The Flow Around High Speed Trains

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    BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications

    Milano, Italy, July, 20-24 2008


    Chris Baker

    School of Civil Engineering University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdon


    Keywords: High speed trains, aerodynamics, cross winds, boundary layers, wakes

    Abstract: This paper considers aspects of the aerodynamic behaviour of high speed trains. It does not specifically address the many aerodynamic problems associated with such vehicles, but rather attempts to describe, in fundamental terms, the nature of the flow field. The ration-ale for such an approach is that the flow fields that exist are the primary cause of the aerody-namic forces on the train and its components which result in a whole range of aerodynamic issues. This paper thus draws on a wide range of model scale and full scale experimental and computational work and attempts to build up a comprehensive picture of the flow field. Atten-tion is restricted to trains in the open air (i.e. tunnel flows will not be considered) for both still air conditions and crosswind conditions. For still air conditions the flow field will be de-scribed for a number of flow regions i.e. around the nose of the train; along the side, roof and underbody of the train; the wake of the train; Calculations of the nature of the wind relative to the train will be presented for a variety of train speeds and wind speeds. For crosswind conditions, the nature of the flow field around typical trains, including surface pressure distributions, will be presented. In addition the aerodynamic admittances / weighting functions for different types of train will be discussed. Finally some remarks will be made as to the relevance of the data that has been presented to current issues in train aerodynamics.

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    1 INTRODUCTION This paper aims to set out a description of the flow field around high speed trains in the

    open air. It will approach this from a fairly fundamental point of view, and will not specifi-cally address practical issues and problems associated with the aerodynamic behaviour of trains, although these will be briefly discussed at the end of the paper. Such an approach is adopted in the hope that such a description will clarify the basic flow mechanisms that exist around high speed trains, and will thus inform future consideration of a range of more practi-cal issues.

    The basic tools in the study of train aerodynamics are full scale testing, wind tunnel testing and CFD calculations, as indeed is the case in other fields of aerodynamics. In the case of the study of train aerodynamics, all of these approaches are fraught with difficulties. Full scale measurements have to be made in very turbulent flows and very often a large number of runs have to be carried out to enable the mean and unsteady flow patterns to be elucidated. Refer-ence [1] describes the technique of ensemble averaging through which the results of a large number of runs are considered together. Results obtained using this technique will be used extensively in what follows. Both wind tunnel tests and CFD calculations are made difficult because of the large length / height ratio of high speed trains that makes wind tunnel models or computational grids very long and thin, and which both require specialist techniques and expertise. This point having been made however, experimental and computational techniques will not be discussed at any length in what follows, although where the nature of the tech-nique has the potential to seriously affect the results that are being presented, then this will be pointed out.

    Section 2 discusses the aerodynamics of high speed trains in conditions of zero cross wind. The discussion is framed in terms of three flow regions, viz.

    the nose region around the front of the train; the boundary layer region along the length of the train (for the train side, train

    roof and train underbody); the wake region behind the train.

    This scheme is based on that developed by the author in [1], although in this paper the number of flow regions is reduced from the five in [1] to the three listed above the upstream and nose region in [1] being considered together here, and the near wake and far wake regions in [1] being similarly combined. For each of the flow regions the work of the author and his co-workers, and the work of other investigators are considered to develop as complete a pic-ture as possible of the flow field around the train.

    Section 3 then goes on to consider the flow field around trains in a cross wind. This begins by a consideration of the nature of the wind flow relative to the train (in terms of the mean velocity profile, turbulence profile and power spectrum. A qualitative picture of the flow around trains is then developed from a consideration of the work of a number of authors, and the nature of the pressure distribution around high speed trains is also discussed, in terms of both steady and unsteady surface pressures. Finally the way in which these pressures sum to give cross wind forces and moments is discussed in terms of the aerodynamic admittances and aerodynamic weighting functions. Some concluding remarks are then made in section 4 and the implications of the results for current issues in high speed train aerodynamics are set out.

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    2.1 The nose region In this section the flow upstream and just downstream of the nose of high speed trains will

    be considered. In this region the variations of air velocity and pressure are essentially inviscid. A typical variation in air velocity is shown in figure 1 around the front of a 14 car ICE service train. This data was obtained from trackside anemometry in full scale experiments designed to measure the slipstreams around such trains. The experiments are reported in outline [2] and discussed in considerable length by the author and his co-workers in [3]. Data from these ex-periments will be used extensively in what follows to illustrate a number of effects. The data in figure 1 is an ensemble average of the data from 17 train passes. This data was aligned (at the point corresponding to the peak of the velocity trace shown in the figure) and the data at all other points averaged over all the runs. Thus x, the position along the train, is defined as measured from this peak in velocity. The lateral distance y is defined as the distance from the rail edge, and the vertical distance z as the distance from the top of the rail. For the results shown the velocities were measured at trackside with no platform present (z=0.5m). The air velocity data, u, is divided by the train speed, v, to give the normalised value U. From figure 1 the velocity peak can be seen to be sharply defined and, as would be expected, decreases away from the train. The standard deviation of the ensemble is small in all cases of the order of 0.02 to 0.03, which indicates that in this flow region there is little run to run variation.

    The velocity changes illustrated in figure 1 are accompanied by pressure changes. Figure 2 shows typical pressure changes caused by an ETR 500 [4]. These measurements were ob-tained from train passing tests carried out as part of the major EU TRANSAERO project. It can be seen that there is a rapid increase and then decrease in pressure around the train nose. Again for any particular train, this effect is highly repeatable from run to run.

    As such flows are inviscid they can be well predicted by reasonably simple calculation methods as shown figure 3 below from the potential flow calculations of Sanz-Andres [5]. More complex panel methods can be used to calculate the details of the pressure and velocity variations around train nose shapes of different types (such as the results for the Euler method shown in figure 2). As would be expected, the blunter the nose shape, the higher are the ve-locity and pressure disturbances.

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    Figure 1 Velocities in the nose region of the ICE service train (z=0.5m)

    Figure 2 Pressure time history measured during the passage of two ETR 500 trains (x axis is an arbitrary time) [4]

    Figure 3 Results of the potential flow calculations of [4] (Pressure coefficient traces are shown for 2D and 3D computations. The x axis parameter T is the time from the passing of the nose of the train normalised by train

    speed and distance from the centre of the train)








    -10 -5 0 5 10


    x (m)




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    2.2 The boundary layer region 2.2.1 Train side

    Over the last few decades a number of investigators have made boundary layer measure-ments on trains, using conventional train based pitot probes, hot wire probes etc. These tests have been carried out at both full scale and model scale for a variety of train types. From these experiments it is possible to derive standard boundary layer parameters such as the displace-ment thickness and the form parameter. The data from some of these experiments is summa-rised in figure 4 below, with data from the wind tunnel and full scale tests of [6] for the UK HST, and the data correlation of model scale results given in [7], reporting the earlier work of [8] for a variety of other trains. All dimensions given in these figures are the equivalent full scale values. Note that the results of [7] and [8] are for the actual, somewhat loosely defined, boundary layer thickness. [7] notes that the ratio between this thickness and the displacement thickness is between 8 and 11, i.e. one order of magnitude.

    It can be seen that all the model scale results are broadly consistent with each other, and show firstly a steady development in the total boundary layer thickness and the displacement thickness along the length of the train, and secondly values of the form parameter that are sig-nificantly below the value of 1.4 that one would expect for an equilibrium boundary layer. The measurements in reference [6], together with a consideration of the momentum integral equation, suggest that the side wall boundary layer is very far from two dimensional, with a divergence of the flow up the side of the train and a convergence over the roof (see below). The full scale HST results are however somewhat different, and show little growth along the train, although the form parameters are consistent with the model scale measurements.

    A different method of obtaining information on the state of the boundary layer on the train comes from measurements made using stationary anemometers at the trackside or on plat-forms. The measurements that were made on the German ICE have already been described above [2], [3]. Figure 5 shows the measurements that were made at all positions along the train. The inviscid velocity peaks around the nose described in the last section can be seen around x = 0m, but the velocities in these peaks can be seen to be small in comparison to the boundary layer velocities. At each distance away from the train the velocity increases steadily along the train up to the wake region around x = 350m. (This region will be discussed in detail below).

    Figure 6 shows the same data, but plotted in the conventional boundary layer velocity pro-file format for different distances along the length of the train. There can be seen to be a grad-ual thickening of the boundary layer as x increases, as would be expected.

    Figure 7 shows the boundary layer displacement thicknesses and form parameters obtained from this data. In addition these parameters are also given for a similar set of full scale meas-urements made above a station platform, and for a set of model scale experiments made at half train height without a platform simulation [3]. Note that for the platform experiments, z is defined as the distance from the top of the platform, and y the distance from the train side. It can be seen that the displacement thicknesses in all three cases grow along the length of the train, with the trackside full scale values being larger than those for the other experiments. This is not surprising, as the former measurements were taken in a region close to the ground exposed to the aerodynamically rough bogies, whereas the latter were obtained from regions closer to smoother areas of the train. The form parameters are again significantly less than the equilibrium values as in figure 4. Perhaps the major point to emerge from this data are the large values of displacement thickness near the front of the vehicle in the full scale measure-

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    ments, suggesting a major flow disturbance around the nose that is not replicated in the model scale measurements shown in either figures 4 or 7.

    Turbulent boundary layers such as those on the side of the train are also characterised by their unsteady flow characteristics with the magnitude of the turbulence being characterised by the turbulence intensity, and the scale by parameters such as the integral time or length scales. In terms of the ensemble average data velocity data from stationary probes that has been obtained for the ICE service train, the turbulence intensity can be approximated by (1 ensemble standard deviation) / ensemble mean. Figure 8 shows a plot of this parameter along the train for both the measurements made at trackside and those made above the platform at broadly equivalent positions. It can be seen that in both cases the turbulence intensity is more or less constant along the train, although, as would be expected, the value is significantly higher for the trackside measurements than for the platform measurements. The values are of the order of 0.05 to 0.1, which are typical values for flat plate boundary layers. Figure 9 shows the autocorrelations of velocity for these two cases. From these plots the integral length and time scales (the scales that contain the most turbulence energy) can be found to be 4.7m and 0.067s for the trackside measurements and 4.1m and 0.059s for the platform measure-ments. The integral length scale is thus of the order of 20% of the length of an individual car-riage.

    The final boundary layer parameter that is of interest is the skin friction coefficient, as the surface skin friction determines to a large extent the overall drag of the train. Figure 10 shows the local skin friction coefficient for the HST model and full scale results of [6]. It can be seen that, as is to be expected, the skin friction is very dependent upon scale and indicates the ne-cessity for as large a scale as possible in either wind tunnel tests or computations if the drag is to be accurately predicted. It is of interest to note that most of the individual values of local skin friction fall on or below the accepted smooth wall correlations of skin friction and local Reynolds number for flow over a two dimensional flat plate, indicating again the non-equilibrium, th...