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A PRÉCIS OF DEVELOPMENTS IN THE AEROACOUSTICS OF FAST TRAINS
Journal of Sound and Vibration (1996) 193(1), 349–358
A PRE CIS OF DEVELOPMENTS IN THE AEROACOUSTICS OF FAST TRAINS W. F. K III German Aerospace Establishment (DLR), Department of Turbulence Research, Mu¨ller-Breslau-Strasse 8, D-10623 Berlin, Germany (Received in final form 20 November 1995) After briefly reviewing the important mechanisms by which aerodynamic sound sources are generated on high speed tracked vehicles, two characteristic train speeds that quantify the significance of this noise are defined. The results of microphone array measurements are used to illustrate sound levels generated by flow interactions with a pantograph. Recent developments in measurement technology, analysis and hardware are then surveyed. 7 1996 Academic Press Limited
1. INTRODUCTION
Until the mid-1970s, the term ‘‘railway’’ noise referred exclusively to wheel/rail (W/R) interaction noise, which is the dominant component of wayside noise at train speeds above about 80 km/h. Aerodynamic noise was discussed very briefly at the first Railway Noise Workshop held in Derby, England, in 1976, but this subject was then more academic than practical. With the introduction into service of truly high speed trains in the 1980s, aerodynamic fluctuations began vying with W/R interactions for the honour of being the predominant source of wayside noise at high train speeds. Technological advances in abating W/R noise levels during the past few decades have further enhanced the significance of the aerodynamically generated component of wayside noise. In the present paper some of the advances made during the past ten years in locating and analyzing the aerodynamically generated component of wayside noise will be outlined. Also, albeit briefly, some of the recent techniques being developed to control aerodynamic noise sources will be discussed.
2. AERODYNAMIC SOUND SOURCES
2.1. To a physicist, the word ‘‘noise’’ means any disturbance that interferes with the intelligibility of a signal. In colloquial usage, ‘‘noise’’, which is derived from the Latin nausea (seasickness), refers to any sound that is noticeably unpleasant or disturbing. To railway acousticians, ‘‘noise’’ has the latter meaning, and ‘‘noise’’ and ‘‘sound’’ are used interchangeably. The common sources of aerodynamic noise generated by fast trains are illustrated in Figure 1. All of these sound sources are a consequence of flow separations caused by either the detachment of the turbulent boundary layer or vortex shedding from structural elements on the vehicle. At high speeds, a boundary layer detachment on the head of the leading car often produces the strongest individual sound source on the train with vortex 349 0022–460X/96/210349 + 10 $18.00/0
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shedding from pantographs and their associated roof equipment generating the second strongest individual sound sources. In countries such as Japan where peak sound levels are the criteria for determing wayside noise levels, these two sound sources are very important, with the latter one being the more important at high speeds when sound barriers are present. Noise generated by pressure fluctuations beneath the turbulent boundary layer per se will not be discussed because this noise is not expected to be significant at train speeds up to at least 400 km/h [1]. In countries where the measure of wayside noise is an equivalent sound level Leq , averaged over some prescribed time period, the two strongest sources of aerodynamic noise, albeit still important, are not usually the dominant flow-generated sound sources on railway trains. Rather, vortex shedding from protuberances and edges in the bogie regions on long trains plays the controlling role in establishing an equivalent sound level at high speeds. Whether or not aerodynamically generated noise is an important constituent of wayside noise for any particular vehicle depends on several factors including the relative level of wheel/rail (W/R) interaction noise and the speed range within which the train operates. In turn, W/R noise levels are strongly affected by the degree of roughness on wheel treads and rail surfaces. In general, as advances are made in controlling W/R noise, the relative importance of aerodynamic noise increases. 2.2. Vortex shedding is the most important mechanism for generating aerodynamic noise on railway trains. As shown in Figure 2, consider a slender cylinder of diameter D and length L moving along the x-axis with constant velocity U0 in such a way that L is normal to U0 and lies in the x–z plane. Vortices shed from this cylinder will generate sound having a dipole radiation pattern whose maximum intensity lies more or less in the y-direction. The shed vortices are coherent over some correlation length lc along L. Sound generated by vortex shedding within any correlation length is statistically independent of sound produced by shedding within any other correlation length. One can derive an expression for modelling this sound by replacing the vortex shedding within a correlation length by an equivalent point dipole sound source the axis of which lies along the y-direction. Let p˜i be the root-mean-square (r.m.s.) sound pressure due to a single correlation length. Then, if Llc and RL, one can calculate the total sound pressure due to vortex
Figure 1. Aerodynamic sound sources on a typical high speed train.
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Figure 2. The co-ordinate system for a moving point-dipole sound source. An observer is located at P, and the dipole axis lies along the y-direction.
shedding on the cylinder by simply summing up the p˜i2 , where i identifies the individual correlation lengths. By using a force distribution term for the equivalent point dipole as the source term in the wave equation, it can be shown that the rms sound pressure due to vortex shedding can be written as p˜ 2 = C L2 Sd2 r 2Llc U06 sin2 u cos2 f/16c 2R 2(1 − M cos u)4,
(1)
where C L is the coefficient of fluctuating lift, r is the fluid density, c is the local sound speed, R is the distance from an observer to the source, and M = U0 /c is the Mach number. The symbol Sd , equal to f0 d/U0 , is the Strouhal number, where d is some characteristic dimension of the body (in the cylinder case D), and f0 is the peak frequency of both vortex shedding and sound. If the cylinder in the example were one of the horns on a pantograph and the observer were positioned along the wayside, one could let f in equation (1) equal zero. For slender cylinders having circular or elliptic cross-sections, the values of C L and lc are dependent upon Reynolds number, defined as Red = U0 d/n, where n is the kinematic viscosity of the fluid. Up to a Reynolds number of about 3 × 105, the higher the Reynolds number, the lower the values of C L and lc . For cylinders having square or rectangular cross-sections, these parameters are only weakly dependent on Reynolds number. 2.3. In Figure 3 are shown two superposed results of sound level distributions measured at the locations of the front and rear pantographs on the ICE/V, the test version of the InterCity Express. The measurements were made with a vertically mounted line array of 15 microphones spaced at equal intervals of 0·24 m, with the middle of the array positioned at approximately the height of the knee on the raised pantograph and at a lateral distance of 5 m from the near rail. Details concerning measurements of railway noise with microphone arrays are given in references [2–5]. The dedicated test train comprised two power cars separated by two middle coaches. Each power car was equipped with a model DSA 350 M pantograph with its associated roof equipment. The results shown in Figure 3 are for a pass-by speed of 300 km/h with the front pantograph retracted and the rear
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pantograph raised. Both results are given in unweighted decibels for the frequency range 200–1400 Hz. As can be seen in the figure, flow interactions with the roof equipment and retracted front pantograph generate a higher sound level than do flow interactions with the head of the raised rear pantograph. The boundary layer on the roof of the front power car is relatively thin, and the folded pantograph and its associated equipment (insulators, switches, and cables) are subjected to essentially the full free-stream velocity U0 . On the roof of the rear power car, the boundary layer is several times thicker than it is on the front power car, and the roof equipment on the rear car is subjected to substantially lower inflow speeds than is the case on the front car. The distribution of sound level on the rear power car shows a high peak value at a height of about 2·7 m. This is the height of the inlet louvres for the cooling fans, which are activated automatically and are therefore not always switched on. The high sound level here is probably not due to the cooling fans per se, but rather is caused by vortex shedding on the louvre inlet vanes [6]. It is also possible that the force of sliding (kinetic) friction Fk between the contact strips and the overhead wire could be responsible for part of the radiated noise. Although laboratory measurements of Fk are not available for the high speeds at which the contact strips interact with the overhead wire, it is known that Fk is essentially independent of both contact area and speed. The force of kinetic friction is, however, proportional to the normal force FN that hold the two bodies in contact. For pantographs, FN has an average value of about 100 N, regardless of speed. Furthermore, for many materials, Fk decreases at very high sliding speeds. In view of these characteristics of Fk , it seems likely that any noise level due to sliding friction would remain fairly constant and would not be a function of train speed. Indeed, any frictional noise level may will decrease at high train speeds.
Figure 3. Sound-level distributions generated by flow interactions with front (down) (– – –) and rear (up) (——) pantographs on a dedicated ICE/V as it passed by at 300 km/h, as measured by an SWV2H micrphone array (Shaded Wayside Vertical High array, where ‘‘2’’ signifies the microphone spacing of 0·24 m; bandwidth 200–1400 Hz). On the ordinate, H = height above rail.
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3. DECOMPOSITION OF WAYSIDE NOISE LEVELS
3.1. It is now well known that the square of the sound pressure generated by a vehicle is proportional to vehicle speed raised to a power a: i.e., p˜ 0 U0a ,
(2)
where a is called the speed exponent. For the total sound pressure measured along the wayside, a is not a constant but depends upon speed and whether or not the sound is A-weighted [7]. Variations in a with speed are, however, quite small and become significant only at high speeds. 3.2. The effect of convective augmentation [8, 9] causes a to increase with increasing vehicle speed. The most simple example of this effect is the case of a moving point dipole sound source. Using equation (1) and considering only the direct change of sound pressure with motion, one can write p˜ 2 = KU06 sin2 u/R 2(1 − M cos u)4,
(3)
where K is a constant. Here the observer is positioned along the wayside, and hence f is set to zero. The factor (1 − M cos u)4 is responsible for convective augmentation. At u equal to 90 degrees there is no additional effect due to convection, and p˜ 2 = KU06 /R 2 for all speeds rather than just for M1. One can find the angle um at which the augmentation is a maximum by differentiating equation (3) with respect to u and setting the result equal to zero. This procedure gives um = arccos M.
(4)
The value of the convective augmentation D is then the difference between the sound levels at um and at u equal to 90 degrees. It can be shown that D = −20 log10 (1 − M 2 ) dB.
(5)
Although equation (5) was derived for a point dipole sound source, the result is the same if one considers a line segment of dipoles and integrates equation (3) over all of them. Thus, equation (5) is a good approximation for the effect of convective augmentation on passby sound levels. If one is interested in the effect of convection on the peak sound level due to a line segment of dipoles, the coefficient in equation (5) should be about 27 rather than 20. 3.3. Pass-by sound pressure levels for the individual W/R and aerodynamic noise contributions to the wayside sound pressure level after the effect of convective augmentation has been removed can be represented by equations of the form Leq,p (i) = 10ai log (U0 /UR ) + Ni dB(A),
(6)
where the index i is equal to 1 for sound due to W/R interactions and to 2 for sound due to aerodynamic fluctuations. The symbol UR denotes a reference speed, and the Ni are empirical constants. The acoustical transition speed Ut is that train speed at which the sound pressure level due to aerodynamic interactions equals the sound level due to all other causes (essentially W/R interactions). At train speeds higher than Ut , aerodynamic noise will dominate
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Figure 4. Measured pass-by sound pressure levels (at 25 m) for a 12-coach ICE (D) [10] and a 2-coach ICE/V (X). – –, W/R noise; . . ., aerodynamic nosie.
wayside noise levels. An expression for Ut can easily be found by using equation (6) and setting Leq,p (1) equal to Leq,p (2). This procedure gives log (Ut /UR ) = 0·1(N1 − N2 )/(a2 − a1 ).
(7)
Another characteristic speed that quantifies the relative importance of aerodynamic noise is the acoustical impact speed UI , defined as that train speed at which the pass-by sound pressure due to aerodynamic fluctuations increases the pass-by sound pressure level caused by W/R interactions by one decibel. Again using equation (6), one finds that UI can be expressed as log (UI /UR ) = 0·1(N1 − N2 − 5·87)/(a2 − a1 ).
(8)
3.4. () Average operating conditions in Germany, what are called here condition 2, means that wheel treads have no obvious pits or scans and rail surfaces appear smooth to the naked eye. Pass-by sound pressure levels (open triangles) for a 12-coach dedicated InterCity Express (ICE) operating under condition 2 are shown in Figure 4. These results were measured by Barsikow [10] with a microphone positioned at a lateral distance of 25 m from the centerline of the track and at a height of 3·5 m above the rails. The ICE is equipped with disc brakes, and the wheels on all coaches are fitted with noise absorbers that abate W/R noise levels by from 5 to 6 dB. For comparison, pass-by sound pressure levels for the two-coach ICE/V are also shown in the figure. All wheels on this test train were fitted with noise absorbers. At high speeds in particular, the power cars on both trains generate somewhat higher sound levels than do the coaches. Thus, since the power cars on the short ICE/V make up a much larger fraction of the total train length than they do on the longer ICE, pass-by sound levels produced by the former are a few decibels higher than they are for the latter at high speeds.
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To obtain an empirical fit to the ICE data, one can first employ equation (5) to remove the effect of convective augmentation from all measured sound levels. Making use of the facts that a for W/R noise lies between 2·8 and 3·2 and that aerodynamic noise is relatively insignificant at low speeds, one can find a1 and N1 in equation (6) for a reference speed of 200 km/h. By extrapolating the sound pressure due to W/R interactions up to a train speed of 280 km/h, the highest speed at which data were available, and subtracting this sound pressure from the average of the measured values, the sound pressure caused by aerodynamic fluctuations was obtained. The results are Leq,p (1) = 28 log (U0 /200 km/h) + 81·6 dB(A),
(9)
Leq,p (2) = 65 log (U0 /200 km/h) + 74 dB(A)
(10)
and
Pass-by sound levels for the W/R and aerodynamic noise components computed with the above equations are shown in Figure 4. The solid curve in the figure represents the energy sum of these two components plus the augmentation due to convection. The acoustical transition and impact speeds can then be computed with equations (7) and (8), respectively. The results of these calculations are Ut 1 320 km/h and UI 1 220 km/h. Therefore, when a 12-coach ICE operates under average conditions, the aerodynamically generated component of noise begins to make a measurable difference to wayside noise levels at a speed of roughly 220 km/h. Although numerous array measurements have shown that the value of the speed exponent for W/R noise lies within a very narrow range, there is a certain degree of arbitrariness in the choices of the parameters in equations (9) and (10). This arbitrariness results in uncertainties in the computed values of the characteristic speeds on the order of 10 per cent. Wayside noise levels can be decomposed with greater accuracy if measured values are available for train speeds up to at least the acoustical transition speed, as they are for the ICE/V. 4. RECENT AND ONGOING DEVELOPMENTS
A few investigators [11–15] have used two-dimensional configurations of microphone arrays to study railway noise during the past five years or so. Use of these arrays has halved the on-site measuring time needed to locate both the vertical and longitudinal co-ordinates of individual, localized sound sources. A true, two-dimensional array of microphones is a planar surface covered with microphones, each of which is separated from its nearest neighbors by some specified displacement. The two-dimensional configurations of microphone arrays used thus far for studying railway noise comprise two linear line arrays of microphones arranged at an angle of 90 degrees to one another so that the middle microphone of each line array is one and the same. When we designate a line array of microphones as ‘‘linear’’ we mean that the microphones are spaced at equal intervals. When such a two-dimensional configuration is arranged along the wayside so that one line array is positioned vertically and the other horizontally, the configuration is referred to as a cross-array [11, 12]. When this array is rotated through an angle of 45 degrees, an X-array is formed [13–15]. By appropriately processing the microphone signals measured with these arrays, a quasi two-dimensional ‘‘viewing window’’ (i.e., the combined main beams of the directivity patterns) can be formed. In principle, these two-dimensional configurations of line arrays can more effectively isolate sound generated by an individual, localized source than can a one-dimensional line array, the resolution of which is restricted to one spatial direction. In practice, however, the conventional Dolph–Tschebyscheff shading technique leads to
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a suppression of side lobes of only 10–12 dB in the directivity pattern of the two-dimensional array configurations compared with a suppression of 20 dB or higher for the one-dimensional line array. The most effective array configuration for a given task, therefore, depends upon the location of the particular sound source of interest and the intensities and positions of its near neighbors. All three of the array configurations described above have been used to study flowgenerated pantograph noise. Ikeda et al. [16] have developed a very innovative low-noise pantograph for fast trains. This pantograph, shown in Figure 5, combines a minimum number of structural elements with a head shape the cross-section of which is elliptic. The coefficient of fluctuating lift in equation (1) for the integrated horns and bow is significantly lower for the elliptic cross-section than it would be for any other geometry. Vortex shedding from the large-diameter yawed support arm also generates negligible sound. Another new ‘‘wing-shaped’’ pantograph [17] also combines a minimum of structural elements with an elliptic head shape and a single vertical support arm. In 1995 this pantograph was tested on the new Japanese WIN 350 high speed train, which is also equipped with wheel skirts to abate vortex-shedding noise generated in the bogie regions. Iida et al. [18] discussed a new ‘‘delta-wing’’ shaped pantograph that generates noise levels about 19 dB lower than do conventional current collectors. These authors used an X-array in their acoustical investigations. Computer models [13, 19] the inputs of which are the intensities, locations and speed exponents of sound sources have proved to be valuable tools for ascertaining the importance of individual aerodynamic and W/R sound sources. The input parameters for these models are taken either from the results of array measurements or from theoretical considerations. Time histories of the sound pressure level, pass-by sound levels and other equivalent sound levels based upon any desired time span can be computed with these models [13]. A number of examples of such calculations illustrating the influence of various sound sources on an ICE are given in reference [19]. Aerodynamically optimized head shapes on the lead car of a tracked vehicle can help reduce radiated noise levels at high speeds by suppressing the tendency of the boundary
Figure 5. The prototype of a low-noise pantograph [16] with elliptic head and horns.
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layer to detach itself in this region [7, 20–22]. A good discussion of the head shape on the new 300-series Shinkansen Nozomi is given in reference [15]. Measurements made with an X-array of microphones are also discussed. According to these authors, the acoustical transition speed for the Nozomi when a sound barrier is present is 220 km/h. A new, improved head shape has recently been installed on the German Transrapid maglev vehicle. Since array measurements [11] demonstrated that flow interactions with the cover plates for the guidance system were also a source of wayside noise, these cover plates have also been changed. With these modifications, the vehicle is now designated as the TR 07-2. Measurements, the results of which are not yet generally available, indicate that this modified maglev vehicle generates wayside noise levels that are between 2 and 3 dB lower than those produced by its immediate predecessor. With its modified head shape and cover plates, the TR 07-2 now generates a lower wayside noise level at a speed of 400 km/h than do the majority of InterCity trains travelling at a speed of only 200 km/h (see references [7, 23]).
5. CONCLUDING REMARKS
Because brevity is one of the criteria placed upon this paper, we have necessarily given rather short shrift to our discussions of recent advances in the aeroacoustics of high speed tracked vehicles. Most of the ongoing work in this field can be grouped into three categories: (1) improvements in measurement techniques designed to locate and quantify sources of aerodynamic noise; (2) the development of computer models to predict effects of abating individual sound sources; and (3) the design of new hardware such as pantographs and head shapes for lead cars. Our selection of published material to illustrate advances in these three areas has only scratched the surface of the available literature, and we hope that authors whose works are not cited here will understand the reasons for these omissions.
REFERENCES 1. W. F. K III 1994 Proceedings of InterNoise ’94, 175–180. On the boundary layer contribution to wayside noise generated by high-speed tracked vehicles. 2. W. F. K III and D. W. B 1979 Noise Control Engineering Journal 13, 13–23. Aerodynamic noise generated by high-speed trains. 3. W. F. K III and D. W. B 1979 Journal of Sound and Vibration 66, 311–332. On the sources of wayside noise generated by high-speed trains. 4. B. B, W. F. K III, and E. P 1987 Journal of Sound and Vibration 118, 99–122. Wheel/rail noise generated by a high-speed train investigated with a line array of microphones. 5. B. B and W. F. K III 1988 Journal of Sound and Vibration 120, 190–196. On removing the Doppler frequency shift from array measurements of railway noise. 6. Y. M, Y. Z, Y. S and K. N 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 45–48. Aerodynamic noise of high-speed railway cars. 7. W. F. K III 1995 Journal of the Transportation Research Board, Washington, D.C., U.S.A. 1475, 59–65. Radiated aerodynamic noise generated by high-speed tracked vehicles. 8. W. F. K III 1977 Physics Letters 62A, 282–284. The effect of motion on acoustic dipole models for aerodynamic noise prediction. 9. D. G. C 1975 Journal of Fluid Mechanics 72, 209–227. Scattering and diffraction of sound by moving bodies. 10. B. B, personal communications. 11. G. H , P. F, K. P. S, A. P and B. B 1994 Proceedings of
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12. 13. 14. 15. 16. 17. 18. 19.
20. 21. 22. 23.
. . InterNoise ’94, 193–198. DEUFRAKO-2: localized sound sources on the high-speed vehicles ICE, TGV-A, and TR 07. P. K. S 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 33–38. Sound measurements on Transrapid 07—methods and results. B. B 1996 Journal of Standard Vibration 193, 283–293. Experiences with various configurations of microphone arrays used to locate sound sources on railway trains operated by the DB AG. G. H 1996 Journal of Sound and Vibration 193, 359–366. Low-noise goods wagons. Y. T, A. T, K. T, M. S, M. H and Y. K 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 39–44. Noise reduction on the new Nozomi Shinkansen cars. M. I, T. M and K. M 1994 Proceedings of InterNoise ’94, 169–174. Development of low aerodynamic noise pantograph for high-speed train. N. Y and E. Y 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 275–279. High-speed testing car ‘‘WIN 350’’. A. I, Y. Y, T. M, K. K and M. H 1994 Proceedings of InterNoise ’94, 163–168. Development of a low-noise electric-current collector for high-speed trains. B. B and B. M 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 49–54. Relevant sound sources generated by the high-speed railway train ICE of the Deutsche Bundesbahn and how they are accounted for in model calculations of wayside noise predictions. W. F. K III, P. A. M and E. P 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 65–69. The aerodynamics and acoustics of high-speed tracked vehicles. J. M and S. H 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 1, 174–179. Aerodynamic design of frontal shape for JR maglev train. T. T and K. S 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 1, 180–185. Aerodynamic design of JR maglev train frontal shape Part II. B. B and B. M 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 1, 227–232. Modal calculations of radiated noise generated by a multiple-section Transrapid maglev TR 07.
A PRE CIS OF DEVELOPMENTS IN THE AEROACOUSTICS OF FAST TRAINS W. F. K III German Aerospace Establishment (DLR), Department of Turbulence Research, Mu¨ller-Breslau-Strasse 8, D-10623 Berlin, Germany (Received in final form 20 November 1995) After briefly reviewing the important mechanisms by which aerodynamic sound sources are generated on high speed tracked vehicles, two characteristic train speeds that quantify the significance of this noise are defined. The results of microphone array measurements are used to illustrate sound levels generated by flow interactions with a pantograph. Recent developments in measurement technology, analysis and hardware are then surveyed. 7 1996 Academic Press Limited
1. INTRODUCTION
Until the mid-1970s, the term ‘‘railway’’ noise referred exclusively to wheel/rail (W/R) interaction noise, which is the dominant component of wayside noise at train speeds above about 80 km/h. Aerodynamic noise was discussed very briefly at the first Railway Noise Workshop held in Derby, England, in 1976, but this subject was then more academic than practical. With the introduction into service of truly high speed trains in the 1980s, aerodynamic fluctuations began vying with W/R interactions for the honour of being the predominant source of wayside noise at high train speeds. Technological advances in abating W/R noise levels during the past few decades have further enhanced the significance of the aerodynamically generated component of wayside noise. In the present paper some of the advances made during the past ten years in locating and analyzing the aerodynamically generated component of wayside noise will be outlined. Also, albeit briefly, some of the recent techniques being developed to control aerodynamic noise sources will be discussed.
2. AERODYNAMIC SOUND SOURCES
2.1. To a physicist, the word ‘‘noise’’ means any disturbance that interferes with the intelligibility of a signal. In colloquial usage, ‘‘noise’’, which is derived from the Latin nausea (seasickness), refers to any sound that is noticeably unpleasant or disturbing. To railway acousticians, ‘‘noise’’ has the latter meaning, and ‘‘noise’’ and ‘‘sound’’ are used interchangeably. The common sources of aerodynamic noise generated by fast trains are illustrated in Figure 1. All of these sound sources are a consequence of flow separations caused by either the detachment of the turbulent boundary layer or vortex shedding from structural elements on the vehicle. At high speeds, a boundary layer detachment on the head of the leading car often produces the strongest individual sound source on the train with vortex 349 0022–460X/96/210349 + 10 $18.00/0
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shedding from pantographs and their associated roof equipment generating the second strongest individual sound sources. In countries such as Japan where peak sound levels are the criteria for determing wayside noise levels, these two sound sources are very important, with the latter one being the more important at high speeds when sound barriers are present. Noise generated by pressure fluctuations beneath the turbulent boundary layer per se will not be discussed because this noise is not expected to be significant at train speeds up to at least 400 km/h [1]. In countries where the measure of wayside noise is an equivalent sound level Leq , averaged over some prescribed time period, the two strongest sources of aerodynamic noise, albeit still important, are not usually the dominant flow-generated sound sources on railway trains. Rather, vortex shedding from protuberances and edges in the bogie regions on long trains plays the controlling role in establishing an equivalent sound level at high speeds. Whether or not aerodynamically generated noise is an important constituent of wayside noise for any particular vehicle depends on several factors including the relative level of wheel/rail (W/R) interaction noise and the speed range within which the train operates. In turn, W/R noise levels are strongly affected by the degree of roughness on wheel treads and rail surfaces. In general, as advances are made in controlling W/R noise, the relative importance of aerodynamic noise increases. 2.2. Vortex shedding is the most important mechanism for generating aerodynamic noise on railway trains. As shown in Figure 2, consider a slender cylinder of diameter D and length L moving along the x-axis with constant velocity U0 in such a way that L is normal to U0 and lies in the x–z plane. Vortices shed from this cylinder will generate sound having a dipole radiation pattern whose maximum intensity lies more or less in the y-direction. The shed vortices are coherent over some correlation length lc along L. Sound generated by vortex shedding within any correlation length is statistically independent of sound produced by shedding within any other correlation length. One can derive an expression for modelling this sound by replacing the vortex shedding within a correlation length by an equivalent point dipole sound source the axis of which lies along the y-direction. Let p˜i be the root-mean-square (r.m.s.) sound pressure due to a single correlation length. Then, if Llc and RL, one can calculate the total sound pressure due to vortex
Figure 1. Aerodynamic sound sources on a typical high speed train.
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Figure 2. The co-ordinate system for a moving point-dipole sound source. An observer is located at P, and the dipole axis lies along the y-direction.
shedding on the cylinder by simply summing up the p˜i2 , where i identifies the individual correlation lengths. By using a force distribution term for the equivalent point dipole as the source term in the wave equation, it can be shown that the rms sound pressure due to vortex shedding can be written as p˜ 2 = C L2 Sd2 r 2Llc U06 sin2 u cos2 f/16c 2R 2(1 − M cos u)4,
(1)
where C L is the coefficient of fluctuating lift, r is the fluid density, c is the local sound speed, R is the distance from an observer to the source, and M = U0 /c is the Mach number. The symbol Sd , equal to f0 d/U0 , is the Strouhal number, where d is some characteristic dimension of the body (in the cylinder case D), and f0 is the peak frequency of both vortex shedding and sound. If the cylinder in the example were one of the horns on a pantograph and the observer were positioned along the wayside, one could let f in equation (1) equal zero. For slender cylinders having circular or elliptic cross-sections, the values of C L and lc are dependent upon Reynolds number, defined as Red = U0 d/n, where n is the kinematic viscosity of the fluid. Up to a Reynolds number of about 3 × 105, the higher the Reynolds number, the lower the values of C L and lc . For cylinders having square or rectangular cross-sections, these parameters are only weakly dependent on Reynolds number. 2.3. In Figure 3 are shown two superposed results of sound level distributions measured at the locations of the front and rear pantographs on the ICE/V, the test version of the InterCity Express. The measurements were made with a vertically mounted line array of 15 microphones spaced at equal intervals of 0·24 m, with the middle of the array positioned at approximately the height of the knee on the raised pantograph and at a lateral distance of 5 m from the near rail. Details concerning measurements of railway noise with microphone arrays are given in references [2–5]. The dedicated test train comprised two power cars separated by two middle coaches. Each power car was equipped with a model DSA 350 M pantograph with its associated roof equipment. The results shown in Figure 3 are for a pass-by speed of 300 km/h with the front pantograph retracted and the rear
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pantograph raised. Both results are given in unweighted decibels for the frequency range 200–1400 Hz. As can be seen in the figure, flow interactions with the roof equipment and retracted front pantograph generate a higher sound level than do flow interactions with the head of the raised rear pantograph. The boundary layer on the roof of the front power car is relatively thin, and the folded pantograph and its associated equipment (insulators, switches, and cables) are subjected to essentially the full free-stream velocity U0 . On the roof of the rear power car, the boundary layer is several times thicker than it is on the front power car, and the roof equipment on the rear car is subjected to substantially lower inflow speeds than is the case on the front car. The distribution of sound level on the rear power car shows a high peak value at a height of about 2·7 m. This is the height of the inlet louvres for the cooling fans, which are activated automatically and are therefore not always switched on. The high sound level here is probably not due to the cooling fans per se, but rather is caused by vortex shedding on the louvre inlet vanes [6]. It is also possible that the force of sliding (kinetic) friction Fk between the contact strips and the overhead wire could be responsible for part of the radiated noise. Although laboratory measurements of Fk are not available for the high speeds at which the contact strips interact with the overhead wire, it is known that Fk is essentially independent of both contact area and speed. The force of kinetic friction is, however, proportional to the normal force FN that hold the two bodies in contact. For pantographs, FN has an average value of about 100 N, regardless of speed. Furthermore, for many materials, Fk decreases at very high sliding speeds. In view of these characteristics of Fk , it seems likely that any noise level due to sliding friction would remain fairly constant and would not be a function of train speed. Indeed, any frictional noise level may will decrease at high train speeds.
Figure 3. Sound-level distributions generated by flow interactions with front (down) (– – –) and rear (up) (——) pantographs on a dedicated ICE/V as it passed by at 300 km/h, as measured by an SWV2H micrphone array (Shaded Wayside Vertical High array, where ‘‘2’’ signifies the microphone spacing of 0·24 m; bandwidth 200–1400 Hz). On the ordinate, H = height above rail.
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3. DECOMPOSITION OF WAYSIDE NOISE LEVELS
3.1. It is now well known that the square of the sound pressure generated by a vehicle is proportional to vehicle speed raised to a power a: i.e., p˜ 0 U0a ,
(2)
where a is called the speed exponent. For the total sound pressure measured along the wayside, a is not a constant but depends upon speed and whether or not the sound is A-weighted [7]. Variations in a with speed are, however, quite small and become significant only at high speeds. 3.2. The effect of convective augmentation [8, 9] causes a to increase with increasing vehicle speed. The most simple example of this effect is the case of a moving point dipole sound source. Using equation (1) and considering only the direct change of sound pressure with motion, one can write p˜ 2 = KU06 sin2 u/R 2(1 − M cos u)4,
(3)
where K is a constant. Here the observer is positioned along the wayside, and hence f is set to zero. The factor (1 − M cos u)4 is responsible for convective augmentation. At u equal to 90 degrees there is no additional effect due to convection, and p˜ 2 = KU06 /R 2 for all speeds rather than just for M1. One can find the angle um at which the augmentation is a maximum by differentiating equation (3) with respect to u and setting the result equal to zero. This procedure gives um = arccos M.
(4)
The value of the convective augmentation D is then the difference between the sound levels at um and at u equal to 90 degrees. It can be shown that D = −20 log10 (1 − M 2 ) dB.
(5)
Although equation (5) was derived for a point dipole sound source, the result is the same if one considers a line segment of dipoles and integrates equation (3) over all of them. Thus, equation (5) is a good approximation for the effect of convective augmentation on passby sound levels. If one is interested in the effect of convection on the peak sound level due to a line segment of dipoles, the coefficient in equation (5) should be about 27 rather than 20. 3.3. Pass-by sound pressure levels for the individual W/R and aerodynamic noise contributions to the wayside sound pressure level after the effect of convective augmentation has been removed can be represented by equations of the form Leq,p (i) = 10ai log (U0 /UR ) + Ni dB(A),
(6)
where the index i is equal to 1 for sound due to W/R interactions and to 2 for sound due to aerodynamic fluctuations. The symbol UR denotes a reference speed, and the Ni are empirical constants. The acoustical transition speed Ut is that train speed at which the sound pressure level due to aerodynamic interactions equals the sound level due to all other causes (essentially W/R interactions). At train speeds higher than Ut , aerodynamic noise will dominate
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Figure 4. Measured pass-by sound pressure levels (at 25 m) for a 12-coach ICE (D) [10] and a 2-coach ICE/V (X). – –, W/R noise; . . ., aerodynamic nosie.
wayside noise levels. An expression for Ut can easily be found by using equation (6) and setting Leq,p (1) equal to Leq,p (2). This procedure gives log (Ut /UR ) = 0·1(N1 − N2 )/(a2 − a1 ).
(7)
Another characteristic speed that quantifies the relative importance of aerodynamic noise is the acoustical impact speed UI , defined as that train speed at which the pass-by sound pressure due to aerodynamic fluctuations increases the pass-by sound pressure level caused by W/R interactions by one decibel. Again using equation (6), one finds that UI can be expressed as log (UI /UR ) = 0·1(N1 − N2 − 5·87)/(a2 − a1 ).
(8)
3.4. () Average operating conditions in Germany, what are called here condition 2, means that wheel treads have no obvious pits or scans and rail surfaces appear smooth to the naked eye. Pass-by sound pressure levels (open triangles) for a 12-coach dedicated InterCity Express (ICE) operating under condition 2 are shown in Figure 4. These results were measured by Barsikow [10] with a microphone positioned at a lateral distance of 25 m from the centerline of the track and at a height of 3·5 m above the rails. The ICE is equipped with disc brakes, and the wheels on all coaches are fitted with noise absorbers that abate W/R noise levels by from 5 to 6 dB. For comparison, pass-by sound pressure levels for the two-coach ICE/V are also shown in the figure. All wheels on this test train were fitted with noise absorbers. At high speeds in particular, the power cars on both trains generate somewhat higher sound levels than do the coaches. Thus, since the power cars on the short ICE/V make up a much larger fraction of the total train length than they do on the longer ICE, pass-by sound levels produced by the former are a few decibels higher than they are for the latter at high speeds.
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To obtain an empirical fit to the ICE data, one can first employ equation (5) to remove the effect of convective augmentation from all measured sound levels. Making use of the facts that a for W/R noise lies between 2·8 and 3·2 and that aerodynamic noise is relatively insignificant at low speeds, one can find a1 and N1 in equation (6) for a reference speed of 200 km/h. By extrapolating the sound pressure due to W/R interactions up to a train speed of 280 km/h, the highest speed at which data were available, and subtracting this sound pressure from the average of the measured values, the sound pressure caused by aerodynamic fluctuations was obtained. The results are Leq,p (1) = 28 log (U0 /200 km/h) + 81·6 dB(A),
(9)
Leq,p (2) = 65 log (U0 /200 km/h) + 74 dB(A)
(10)
and
Pass-by sound levels for the W/R and aerodynamic noise components computed with the above equations are shown in Figure 4. The solid curve in the figure represents the energy sum of these two components plus the augmentation due to convection. The acoustical transition and impact speeds can then be computed with equations (7) and (8), respectively. The results of these calculations are Ut 1 320 km/h and UI 1 220 km/h. Therefore, when a 12-coach ICE operates under average conditions, the aerodynamically generated component of noise begins to make a measurable difference to wayside noise levels at a speed of roughly 220 km/h. Although numerous array measurements have shown that the value of the speed exponent for W/R noise lies within a very narrow range, there is a certain degree of arbitrariness in the choices of the parameters in equations (9) and (10). This arbitrariness results in uncertainties in the computed values of the characteristic speeds on the order of 10 per cent. Wayside noise levels can be decomposed with greater accuracy if measured values are available for train speeds up to at least the acoustical transition speed, as they are for the ICE/V. 4. RECENT AND ONGOING DEVELOPMENTS
A few investigators [11–15] have used two-dimensional configurations of microphone arrays to study railway noise during the past five years or so. Use of these arrays has halved the on-site measuring time needed to locate both the vertical and longitudinal co-ordinates of individual, localized sound sources. A true, two-dimensional array of microphones is a planar surface covered with microphones, each of which is separated from its nearest neighbors by some specified displacement. The two-dimensional configurations of microphone arrays used thus far for studying railway noise comprise two linear line arrays of microphones arranged at an angle of 90 degrees to one another so that the middle microphone of each line array is one and the same. When we designate a line array of microphones as ‘‘linear’’ we mean that the microphones are spaced at equal intervals. When such a two-dimensional configuration is arranged along the wayside so that one line array is positioned vertically and the other horizontally, the configuration is referred to as a cross-array [11, 12]. When this array is rotated through an angle of 45 degrees, an X-array is formed [13–15]. By appropriately processing the microphone signals measured with these arrays, a quasi two-dimensional ‘‘viewing window’’ (i.e., the combined main beams of the directivity patterns) can be formed. In principle, these two-dimensional configurations of line arrays can more effectively isolate sound generated by an individual, localized source than can a one-dimensional line array, the resolution of which is restricted to one spatial direction. In practice, however, the conventional Dolph–Tschebyscheff shading technique leads to
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a suppression of side lobes of only 10–12 dB in the directivity pattern of the two-dimensional array configurations compared with a suppression of 20 dB or higher for the one-dimensional line array. The most effective array configuration for a given task, therefore, depends upon the location of the particular sound source of interest and the intensities and positions of its near neighbors. All three of the array configurations described above have been used to study flowgenerated pantograph noise. Ikeda et al. [16] have developed a very innovative low-noise pantograph for fast trains. This pantograph, shown in Figure 5, combines a minimum number of structural elements with a head shape the cross-section of which is elliptic. The coefficient of fluctuating lift in equation (1) for the integrated horns and bow is significantly lower for the elliptic cross-section than it would be for any other geometry. Vortex shedding from the large-diameter yawed support arm also generates negligible sound. Another new ‘‘wing-shaped’’ pantograph [17] also combines a minimum of structural elements with an elliptic head shape and a single vertical support arm. In 1995 this pantograph was tested on the new Japanese WIN 350 high speed train, which is also equipped with wheel skirts to abate vortex-shedding noise generated in the bogie regions. Iida et al. [18] discussed a new ‘‘delta-wing’’ shaped pantograph that generates noise levels about 19 dB lower than do conventional current collectors. These authors used an X-array in their acoustical investigations. Computer models [13, 19] the inputs of which are the intensities, locations and speed exponents of sound sources have proved to be valuable tools for ascertaining the importance of individual aerodynamic and W/R sound sources. The input parameters for these models are taken either from the results of array measurements or from theoretical considerations. Time histories of the sound pressure level, pass-by sound levels and other equivalent sound levels based upon any desired time span can be computed with these models [13]. A number of examples of such calculations illustrating the influence of various sound sources on an ICE are given in reference [19]. Aerodynamically optimized head shapes on the lead car of a tracked vehicle can help reduce radiated noise levels at high speeds by suppressing the tendency of the boundary
Figure 5. The prototype of a low-noise pantograph [16] with elliptic head and horns.
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layer to detach itself in this region [7, 20–22]. A good discussion of the head shape on the new 300-series Shinkansen Nozomi is given in reference [15]. Measurements made with an X-array of microphones are also discussed. According to these authors, the acoustical transition speed for the Nozomi when a sound barrier is present is 220 km/h. A new, improved head shape has recently been installed on the German Transrapid maglev vehicle. Since array measurements [11] demonstrated that flow interactions with the cover plates for the guidance system were also a source of wayside noise, these cover plates have also been changed. With these modifications, the vehicle is now designated as the TR 07-2. Measurements, the results of which are not yet generally available, indicate that this modified maglev vehicle generates wayside noise levels that are between 2 and 3 dB lower than those produced by its immediate predecessor. With its modified head shape and cover plates, the TR 07-2 now generates a lower wayside noise level at a speed of 400 km/h than do the majority of InterCity trains travelling at a speed of only 200 km/h (see references [7, 23]).
5. CONCLUDING REMARKS
Because brevity is one of the criteria placed upon this paper, we have necessarily given rather short shrift to our discussions of recent advances in the aeroacoustics of high speed tracked vehicles. Most of the ongoing work in this field can be grouped into three categories: (1) improvements in measurement techniques designed to locate and quantify sources of aerodynamic noise; (2) the development of computer models to predict effects of abating individual sound sources; and (3) the design of new hardware such as pantographs and head shapes for lead cars. Our selection of published material to illustrate advances in these three areas has only scratched the surface of the available literature, and we hope that authors whose works are not cited here will understand the reasons for these omissions.
REFERENCES 1. W. F. K III 1994 Proceedings of InterNoise ’94, 175–180. On the boundary layer contribution to wayside noise generated by high-speed tracked vehicles. 2. W. F. K III and D. W. B 1979 Noise Control Engineering Journal 13, 13–23. Aerodynamic noise generated by high-speed trains. 3. W. F. K III and D. W. B 1979 Journal of Sound and Vibration 66, 311–332. On the sources of wayside noise generated by high-speed trains. 4. B. B, W. F. K III, and E. P 1987 Journal of Sound and Vibration 118, 99–122. Wheel/rail noise generated by a high-speed train investigated with a line array of microphones. 5. B. B and W. F. K III 1988 Journal of Sound and Vibration 120, 190–196. On removing the Doppler frequency shift from array measurements of railway noise. 6. Y. M, Y. Z, Y. S and K. N 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 45–48. Aerodynamic noise of high-speed railway cars. 7. W. F. K III 1995 Journal of the Transportation Research Board, Washington, D.C., U.S.A. 1475, 59–65. Radiated aerodynamic noise generated by high-speed tracked vehicles. 8. W. F. K III 1977 Physics Letters 62A, 282–284. The effect of motion on acoustic dipole models for aerodynamic noise prediction. 9. D. G. C 1975 Journal of Fluid Mechanics 72, 209–227. Scattering and diffraction of sound by moving bodies. 10. B. B, personal communications. 11. G. H , P. F, K. P. S, A. P and B. B 1994 Proceedings of
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12. 13. 14. 15. 16. 17. 18. 19.
20. 21. 22. 23.
. . InterNoise ’94, 193–198. DEUFRAKO-2: localized sound sources on the high-speed vehicles ICE, TGV-A, and TR 07. P. K. S 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 33–38. Sound measurements on Transrapid 07—methods and results. B. B 1996 Journal of Standard Vibration 193, 283–293. Experiences with various configurations of microphone arrays used to locate sound sources on railway trains operated by the DB AG. G. H 1996 Journal of Sound and Vibration 193, 359–366. Low-noise goods wagons. Y. T, A. T, K. T, M. S, M. H and Y. K 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 39–44. Noise reduction on the new Nozomi Shinkansen cars. M. I, T. M and K. M 1994 Proceedings of InterNoise ’94, 169–174. Development of low aerodynamic noise pantograph for high-speed train. N. Y and E. Y 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 275–279. High-speed testing car ‘‘WIN 350’’. A. I, Y. Y, T. M, K. K and M. H 1994 Proceedings of InterNoise ’94, 163–168. Development of a low-noise electric-current collector for high-speed trains. B. B and B. M 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 49–54. Relevant sound sources generated by the high-speed railway train ICE of the Deutsche Bundesbahn and how they are accounted for in model calculations of wayside noise predictions. W. F. K III, P. A. M and E. P 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 2, 65–69. The aerodynamics and acoustics of high-speed tracked vehicles. J. M and S. H 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 1, 174–179. Aerodynamic design of frontal shape for JR maglev train. T. T and K. S 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 1, 180–185. Aerodynamic design of JR maglev train frontal shape Part II. B. B and B. M 1993 Proceedings of the International Conference on Speed-Up Technology (STECH), Yokohama, Japan 1, 227–232. Modal calculations of radiated noise generated by a multiple-section Transrapid maglev TR 07.