Some Thoughts on Initial Flow Conditions for Fire Modelling in Tunnels
By: Wojciech Węgrzyński, Building Research Institute (ITB), Poland
Paulina Jamińska-Gadomska, Building Research Institute (ITB), Poland
Tomasz Burdzy, Building Research Institute (ITB), Poland
Jakub Bielawski, Building Research Institute (ITB), Poland
Aleksander Król, Silesian University of Technology, Poland
Małgorzata Król, Silesian University of Technology, Poland
Introduction
Fire safety of tunnels is paramount in their development. Engineering analyses, often including advanced numerical tools like CFD modelling, are common in assessing safety. However, based on recent first-hand experience delivering two large tunnelling projects in Poland, some reservations regarding the common approach to initial conditions in CFD simulations can be formed.
A common practice is initializing the flow field inside a CFD model in a quiescent state. That means that upon initialization of the numerical analyses (t = 0 s), there are no significant flows in the model. Then, as the simulation is solved, the resulting flow field results from the fire and the operation of the smoke control systems in the tunnel. External conditions such as wind are not always considered and are sometimes implemented as a flow boundary condition (but rarely as an initial condition). Interestingly, a similar “image” of a flow in a quiescent tunnel is often observed in the commissioning stage, where the tests are also carried out in an empty tunnel in favorable flow conditions, Fig. 1, similar to those observed in CFD modelling. This usually includes the formation of an axisymmetric smoke plume, symmetric flow into both directions (in some cases one, dependent on inclination) and the formation of a smoke layer underneath the tunnel ceiling. Formation of the latter is often considered a prerequisite for the safe evacuation of the tunnel – if an undisturbed smoke layer is floating above the occupants' heads, there is a good chance that tenable evacuation conditions may be achieved.
Figure 1. Hot smoke test in an empty tunnel, visible buoyant axisymmetric plume above the source of heat (approx. 1,5 MW)
Contrary to the description above, the tunnels in their operation are not a quiescent environment. A case can be brought that the combined action of wind and traffic (piston effect) will always result in a flow in the tunnel. However, based on the Authors’ experience, the wind condition is usually considered irrelevant, or one arbitrary wind velocity and direction is considered. In the case of commissioning, we get to work with whatever wind occurred on the day of the test. It would also not be uncommon to fit the testing schedule to the weather forecast, so the most adverse winds are avoided. The second missing element is the traffic. Tunnels are never quiescent unless there is no traffic in them. However, in that case, whose safety are we worried about? The scenarios important for the fire safety engineer usually refer to traffic jams (though please note, a full stop is rare) or peak traffic with the maximum number of potential victims for the fire [1]. In such scenarios, the flow in the tunnel is immanent to the traffic.
The momentum equation
If one tries to determine the flow in the tunnel, it is possible by calculating the pressures (forces) acting in the tunnel and resistances posed by the walls and other obstacles. In essence, this is a solution of the momentum transfer equation and allows to approximate the flow velocity relevant to input variables. This approach is usually applied to determine the performance characteristics of longitudinal ventilation (for detailed methodology, please refer to section 12.3 of [2]). In addition, it may be directly used to compare the resulting velocity to the primary performance characteristic of the longitudinal system – the critical velocity [3]. The constituents of the estimation are:
- Smoke control operation (jet-fans);
- Wind pressure at the portals;
- Chimney effect;
- Piston or drag effect per traffic lane;
- Pressure loss at the entrances to the tunnel;
- Pressure loss at the walls of the tunnel;
- Pressure loss at the stopped vehicles;
- Fire throttling effect;
- Atmospheric pressure difference.
Keep in mind that fire considerations are usually done for a steady-state. Thus, traffic drag is not considered a source of momentum; instead, stopped vehicles are considered a resistance. In this setting, the wind is the most significant force acting on the flow in the tunnel.
Wind
A comprehensive review of the literature on wind research for tunnels was given in [4]. Wind action may create an overpressure (or underpressure) at the tunnel portals. The pressure rise at the tunnel portal forces a flow into the tunnel. The effectiveness of this action is related to the type of the tunnel portal and its surroundings [5]. An example solution of the pressure rise at the tunnel portals of Martwa Wisła Tunnel in Gdańsk is presented in Fig. 2. For an extreme case wind velocity of 15 m/s and a flow direction perpendicular to the tunnel portal (0°), we have estimated that the pressure rise at the portal can exceed 150 Pa. However, that is for a rare wind condition case. If one resorts to the 95th percentile of wind in this region, which correlates to 7 m/s (Fig. 2), this pressure increase will be in the range of 25 Pa, which is a much lower but still considerable value.
Furthermore, one must also realize that wind impact on this tunnel portal can be an issue only for a specific angle of wind attack. In the analyzed case, the overpressure at the tunnel portal is observed only for 1/3rd of the wind directions. The complexity related to wind velocity and direction introduces significant issues with identifying the representative scenarios for analyses of the safety in the tunnels. With hand calculations or 1D models, the probabilistic approach can be used. However, this is not feasible for CFD modelling, and just using the most unfavorable probable wind seems to be the best solution. Alternatively, employing steady-state wind analyses without fire and then using the worst-case scenario as the input to the fire analysis may be a sound approach [6].
Figure 2. Wind pressure at the tunnel portal for different wind speeds and wind angles, a case study of Martwa Wisła Tunnel in Gdańsk, Poland
An example of the impact of the unfavorable wind on the flow inside of an empty tunnel is shown in Fig. 3. We have approximated air velocities in an empty tunnel from the dynamic pressure at the tunnel portal, given the discharge coefficient of a portal of Cd = 0,4 [-] and ignoring all resistances (walls, stopped vehicles) and thermal effects. In this simple case, a wind velocity of just 4.00 m/s (in Poland – commonly the median wind velocity) can create flow inside a tunnel exceeding 2.00 m/s, which is sufficient to disturb a buoyant thermal plume. In consequence, the idealistic conditions of an axisymmetric plume and a stable hot smoke layer, as seen in Fig. 1, may not be achieved. This may lead to dangerous mixing of hot smoke with air, which fills the tunnel’s cross section, as shown in Fig. 4.
Figure 3. Air velocity in the tunnel approximated from wind velocity, ignoring wall and local resistance
Figure 4. Hot smoke test performed in strong wind conditions, the flow inside the tunnel exceeds 2.00 m/s and creates a mixing of the smoke and airflow in the tunnel, disturbing the plume and smoke layer
Traffic
The second “missing” aspect of fire simulations is the inclusion of traffic. A common explanation is that the traffic stops in the event of a fire and thus becomes irrelevant. Nevertheless, this being true, due to the inertia of the air moved by the running vehicles, it may take a few minutes for the flow to come to a complete stop [7]. It is these critical minutes in which the evacuation takes place, thus as posed in the title of this paper – it becomes a critical initial condition often overlooked in the CFD modelling.
The existing guidelines, such as the previously mentioned PIARC recommendations, give an approximate solution to the piston effect introduced by the traffic.
(1)
In equation 1, the value of the aerodynamic drag coefficient c_x ranges, in open space, from about 0.3 (for modern passenger cars) to almost 1 (for box-shaped vehicles like trucks, HGVs, and buses). The total force of the aerodynamic drag acting on the vehicle also depends on its cross-sectional area in the direction of movement. This is the same force that sets the tunnel’s air in motion. If there are many (n) vehicles moving in the tunnel at the same speed, the momentum transferred to the air (Δp_veh) in a period Δt is (Av denotes the area of a vehicle cross-section in the direction of movement, ϱ is air density):
. (2)
This approach can be used for steady traffic with a known speed. However, our recent research has shown that this approach can be further improved by incorporating the effects of multiple vehicle aerodynamics in the tunnel, which significantly change the drag coefficient with an increased traffic intensity in the tunnel. The results of this work will be published shortly [8]. Some initial results of this study correlating the air velocity in the tunnel with traffic intensity and average vehicle speed with the use of a novel improved methodology for the Martwa Wisła Tunnel (unidirectional, 2 + 1 traffic lanes, 1378 m long) in Gdańsk, Poland is shown on Fig. 5.
Figure 5. Theoretical relation between traffic intensity and air velocity due to the piston effect, a) dependence on traffic intensity, b) dependence on vehicle speed [8]
Wind and Traffic
Based on the abovementioned considerations, it may be interesting to investigate the traffic and wind together as a complete initial condition in the numerical analysis. When wind and traffic are in the same direction, the flows generated by these phenomena add up together. When the wind is acting against the traffic, it is interesting to understand in which direction the flow in the tunnel will occur. In the case of unidirectional tunnels, the most dangerous flow caused by the wind is the flow in the direction opposing the traffic direction. This means that the wind may push the smoke toward people in vehicles stopped behind the fire.
Based on our observations and preliminary calculations (see Fig. 5), even at a very low traffic intensity, the flow from vehicle drag can overcome the flow created by the wind. This was a subject of an experimental study performed in the S2 POW Tunnel (unidirectional, 3 + 1 lanes, 2335 m long) in Warsaw, Poland. On an experimental day, we had a very high average wind velocity (approx. 7 - 8 m/s) and the direction opposite the traffic direction in the tested tube and perpendicular to the tunnel portal. During the experiment, we conducted a drive through the tunnel with 20 passenger vehicles of different sizes at 3 s intervals (traffic intensity of approx. 400 veh/h), and at a different speed. Without the traffic created by us, the average velocity in the tunnel ranged between 3,5 – 4 m/s. During an 80 km/h drive-through, this was reduced to approximately 2.00 m/s, indicating that vehicles easily overcome the wind effect in the tunnel. Based on the results of [8], one could expect that at higher traffic intensities, the wind effect could be neglected entirely, and the flow reversed. The resulting air velocity for drive-through with 80 km/h, 50 km/h and 30 km/h are shown on the graph, Fig. 6.
Figure 6. Reduction of air flow velocity in a tunnel tube after passing of 20 vehicles with constant speed
Conclusions
Road tunnels are not a quiescent environment. A constant flow of air seems an intrinsic property of the tunnel environment, yet it is rarely reflected as an initial condition in the engineering analyses. In our opinion, the realism of simulations could be significantly improved if the initial airflow in the tunnel is an outcome of a preliminary analysis. As we consider how to implement better initial conditions, new challenges appear - what wind and traffic conditions should be considered as representative / most onerous? The answer to the first one is the critical question in the research grant OPUS 19 carried in the Building Research Institute. The questions related to the traffic structure in road tunnels and the impact of the traffic on airflow are in the focal point of the researchers at the Silesian University of Technology. We hope that by combining our expertise and further efforts in both directions, we will be able to propose a framework for generating the initial conditions for road tunnel simulations, both for the probabilistic or risk-based approach with simple tools and for the advanced numerical modelling with the use of CFD.
Funding disclaimer
Part of the research presented in this paper was financed by the National Science Centre, Poland, based on a contract for the implementation and financing of research project No 2020/37/B/ST8/03839
References
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[2] PIARC Committee on Road Tunnels Operation (C3.3), SYSTEMS AND EQUIPMENT FOR FIRE AND SMOKE CONTROL IN ROAD TUNNELS, 2007.
[3] NFPA, NFPA 502: Standard for Road Tunnels, Bridges, and Other Limited Access Highways, (2017).
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