Flow-induced Vibration of High-Speed Trains inTunnels

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 asubject of discussions concerning riding comfort. The paper describes the phe-nomenon, its mechanism and countermeasures.

First, running tests revealed that the aerodynamic force in tunnel sections ismuch greater than that in open sections. The aerodynamic force and the vi-bration in tunnel sections gradually increased from the head toward the tail ofa train set; and the yawing vibration of cars had a close relation with the aero-dynamic force.

Second, to clarify the interaction between the vehicle dynamics and theaerodynamic force, the flow field around a scale model, which was forcibly vi-brated, was analyzed by a wind tunnel experiment. The results showed that apressure field that had the same properties as those of real trains was foundeven though the train model did not vibrate. The effect of vibration on theflow field was small and thus the phenomenon was considered as a forced vi-bration by the aerodynamic force.

Third, to investigate the aerodynamic force, numerical simulations wereconducted. The computation proved that the cause of the large pressure fluc-tuation at the tail is the flow separation by the sudden expansion of the effec-tive 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 thenthe unsteady aerodynamic force is generated when the vortices pass.Finally, to derive an optimal shape, which suppresses the unsteady aerody-namic force, scale model tests were conducted. The results showed that a longnose effectively decreases the large pressure fluctuation at the tail. Roundingthe lower section of the car and installing fins under the train were also shownto 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 ofthe trains has recently become a subject of discussion especially concerningriding comfort. This phenomenon has the following characteristics (Fujimotoet al. 1995). (1) The vibration amplitude of the train in tunnel sections ismore noticeable than in open sections (fig. 1), (2) it gradually increases fromthe head toward the tail of the train set, and (3) the yawing vibration is moreprominent than the other vibrations.

Fig. 1. Time history of yawing angular acceleration of a train entering a tunnel (train speed: 300km/h).

Since mountains account for about 70 % of Japan's total land area, thereare a large number of tunnels in its railway system. For example, half of theSanyo Shinkansen line, which connects Osaka and Hakata (622.3 km), is intunnels. So, the riding quality in tunnel is critical for service. Therefore, in-tensive studies have been carried out to solve the problem of vibration in tun-nels.

Track irregularity was considered at the initial stage as one of the factorscausing the phenomenon. However, there was no correlation between the vi-bration and the track irregularity in the tunnel sections (Takai 1989). Anotherfactor, namely aerodynamic force, has also attracted attention. As for theaerodynamic force, the effect of Karman-like vortices on the vibrations of thetrain had been suggested. But, no mechanisms had been clarified in detail atthis first stage. Thus, we have been extensively investigating flow around thetrains in tunnel by running tests, wind tunnel experiments and computersimulations.The paper describes the phenomenon, its mechanism and countermeasuresfrom our studies.

2. Characteristics of the phenomenon

In this section, we describe some characteristics of the phenomenon that havebeen revealed by the analysis of the running test data (Suzuki 2000).

Flow-induced Vibration of High-Speed Trains in Tunnels 445

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 thetrain side in a running test. From the pressure data, we calculated aerody-namic yawing moment (fig. 2). The train speed was 300 km/h. When thetrain ran in the open section, the aerodynamic force was small. However, oncethe train went into the tunnel, the aerodynamic force suddenly increased.

Figure 3 shows the work done by the aerodynamic force on a car. Whenthe train ran in the open section, the work was nearly zero. In the tunnel sec-tion, however, the aerodynamic force clearly vibrated the train.

Figure 4 is a typical chart of the pressure on each side of a train entering atunnel. The course of the train deviates from the tunnel center, as it runs onone of the double tracks. The side of the train nearest the tunnel wall is calledthe Tunnel wall side Tunnelcenter side

, and that nearest the tunnel center is called the. 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 centerside (hereafter referred to as pressure difference) acts on the vehicle as an aero-dynamic lateral force and yawing moment. Since the pressure fluctuation on

Fig. 2. Time history of aerodynamic yawing moment acting on a train entering a tunnel (trainspeed: 300 km/h).

446 M. Suzuki

the tunnel wall side is much larger than that on the tunnel center side, thepressure difference is mainly dependent on the pressure on the tunnel wallside.

Fig. 4. Time histories of pressure on each side of a train entering a tunnel (train speed: 300km/h)

To investigate the pressure on the tunnel wall side, we set pressure sensorson the sides of two consecutive cars, the 4th and 5th cars. Figure 5 showspressure as a function of time. The pressure fluctuation that travels leewardwhile keeping its shape does not decay even when it passes the gap betweentwo cars. The speed of this propagation is equivalent to approximately 80 per-cent of the train speed.

Running test data of various series of trains were analyzed to find that thereis coherence in the data. The pressure fluctuation does not appear locally butdevelops along the whole length of the train (the typical train length was 400mwith 16 cars) irrespective of the train types. Figure 6 displays pressure fluctua-tion developing along the whole set of train. The pressure fluctuation in-creases from the head to the 6th car (125~150m from the head), then remainsconstant and finally drastically increases at the tail of the train set. The peakfrequencies 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) andremain at the same level to the tail of the train set.

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 non-dimensional frequency based on train speed and train width).

From the above, the following are presumed. Some large organized pat-terns exist in the space between the tunnel wall and the train. These flow pat-terns 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 pres-sure fluctuation.

3. Mechanism

In this section, some mechanisms of generating these aerodynamic forces areexplained.

3.1 Interaction between vehicle vibration & aerodynamic force

First of all, we investigated the interaction between vehicle vibrations andaerodynamic force (Suzuki et al. 2001). There was some potential for self-induced vibrations in which lateral movements of the train have an effect onthe flow field around the train. The flow field around a vehicle model, whichwas forcibly vibrated in the yawing direction, was analyzed by a wind tunnelexperiment. The result showed that a pressure field that has the same proper-ties 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 thatare normally observed in real trains. We concluded that the phenomenon isconsidered as a forced vibration by the aerodynamic force. Therefore we donot 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 Na-vier-Stokes simulation was carried out with a short train model that has alength of 2.5 cars (Suzuki et al. 1996). The simulation successfully obtainedunsteady flow separation on the rear nose, which causes fluctuations of theyawing moment of the tail car. In the tunnel section, the simulation provedthat the tunnel wall makes the flow separation asymmetric and that the expan-sion of the effective flow area along the rear nose causes a greater pressurefluctuation.

3.3 Coherent structure along middle cars

As described in section 2, aerodynamic force occurs not only at the train tailbut also along the middle cars. In general, flow structures such as vortices arediffused and dissipated in the turbulent boundary layer. However, the coher-ent patterns develop and remain along the train. Here, the numerical simula-tion was performed (Suzuki 2001). The model has a length of six cars in thecomputation. The computation revealed that there are vortices generatingaround the floor of the train (fig. 7). These vortices develop from the headtoward the tail. They stay around the floor on the 1st car, while they cover the

whole side of the train after the 4th car. The unsteady aerodynamic force isgenerated 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 intunnels. First, a yaw damper between cars, which is proportional to the angu-lar 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 controllingdamping-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 improvethe riding quality. However, these are regarded as stopgap measures. To fur-ther speed up improvement, we need to decrease the aerodynamic force itself.Therefore we explored the optimal aerodynamic shape by using a movingmodel 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 di-mensional short shape, a two-dimensional long nose, a three-dimensional shortnose, a three-dimensional long nose and square cornered nose. The two-dimensional nose is a so-called wedge-shaped nose. Sides of the three-dimensional noses are rounded. The result shows the three-dimensional shortnose is the worst. This is because the flow separates around the sides of noseand 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 ofthe train. The shapes of the train bottom were supposed to be critical for re-ducing the aerodynamic force on middle cars. Here, two kinds of shapes wereprepared; a train with rounded bottom corners and one with fins under thebody. The effects of these shapes are illustrated in figure 9.

Fig. 9. Effects of rounding lower corners and installing fins. (Cyaw is a coefficient of aerody-namic yawing moment.)

5. Conclusions

The flow-induced vibration of the high-speed trains in tunnels was investi-gated by the running tests, wind tunnel experiments and numerical simula-tions. The running test revealed the development of coherent flow patternsalong the whole set of the train. The wind tunnel experiment confirmed thatthe train vibration in tunnels is a forced vibration by aerodynamic force. Thecomputation demonstrated the vortices on the train side and the sudden ex-pansion of flow area at the tail generate the aerodynamic force. The wind tun-nel experiment showed the long nose, rounding the lower section of the car,and installing fins under the train, which decrease the aerodynamic force, areeffective countermeasures.

References

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Fujimoto H, Miyamoto M, Shimamoto Y (1995) Lateral vibration of aShinkansen and its decreasing measure (in Japanese). RTRI Report, Vol 9-1, pp 19-24

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Sasaki K, Kamoshita S, Shimomura T (1996) Development and field results ofsemi-active suspension high speed train (in Japanese). RTRI Report, Vol10-5, pp 25-30

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Suzuki M, Maeda T, Arai N (1996) Numerical simulation of flow around atrain. in: Deville M, Gavrilakis S, Ryhming IL (eds) Notes in numericalfluid mechanics, Vol 53. Vieweg, Braunschweig, pp 311-317

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