- 56 - CONSIDERATION OF DENSITY VARIATIONS IN THE DESIGN OF A VENTILATION SYSTEM FOR ROAD TUNNELS Gloth O., Rudolf A. ILF Consulting Engineers Zürich, Switzerland ABSTRACT This article investigates the effects of varying density on the design of a ventilation system. In particular the effect of strong local heat sources (e.g. fires) on the system behaviour will be discussed. Changes in density have different effects. If a given flow rate has to be achieved at a certain point in a tunnel system the density at this very point might be different from the density at a ventilator station. Hence, if the density at the ventilator station is higher, the volumetric flow rate achieved by the fan can be lower than the required flow rate at a particular point in the tunnel. Since the volumetric flow rate is directly related to the size of a turbo-machine, it can be an important reduction in investment costs. Another important effect is buoyancy. Temperature changes can lead to strong flows induced by the natural buoyancy of the air. The intention of this article is to highlight a few impacts these effects might have on the design of a ventilation system. 1. INTRODUCTION 1.1. Symbols The following symbols have been used in this article: p pressure [Pa] h elevation [m] T temperature [K or C] R individual gas constant of air [J kg -1 K -1 ] Re Reynolds number [1] Pr Prandtl number [1] Nu Nusselt number [1] g acceleration due to gravity [m s -2 ] ρ density [kg m -3 ] c specific heat [J kg -1 K -1 ] k heat conductivity [W K -1 m -1 ] V & volumetric flow rate [m 3 s -1 ] Q & heat flux [W] 1.2. Density Changes in Air Flow In the scope of this article air is considered to be a perfect gas. The relation between pressure, density and temperature is given by the ideal gas law p p = ρ RT ρ =. (1) RT For flow problems in tunnels, the influence of the temperature in (1) is more important than the pressure dependency of the density. Figure 1 shows the relation between pressure and density for a constant temperature of 20 C, as well as the temperature dependency for a constant pressure of 1013.25 mbar.
- 57-1.50 1.50 1.40 1.40 1.30 1.30 1.20 1.20 ρ [kg/m³] 1.10 1.00 ρ [kg/m³] 1.10 1.00 0.90 0.90 0.80 0.80 0.70 0.70 0.60 900 950 1000 1050 1100 0.60-20 30 80 130 180 p [mbar] T [ C] Figure 1: Temperature and pressure dependency of air density While pressure fluctuations of 100 mbar or more are a rare exception in tunnel aerodynamics, temperature variations of 200 C and more are very common design cases in case of emergencies. Because of the strong influence of the temperature great care has to be taken to model heat exchanges correctly. Pressure, density and temperature also vary with altitude. All computations in this article have used the following equation to determine the atmospheric conditions at a given elevation gh p = psea exp, (2) RT where p sea is the pressure at sea level. Under normal conditions a gradient of -6.5 Kkm -1 can be assumed for the temperature distribution. Figure 2 shows the density variations depending on the elevation. isothermal dt/dh = -6.5 K/km 1.30 1.30 1.20 1.20 1.10 1.10 ρ [kg/m³] 1.00 0.90 ρ [kg/m³] 1.00 0.90 0.80 0.80 0.70 0.70 0.60 0 1000 2000 3000 4000 5000 6000 0.60 0 1000 2000 3000 4000 5000 6000 h [m] h [m] 2. BUOYANCY EFFECTS Figure 2: Density variations with altitude This section shows what happens if a ventilation system is designed without buoyancy considerations and then is exposed to temperature differences between inside and outside. A computer model of a simple road tunnel has been created to show the effects of buoyancy. It is a fairly standard road tunnel with a cross section of 50 m 2 and a length of 2 kilometres. To illustrate buoyancy effects, it has an uphill grade of 2% and hence the difference in elevation between the two ends is 40 metres. The tunnel and the exhaust air channel are connected by three vents which split the tunnel in an upper and a lower half. Figure 3 shows a sketch of the
- 58 - model with the arrows indicating the airflow. The exhaust channel has a cross sectional area of 20 m 2 and is extended 100 metres sideways on either end (see also Figure 4). An axial fan is situated on both ends of the exhaust channel. Two additional jet fans are placed in the tunnel at 500 and 1500 metres. These jet fans will only be used if the flow velocities in the two branches of the main tunnel differ significantly. Figure 3: Schematic sketch of model tunnel Figure 4: Computer model of a generic road tunnel Both axial fans deliver a volumetric flow rate of 75 m 3 s -1. In absence of buoyancy this leads to an air velocity of 1.5 ms -1 in both branches towards the extraction point. A first simulation has been made with the design conditions (i.e. no temperature variations considered). This is mainly a check for the computational setup. As can be seen in Table 1 (scenario A), the velocities in the upper and lower half of the tunnel are almost equal. The yet existing small differences are caused by tiny density differences in the ambient conditions at the tunnel ends (see Figure 2). Density variations due to altitude differences can be neglected for most road tunnel applications. Only in nearly vertical shafts, they may have a significant influence. To show the impact of temperature differences between tunnel walls and ambient air, the tunnel wall temperature has now been set above (scenarios B, C and D), or below the ambient temperature (scenarios E, F and G). Table 1 gives an overview of the computed results. The
- 59 - average velocity varies significantly between the upper and lower branch. In the scenarios B and E, the velocity distribution is particularly asymmetric. Only if additional measures are taken (i.e. using the jet fans) a better flow can be achieved (scenarios C and F). An interesting alternative can also be to let buoyancy be the only driving force (i.e. all fans switched off). In the scenarios D and G it shows that a velocity above 1.5 ms -1 can be achieved by this strategy. This little example shows that natural buoyancy cannot be neglected for the design of a ventilation system. Please refer to Table 1 for a detailed summary of the results. The scenarios B, C and D represent conditions as they might be found in winter, and the scenarios E, F and G represent typical summer conditions. Table 1: Overview of different scenarios scenario A B C D E F G T wall C 10.0 10.0 10.0 10.0 15.0 15.0 15.0 T ambient C 10.0 0.0 0.0 0.0 25.0 25.0 25.0 lower jet fan d jet m 1.0 1.0 1.0 1.0 1.0 1.0 1.0 v jet ms -1 0.0 0.0 0.0 0.0 0.0 15.0 0.0 upper jet fan d jet m 1.0 1.0 1.0 1.0 1.0 1.0 1.0 v jet ms -1 0.0 0.0-15.0 0.0 0.0 0.0 0.0 lower fan Δ p Pa 35.8 37.7 35.6 0.0 34.1 32.1 0.0 V & m 3 s -1 75.0 75.0 75.0 0.0 75.0 75.0 0.0 upper fan Δ p Pa 35.6 27.5 25.2 0.0 42.7 40.9 0.0 V & m 3 s -1 75.0 75.0 75.0 0.0 75.0 75.0 0.0 lower half v ms -1 1.50 2.10 1.58 1.70 0.96 1.46-1.68 upper half v ms -1-1.50-0.83-1.35 1.73-2.09-1.60-1.71 3. INFLUENCE OF DENSITY VARIATIONS FOR EMERGENCIES The position of a ventilator station with respect to the position of a strong heat source (i.e. a fire) can have a strong influence on the design choices. If the fan is positioned close to a fire, it has to be capable of withstanding the hot gases from the fire. Also, due to the higher temperature, the density is significantly lower than in other areas. Thus, a machine which needs to deliver a given mass flow rate at one particular point in a tunnel system, can be smaller if it is placed where the density is expected to be higher. To illustrate this behaviour, a single gallery with a cross section of 20 m 2 and a length of 1000 metres shall be used. A computer simulation of this simplified example demonstrates the effects. The main relevant effects (i.e. convective heat transfer and heat conduction into the rock) shall be considered. On one side air with a temperature of 400 C enters the gallery. A flow rate of 200 m 3 s -1 has to be achieved. The difference between placing a fan 50 metres from the entrance or 50 metres from the exit is investigated. Operation of this exhaust fan shall be computed for two hours after the event. During this time, heat exchange between the hot air and the tunnel walls plays a decisive roll. Unlike real tunnel fires, this test case assumes a constant feed of air with a temperature of 400 C. This simplified example considers a homogeneous rock and air temperature of 20 C at the beginning of the test, i.e. the tunnel walls, as well as the rock behind them, initially have the same temperature. With time the heat penetrates into the rock. This penetration is governed by the equation for radial heat conduction.
- 60 - T k = t ρ c rock rock 2 T 2 r 1 T +. (3) r r For r the temperature remains constant, but the wall temperature and the temperature distribution inside the rock is left free to change. The heat exchange between the tunnel walls and the air flow has been modelled using the following empirical expression for the turbulent Nusselt number ( 0.78ln Re 1.5) 2 ( 0.78ln Re 1.5) RePr Nu =. (4) 2 3 8 1+ 12.7 Pr 8 2 The Nusselt number depends on the Reynolds and on the Prandtl number. The latter has been assumed to be 0.7 throughout this article. 3.1. Ventilator Operating in Hot Air A first case shall be simulated where the ventilator operates in hot air (50 metres from the entry). Figure 5 illustrates this setup. Figure 5: Fan operating in hot air The flow through this model gallery will be simulated for two hours of physical time. In Figure 5 the other possible position for the fan is indicated (50 metres from the exit). Probably a lower volumetric flow rate will be required at this point in order to achieve the same flow rate at the entry. The required flow rate will change over time. As the tunnel walls warm up the heat exchange between air and rock decreases. This heat exchange, however, is the reason for the higher density at the end of the gallery. If the conditions are kept up for an infinite time, the whole rock and the air will have the same temperature. In this case the difference in density is minor, because it is only related to the pressure drop along the tunnel. This difference can be neglected safely. In this example a maximal power of 15 kw is required to operate the fan. This maximal value occurs at the end of the two hour period. 3.2. Ventilator Operating in Colder Air To show the difference between operating a fan in cold or in hot air, the fan will now be placed closer to the exit. Figure 6 shows the new setup. The required volumetric flow rate can be extracted from the previous simulation (V & =160 m 3 s -1 ). For this setup a maximal power of 13 kw at the beginning of the two hour period is required.
- 61 - Figure 6: Fan operating in colder air 3.3. Comparison Between Hot and Cold Operation The power requirement for the ventilator close to the exit is significantly lower. Figure 8 shows the evolution of the power consumption over time for both ventilator positions. In Figure 7 the volumetric flow rate at the position 50 metres from the entry can be viewed. It can be observed that for the two hours of operation the flow rate is higher if the fan is placed close to the exit. This could potentially give more security, while still requiring a smaller investment. The size of the machine, the maximal power requirement and the resistance to heat are all in favour of a position close to the exit. Figure 10 and Figure 11 show the evolution of air and wall temperature along the gallery. The lines represent different points in time (t = 20 min, 40 min, 60 min, 80 min, 100 min and 120 min). With increasing time the temperature increases as well. Initially both setups require the same power. As the tunnel heats up, the required power for the fan on the entry side increases. For the alternative fan position, on the other hand, the power decreases. Most of the time, the volumetric flow rate is significantly higher than for the hot fan position. Note has to be taken that the transient behaviour of the fans has not been modelled correctly. Thus the first fifteen minutes are left out of Figure 7 and Figure 8 due to the strong transient effects in this period. The volumetric flow rate has been enforced in the computer model. This can lead to unrealistically high forces. To model this phase accurately, the detailed fan behaviour (i.e. the compressor map) needs to be put into the computer model. It is, however, believed that the general trend and the maximal and minimal values are represented correctly. 4. CONCLUSIONS Density variations in tunnel systems can lead to strong effects. These effects cannot be neglected during the design phase of such a system. The comparison between a hot and a cold position for a ventilator station highlights a few important facts. The cold fan saves about 13% for the installed power requirement A cold fan could have a roughly 10% smaller diameter (based on the lower volumetric flow rate) A fan in a cold area experiences lower temperatures (see Fehler! Verweisquelle konnte nicht gefunden werden.) All these points could cut investment costs, if axial smoke extraction fans are positioned as far away from potential fires as possible.
- 62-230 fan 50 m from entry fan 50 m from exit 220 P [kw] 210 200 190 0 15 30 45 60 75 90 105 120 t [min] Figure 7: Volumetric flow rate 50 metres from the entry 15 fan 50 m from entry fan 50 m from exit 14 P [kw] 13 12 0 15 30 45 60 75 90 105 120 t [min] Figure 8: Power consumption of the two different ventilator stations 450 400 fan 50 m from entry fan 50 m from exit 350 T [ o C] 300 250 200 150 0 15 30 45 60 75 90 105 120 t [min] Figure 9: Temperature at ventilator stations
- 63-400 350 T [ o C] 300 250 200 0 200 400 600 800 1000 x [m] Figure 10: Air temperature evolution 250 200 T [ o C] 150 100 50 0 200 400 600 800 1000 x [m] Figure 11: Wall temperature evolution