Aerodynamic Effects in Railway Tunnels
as Speed is Increased
V. Bourquin, C. Béguin, and P.A. Monkewitz
Swiss Federal Institute of Technology, Laboratory of Fluid Mechanics, EPFLLMF, CH-1015 Lausanne, Switzerland. bourquin@mac.com
Abstract
The aerodynamic effects occurring in a tunnel as a train moves into or through
it are totally different from those observed in the open air and their amplitude
and severity grow as the train speed is increased. The flow in the whole tunnel
needs to be considered in the same time as the flow in the vicinity of the vehicle. Aerodynamic forces, pressure waves and acoustics have a strong impact on
safety and comfort issues.
When a train enters into a tunnel, a compression wave is generated, propagates through the tunnel and is reflected at the tunnel extremity. During the
reflection process a part of the wave is transmitted outside the tunnel in the
form of a micro-pressure wave, which may generate a “sonic boom” problem,
depending on the shape of the incident wave, in particular the gradient of the
wavefront. The shape of the wave changes as it propagates through the tunnel
under the influence of the unsteady viscous effects (in particular skin friction
at the tunnel wall), the non-linear effects and the presence of material and
components in the tunnel (for example, ballast or niches). Measurements of
the skin friction behind a pressure wave are presented.
Introduction
The development of improved transportation systems is highly desirable and is
corroborated by the necessity to satisfy long-term sustainable objectives, in
particular more environmental responsibility [2]. In this context, solutions
need to be found to lower the energy consumption, the emission of pollutants
and the environmental impacts. This effort is characterized by both the improvement of existing ground transportation systems (with new generations of
railway systems, for example), as well as the emergence of new transportation
technologies and systems (Swissmetro, ET3, MLX, Transrapid, etc.)[3]. For
railway systems, these developments, aiming at increasing the competitiveness
of the railway systems, have lead to a significant increase of the commercial
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V. Bourquin, C. Béguin, and P.A. Monkewitz
speed and the building of more and more tunnels of increasing length. The essential advantage of a tunnel is that the environmental impacts observed in the
open air are reduced. A new one, the “sonic boom”, may appear and impair
the comfort of people living in residential area close to the tunnel portals.
The presence of the tunnel confines the air flow to a finite domain and constrains the air perturbations generated by the vehicle to propagate along the
axis of the tunnel only. The general flow can be divided in two different flow
domains, which are the near-field flow (in the vicinity of the vehicle) and the
far-field flow (far from the vehicle, corresponds to the flow in the tunnel).
Both domains are strongly dependant to each other.
The near-field flow is strongly influenced by the blockage ratio ß defined as:
ß = Av / At
(1)
In which Av is the cross-section of the vehicle and At the cross-section of the
tunnel. In long tunnels, at moderate speeds and blockage ratios (railways
situation), the flow in the annular space1 is essentially driven by the pressure
gradient and the relative speed between the train and tunnel walls (see Eder &
Sockel, 1985 [7]). As the speed or/and the blockage ratio are increased, the air
flow velocity increases, as well as the momentum loss along the vehicle. Drag
becomes a key issue. The amount of energy necessary to overcome the aerodynamic drag at 300 km/h in the open air is of the order of 80% of the total resistance. In a tunnel, it easily exceeds 90%. This substantial increase is essentially due to the presence of a flow in the tunnel, increasing the pressure in
front of the vehicle and decreases it behind. The drag does not only depend on
the train characteristics, but also significantly on the tunnel characteristics.
This dependency on the train and environment characteristics associated with
the high length to width of trains makes it necessary to use rigs with moving
models such as the MMR (Moving Model Rig) operated by AEA Tech. Rail in
Derby (UK), see [20],[21] and [24].
As speed, train length and blockage ratio are increased, compressibility effects become significant and the flow at the end of the annulus may even
choke (i.e. it reaches the sonic speed), see [4], [8] and [12]. Such complex
flows have been studied in the framework of projects of vehicles operated in
evacuated tunnels (5 to 10% of the atmospheric value for the case of the
Swissmetro project). The low pressure allows to reduce the size of the tunnel
and to lower the total energy consumption of the system.
The transverse forces are another category of force-related effects induced by
side-winds, train passing or flow instabilities. Usually unsteady, the transverse
forces have an impact on the stability (safety), the ageing of the structure (fatigue) and the dynamic comfort of the passengers (transverse accelerations).
The far-field flow is considered as essentially one-dimensional and unsteady
(see Hammitt, 1975 [9] and Sockel, 1989 [10]). In tunnels of short to me1
The annular space (also referred to as annulus) is defined as the volume between the vehicle and tunnel walls: following the flow, it starts at the end of the nose and ends at the start
of the tail.
Aerodynamic Effects in Railway Tunnels as Speed is Increased
433
dium length, the unsteadiness of the flow is due to the train-tunnel entry pressure waves. The transmission of these pressure waves inside coaches generates a
comfort problem since the internal ear of the human being is very sensitive to
pressure level changes (amplitude and rate). This problem can be a limiting
factor while defining speed and blockage ratio. The sealing efficiency and the
stiffness of coaches can be increased to limit the pressure variations at the ear
of passengers during tunnel travel. In long tunnels, these pressure waves are
strongly attenuated and, after a given travel time, the unsteady effects are essentially associated with the motion of the train. In this situation, the dragrelated effects become dominant.
The oncoming of a high-speed train in an underground station can induce
high air velocities, which must be controlled by an appropriate design in order
to satisfy the comfort and safety criteria for the passengers on the platforms
and in the station. Ventilation is another key aspect to preserve the air quality
and to maintain the temperature within acceptable values.
Pressure wave effects in tunnels
In the open air, pressure effects are associated with the pressure distribution in
the near-field flow of the moving train (in particular at its extremities): when a
train passes another train or a stationary object, an unsteady pressure loading
appears, which is associated with the train motion. In tunnels, two types of
pressure waves related effects should be considered: (1) The short term situation is essentially characterized by the pressure waves provoked by the traintunnel entry or the acceleration of a train in a tunnel; (2) The long term situation is characterized by a strong attenuation of the pressure waves and the
buildup of a pressure profile in the tunnel moving with the train (the characteristic length of this profile is much longer than the train length). The shortterm effects are dominating in tunnels shorter than 15 km. It depends essentially on the initial amplitude of the wave and on how waves are influenced by
the presence of ballast, the friction and heat transfer effects, as well as by the
presence of connections to another tunnel (pressure relief ducts) or to the atmosphere (shafts).
Focusing on waves produced by the train-tunnel entry in tunnels of medium length, it is useful to consider separately the pressure wave generation, its
propagation and the reflection process including the emission of micropressure waves.
Pressure wave generation
Pressure waves are generated during the train-tunnel entry or exit. Additional
pressure waves are generated when the train passes a location in the tunnel
where a change of the cross-sectional area occurs or near an airshaft of important cross-section, as well as in the case of a train-passing situation inside the
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V. Bourquin, C. Béguin, and P.A. Monkewitz
tunnel. The initial gradient of the wavefront is directly related to the nose
shape, the portal shape, blockage ratio and the speed of the train.
A typical shape of the pressure signal recorded in a tunnel, as a train enters
into it, is shown in the following figure (from the TRANSAERO project, see
e.g. [11]):
Pressure
Secondary pressure
rise due to the friction
effects in the annular
space
Primary pressure
rise due to nose entry
Pressure drop due to
the passage of the nose
in front of the
transducer
Preliminary pressure
rise due to the flow
ahead of the train nose
0
Actual train entry
Time
Fig. 1. Pressure history measured close to the tunnel entry (typical amplitude
1’500 Pa)
The maximal amplitude generated as the train enters into the tunnel depends essentially on the speed and the blockage ratio. State-of-the-art numerical methods and the use of a facility such as the MMR allow an accurate prediction of the pressure wave profile during the generation process [24].
Pressure wave propagation
As the wave propagates, changes in its amplitude and gradient are influenced
by the nonlinear effects, the friction and the heat transfer to the tunnel walls as
well as mass transfer (through ducts or ballast). The tunnel characteristics are
of primary importance (mainly roughness, perimeter, length, presence and
characteristics of ballast or niches, tunnel equipment, connections to the atmosphere or to another tunnel, changes of cross-section). The presence of
other vehicles and their associated pressure waves will also affect the unsteady
pressure profile in the tunnel. One problem is the superposition of the waves,
in particular for short tunnels (see Schultz & Sockel, 1991 [13]), that may lead
to severe unpleasant peak-to-peak amplitudes. The phenomena involved in the
propagation problem will be addressed later in this article.
Pressure wave reflection at the portals
The waves are reflected at the open extremities of the tunnel and part of their
energy is transmitted out of the tunnel in the form of micro-pressure waves.
Aerodynamic Effects in Railway Tunnels as Speed is Increased
435
Their amplitude depends on the ratio between the wavelength and the tunnel
diameter. This may lead, under some circumstances, to a “sonic boom”, an
unpleasant noise for people living in the vicinity of a tunnel portal. Accounting for the unsteady viscous effects appearing during this wave reflection process (shear flow, vortices, etc.), the flow is actually quite complex. The problem
of the emission of micro-pressure waves at the exit of a tunnel has been studied
since the 70’s in Japan. Descriptions can be found in Hammitt, 1973 [4],
Matsuo et al., 1997 [5] and Ozawa et al., 1995 [138]. This problem has been
addressed in the framework of the TRANSAERO project [11]. Very accurate
predictions have been obtained by Reiterer, Ehrendorfer and Sockel, 2002
[16].
Experimental measurements associated with the propagation of a
pressure wave
The behavior of pressure waves in full-scale tunnels has been investigated by
several authors (see e.g. Ozawa et al., 1994 [14], Grégoire et al., 1997 [15]).
The attenuation of the amplitude and the change in the gradient are of primary importance for the tunnel design. Non-linear effects tend to steepen the
wavefront and viscous and additional effects tend to weaken the wavefront.
Tests were carried out on a shock tube by Matsuo et al., 1991 [17]. The
scale of the facility is approximately 1/310 and its length is about 20 m. The
effect of the unsteady friction could be noticed particularly for pressure steps of
low amplitudes. These authors have shown that a pressure wave amplitude exists at which the gradient is stabilized at a constant value during the propagation (7 kPa for this facility). Comparing with full-scale data, it appears that the
attenuation of the waves is more than an order of magnitude smaller. A real
tunnel is actually much more complex than most experimental facility (presence of equipment, niches, rails, wires, pipes, etc.). The presence of ballast has
also a strong influence on the pressure shape and wavefront, but in this case a
dynamic effect occurs in the void space of the ballast ([12] and [19]). Oda et
al., 1997 [18], have recorded pressure waves in a tunnel on their highperformance moving model facility (the propagation of a wave over 62.3 m has
been analyzed at scale 1/30 and compared with numerical results). A.E. Vardy
has proposed different models that can be used in numerical methods to account for the propagation effects (see e.g. [22], [23]).
The STARLET facility has been built at EPFL to study the propagation of
pressure waves in long tunnels. The length of the facility is 120 m. The inner
diameter is 176.2 mm (typical scale 1/50). Two devices are used to generate
pressure waves: (1) Diaphragm: the facility is used as a shock tube with a paper
diaphragm separating a high-pressure zone from the rest of the facility (atmospheric pressure). With this method, essentially pressure steps (weak shocks)
can be generated. (2) Valve: the facility is kept at low pressure and pressure
waves are generated as the valve opens and let air at atmospheric pressure
flowing into the tube.
436
V. Bourquin, C. Béguin, and P.A. Monkewitz
Fig. 2.
Picture of the STARLET facility located in a service tunnel at EPFL,
Lausanne
Pressure measurements are done using Kulite XT-190 pressure transducers
with a specific data acquisition module developed by the company Gillièron
électronique Ltd (Morges, Switzerland). The measurement of the skin friction
is done using a transducer developed at EPFL specifically for this application.
The measurement makes use of the analogy between the heat transfer at the
wall and the skin friction. An electrical current heats a thin film of platinum at
the wall. An appropriate electronic regulating device (hot-wire anemometer of
type TSI-1054a) keeps the temperature of this film constant. The magnitude
of the skin friction is related to the electrical power required to keep the platinum film at a constant temperature. The sensor is made of a thin platinum
film (800 x 50 mm, thickness: 0.1 mm) deposited on a pyrex substrate (see
Figure 3). The electrical connections are thin gold contact areas deposited by
vacuum evaporation (triangles on figure 3, thickness: 0.3 mm). The time response of the transducer is 0.05 ms. The overheat ratio is set at 1.4. The transducer has been calibrated in a wind tunnel [25].
Fig. 3.
Picture of the transducer used to measure skin friction
Experimental results
Figure 4 shows the superposition of the pressure histories of 3 weak shock
waves of different amplitudes (6’100 Pa, 7’800 Pa and 16’600 Pa) recorded at
two different locations along the facility. The first location (IB-1) is located at
Aerodynamic Effects in Railway Tunnels as Speed is Increased
437
a distance of 10.19 m from the diaphragm. The second one (IB-2) is located at
a distance of 50.95 m from IB-1. IB is an acronym for Instrumentation Block.
Fig. 4. Pressure histories for three different pressure levels at 50.95 meter distance, see [11]
The pressure histories recorded close to the diaphragm (IB-1) shows a typical step shape for a shock tube experiment. The pressure histories recorded at
the IB-2 location are characterized by slight differences close to the wavefront,
as well as lower amplitude due to dissipative effects. A “rounding” of the “corner” can be noticed on the two low-amplitude pressure steps (6’100 & 7’800
Pa). This is due to the unsteady friction. The flow just behind the pressure
step is laminar and the value of the unsteady friction is very high close to the
pressure step and decreases until the start of the transition to turbulence. As
the flow is getting turbulent, higher values of the skin friction are reached.
This unsteady skin friction profile behind the pressure wave has a significant
impact on the shape of the pressure wave close to the wavefront as the wave
travels over long distances (kilometers in the case of railway tunnels).
The definition of the transitional Reynolds number Retr can be done as follows:
In which, uw = wave velocity; u0, w0 = flow velocity (u in the tube referential, w in the wave referential); x = distance between the wave front and the
transition point; ttr time to transition after the passing of wavefront; nt = kinematic viscosity.
For weak pressure waves the flow velocity is proportional to the amplitude
of the pressure step and therefore the transition time is inversely proportional
to the square of the pressure step amplitude. Works undertaken by Hartunian
et al. [26], 1960 and Aoki, 1996 [27] have shown that the transition appears at
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V. Bourquin, C. Béguin, and P.A. Monkewitz
a distance from the wavefront characterized by a Reynolds number Retr of approx. 106. For the profiles shown on Fig. 4, the time values to transition are
(from low to high pressure amplitude): 0.068 s, 0.041 s and 0.0093 s. The
laminar part of the pressure step of highest amplitude is very small and is close
to the maximal value of the pressure history recorded on IB-2.
Figure 5 shows the measured history of the skin friction for a pressure step
of an amplitude of 5’800 Pa. The air velocity induced by this wave is approx.
14.5 m/s. The laminar part is clearly visible on the left. It can be seen that the
flow is fully laminar until a time of 0.012 s (corresponding to a Retr of 2.105).
Then, instabilities appear and a transitional zone starts.
Fig. 5. Measurement of skin friction 10.19 m away from the diaphragm. The
pressure step amplitude is 5’800 Pa (shape is similar as what was recorded on
IB-1 location, see Fig. 4).
It is difficult to define at what time the flow is fully turbulent on this graph.
The expansion wave limits the recording time. A longer pressure step would be
required to analyze the transition and turbulence zone in deeper details. This
can be obtained by an increase in length of the facility.
It is interesting to note that the shape of the first two peaks in the first part
of the transition zone (up to 0,02 s) is different from the following ones. This
can be compared to the observations of “turbulent bursts” by Dillon and Nagamatsu, 1984, [28]. The precision of the measurement technique is approx.
5%. But it must be stated that the flow is very sensitive to small geometrical
perturbations close to the transducer, as well as difference in level between the
transducer and the tube wall. Attention has been paid to minimize these perturbations, but a systematic error may appear and it is difficult to evaluate it
precisely. Based on wind tunnel experience and the shock tube peculiarities,
Aerodynamic Effects in Railway Tunnels as Speed is Increased
439
the uncertainty was estimated at 40%. Further development of the measurement technique is necessary to evaluate more precisely and reduce this uncertainty.
Considering the railway systems, the pressure waves generated by a train is
of slightly lower amplitude and the wavefront is not a pressure step, but a pressure wave. Additional experiments are necessary to evaluate the effects of a
gradual pressure increase on the shape of the unsteady skin friction profile. It
appears nevertheless that the wavefront is probably influenced at least by the
laminar and transitional part of the unsteady skin friction profile. The modeling of the unsteady laminar and turbulent skin friction in numerical codes
have been studied by many authors [12],[23],[29]. Improving these models
also requires experimental data, in particular to account for the transition and
to model the turbulent part more accurately.
Conclusion and prospects
The aerodynamic effects appearing in railway tunnels have been described and
the preliminary results of a study on the propagation of pressure waves in tunnels have been presented. The context of this work is the research effort done
to understand and model tunnel flows for railway systems and new transportation systems, such as Swissmetro or ET3. The importance of the unsteady skin
friction behind a pressure wave appears clearly from the measurements, in particular, the importance and peculiarities of the transition from a laminar to a
turbulent flow.
This research has been motivated by the importance of improving models to
predict the propagation of pressure waves for the design and operation of railway tunnels. Another area in which similar effects can be observed is during
the repressurisation (for safety reasons) of an initially evacuated tunnel, for the
case of vacuum-based transport system in development. The constraints due to
aerodynamic effects have a significant impact on the costs of both tunnels and
trains. Aerodynamics is as well a key issue in the performance of high-speed
systems, in terms of energy consumption and performance.
Research projects such as TRANSAERO have provided an opportunity to
develop methodologies and tools for the improvement of the performances of
existing railway systems. On the other hand, projects as Swissmetro or ET3
show that there is a potential for new transport systems to address sustainability issues and opening new fields for aerodynamic research.
The results presented in this paper have shown the limits of the Starlet facility. In order to investigate in more details the skin friction behind a pressure
wave, it is necessary to improve the following points: 1) to increase the length
of the facility to be able to record pressure histories over a longer time behind
the pressure wave; 2) to generate different shape of pressure waves in order to
measure the influence of the gradient on the transition; 3) to investigate in
deeper details the transition; 4) to improve the unsteady skin friction measurement and to apply other techniques as well.
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V. Bourquin, C. Béguin, and P.A. Monkewitz
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