Schulte-Werning, B.; Heine, C.; Matschke, G.

Unsteady Wake Flow Characteristics of High-Speed Trains

1. IntroductionThe tendency to increased cruising velocity of high-speed trains is unbroken, although stabilising the level

already reached is dominant [1]. In parallel the weight of the end coaches in the future train sets is decreasedbecause of replacing the power car concept by the distributed traction, this allows both for a less overall weightof the train with its reduced energy consumption effect and for an end car equipped with passenger seats, thusincreasing the transport capacity of the train.

2. Main ResultsHigher speed results in higher aerodynamic forces acting on vehicles with lower mass. Therefore the vehicle

reaction to unsteady aerodynamic excitation, e.g. of the end car in trailing position, have come into the view of therailway operators. When the thick turbulent boundary layer separates at the end of the train the location of flowseparation on the train surface shift periodically in time, thereby causing excitation of oscillations of the last coacharound the longitudinal axis. This phenomenon was firstly detected by the Japanese railways some years ago [2]. Thefrequency of the so-called last car oscillations (LCO) and the related amplitude may cause discomfort to passengersin the rear coach because of its nauseaeffect. Confirmation of this effect has been given by Japanese measurementson the STAR21 experimental train with speeds up to 315 km/h, showing the frequency of these lateral oscillationsto be at several Hertz.

In the EU-funded research project RAPIDE (Railway Aerodynamics of Passing and Interaction with DynamicEffects, 1998-2001) the railway undertakings Deutsche Bahn AG (DB), the French SNCF and the Italian FS, joinedtheir forces to investigate the boundary layer flow of a modern high-speed train and the wake flow characteristicsby means of currently available off-the-shelf CFD-codes. In the related full scale tests with an ICE 2 control carrunning in trailing position up to 280 km/h no LCO was found [3]. The vehicle accelerations were clearly dominatedby the track irregularities and they were not correlated to the periodic pressure fluctuations. To further supportthis fortunate result, the 3-dimensional and unsteady wake flow was analysed numerically. Both the steady and theunsteady low Mach-Number Navier-Stokes equations were solved numerically for 1:1 scale conditions with Re107.Standard turbulence models were applied and for unsteady runs a procedure 1st order implicit in time was used.Some results of the steady calculations are already reported in [4].

Both the steady and the unsteady calculations with the FLUENT code show streamline convergence on the vehicleshoulders as illustrated in Figure 1.

Figure 1: One of the two limit flow pattern in the unsteady calculations (left) and the flow pattern in the steadycalculations (middle) on the surface of the ICE 2 nose in trailing position (right) for Re 107.

PAMM · Proc. Appl. Math. Mech. 2, 332–333 (2003) / DOI 10.1002/pamm.200310150

To come to a clear understanding of the train wake flow phenomena, the analysis methods of flow topology are used(see e.g. [5]). The surface flow field structure is represented due to its skeleton via the detection of the ßingularpointsın which in the wall plane the skin friction vector vanish identically. These singular points can essentially be ofthe so-called nodal, saddle and focus type. Once having located these points on the train surface and the separatingstreamlines connecting them, the visualisation of separating and reattaching shear layers as well as vortical flowstructures leads to a clear portrait of the wake flow situation.

In the unsteady calculations, the flow pattern alternates smoothly between two asymmetrical limit states withone vortex starting on the nose surface. The vortex is fed by two lines of strong streamline convergence. Thisstreamline convergence evolves into a multiple critical point (saddle-node point) which bifurcates then further on intoa topologically stable saddle-focus connection, this focus is the footprint of the new second vortex. The symmetricalstate of the unsteady flow exhibits 2 vortices, whereas the flow pattern in the steady calculations shows 6 vortices ina complex topological arrangement! Figure 2 exhibits the unsteady skin friction pattern on the surface of the ICEtrailing car. The different instantaneous flow pattern appearing in the temporal cycle of the vortex shedding processcan be directly linked to the variation of the side force amplitude.

Figure 2: Cycle of the vortex shedding on the surface of the ICE trailing car expressed by instantaneous skinfriction pattern

The amplitude of the side force is approximately 500 N and the vortex shedding frequency is 1.4 Hz , i.e. Sr =0.14 based on the hydraulic diameter. Regarding the rolling moment, the side force operates with a small leverbecause the vortices shed at the nose tip and the resulting moment is small, too. Although the Eigenfrequency ofthe vehicle body is met, the minor variation in side force and rolling moment is negligible for LCO. The CFD studythus identifies the aerodynamic excitation mechanism, but also that the magnitude of the excitation forces is beyondthe threshold value for the LCO phenomenon. This is in line with the 1:1 scale test.

3. References

1 Taylor C.: Quantity not quality, as high-speed operators mark time; Railway Gazette Int., October 19992 Kohama Y., Koshikawa T. & Okude: Wake Characteristics of a High Speed Train in Relation to Tail Coach Oscillations,

Vehicle Aerodynamics Conference, Loughbrough University, UK (1994)3 RAPIDE Workshop: Synthesis Report, Cologne Nov 29 (2001)4 Schulte-Werning B., Heine C. and Matschke G.: Slipstream Development and Wake Flow Characteristics of modern

High-Speed Trains, ZAMM Z. Angew. Math. Mech. 81 (2001) S35 Peake D.J. and Toback M.: Three Dimensional Interaction and Vortical Flows with Emphasis on High Speeds, AGAR-

Dograph No. 252, (1980)

Dr. Burkhard Schulte-Werning, Dr. Christoph Heine, Gerd Matschke, Deutsche Bahn AG, DB Sy-stemtechnik, Volkerstraße 5, 80939 Munchen, Germany.

Section 10a: Viscous Flow 333