampers when vertical barriers are placed just downstream of the vents (see Fig. 1e). As extensively discussed in studies on empty tunnels [28,30], the presence of barriers improves the efficiency of extraction, especially for square-shaped dampers. In this case, the efficiency of RSD and SSD-PC
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** (a) $Fr_{e,c}$ values for different damper shapes as a function of the block size, i.e. no blocks (NoB), small blocks (SB), and large blocks (LB). The gray bar corresponds to the transition zone between the stratified and unstratified regimes, evaluated from flow visualizations. (b–d), (e–g), (h–j) Flow visualization of the confined smoke for the RSD, SSD-PC, and SSD-PS configurations, respectively. The blue arrows show the position of the extraction damper.</figcaption></figure>

is similar, while the SSD-PS requires a higher $Fr_{e,c}$ for confinement. However, when small or large blocks are placed in the tunnel, even the behavior of SSD-PS becomes closer to the one of RSD and SSD-PC. This means that with vertical barriers, in the realistic case where cars or trucks are present in the tunnel, both the shape (RSD or SSD) and the position (PC or PS) of the damper almost do not affect the ventilation efficiency. The enhanced efficiency due to barriers can once again be understood through flow visualizations of the confined smoke (Fig. 5b–j). In the flow visualization, the dark area beneath the ceiling corresponds to the shadow cast by the barrier positioned directly downstream of the extraction point.

For all the dampers tested, when small or large blocks are present, the vertical barriers prevent the formation of a completely unstratified regime. They block the smoke that accumulates close to the dampers, maintaining the stratified layer of light mixture.

While the vertical barriers do not increase the RSD efficiency in an empty tunnel [28,30], they become very useful for maintaining a stratified regime (and increasing the ventilation efficiency) with this same damper geometry when realistic traffic conditions are considered.

## 3.2. Combined ventilation

Now we examine the impact of realistic traffic conditions on tunnel ventilation efficiency in the presence of two concurrent inertial forces: a transverse extraction system and a longitudinal airflow. Although the imposed vertical extracted flow rate is the same for the two vertical fans, the symmetric flow hypotheses made in Section 3.1 do not hold anymore, so that $\rho_{e,1} \neq \rho_{e,2}$ and $Q_{in} \neq Q_{out}$ (Fig. 1a). Therefore,

in order to evaluate the ventilation efficiency, we adopt the same criterion of Salizzoni et al. [30]: at a fixed $Fr_t$ induced by the combined ventilation system, we identify the best configuration as the one that guarantees the buoyant release confinement with the minimal $Fr_{e,c}$. As for the symmetric case, we are also interested in the description of the stratification regime of the confined smoke for the different configurations. Four different stratification regimes for an increasing value of $Fr_t$ were identified for an empty tunnel (see [30] for a detailed description of the regimes). The possible stratification conditions are:

* Regime I: stratified flow layer on both sides of the source;

* Regime II: intermediate condition, i.e. the buoyant fluid is un-stratified on the upwind side and stratified at the downwind side;

* Regime III: unstratified flow at both sides of the source;

* Regime IV: the buoyant fluid is only observable downstream of the source, primarily due to the dominant influence of the longitudinal velocity. The upstream damper does not extract the light mixture.

The four different regimes are identified by different markers employed in the plots, namely: circle, square, triangle, and diamond, respectively. All the results are obtained for a fixed source condition (see Section 2.3).

In Fig. 6, we examine how the presence of blocks in the tunnel affects the efficiency of combined ventilation for various damper types in the absence of vertical barriers. For completeness, the reference results by Salizzoni et al. [30] with the same source conditions in an empty
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** (a) $Fr_{e,c}$ values, when barriers are installed in the tunnel, for different damper shapes as a function of the block size, i.e. no blocks (NoB), small blocks (SB), and large blocks (LB). The gray bar corresponds to the transition zone between the stratified and unstratified regimes, evaluated from flow visualizations. (b–d), (e–g), (h–j) Flow visualization of the confined smoke for the RSD & Bar, SSD-PC & Bar, and SSD-PS & Bar configurations, respectively. The blue arrows show the position of the extraction damper. The red bars show the position of the vertical barrier.</figcaption></figure>

tunnel (NoB) are shown in Fig. 6a. In Fig. 6b,c, for each experimental configuration, the point with the smallest $Fr_{e,c}$ corresponds to the pure transverse ventilation experiment (Fig. 4a). As for the empty tunnel, when small blocks, SB (Fig. 6b), and large blocks, LB (Fig. 6c), are considered, the $Fr_{e,c}$ and $Fr_t$ relation for the RSD and SSD-PC is well fitted by a straight line. The presence of an initial non-zero longitudinal velocity requires greater vertical suction power (i.e. $Fr_{e,c}$) to confine the smoke and, with SSD-PS, our ventilation system can only confine the smoke in the pure transverse ventilation condition, i.e. when the initial longitudinal velocity in the tunnel is zero. When the tunnel is empty, for a given value of $Fr_t$, the results for SSD-PC are always at higher $Fr_{e,c}$ values compared to the results for RSD. The gain in ventilation efficiency of RSD over SSD-PC diminishes when small blocks are placed into the tunnel and is canceled by the presence of large blocks. Similar to the pure-transverse condition, the convergence of performance between RSD and SSD-PC in the LB case is attributed to a reduction in the efficiency of the rectangular damper. The presence of obstacles has a minor impact on the straight-line slope for RSD but instead causes a vertical shift towards higher $Fr_{e,c}$ values. The magnitude of this shift does not depend on $Fr_t$.

Furthermore, the presence of obstacles also affects the stratification of the confined smoke. With RSD, stratification regimes I and II can be achieved (under low longitudinal velocities in the tunnel before the release of the buoyant plume) only when the tunnel is empty or with

small obstacles. However, when large blocks are present, achieving a stratified regime is not feasible in any experiment.

The effects of obstacles on combined ventilation systems when vertical barriers are placed in the tunnel (Fig. 1e) is shown in Fig. 7. Similar to the case without barriers, we consider the experiments performed without blocks by Salizzoni et al. [30] as the results for the NoB case (Fig. 7a). When obstacles are absent, the behavior of RSD is very similar to that of SSD-PC, while the experimental results of SSD-PS regularly exhibit higher values of $Fr_{e,c}$. Interestingly, with small obstacles (Fig. 7b), the difference between SSD-PC and SSD-PS is reduced and it is completely canceled with large obstacles (Fig. 7c). With vertical barriers and LB, neither the geometry nor the position of the damper affects the efficiency of the combined ventilation system.

The damper that benefits most from the presence of obstacles and barriers is SSD-PS, which is the less-performing damper in an empty tunnel but becomes comparable even to RSD in this situation. Furthermore, even with this vent geometry and position, the presence of barriers allows the smoke to be confined with different longitudinal velocities in the tunnel. The presence of barriers and obstacles affects the stratification regimes. Unlike in experiments without barriers, when barriers are present, stratification regimes I and II can be achieved even with LB.

In Fig. 8, for each one of the nine possible combinations of damper type and obstacle size, we make a direct comparison between experiments with and without vertical barriers. Salizzoni et al. [30]
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Relation between the tunnel Froude number $Fr_t$ and the extraction Froude number $Fr_{e,c}$ without vertical barriers considering different dampers (a) in the empty tunnel (NoB), (b) in the tunnel with small blocks (SB), and (c) in the tunnel with large blocks (LB). All the points plotted in panel (a) are taken from [30]. The marker shape is related to the different stratification regimes: circle (Regime I), square (Regime II), triangle (Regime III), and diamond (Regime IV).</figcaption></figure>

observed that, without obstacles, the barriers significantly enhance the aspiration efficiency for SSD-PC and SSD-PS (Fig. 8d,g), while they have not a significant impact when used with RSD (Fig. 8a). This is no longer true when obstacles are placed in the tunnel. For RSD, both with small and large obstacles (Fig. 8b,c), the segment obtained from the linear regression of the data shows lower $Fr_{e,c}$ values when barriers are present compared to when they are not employed. As for the NoB case, for SSD-PC and SSD-PS, barriers enhance the vent efficiency even when small (Fig. 8e,h) or large (Fig. 8f,i) obstacles are present. Therefore, in the realistic scenario with vehicles in the tunnel, the presence of vertical barriers positioned just downstream of the transverse dampers improves the aspiration efficiency for all RSD, SSD-PC, and SSD-PS dampers. However, while barriers significantly enhance the damper efficiency in the event of a fire, their placement within the tunnel, along with the integration of software and hardware systems to ensure reliable activation after smoke detection, poses several technical challenges. Determining the overall suitability of vertical barriers' implementation requires a comprehensive evaluation that is beyond the scope of the present study. In addition, the barrier height that we investigated is not necessarily optimal and should be selected on a case-by-case basis.

## 4. Conclusions

We conducted experiments using a reduced-scale tunnel to investigate the fluid dynamics of a fire plume, modeled by an isothermal buoyant release. We presented the limitations and advantages of this

approach, together with a list of conditions that must be met to reliably up-scale the experimental results to a real scenario. In the experimental facility, two extraction fans connected to ceiling vents on either side of the source were regulated to confine the plume between these vents. Various tunnel configurations were tested, including different vent geometries and positions, as well as the presence or absence of vertical barriers downstream of the extraction points.

To assess how vehicles in the tunnel impact ventilation performance, we used cubic blocks of two different sizes to represent vehicles, placing them on either side of the buoyancy source. For each tunnel configuration and block size, we conducted experiments under two conditions: null initial longitudinal velocity (pure transverse ventilation) and varying longitudinal velocities (combined ventilation). Here, we present our main findings:

1. In pure transverse ventilation, the presence of vehicles in the tunnel reduces the effectiveness of rectangular extraction dampers, while it has minimal impact on the performance of square dampers, regardless of their placement in the center or at the side of the tunnel ceiling. In the presence of large obstacles, the dimensionless extracted volume flux, $Fr_{e,c}$, required to confine the smoke is similar for both rectangular vents and central square ones. According to well-established literature [27,28,30,62], rectangular vents outperform square ones in an empty tunnel, but this advantage does not necessarily persist under realistic traffic conditions.

2. The reduced efficiency of rectangular vents under pure transverse ventilation and realistic traffic conditions is primarily due
<figure><img src="image_9.png" /><figcaption>Fig. 7. Relation between the tunnel Froude number $Fr_t$ and the extraction Froude number $Fr_{e,c}$ considering different dampers (a) in the empty tunnel (NoB), (b) in the tunnel with small blocks (SB), and (c) in the tunnel with large blocks (LB) when vertical barriers are present. All the points plotted in panel (a) are taken from [30]. The marker shape is related to the different stratification regimes: circle (Regime I), square (Regime II), triangle (Regime III), and diamond (Regime IV).</figcaption></figure>

to a change in the stratification regime of the confined smoke. The presence of obstacles, particularly those simulating heavy goods vehicles, disrupts the thin stratified layer of light mixture beneath the ceiling that typically characterizes the confined smoke in an empty tunnel. Consequently, the mixture spreads throughout the entire height of the tunnel and becomes well-mixed with the ambient air. This increased mixing requires a higher extracted volume flow rate to achieve the confinement of the buoyant flow. In contrast, with square dampers, the flow is already unstratified and occupies the entire height of the tunnel, even when empty. Therefore, the presence of obstacles has a minimal effect on the extracted volume required for confinement.

3. Under pure transverse ventilation, the presence of vertical barriers positioned immediately downstream of the extraction points significantly improves the efficiency of all dampers, regardless of whether small or large blocks are used. The lateral square dampers benefit the most from the presence of these barriers, achieving $Fr_{e,c}$ values comparable to those of other vents. The barriers help maintain the buoyant release in stratified conditions, thereby limiting its mixing with the ambient air. While barriers do not affect the efficiency of rectangular dampers in an

empty tunnel, they enhance their performance when obstacles are present.

4. Similarly to pure transverse ventilation without vertical barriers, even when the horizontal fan is employed (i.e. combined ventilation condition), the presence of obstacles worsens the efficiency of the rectangular damper (i.e., for a fixed $Fr_t$, $Fr_{e,c}$ increases). With large obstacles, the behavior of these vents becomes comparable to that of the squared-centered ones. While a stratified regime of confined smoke can be achieved in an empty tunnel across various longitudinal velocities, this regime is unattainable when large obstacles are present.

5. Under combined ventilation, the simultaneous presence of obstacles and vertical barriers minimizes the performance differences among the three tested dampers. These differences are completely eliminated when large blocks are present. Additionally, barriers consistently enhance the combined ventilation performance in a tunnel with obstacles.

In conclusion, we have demonstrated that in the absence of vertical barriers, the efficiency gap between rectangular and centrally positioned square vents diminishes or disappears when cubic blocks are introduced into the tunnel. However, when vertical barriers are
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Direct comparison for each possible combination of damper type and obstacle size for the experiments with and without vertical barriers. All the points plotted in panels (a), (d), and (g) are taken from [30]. The marker shape is related to the different stratification regimes: circle (Regime I), square (Regime II), triangle (Regime III), and diamond (Regime IV).</figcaption></figure>

included alongside obstacles, they enhance the extraction performance for all damper configurations, resulting in similar behavior among all three types of vents.

Our findings highlight how outcomes from literature on empty road tunnel ventilation can be significantly altered by realistic traffic conditions. They underscore the critical importance of accounting for vehicle-induced turbulence when designing and implementing strategies for smoke confinement.

### CRediT authorship contribution statement

**Stefano Lanzini:** Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. **Cosimo Peruzzi:** Writing – original draft, Visualization, Validation, Supervision, Software, Methodology, Investigation, Formal analysis, Data curation. **Massimo Marro:** Writing – review & editing, Validation, Supervision, Software, Resources, Methodology, Investigation. **Livia Grandoni:** Writing – review & editing, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation. **Thierry Kubwimana:** Writing – review & editing, Project administration, Funding acquisition. **Antoine Mos:** Writing – review & editing, Project administration, Methodology, Funding acquisition. **Pietro Salizzoni:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization.

### Funding

This work was supported by the Région Auvergne-Rhône-Alpes (France) within the COVENTU Project (grant number: GFC 2020–043).

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The authors are grateful to the assistant-engineer Horacio Correia (LMFA) for the technical aid in the realization of the experimental set-up.

### Data availability

Data will be made available on request.
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