Numerical Simulation of the Flow about a Train
Model
Samira Barakat and Dieter Schwamborn
DLR, Institute for Aerodynamic and Flow Technology, Göttingen, Germany
Summary
This paper presents results from flow simulations about a simple train model
to be used in an upcoming experiment. The simulations are made with the unstructured Navier-Stokes solver TAU employing hybrid grids. The influence of
wind tunnel walls as well as a ground plate with and with out a boundary layer
is examined. The results obtained so far indicate that the influence of the wind
tunnel wall can be neglected in the computation, while the boundary layer on
the ground plate might become critical in the experiment. Furthermore the
influence of cross wind on the train is studied by yawing the train up to 30° to
the oncoming flow.
1. Introduction
Amongst different kinds of trains used in Germany are the fast trains called
ICE (Inter City Express). While the front and rear cars with the engines were
quite heavy in the first generation trains, they are quite light weighed in the
new generation since the engines are now distributed over all bogies. Travelling
at very high speeds while encountering strong side winds can be hazardous
causing derailment of the train especially at the instance of exiting a tunnel or
crossing a bridge. Therefore the study of high speed trains under different cross
wind angles is of great significance. The objective of this particular preliminary
analysis has been the determination of suitable wind tunnel conditions for future tests and studies of stability and derailment of the ICE trains. Therefore a
simple geometry of the train without bogies is considered to examine both the
influence of the tunnel walls in the experiment and of the boundary layer developing on a ground plate below the model. Once the computer simulation
and the wind tunnel test results to be available in the near future are within
reasonable agreement, more complex geometries will be studied.
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2. Numerical approach
In this study the DLR-TAU Code which solves the Reynolds-averaged NavierStokes equations (RANS) on hybrid grids (Gerhold and Evans 1999;
Schwamborn et al. 1999) is used. The three major modules of this code are:
the pre-processing for the unstructured hybrid grid, the flow-solver which
works on a dual grid with an edge-based data structure and the adaptation
which allows for an automatic adaptation of the grid to the solution. Both preprocessing and solver are fully parallelized for distributed memory machines
such as the LINUX cluster used in this exercise. Parallelizing the adaptation is
currently under development.
The pre-processing supports tetrahedral, prismatic, pyramidal and hexahedral elements thus enabling the use of efficient and flexible modern grid generators for the generation of meshes about complex geometries within days.
Besides producing the dual grid, the pre-processing also takes care of the domain decomposition for the case of parallel computation, the agglomeration of
coarser grids to be used in the multi-grid acceleration and the optimisation of
the data structure for vector or cache-based computers.
TAU is based on a finite volume technique, and it integrates the solution in
time using a Runge-Kutta method. It employs different central and upwind
discretisations for the convective fluxes and a number of one- and twoequation turbulence models. In the current investigation, central discretisation
and a Spalart-Allmaras one-equation model (Edwards 1996) is used. For timeaccurate calculations a dual-time stepping approach can be enabled.
The resolution of flow features can be taken automatically into account by
the adaptation which allows for local refinement of the hybrid grids based on
different refinement sensors. Additionally a redistribution of grid points in
structured sub-layers (composed of prisms or hexahedrons) is possible in order
to adapt the mesh along wall-normal rays for an improved boundary-layer
resolution.
3. Computer Simulation
A geometry representing a German ICE train is used in the simulation which
considers only the leading car where the engine is located plus a connector
section and the front part of a second car. The physical specifications and
condition of the train are given below:
• Length of the part of the train that was simulated: 45 m
• Speed: 282 km/h
• Cross sectional area: 10 m2
• Standard condition (ambient pressure and temperature)
• Reynolds number: 2.2 108 (based on length)
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Fig.1. Overview of the mesh near the train
The commercial grid generation tool CENTAUR was used in creating the
hybrid unstructured grid. The near wall grid of the train consists of prismatic
layers to resolve the boundary layer, while the remainder of the computational
domain is filled with tetrahedrons except for the area of the ground plate below the train where the grid was also prismatic to allow the simulation of a viscous ground plate
Fig.2. A close-up of the surface grid at the train nose
in the experiment. The grid consists of about 2 million elements of which
about one million are prisms, while seven hundred thousand are tetrahedral
and twelve thousand are pyramidal elements. A view of the surface mesh near
the engine car is given in figure 1 indicating the increased grid resolution near
the train and in areas of high surface curvature, while figure 2 gives a close-up
of that the train nose.
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3.1 Analysis and Results
The objective of the analysis has been the determination of the influences
coming from wind tunnel conditions compared to “free air” conditions in order to obtain close to reality results in future studies. In order to achieve this
objective the following cases are studied:
• Influence of boundary conditions
• Influence of different yaw angles
3.1.1 Influence of boundary conditions
The boundary condition influences that are analysed here are the effect of the
wind tunnel walls and the turbulent boundary layer along the ground plate.
During this first part of this study the yaw angles are kept at zero degrees.
In order to determine the effect of the wind tunnel, the flow simulations are
made for the train once in the free air and then inside the wind tunnel. In both
cases the ground below the train is treated as inviscid. Of course, the computational domain had to be reduced in size in the wind tunnel case and the
boundary conditions at the wind tunnel walls were set to inviscid wall conditions omitting the effect of the tunnel wall boundary layer for simplicity. The
original geometry is taken from the test section of the High Pressure Tunnel in
Göttingen. This tunnel will be used in the experiments since it allows for realistic Reynolds numbers. The cross-sectional area of the tunnel is 60 by 60 cm,
but for this experiment the the blockage of the tunnel compared to the crosssectional area is about .36 per cent.
In wind tunnel
inviscid ground
Free air
inviscid ground
Free air
viscous ground
Fig.3. Streamline distribution, isometric view
In the case of the viscous ground plate, a no-slip condition was used along
the ground below the train starting at one reference length (considered train
length 45m) in front of the nose. The prismatic layers on the ground plate are
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now additionally redistributed by the adaptation in the solution process in order to arrive at a y+ of one in the boundary layer.
Figures 3 and 4 show a comparison of the streamline distribution for the
three mentioned boundary conditions on the front part and along the bottom
of the train, respectively. No substantial difference in the streamline distribution is observed for the cases inside and outside the wind tunnel indicating the
tunnel wall are far away enough to have no effect on the flow in the vicinity of
the train. This can also be seen from Table 1, which summarizes the drag coefficient and its components for these cases. The influence of wind tunnel
walls compared to the free air case is very small and much smaller than that of
the viscous ground plate.
In wind tunnel
inviscid ground
Free air
inviscid ground
Free air
viscous ground
Fig.4. Streamline distribution, bottom view
In the case of a viscous ground; however, the stagnation point at the nose of
the train is shifted upwards (fig.3) due to the displacement effect of the oncoming boundary layer. In Figure 4 it can be seen that the streamlines tend to
diverge along the bottom due to the increase in boundary layer thickness along
the ground.
The influence of the boundary layer on the pressure distribution in the
symmetry plane of the train can also be seen in Figure 5 where the cases with
and without ground plate are compared for free-air boundary conditions in the
far-field. Due to the displacement effect of the boundary layer the stagnation
point is moved upward, and the pressure on the upper nose is increased. At the
same time the suction peak below the nose is reduced. Thus the average pressure on the frontal area rises resulting in an increase of the pressure drag.
From this it is concluded that the effect of the wind tunnel can be neglected
at the low blockage for the case of zero yaw. Although a nonzero yaw angle
would increase the blockage effect to a certain extent, this increase would not
be substantial. Although this has still to be proven in a future calculation, it is
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concluded for the moment that the wind tunnel simulation would not be
negatively influenced by wall effects. Thus it seems not necessary to simulate
the wind tunnel in future computations.
Table 1. Drag Coefficient Comparisons between the Train inside the Wind Tunnel, Outside the
Wind Tunnel and Viscous Ground
Train in Free Air
Train in Tunnel
Percent Difference
Viscous Ground
Percent Difference
Cd (pressure)
0.0118
0.0120
2.0%
0.0558
78.9%
Cd (viscous)
0.0629
0.0608
3.4%
0.0561
10.8%
Total Cd
0.0746
0.0728
2.5%
0.1119
49.9%
Train contour
Fig. 5. Comparison of pressure distribution in the symmetry plane of the train
However, the ground plate might play a critical role in the experiments. In
the current calculation the running length of the boundary layer in front of the
train was equal to the simulated length of the train. Since the front edge of the
plate will be much closer to the nose of the train (approximately one train
height) in the experiment, the effect of the boundary layer would be much
smaller at least at the nose of the train and at zero yaw. However, at higher yaw
angles the running length of the boundary layer is increased again. Additionally the boundary layer height will then vary along the train causing effects in
the flow about the train that cannot be neglected.
3.1.2 Influence of different yaw angles
In order to study the effect of yaw, four different cross wind (yaw) angles were
considered: zero, 15, 25 and 30 degrees. The angle of 30 degrees is included
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to cover the worst case scenario which is unlikely to occur in reality at train
speeds above 200 km/h.
Fig.6. Streamlines distribution on the train seen from the windward side for yaw angles of 0°,
15°, 30° (top to bottom)
Figure 6 depicts streamlines on the surface of the train as the yaw angle
changes. (Please note that the train in the picture is see-through, i.e. the
streamlines from both sides of the train could be viewed). Looking at this figure it can be concluded that separation occurs along both the top and bottom
leeward edge of the train in all cases of nonzero yaw. This separation leads to
the formation of leeward vortices which are visualized in Figure 7 for the case
of 25° yaw in a cut 11m behind the train nose using lines of constant vorticity.
It can also be seen from Figure 6 that the top separation is moving upstream
as the yaw angle increases, finally arriving at the very nose of the train.
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Fig.7. Vortices separating from top and bottom of the train indicated by vorticity contours in a
cut a 11m behind the train nose
3.2 Comparison with preliminary experiments
In order to get an idea about the validity of the present computer simulation
before the corresponding experiment has taken place, the results are compared
with an earlier experiment. However, this experiment was performed using a
train with a slightly different nose (Loose 2002). Unfortunately, in this experiment some problems were found with respect to the accuracy of the drag
force measurements, but the results are used here due to unavailability of a
better data for a similar simulation.
Comparisons of the numerically obtained drag and side force coefficients
with the experimental data as a function of the yaw angle are shown in Figures
8 and 9. While the experimental data are given in the body-fixed coordinates
only, the numerical data are presented additionally in the aerodynamic system
distinguishing between pressure and viscous components. As can be seen, the
viscous part of the drag is almost independent of the angle of cross wind and
already at moderate angles (about 4°) the pressure drag, which increases
strongly with yaw, becomes larger than the viscous drag.
Due to the fact that there isn’t a large base pressure area on the engine car,
the drag in body-fitted coordinates very quickly turns into a suction force with
increasing yaw angle. The experimental drag shows the same trend although it
can not be used for a real judgement due to the error involved (indicated by
the fact that is doesn’t start with a positive value at zero yaw).
With respect to the side force in the body-oriented system both experimental and theoretical data follow the same trend in increasing forces with increasing yaw angle. Experiments and simulation are in relatively good agreement despite the slight difference in nose geometry. But, of course, it is not
clear how much of the discrepancy between experiment and computation is to
be attributed to that difference.
Numerical Simulation of the Flow about a Train Model
Fig. 8 Drag force coefficient in wind and body fixed coordinates
Fig. 9 Side force coefficient in wind and body fixed coordinates
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4. Conclusion and future work
Trying to investigate the influence of wind tunnel condition using a simulation on a German ICE train, the following can be concluded:
The in-house Navier-Stokes solver TAU which was originally intended for use
in the aerospace industry is perfectly capable of handling the flow simulation
of ground-based vehicles such as trains.
In the train simulation it could be shown that the blockage effect can be expected to be low for the configuration considered. Thus it seems reasonable
not to simulate the tunnel in most of the future calculations. This will, however, be checked at least with one additional computation at a reasonably high
yaw angle.
The ground plate boundary layer, however, has considerable effects on the
flow solution as it moves the stagnation point upwards and increases the pressure on the nose of the train resulting in an increase in the drag. Even with a
shorter ground plate using the correctly scaled distance between model and
ground as it is planned in the upcoming experiment, it is quite likely that some
effects would still exist.
For yaw angles greater than zero it was found that separation occurs both
along the upper and lower leeward side of the train generating a pair of vortices. It was seen that the upper separation starts to move to the front of the
train when the yaw angle is increased.
Despite the differences in the experiment and simulation, the preliminary
comparison seems quite promising.
Further studies will be performed regarding influence of grid refinement as
well as turbulence modelling on the results.
References
Edwards JR, Chandra S (1996) Comparison of Eddy Viscosity Transport Turbulence Models for Three-Dimensional Shock-Separated Flow Fields.
AIAA J. Vol. 34, pp 756–763
Gerhold T, Evans J (1999) Efficient Computation of 3D-Flows for Complex
Configurations with the DLR TAU-Code Using Automatic Adaptation.
In: Notes on Numerical Fluid Mechanics, Vol. 72, Vieweg
Loose S (2002) Private communication
Schwamborn D, Gerhold T, Hannemann V (1999) On the validation of the
DLR TAU-Code. In: Notes on Numerical Fluid Mechanics, Vol.
72,Vieweg