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BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications

Milano, Italy, July, 20-24 2008

THE FLOW AROUND HIGH SPEED TRAINS

Chris Baker

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

e-mail: c.j.baker@bham.ac.uk,

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 THE FLOW AROUND TRAINS WITH NO CROSS WIND

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)

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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, three dimensional nature of the side wall boundary layers. Similar coefficients could also be determined from the model scale moving model measurements for the ICE re-ported in [1], through a fit of the logarithmic law to the velocity profiles. The authors of this paper acknowledge that this procedure was not an accurate one, but average values of 0.0029 were obtained, which is again somewhat below the smooth flow flat plate value at that Rey-nolds number. These values are broadly consistent with those shown in figure 10. Similarly the full scale ICE slipstream measurements can be used to obtain values of skin friction, through the fitting of a logarithmic law to the velocity profiles from which the shear velocity and thus the skin friction coefficient can be determined. The log law is however a poor fit to many of the velocity profiles and thus this procedure is a an approximate one. The average value for the measurements, above the platform for the centre of the train from x = 100 to x = 300m where the log law fit was reasonable is 0.0046, rather higher than would be expected from the results presented above. For the measurements at trackside, exposed to the rough bo-gies, the equivalent skin friction coefficient is, predictably, much higher at 0.038.

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(a) (b)

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Figure 4 Synthesis of boundary layer measurements boundary layer thickness , displacement thicknesses d*, and form parameter H [6, 7, 8]

Figure 5 ICE service car velocity measurements (z=0.5m; measurements made at trackside with no platform) [3]

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Figure 6 ICE service car velocity measurements (z=0.5m; measurements made at trackside ) [3]

Figure 7 Boundary layer parameters for ICE service train [3]

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Figure 8 Turbulence intensity for boundary layers on the side of the ICE service train [3]

Figure 9 Autocorrelations for boundary layers on the side of the ICE service train [3]

Figure 10 Local skin friction coefficients for HST model and full scale tests of [6]

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2.2.2 Train roof There is not a great deal of experimental data for the boundary layer development over the

train roof. Figure 11 shows a compilation of the conventional boundary layer measurements of [6]. This data indicates a displacement thickness that is considerably thicker than the corre-sponding side wall boundary layers, which leads to the conclusion that there is a diverging flow up the side of the wall and a converging flow over the roof of the train.

[1] describes some measurements made using the alternative approach of stationary probes and a moving model, for a 1/25th scale ICE vehicle. The results for displacement thickness and form parameter are shown in figure 12. The x axis in these figures is a normalised time, with the normalisation being with vehicle speed and vehicle length. T=0 is when the train nose passes, and T=4 is when the tail of the four coach train passes. There can be seen to be little difference in the displacement thickness results between the side wall data (already in-cluded in figure 7) and the roof data , which is not consistent with the results of figure 10. Again the form parameters are significantly below the equilibrium boundary layer value of 1.4.

Figure 11 Boundary layer displacement thickness on 1/76th model scale HST roof from [6]

a) Displacement thickness b) Form parameter

Figure 12 Boundary layer on train roofs from moving model tests for 1/25 scale ICE model [1]

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2.2.3 Train underbody The flow underneath high speed trains has not been extensively studied in the past, but has

recently come to prominence as a result of the ballast flying issue that can cause a variety of problems to the train and to the track. The investigations into this problem have resulted in a number of investigations taking place which have measured the velocity and pressure field beneath high speed trains. The results of a number of these investigations are considered here those of reference [9] for the Korean high speed train, reference [10] for the Eurostar trains on the Channel Tunnel Rail Link, and the experiments reported in [11] for the Japanese Shinkansen train. Figure 13 shows the velocities beneath the Korean train for a number of heights, measured at full scale with pitot probes. The train speed was 300kph, about 83m/s. The velocities at various distances form the upper rail surface are shown. It can be seen that these velocities reach high levels of around 40% of the train speed at heights of 0.18m. A small peak in the velocities can be seen as the train nose passes, but for most of the trace the velocities are highly turbulent and fluctuating as would be expected from the rough under -train environment. Figure 14 shows vertical and horizontal velocity profiles for the same tests. The results for the vertical profile imply some sort of annular flow profile (with an inflexion point between the track and the train), rather than a conventional boundary layer profile. There velocities can also be seen to peak on the train centre line and fall off towards the out-side of the track.

The velocity and pressure fields were measured beneath the Eurostar train and are reported in reference [10]. The velocity traces are similar to those described above and are not shown here. The pressure trace is shown in figure 15, both for the entire train and for the first quarter of the train. One unit of normalised time represents the passage of one carriage of the train. These are ensemble averages of 20 nominally identical train passes. A prominent nose maxi-mum and minimum can be seen in both traces that is similar to those shown in section 2.1. However regular minima are also seen along the vehicle that seem to be associated with the passage of the middle of each coach between the bogies. A tail peak can also be seen. From the Eurostar velocity data it was also possible to obtain autocorrelation functions, and thus the integral length scales and time scales. The length scales were found to be between 1.8 and 2.0m, and the time scales between 0.02 and 0.03 seconds. These values are rather smaller than those for the side boundary layer, as may be expected because the flow is significantly con-strained.

The flow field beneath a full scale 16 car Shinkansen test train and a three car wind tunnel model are reported in [11]. The wind tunnel tests were carried out with a moving ground belt beneath the middle car only, and this may have some influence on the results that are shown in figure 16 below. The results of figure 16 look rather different to those of figure 14, but this is because of the frame of reference that is used and in fact they are identical in form. Those of figure 16 show clearly the inflexion point profile that could only be inferred from figure 14. There is good agreement between the model scale and full scale data. Reference [11] also goes on to look at a number of different underbody geometries bogie fairings etc and shows that the underbody flow is, unsurprisingly, quite sensitive to geometric changes.

Finally, similar information is also presented for tests on the ICE in [12]. However the ve-locity profile information has been normalised in an arbitrary way, and is not amenable for comparison with the other results presented here. It is also of interest to note that the ballast flying problem has also driven wind tunnel and computational research on the flow in and around bogies [11], [12]. This work is at an early stage, and is very challenging both experi-mentally and computationally, with the results being very sensitive to both the experimental set up and the computational configuration (including the turbulence model). Further progress can be expected in this area in the future.

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Figure 13 Velocity traces beneath Korean high speed train [9]

Figure 14 Vertical and horizontal velocity profiles beneath Korean high speed train [9]

Figure 15 Pressure coefficients beneath Eurostar train [10]

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Figure 16 Velocity profiles measured below Shinkansen train [11]

2.3 The train wake In the last few decades there has been a great deal of work carried out on the nature of the

wakes of road vehicles primarily with a view to being able to minimise drag which is of course dominated by wake effects for road vehicles. It is clear from the literature that the pre-cise nature of the wake varies from vehicle to vehicle, but there seem to be a relatively small number of flow mechanisms that can exist in some combination or other shear layer separa-tions, longitudinal helical flows, vortex streets and a separation cavity (references [13], [14], [15]). All of these phenomena are subject to instabilities with Strouhal numbers (based on ve-hicle velocity and some representative frontal dimension) between 0.05 and 0.4. Now whilst the tail shape of trains is rather different to those of cars, one might expect equally complex flows. The major physical difference will be that the thickness of the boundary layer around the train will be relatively much greater than for cars, and thus any separated shear layers will also be much thicker.

With these points in mind, let us now consider the experimental data and computational work that is available to describe the wakes of high speed trains. Figure 17 shows experimen-tal velocity vectors for a model TGV [16] and a model ICE [1], together with a visualisation of the flow around an ICE using standard RANS CFD methods [17]. It can be seen in each case that there is strong evidence of helical vortices behind the train, which extend a consider-able distance into the vehicle wake. Reference [18] takes the CFD work somewhat further and investigates the unsteadiness of these helical structures through the use of unsteady RANS techniques. The results are illustrated in figure 18. A well defined oscillation can be seen with a Strouhal number of 0.14.

Now the full scale slipstream data presented in reference [3] has been analysed intensively to attempt to determine the wake characteristics. Figure 5 shows the ensemble average veloc-ity traces, and for those nearest to the train there can be seen to be a noticeable peak in the ve-locity in the near wake (i.e. 350m to 400m). These velocities were measured 1m above the

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track with no platform in place. The equivalent model scale experiments of reference [1], measured half way up body height, do not show this peak. The experiment and simulation of figure 17 indicate that the helical vortex occurs close to the ground, and it thus seems likely that this is what is observed in the full scale slipstream measurements. Further investigation of the full scale data however showed that the technique of ensemble averaging was, in this case, actually hiding a physical effect, and that this peak did not appear on around half of the indi-vidual velocity traces that were used. Careful re-analysis revealed that the slipstream meas-urements were picking out some type of vortex shedding oscillation with a Strouhal number of 0.11, which is close to the computational value of 0.14 reported above. It thus seems that the helical vortices in the train wake undergo some sort of regular oscillation with a Strouhal number of around 0.11 to 0.14.

The situation is further complicated however when the model scale data of [1] is consid-ered in more detail. The wake velocities just behind the train showed a very great deal of run to run variation with high ensemble standard deviations. A wavelet investigation of the turbu-lence scales suggested peaks at two Strouhal numbers 0.03 (hypothesised to be due to wake cavity pumping) and 0.5 (taken to be due to shear layer instability). As the model measure-ments were made higher up the train than the full scale measurements, it may be that the un-steady helical vortex motion is more important close to the ground, and other types of unsteadiness higher up the vehicle. Further work is required in this area.

Up to this point we have implicitly been considering the near wake of trains within a few vehicle heights of the train tail. One would expect that any large scale flow structures that ex-ist would decay fairly rapidly and that the far wake of the train would show a gradual decrease in velocity. This effect can be seen in the ensemble average velocity traces for the ICE in fig-ure 5 for a value of x> 420m (the tail of the train is at x = 365m). The velocity measurements made nearest the train decay steadily, whilst the measurements made furthest away first in-crease and then decrease showing the lateral spread of the wake. This effect can also be seen in the model scale wake measurement for the ICE of figure 19 below [1]. The x axis variable is a time normalised by the vehicle speed and the length of a single car of the four car model train. In this case the origin is at the train tale. A model for the longitudinal, lateral and verti-cal velocities in this decaying wake was developed in reference [19] based on the similarity method of [20]. The expressions for the velocities are simple algebraic functions of the dis-tance along and across the wake, and governed by two parameters. Figure 20 shows the best fit curves to the model scale ICE data. The agreement can be seen to be good, and suggest that the wake velocities are self similar when expressed in a suitably dimensionless format.

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Figure 17 Helical vortices in the wake of trains [1], [8], [17]

Figure 18 Computations of wake oscillations for the ICE [18]

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Figure 19 ICE 1/25th model scale wake measurements (y is the distance from the side of the train, h is the train h) [1]

Figure 20 Best fit curves to wake velocities using model of [19] ((a) y/h = 0.033, (b) y/h = 0.2, (c) y/h = 0.533)

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3 THE FLOW AROUND TRAINS WITH A CROSS WIND

3.1 The natural wind relative to a train In this section we consider how the natural wind appears to a train moving though it, for

the fundamental case of a train moving over a flat ground. We assume for the sake of simplic-ity that the wind is normal to the train track and that the vertical velocity profile is given by the usual logarithmic law with a surface roughness length of z0 [21]. We further assume that the turbulence intensity is given by the values given in that same reference, and is again a function of the surface roughness length. To calculate the velocity profile and turbulence in-tensity with respect to a train the train velocity must also be considered. This is straightfor-ward and the method has been frequently rehearsed in the past ([22] for example) and one can easily obtain the velocity profile, yaw angle, and turbulence intensity relative to a moving train. Sample calculations are shown in figure 21 below for a cross wind speed u, 3m above the ground of 20 m /s and various train speeds (v), for a value of z0 of 0.03m, typical of a ru-ral upstream fetch. The turbulence intensity with respect to the train is defined as the atmos-pheric turbulence level divided by the wind velocity relative to the train. It can be clearly seen that at low train speeds, the velocity profile takes on the appropriate boundary layer form, with a significant velocity variation across the train, the yaw angle is close to 90 degrees and the turbulence intensity is high. At high train speeds, the velocity profile is more uniform, and the yaw angle is low and varies somewhat over the height of the train. The turbulence inten-sity is low of the order of a few percent. Clearly these results have implications for the type of wind tunnel or computational simulation that is used if there is a desire to model trains moving at high speeds, then these tests can reasonably be carried out in low turbulence wind tunnels, with no velocity shear (although the yaw angle twist would not be simulated). If low vehicle speed conditions are required, then atmospheric turbulence and shear needs to be simulated, although it needs to be recognised that any simulation will only model one specific set of wind speed / vehicle speed conditions. The same comments can be made for the critical case of a train on an embankment, where the wind profile speeds up close to the ground, al-though in this case the wind shear and turbulence intensities are rather less in all cases

As well as the mean velocity profiles and the turbulence intensity, the turbulence spectrum experienced by a moving train will be different to that experienced by a stationary train. This was investigated in [23] and typical results are shown in figure 22. In this figure the spectra are shown for a range of train speed / wind speed ratios from 0 to infinity, for a pure cross wind. The x axis is a frequency normalised with the atmospheric turbulence length scale and the wind velocity relative to the train, and the y axis is the spectral density normalised with the frequency and the wind velocity variance. Plotted in this way the spectra show a remark-able level of similarity, which thus implies that, to a first approximation, they scale on the wind velocity relative to the train

Whilst the above figures give some indication of the wind statistics relative to the train, it is not unusual when looking at train cross wind stability to specify, in varying degrees of de-tail, an extreme wind gust, on the basis that such wind gusts will cause train stability problems. The question thus arises as to the nature of these gusts, which vary both in space and in time. The author and his co-workers have in recent years investigated a number of velocity and sur-face pressure datasets obtained on the University of Birmingham Wind Engineering field site at Silsoe in Bedfordshire, and, of particular relevance to the current discussion, have adopted the technique of ensemble averaging of extreme gusts i.e. identifying the gusts in the time se-ries and then averaging the gusts to produce an average time series. Figure 23 shows the aver-

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age streamwise, lateral and vertical velocity fluctuations measured 1m above ground level at the site [24] (although the results are similar to those measured at a range of heights up to 10m). It can be seen that the peak streamwise gusts, have a magnitude of about three to four times the standard deviation of the wind velocity fluctuations and last for about one second either side of the maximum peak. These gusts are superimposed upon a longer term gust with a magnitude of around one standard deviation above the mean. The corresponding vertical fluctuations show a negative peak at the maximum gust, indicating that these gusts are associ-ated with sweep events in the atmospheric boundary layer. In terms of the spatial correla-tion of such gusts, the results show that the short term peaks are only correlated over heights of a few metres, and extreme pressure coefficients measured on a 2m high horizontal wall at the same site [25], also indicate that the horizontal correlation of such peaks is similar. How-ever the longer term, underlying and less intense peaks, seem to be correlated over lengths of tens of metres.

There are two general approaches in dealing with extreme gusts in crosswind stability con-siderations the first is to define a time period for these gusts of, say 1 second or 3 seconds, on the basis that such a gust period would be required for any train to blow over. It can be seen that such an approach would significantly filter the short term gust peak shown in figure 23. Another approach is to define a specific type of peak, such as the Chinese hat used in [26] and shown in figure 24. This is a spatially distributed peak only, and lacks the temporal variation shown in figure 24, although its spatial spread of around 100m either side of the peak corresponds roughly to the longer term base peak referred to above. This gust profile has been obtained from a study of the time and spatial averaged wind statistics and as such reflects all the information within these statistics rather than just the information describing the extreme gusts. Either of the above approaches is clearly a simplification of the nature of the gust, although both have practical merits.

An alternative approach to using a simplified extreme gust has been outlined in [27] and [28] where a correctly spatially and temporally correlated wind field has been simulated to match the required wind correlations. The wind velocities seen by a train as it passes through this simulated wind field will then contain the necessary spatial and temporal information concerning the extreme gusts in a more realistic way.

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(a) (b)

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Figure 21 The wind characteristics seen by a moving train over a flat ground (u = 20m/s)

Figure 22 Wind spectra relative to a moving train over a flat ground [23]

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Figure 23 Extreme gust profiles [24] (ds indicates dataset number; velocities normalised by the corresponding standard deviation)

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Figure 24 The Chinese hat gust profile [26]

3.2 Wake flow structure in cross winds In the last few decades a number of wind tunnel tests and computational simulations have

elucidated the flow structure around high speed trains in cross winds. The wind tunnel work of [29], [30]. [31] and [32] in the 1970s and 1980s used an idealised train model , and it was found that the dominant flow pattern was a series of inclined wake vortices such as might be found around a missile at high angles of attack (figure 25a). At higher yaw angles a more conventional vortex shedding pattern was observed, with some switching of the flow at inter-mediate angles. Recent computations, using both RANs and LES techniques on various ICE configurations [33], [34], [35] have also shown similar patterns (figures 25b to 25d). There is broad agreement both qualitatively and quantitatively between the wind tunnel tests and the CFD results - see the surface streamline patterns from [31] and [33] in figure 26. There is some evidence, particularly from the LES results of wake unsteadiness [33] that indicates two modes of wake unsteadiness - a horizontal wake oscillation with a Strouhal number of 0.1, and a weak vortex shedding motion with a Strouhal number of 0.15 to 0.2. It has to be said however that these frequencies are not always well defined in the LES simulations, and do tend to vary somewhat with the type of calculation used.

Measurements of a different kind are reported in [36] which presents data from moving model experiments on a four car ICE train, with rather a crude cross wind generator placed normal to the track. The x axis unit is time normalised by train velocity and carriage length with zero being the point at which the train nose passes the measurement point, and 4 being the point at which the train tail passes that point. The y axis is the slipstream velocity normal-ised by the train velocity. The slipstream velocities were measured in the wake of the vehicle and ensemble averaged in a manner that has been previously described. These results are shown in figure 27 in two formats one for the velocities themselves (figure 27a) and one for the velocities minus the velocities measured with no cross wind (figure 27b). In the first of these the crosswind magnitude can be seen before the train nose has passed, and the inviscid nose peak is clearly visible. This is followed by a dip in the velocities, due to the sheltering effect of the train. A maximum in the velocity can then be seen before a gradual decay. In the wake the crosswind velocities are again seen. In the alternative method of presentation any value of the relative velocity that exceeds the upstream wind speed indicates an enhancement of that wind speed by the train wake. This can be seen to occur at a position that corresponds

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to the passing of the second car of a four car vehicle, with lower values elsewhere. [36] argues that this is consistent with the presence of inclined vortices in the wake of the train. Finally figure 28 shows the maximum wake velocities (one second averages) that were measured for a wide variety of high speed trains in full scale test in the UK, normalised by the train speed. There is, inevitably, a great deal of scatter but it can be seen that there is a general increase in the maximum normalised velocities as the cross wind speed increases.

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Figure 25 Wind tunnel tests and CFD computations of wake vortex flows behind trains in a cross wind. (a idea-lised train [30]; b - 2 car ICE [33]; c ICE [35])

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Figure 26 Computed and measured surface streamline patterns [31], [33]

(a) (b)

Figure 27 Wake velocity measurements from moving model experiments for ICE model [36]

Figure 28 Maximum slipstream velocities for high speed passenger trains [36]

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3.3 Pressure distributions in cross winds The idealised train low turbulence wind tunnel measurements of [29], [30], [31] made ex-

tensive measurements of the pressure distributions around the model, and sample results are shown in figure 29a [31] together with the results of simple panel method calculations Figure 29b shows equivalent measurements for a 2 car ICE 2 model [34], which also shows the LES calculations of [35]. Pressure coefficients are shown on loops around the vehicle, for a variety of different distance (x) from the train nose, normalised with the model diameter D or length L. The results are plotted with a negative pressure coefficient in the positive direction. For all values of x that are not near the nose, it can be seen there is a suction peak on the windward roof corner (45 degrees in figure 29a, 315 degrees in figure 29b), small suctions over the rest of the roof, leeside and underside, and a positive pressure coefficient on the windward wall. Near the nose however, for small values of x there is a suction peak on the leeward side, that can be expected to give a major contribution to the overall side force. In general the numerical solutions show a good level of agreement with the experiments.

A similar set of results, from [37] are shown for a wind tunnel model of a UK Class 365 electrical multiple unit in figure 30. These measurements were made in a simulation of the atmospheric boundary layer i.e. in a highly turbulent flow. They are plotted with the positive pressure coefficient in the positive direction in a manner similar to, but confusingly different from, figure 29. The pressure coefficients are shown on loops around the vehicle (with loop B being near the front of the leading vehicle and loop H near the back of that vehicle. Results are shown for yaw angles of 45 degrees and 90 degrees (results for other yaw angles are given in [37]). The large suction peak on the windward corner can again be seen for all of the loops at both yaw angles. Figure 30 also shows the standard deviation of the pressure coefficients, which gives an indication of the steadiness or otherwise of the flow. It can be seen that this parameter peaks at the windward roof corner, perhaps indicating some unsteady separated flow in this region. Figure 31 shows a proper orthogonal decomposition (POD) analysis of the pressure detail. A full description of this type of analysis is given in [38] and [39]. It shows that the first and most energetic POD mode seems to be concentrated at the windward roof of the vehicle, and thus physically corresponds to the pressure fluctuations on the windward roof. The second mode has the characteristics of the mean pressure distribution and thus physically corresponds to quasi-steady pressure fluctuations around the model. A fuller discussion of this analysis is given in [37].

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(a) (b)

Figure 29 Pressure distributions around trains (a Idealised train, lines are panel method results and points are experimental results [31], front of windward face is at 0 degrees; b - 2 car ICE - lines are LES results of

[33], points are experimental results of [34], front of windward face is at 270 degrees)

(a) 90 degrees yaw (b) 45 degrees yaw

Figure 30 Mean and standard deviations of pressure coefficient distributions around a model class 365 e.m.u.

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[37]

Figure 31 POD analysis of fluctuating pressures around a model class 365 e.m.u. [37]

3.4 Aerodynamic admittances and weighting functions The overall forces on trains are composed of the sum of the mean and fluctuating pres-

sures over the train surface. One would expect that small scale fluctuations that only affect small parts of the surface of the vehicle would be damped out in this summation (integration) process, and thus the force fluctuations would be smaller than the upstream velocity or pres-sure fluctuations. This effect is important in calculating cross wind stability in a number of related ways. If calculations of stability are carried out in the frequency domain to use the terminology of [40] and [41] (as in [42] for example) then the force coefficient spectra can be obtained from the wind spectra through the use of aerodynamic admittance functions, which are effectively normalised ratios of force coefficient spectra to wind spectra. Figure 32 shows the curves for aerodynamic admittance from the work of reference [23] that corresponds to the velocity spectra relative to the vehicle shown in figure 22. Aerodynamic admittance val-ues are plotted against normalized frequency, for a ratio of train speed to normal wind speed of 4.0, and for two different vehicle heights. It can be seen that all the curves (for different ratios of the vehicle length to the turbulence integral length scale) all approach unity at low frequencies (showing that large turbulent eddies are correlated over the entire vehicle) but fall rapidly at high frequencies for the reason set out above, and thus will act as a filter on high frequency wind fluctuations, and thus the energy available to excite suspension frequencies that lie in this range. Similar experimental curves, from the Class 365 e.m.u. results men-tioned above are shown in figure 33 [43]. The reduced frequency is the actual frequency normalized by the wind tunnel velocity and the carriage length. It can be seen that some of the experimental curves tend to values other than unity at low frequencies. [43] suggest that this is because of a number of reasons primarily because the concept of admittance implicitly assumes that the flow is not significantly affected by the body on which the forces are meas-

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ured, and because the streamline passing through the reference point is not the significant streamline defined as the streamline on which the turbulent characteristics mostly influence the unsteady forces on the body. [43] shows that this streamline is usually significantly below the reference position of 3m, which is not unreasonable. That being said, as long as the same reference position is used in any model tests in which the admittances were measured, and in any calculation using these admittances, then the calculations will be valid. Now assuming suitable values of the physical parameters that determine the admittance functions (i.e. wind and vehicle velocities, vehicle length and turbulence length scales, indicates that the admit-tance falls to values of 0.5 at around 1to 2Hz, suggesting that wind fluctuations above these values will be filtered out by the lack of correlation of surface pressures.

Now whilst this frequency domain analysis is useful, in any calculation of train behaviour that considers suspension dynamic effects including discrete track irregularities, the time domain equivalent is required [28]. This is known as the aerodynamic weighting function and can be shown to be the Fourier transform of the aerodynamic admittance, and vice versa. The derivation of such functions from experimental data is far from straightforward, and is discussed in detail in [44]. Typical values are given in figure 34 for side and lift force coeffi-cient weighting functions for the class 365 e.m.u referred to above. Effectively these functions weight the relative wind velocities and train force coefficients over a period leading up to the time of application. The main points to note about these functions are firstly that the values of weighting function for the high speed case are smaller than for the low speed case, which re-flects the fact that the wind velocity fluctuations relative to the train are smaller the faster the train velocity, and secondly that they are only non-zero for values less than around 0.5s i.e. the train side and lift force coefficients are fully determined by the values of the relative wind velocity over the previous 0.5 seconds. These effects are illustrated in the results of figures 35, which show wind time series generated by the method of [27] and the side forces and the lift forces for the class 365 corresponding to the weighting functions shown in figure 34. The fil-tering effect of the higher frequency fluctuations in velocity is very clear, particularly at the higher vehicle speeds.

Finally if calculations are carried out in the amplitude domain, then the extreme values of the force coefficients, based on extreme values of the forces and extreme values of the up-stream velocities, might also be expected to be less than the mean values of these coefficients, as the high frequency fluctuations will have been filtered out. This effect is illustrated in fig-ure 36, for the static wind tunnel model tests carried out on a UK Class 390 Pendolino train [45] for the extreme coefficients based on a gust averaging time of 1s. At first sight the fact that the extreme / mean ratio is significantly below unity seems inconsistent with the admit-tance and weighting function results above which suggest that such effects due to lack of cor-relation of surface loads, should be confined to averaging times less than 0.5 to 1.0s. However more recent calculations carried out by the author suggest that the results of figure 36 are ef-fected, to a significant degree, by the specification of wind velocities at the reference stream-line rather than on the significant streamline defined above. Nonetheless, as with the admittances, if the same reference height is used in any stability calculations as was used in the experiments that measured extreme values, then the results will still be valid.

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Figure 32 Aerodynamic admittances from reference [23] (L = vehicle length, H = vehicle height, xLu = turbu-lent length scale, VT= train speed, x axis is frequency normalised with turbulence length scale and wind velocity

relative to the train)

Figure 33 Experimental measurements of aerodynamic admittances for Class 365 emu side force coefficients (x axis is frequency normalised with length of vehicle and wind velocity relative to the train)

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Figure 34 Aerodynamic weighting functions for the class 365 e.m.u (left v=55.9m/s, u=15m/s, right v=17.9m/s , u = 15m/s)

Figure 35 Wind velocity and force time histories for the class 365 e.m.u (left v=55.9m/s, u=15m/s, right v=17.9m/s , u = 15m/s)

Figure 36 Ratio of extreme to mean side force coefficients for the Class 390 Pendolino full scale experiments [45] legend indicates different train / track configurations

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4 CONCLUDING REMARKS IMPLICATIONS FOR PRACTICAL ISSUES In this section some brief remarks are made on the implications of the flow field descrip-

tions of previous sections for a number of practical issues of current concern. a) It is clear that the boundary layer measurements made on model vehicles are not fully

consistent with those made at full scale, partly due to the expected effects of scale (i.e. Rey-nolds number) and partly because at full scale there would appear to be a very rapid growth of the boundary layer near the nose. These effects will affect the skin friction drag, and thus the overall drag on the train, and the nature of any model scale slipstream measurements in the boundary layer region. More work is required in this area to determine the appropriate way of representing the train boundary layer at model scale in both wind tunnel and moving model experiments.

b) The integral time scale at the train side is less than 0.1s, and thus flow unsteadiness in this region is unlikely to have any effect on the stability of passengers or trackside workers, who have a minimum response time of around 0.3s [46]. Instability in this region will rather be caused by mean flow effects. (Note however that this conclusion is only true for smooth high speed passenger train [3] shows that for freight trains the integral time scales on the train side are rather larger and turbulent flows along such trains could affect passenger and trackside worker stability.)

c) The integral time scales in the underbody gap are very short at 0.02 to 0.03s, with asso-ciated integral length scales of the order of 2m. Unpublished calculations of ballast flight paths beneath the train by the author suggest time scales of the order of 0.3s and path lengths of the order of 3m. This mismatch of times and scales suggest that the flight path of train bal-last will be primarily determined by the mean flow field beneath the train.

d) The large scale unsteady flow structures in the near wake of the train have time and length scales that are potentially hazardous to waiting passengers, and in addition are a poten-tially large cause of train drag. It is possible that careful optimisation of train nose / tail design could reduce the intensity of these vortices and help in the alleviation of both issues.

e) Trains in cross winds experience quite different wind conditions (in terms of shear and turbulence) when they are operating at full speed than when they are operating at low speed. There is a divergence of view as to which effects are most important i.e. is the critical condi-tion when trains are moving at line speed, as trains ought to operate in all weather conditions, or can it be expected that in such conditions effects external to the railway environment (such as flying debris) will cause trains to operate at low speeds, and potentially to come to a stand? The answer to this question will determine which type of wind tunnel test is most appropriate to determine cross wind forces and moments for the purposes of risk calculations.

f) The longitudinal vortices in the wake of trains in cross winds can cause an enhancement of slipstream velocities. It is possible that the cross wind condition represents the most serious safety risk when considering the effects of train slipstreams.

g) When modelling the effects of cross winds on trains, if short period gusts are modelled with time scales of less than 0.5s, or if suspension effects with frequencies greater than 1 or 2Hz are modelled, then it is necessary to include the filtering effects represented by the aero-dynamic admittances or aerodynamic weighting functions. If effects with rather larger time scales are being considered (say the gross overturning of a vehicle with a time scale of 2 to 3 seconds), then the force fluctuations on the train can be assumed to be quasi-steady and to fol-low the wind velocity fluctuations

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AKNOWLEDMENTS Much of the material presented in this paper has been taken from the results of the authors collaborators over the last two decades (research students and fellows, former and present col-leagues), who are too numerous to name individually. Nonetheless their implicit contribution to this work is gratefully acknowledged.

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[46] S.C. Jordan, T. Johnson, M. Sterling, C.J. Baker, Evaluating and modelling the response of an individual to a sudden change in wind speed. Building and Environment 43 15211534, 2008