Flow-induced Vibration of High-Speed Trains in
Tunnels
Masahiro Suzuki
Railway Technical Research Institute, 2-8-38 Hikari-cho, Kokubunji-shi,
Tokyo 185-8540, JAPAN
Abstract
The lateral vibration of high-speed trains in tunnels has recently become a
subject of discussions concerning riding comfort. The paper describes the phenomenon, its mechanism and countermeasures.
First, running tests revealed that the aerodynamic force in tunnel sections is
much greater than that in open sections. The aerodynamic force and the vibration in tunnel sections gradually increased from the head toward the tail of
a train set; and the yawing vibration of cars had a close relation with the aerodynamic force.
Second, to clarify the interaction between the vehicle dynamics and the
aerodynamic force, the flow field around a scale model, which was forcibly vibrated, was analyzed by a wind tunnel experiment. The results showed that a
pressure field that had the same properties as those of real trains was found
even though the train model did not vibrate. The effect of vibration on the
flow field was small and thus the phenomenon was considered as a forced vibration by the aerodynamic force.
Third, to investigate the aerodynamic force, numerical simulations were
conducted. The computation proved that the cause of the large pressure fluctuation at the tail is the flow separation by the sudden expansion of the effective flow area. It also revealed that the flow becomes unstable under the train.
The resulting vortices are spread on the train side by the tunnel wall, and then
the unsteady aerodynamic force is generated when the vortices pass.
Finally, to derive an optimal shape, which suppresses the unsteady aerodynamic force, scale model tests were conducted. The results showed that a long
nose effectively decreases the large pressure fluctuation at the tail. Rounding
the lower section of the car and installing fins under the train were also shown
to be effective countermeasures for reducing the unsteady aerodynamic force.
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1. Introduction
As the maximum speed of Shinkansen trains in Japan increases, vibration of
the trains has recently become a subject of discussion especially concerning
riding comfort. This phenomenon has the following characteristics (Fujimoto
et al. 1995). (1) The vibration amplitude of the train in tunnel sections is
more noticeable than in open sections (fig. 1), (2) it gradually increases from
the head toward the tail of the train set, and (3) the yawing vibration is more
prominent than the other vibrations.
Fig. 1. Time history of yawing angular acceleration of a train entering a tunnel (train speed: 300
km/h).
Since mountains account for about 70 % of Japan's total land area, there
are a large number of tunnels in its railway system. For example, half of the
Sanyo Shinkansen line, which connects Osaka and Hakata (622.3 km), is in
tunnels. So, the riding quality in tunnel is critical for service. Therefore, intensive studies have been carried out to solve the problem of vibration in tunnels.
Track irregularity was considered at the initial stage as one of the factors
causing the phenomenon. However, there was no correlation between the vibration and the track irregularity in the tunnel sections (Takai 1989). Another
factor, namely aerodynamic force, has also attracted attention. As for the
aerodynamic force, the effect of Karman-like vortices on the vibrations of the
train had been suggested. But, no mechanisms had been clarified in detail at
this first stage. Thus, we have been extensively investigating flow around the
trains in tunnel by running tests, wind tunnel experiments and computer
simulations.
The paper describes the phenomenon, its mechanism and countermeasures
from our studies.
2. Characteristics of the phenomenon
In this section, we describe some characteristics of the phenomenon that have
been revealed by the analysis of the running test data (Suzuki 2000).
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Fig. 2. Time history of aerodynamic yawing moment acting on a train entering a tunnel (train
speed: 300 km/h).
Fig. 3. Time histories of work done by aerodynamic force (train speed: 300 km/h).
To clarify the effect of aerodynamic force, we set several sensors on the
train side in a running test. From the pressure data, we calculated aerodynamic yawing moment (fig. 2). The train speed was 300 km/h. When the
train ran in the open section, the aerodynamic force was small. However, once
the train went into the tunnel, the aerodynamic force suddenly increased.
Figure 3 shows the work done by the aerodynamic force on a car. When
the train ran in the open section, the work was nearly zero. In the tunnel section, however, the aerodynamic force clearly vibrated the train.
Figure 4 is a typical chart of the pressure on each side of a train entering a
tunnel. The course of the train deviates from the tunnel center, as it runs on
one of the double tracks. The side of the train nearest the tunnel wall is called
the Tunnel wall side, and that nearest the tunnel center is called the Tunnel
center side. When the train enters a tunnel, a pressure wave occurs. Besides
the propagation of this pressure wave, continuous pressure fluctuation appears.
The difference in pressure between the tunnel wall side and the tunnel center
side (hereafter referred to as pressure difference) acts on the vehicle as an aerodynamic lateral force and yawing moment. Since the pressure fluctuation on
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the tunnel wall side is much larger than that on the tunnel center side, the
pressure difference is mainly dependent on the pressure on the tunnel wall
side.
Fig. 4. Time histories of pressure on each side of a train entering a tunnel (train speed: 300
km/h)
To investigate the pressure on the tunnel wall side, we set pressure sensors
on the sides of two consecutive cars, the 4th and 5th cars. Figure 5 shows
pressure as a function of time. The pressure fluctuation that travels leeward
while keeping its shape does not decay even when it passes the gap between
two cars. The speed of this propagation is equivalent to approximately 80 percent of the train speed.
Running test data of various series of trains were analyzed to find that there
is coherence in the data. The pressure fluctuation does not appear locally but
develops along the whole length of the train (the typical train length was 400m
with 16 cars) irrespective of the train types. Figure 6 displays pressure fluctuation developing along the whole set of train. The pressure fluctuation increases from the head to the 6th car (125~150m from the head), then remains
constant and finally drastically increases at the tail of the train set. The peak
frequencies of the pressure fluctuation which are recognized after the 3rd car
(50~75m) decrease from the 3rd car toward the 6th~8th cars (125~200m) and
remain at the same level to the tail of the train set.
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Fig. 5. Time histories of pressure on the tunnel wall side of two consecutive cars (train speed:
296 km/h, t’ indicates non-dimensional time based on train speed and train width).
Fig. 6. Development of pressure fluctuation on the whole set of train (f’ indicates nondimensional frequency based on train speed and train width).
From the above, the following are presumed. Some large organized patterns exist in the space between the tunnel wall and the train. These flow patterns develop from the head toward the 6th~8th cars and become steady there-
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after to the tail of the train set. The flow separates at the tail with a large pressure fluctuation.
3. Mechanism
In this section, some mechanisms of generating these aerodynamic forces are
explained.
3.1 Interaction between vehicle vibration & aerodynamic force
First of all, we investigated the interaction between vehicle vibrations and
aerodynamic force (Suzuki et al. 2001). There was some potential for selfinduced vibrations in which lateral movements of the train have an effect on
the flow field around the train. The flow field around a vehicle model, which
was forcibly vibrated in the yawing direction, was analyzed by a wind tunnel
experiment. The result showed that a pressure field that has the same properties as those of real trains is found even though the train model is not vibrated.
The effect of vibration on the flow field is small for vibration accelerations that
are normally observed in real trains. We concluded that the phenomenon is
considered as a forced vibration by the aerodynamic force. Therefore we do
not need to consider the car vibration when we investigate the flow field.
3.2 Flow separation around train tail
To clarify the flow field around a train tail, a three-dimensional unsteady Navier-Stokes simulation was carried out with a short train model that has a
length of 2.5 cars (Suzuki et al. 1996). The simulation successfully obtained
unsteady flow separation on the rear nose, which causes fluctuations of the
yawing moment of the tail car. In the tunnel section, the simulation proved
that the tunnel wall makes the flow separation asymmetric and that the expansion of the effective flow area along the rear nose causes a greater pressure
fluctuation.
3.3 Coherent structure along middle cars
As described in section 2, aerodynamic force occurs not only at the train tail
but also along the middle cars. In general, flow structures such as vortices are
diffused and dissipated in the turbulent boundary layer. However, the coherent patterns develop and remain along the train. Here, the numerical simulation was performed (Suzuki 2001). The model has a length of six cars in the
computation. The computation revealed that there are vortices generating
around the floor of the train (fig. 7). These vortices develop from the head
toward the tail. They stay around the floor on the 1st car, while they cover the
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whole side of the train after the 4th car. The unsteady aerodynamic force is
generated on the side of the train when the vortices pass.
Fig. 7. Vortices developing around the train running in tunnel.
4. Countermeasures
Some of countermeasures to solve this problem are presented in this section.
4.1 Present countermeasures
Several countermeasures have been developed to improve the riding quality in
tunnels. First, a yaw damper between cars, which is proportional to the angular velocity between cars (Fujimoto et al. 1995), was introduced.
A semi-active suspension system has also been developed (Sasaki et al.
1996). The semi-active suspensions reduce the vibration by controlling
damping-coefficients, instead of using external energy.
Both systems have already been installed in new series Shinkansen trains,
the 500 and 700 series.
4.2 Aerodynamic countermeasures
The yaw damper between cars and the active suspension effectively improve
the riding quality. However, these are regarded as stopgap measures. To further speed up improvement, we need to decrease the aerodynamic force itself.
Therefore we explored the optimal aerodynamic shape by using a moving
model test facility (Haga et al. 2001) and a wind tunnel (Suzuki et al. 2002).
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(1) Nose shape
Since nose shapes are crucial to flow separation, nose shapes were tested first.
Five different types of nose shape were prepared (fig. 8). These are a two dimensional short shape, a two-dimensional long nose, a three-dimensional short
nose, a three-dimensional long nose and square cornered nose. The twodimensional nose is a so-called wedge-shaped nose. Sides of the threedimensional noses are rounded. The result shows the three-dimensional short
nose is the worst. This is because the flow separates around the sides of nose
and reattaches again. These separation and reattachment points fluctuate.
Thus pressure around the nose vibrates and the yawing moment changes.
Fig. 8. Effects of nose shapes. (Cyaw is a coefficient of aerodynamic yawing moment.)
(2) Shape of lower section and fins
As described in section 3.3, there are vortices generating around the floor of
the train. The shapes of the train bottom were supposed to be critical for reducing the aerodynamic force on middle cars. Here, two kinds of shapes were
prepared; a train with rounded bottom corners and one with fins under the
body. The effects of these shapes are illustrated in figure 9.
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Fig. 9. Effects of rounding lower corners and installing fins. (Cyaw is a coefficient of aerodynamic yawing moment.)
5. Conclusions
The flow-induced vibration of the high-speed trains in tunnels was investigated by the running tests, wind tunnel experiments and numerical simulations. The running test revealed the development of coherent flow patterns
along the whole set of the train. The wind tunnel experiment confirmed that
the train vibration in tunnels is a forced vibration by aerodynamic force. The
computation demonstrated the vortices on the train side and the sudden expansion of flow area at the tail generate the aerodynamic force. The wind tunnel experiment showed the long nose, rounding the lower section of the car,
and installing fins under the train, which decrease the aerodynamic force, are
effective countermeasures.
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