Evaluation of Aeroacoustic Noise Source Structure. around Panhead of a Pantograph in High-Speed Railway

Transcription

1 Evaluation of Aeroacoustic Noise Source Structure around Panhead of a Pantograph in High-Speed Railway 1 M. Ikeda, 1 T. Mitsumoji 1 Railway Technical Research Institute, Tokyo, Japan Abstract: As the maimum speed of high-speed trains has reached 300km/h, performance of a pantograph has been strongly influenced by aerodynamic effects. Aeroacoustic noise generated by the pantograph during high-speed running has become one of the main noise sources on the highspeed trains in Japan. There has therefore been a strong demand for reductions in the aeroacoustic noise of the pantograph in order to decrease wayside noise, and continuous efforts toward this goal have brought about the evolution of a low-noise pantograph. The low-noise pantograph is composed of members with aerodynamically smooth shapes, contributing significantly to wayside noise reduction. Although aerodynamic push-up force characteristics of the pantograph have also a strong effect on the current-collection performance in high-speed running, the contact force between pantograph and contact wire has to be maintained within a suitable range to ensure steady current collection. Hence, the aerodynamic push-up force of the pantograph has to be controlled within acceptable range. A panhead, one of the main components of the pantograph, is placed on the top of an articulated frame; contact strips fied on the upper surface of the panhead is in contact with a contact wire to supply electric power to a traction unit of the train. The panhead has a relatively large projected area compared with that of other components such as the articulated frame; aeroacoustic noise generated by the panhead dominates the whole aeroacoustic noise of the pantograph. In the same reason, lift force acting on the panhead governs dynamic push-up force of the pantograph. Consequently, the aeroacoustic and lift force characteristics of the pantograph on the high-speed train depend largely on the design of the panhead, or the panhead shape. However, it is difficult to achieve a drastic reduction in the aeroacoustic noise of the panhead while also ensuring the stability of its lift force, as these two demands often trade off each other. Up to now, a trial-and-error method involving many eperiments plays an important role in the panhead design. Many time-consuming and epensive wind tunnel tests and line tests have to be conducted to obtain a suitable panhead shape. To make the panhead design more efficient and rational, understanding the physical natures of aeroacoustic noise sources is very important. In this paper, a new method is proposed to identify spatial structure of aeroacoustic noise sources around the body moving at high speed on condition that the compact approimation can be applied. This approimation is reasonable to discuss the aeroacoustic noise generated by the panhead. In many case, low-mach-number aeroacoustic problems are solved by using Lighthill s acoustic analogy. The strength of noise sources, which are distributed around the body, can be evaluated by using Howe s vorte sound theory from flow field quantities obtained by numerical simulation or eperimental result. Although this method ensures the acoustic pressure in the far field, contribution of each noise source to the acoustic radiation cannot be identified. Intensive noise cancellation occurs among mutual noise sources in the vicinity of the body, therefore, It is difficult to identify spatial structure of aeroacoustic noise sources. The newly proposed method calculates cross-correlation between the strength of local noise source around the body and the far-field acoustic pressure. In this way, net contribution of each noise source to the acoustic radiation in the far-field can be evaluated; the characteristic spatial structure of the aeroacoustic noise sources around the body is clarified. This information is valuable to design and modify the body shape for the purpose of decreasing aeroacoustic noise. In this study, this method is applied to identify spatial structure of aeroacoustic noise source around the panhead of the high-speed pantograph. Flow field quantities, which are necessary to derive noise sources strength, are obtained by means of numerical flow simulation. Wind tunnel tests is also conducted to verify the results of the flow simulation as well. Estimation results of the noise source contributions by means of the newly proposed method eplicitly indicate spatial noise source structures that correspond with vorte shedding patterns. In particular, the results clarify the Aeolian

2 tone generated by the Karman vorte sheets has strictly ordered large-scale structure of noise sources in the wake of the panhead. This technique has an advantage that net contributions of the noise source around the panhead to the noise radiating to the far-field can be evaluate quantitatively. Furthermore, the spatial structure of aeroacoustic noise source around the panhead can be identified. This method can gives many physical information about aeroacoustic property of the panhead; it promises to be a powerful tool for design and modification of the panhead shape that generates less aeroacoustic noise. 1. Introduction High-speed railways are epected further progress in the world as environmentally-friendly transportation systems which emit fewer CO2 than other high-speed transportation systems such as car vehicles or aircrafts. However, some environmental problems remain a matter of grave concern for high-speed railways. Japanese high-speed trains (Shinkansen) have been operated above 270km/h passing through the area of dense population due to geographic features of Japan. Wayside noise of Shinkansen trains in a residential area has been controlled by the governmental regulation which requires the maimum wayside noise level shall be lower than 75dB(A). This regulation is very strict compared with that of European countries. Therefore, reduction of the wayside noise of Shinkansen trains has been an important task for railway operators. Continuous efforts to reduce the wayside noise make it possible for Shinkansen trains to run at 300km/h in compliance with this regulation. However, further noise reduction is demanded to increase maimum speed of Shinkansen trains. In the speed-range above km/h, aeroacoustic noise dominates the wayside noise of highspeed railways. A rapidly moving object in the air emits aeroacoustic noise, which is induced by the accelerated motion of vortices shedding from the object. In general, the energy of aeroacoustic noise is proportional to the 6-8 th power of relative flow velocity between the object and air. In this reason, as train velocity becomes faster, the aeroacoustic noise becomes to increase seriously. Shape of the moving object has large influence on the formation of vortices, which causes aeroacoustic noise. Reduction of the aeroacoustic noise is often achieved by smoothing the object shape, because the smooth-shaped objects inhibits formation of strong vortices in the wake. In this sense, the shape design is very important for the high-speed train. However, deductive design of the object shape to reduce aeroacoustic noise is a difficult work. Lighthill s acoustic analogy [4], which describes behaviour of aeroacoustic noise, is hard to be solved; the analytical treatment of the aeroacoustic noise generation is not easy. In practice, repetitive wind tunnel tests and on-line tests determine final shape of the high-speed train to achieve further aeroacoustic noise reduction after much trial and error. However, this approach is generally epensive and takes a long time. RTRI (Railway Technical Research Institute) has been working on numerical simulation of aeroacoustic noise by using CFD (computational fluid dynamics) to design low noise-emission highspeed vehicles effeciently. Takaishi et al. proposed the new technique, which could evaluate noise source distribution of dipole sound emitting from an object in air flow by using CFD analysis in combination with an acoustic analysis technique based on Howe s vorte sound theory [3]. Dipole noise is low-frequency aeroacoustic noise emitted from an object in low-mach-number flow which satisfies the approimation of acoustical compactness. This technique has the advantage that evaluated noise source distribution is directly related to the flow field around the objects. In the contrast, commonly-used aeroacoustic noise evaluation technique based on Curle s equation [1,2] estimates noise source as being related to surface pressure fluctuation of the object. In the process of the dipole sound emission, however, the mutual noise-cancellation occurs significantly between different noise sources in the flow. The evaluation of noise source distribution with no thought of such a cancellation effects should includes many pseudo contributions. In this paper, dipole noise source contributions in the flow are evaluated by the new method, which is epanded from Siddon s method giving noise source evaluation on the surface with Curle s equation [5]. This new method derives noise source contributions by calculating cross spectrums between dipole sound observed in the far-field and dipole noise source strengths at each position around the

3 object. By this method, net contribution of noise source to dipole noise radiating to the far-field can be evaluated; the characteristic spatial structure of the aeroacoustic noise sources around the object is clarified. This information is valuable to design and modify the object shape for the purpose of decreasing aeroacoustic noise. This paper focuses on aeroacoustic noise source evaluation of a panhead on a pantograph. The pantograph is mounted on the roof of the train just like a projection; it is greatly influenced by aerodynamic effects including aeroacoustic noise emission. This is making the pantograph one of the main noise sources on the Shinkansen train set. In particular, the panhead, which is set on the top of an articulated system of the pantograph, is a significant noise source of the pantograph. Lift force acting on the panhead also governs dynamic push-up force of the pantograph. Consequently, the aeroacoustic and lift force characteristics of the pantograph on the high-speed train depend largely on the design of the panhead, or the panhead shape. However, it is difficult to achieve a drastic reduction in the aeroacoustic noise of the panhead while also ensuring the stability of its lift force, as these two demands often trade off each other. To make the panhead design more efficient and rational, identification of aeroacoustic noise sources structure is very important. 2. Method to evaluate dipole noise source contributions In this study, quantitative analysis of aeroacoustic noise generated by an object in low Mach number flow is carried out by so-called the decoupled approach, which combines the incompressible unsteady CFD analysis with the acoustic analogy, assuming that the acoustical compactness approimation is satisfied. Since purpose of this study is to identify noise source structure in the flow field, Howe s vorte sound theory is applied as an acoustic analogy. The aeroacoustic noise is evaluated by using flow field data calculated by CFD analysis: in this paper, the following equation proposed by Takaishi et al. is applied, which gives dipole noise observed in the far-field by using flow information within finite region. ρ0 i pa (, t) = ( 2 ω u)( y, t- /c0 ) ϕidy 4πc Ωint t (1) 0 Where P a is sound pressure of dipole noise, is position vector of the observation point in the far-field, t is time, ω is vorticity vector, u is flow velocity vector, ρ 0 is aerial density, c 0 is sound speed, and Ω int indicates finite computational domain around the object as shown in Fig. 1. φ i is velocity potential around the object moving at unit velocity in the i-direction; this can be obtained by solving the Laplace equation. Far-field Noise observation point Computatinal domain y 2 y 1 Ω int flow velocity u vorticity ω Flow Object Fig. 1 Computational domain and observation point of dipole noise The integrant of Equation (1) can be regarded as noise source strength at point y near the object. Therefore, dipole noise source strength D i (y,t) can be defined as the following equation. Di( y, t) = ( ω u )( y, t ) ϕi (2) t c 0

4 This equation indicates that appearance of strong noise source need two conditions; one is large fluctuation of flow velocity and vorticity, and the other is location near the sharp corner on the surface of the object. Substituting Equation (2) in Equation (1), the dipole noise observed at the point in the far-field can be epressed with the dipole noise source strength D i (y,t) as following. ρ ( ) 0 i pa, t = (, ) 2 Di y t dy 4πc Ω (3) int 0 However, spatially distributing dipole noise sources significantly cancel out each other. The integrant of Equation (3) includes Insubstantial dipole noise sources that have little contribution to the far-filed sound. Therefore, observing only RMS distribution of noise source strength does not give reasonable eplanation. Auto-correlation function of dipole sound p a (,t) observed at the point in the far-field is epressed as followings, pa(, t) pa(, t+ τ ) ρ0i = pa(, t) (, ) 2 Ω D int i y t+ τ dy 4π c0 ρ0 (4) i = pa(, t) D (, ) 2 i y t+ τ dy Ωint 4π c0 = p, t D (, y, t+ τ ) dy Ωint a ( ), where operator and function D (,y,t) are defined respectively as follows. 1 T f () t g( t + τ ) lim f() t g( t+ τ ) dt T T 0 (5) ρ0i D(, y, t) D (, ) 2 i y t 4π c (6) 0 Substituting Equation (2) and Equation (6) into Equation (1), the aeroacoustic noise observed at the point in the far-field can be epressed as spatial integral of D (,y,t). Equation (4) indicates that the auto-correlation of sound pressure of dipole noise p a (,t) observed at the point can be epressed by the cross-correlation between sound pressure of dipole noise observed at the point and the function D (,y,t). Fourier transformation of Equation (4) yields the following equation. SPa, Pa (, ω) = SPa, D (, y, ω) dy Ω (7) int The symbol S fg indicates the cross spectrum as 1 iωτ Sf, g( ω) f( t) g( t τ) e dτ 2π + (8) Equation (7) indicates the power spectrum of sound pressure of the dipole noise observed in the farfield is obtain by calculating the cross spectrum of the sound pressure of the dipole noise observe in the far-field with the function D (,y,t). In addition, value of power spectrum is real numbers; the integral in the right-hand side of Equation (7) has to be a real number. This means that imaginary parts of integrants in Equation (7) cancel out each other. In other words, only real parts of the integrants indicate substantial contributions for the dipole noise. Hence, dipole noise source contribution at the point y near the object to the dipole noise observed at the point in the far-field, or D p (,y,ω) can be defined as follows. Dp(, y, ω) = Re ( SPa, D (, y, ω) ) (9) Aeroacoustic noise source structure in the flow can be evaluated by showing distribution of dipole noise source contributions. In the nest chapter, aerodynamic noise source structure of the panhead on the pantograph will be discussed by calculating distribution of the dipole noise source contributions.

5 3. Distribution of dipole noise source contributions around a panhead 3.1 Method and target of flow field analysis By the previous researches, it is clarified that the panhead is the most strong noise source on the pantograph shown in Fig. 2. Furthermore, flow field around the panhead can be regarded as twodimensional flow ecept for its central region. Therefore, it is reasonable for the panhead to be modelled as a two-dimensional pillar in order to investigate aeroacoustic noise source structure around the panhead. The procedure for evaluating noise source structure is describes below. First of all, flow field around the panhead model is calculated by incompressible unsteady CFD analysis. Then, the aeroacoustic sound observed in the far-field is calculated by Equation (1). Finally, distribution of dipole noise source contributions is evaluated by using Equation (7), indicating the noise source structure around the object. Figure 3 shows the cross-sectional shape to be investigated in this study, which is based on the currently-used panhead. By using the FLUENT solver with large eddy simulation model, incompressible unsteady three-dimensional flow field was calculated. Figure 4 shows a schematic diagram of the computational domain. The computational grids are arranged around the panhead model in y 1 -y 2 plain; the minimum grid size in y 1 -y 2 plain is 0.1mm. Grids in the y 1 -y 2 plain are arranged in line along the y 3 direction with equal intervals of 5mm; the grid number along the y 3 direction is 20. Total number of the computational cells is about A uniform flow of 42m/s without turbulent disturbance is assumed for the inlet boundary. The Reynolds number is At the upper and lower boundaries of the panhead model, symmetry condition is applied; at the boundary in the span-wise direction of the panhead model, asymmetric boundary condition is applied. The no-slip condition for velocity is applied at the model surface. The outlet is set to an outflow boundary condition, which dictates a zero diffusion flu Fig. 2 Eample of a pantograph for Shinkansen trains Fig.3 Cross-section of panhead model Fig. 4 Computational domain

6 3.2 Computational and eperimental result of sound pressure level in the far-field The CFD analysis was eecuted in the 1050 steps. Calculated flow fields yielded the sound pressure of the dipole noise observed at the point 0 in the far-field, that was set at (y 1,y 2,y 3 ) = (2000, 2000, 0), by Equation (1). Subsequently, power spectrum density of the sound pressure level was evaluated on condition that sampling frequency was 10kHz, Hanning window was chosen as a window function, the number of sampling points of the window was 512, and overlap for averaging was set at 50%. To verify the numerical simulation, a wind tunnel test with a two-dimensional panhead model was conducted by the small-scale anechoic wind tunnel of RTRI. Figure 5 shows the outline of the eperimental apparatus. The panhead model for the wind tunnel test had the same cross-section as the panhead model of the numerical simulation shown in Fig. 3. The span-length of the eperimental model was 600mm. Aeroacoustic noise emitted from this model was measured at the flow velocity of 42m/s by a microphone set at the point e = (1414, 1414, -300). Accuracy of numerical simulation of the dipole noise is evaluated by comparing with the eperimental result. However, the span length of the eperimental model is 600mm, while that of the numerical model is 100mm; therefore, the sound pressure level obtained by numerical simulation has to be converted according to the eperimental condition. For the adequate conversion, evaluation of the correlation length of the flow field in the span-wise direction is very important. To obtain the correlation length, an additional wind tunnel test were conducted and the flow velocity distribution in the span-wise direction at the point of (y 1, y 2 )= (117, 27.5 ), that is in the wake region of the panhead model, was measured. In this way, dipole noise generated by the panhead with the span length of 600mm is numerically evaluated. Furthermore, the noise observation point in the numerical simulation is different from that in the eperiment; the eperimental result is converted into the noise level observed at the point e according to the law of inverse-square. Figure 6 shows the comparison between the numerical and eperimental results of sound pressure level of the dipole noise radiated from the two-dimensional panhead model. The dipole noise has a keen peak at the frequency of 146Hz. This narrow-band noise is called the Aeolian tone, generated by the Karman vorte street shedding from the panhead periodically. Although the frequency of the Aeolian tone obtained by the numerical simulation agrees well with that measured eperimentally, there is some difference between numerical and eperimental sound pressure levels. This is because etent and spatially resolution of the computational grids in the span-wise direction is not enough to calculate intensity of the Karman vortees with satisfactory accuracy. However, it is difficult to increase calculation accuracy due to limitation of computational resource of RTRI in practice. Although accuracy of the numerical analysis of the flow field is not enough, good agreement on the peak frequency of the Aeolian tone indicates that macro-scale behaviour of the Karman vortees in the wake region is well calculated. Hence, it is reasonable to make quantitative estimation of the noise source structure from the numerical calculation by the method stated in Chapter 2. Fig. 5 Eperimental apparatus of wind tunnel test Fig. 6 Comparison of sound pressure level

7 3.3 Dipole noise source contributions to the Aeolian tone At first, power spectrum density of the function D ( o, y, t) defined as Equation (6), S D,D, is calculated. Observation point of the dipole noise is set at 0 = (2000, 2000, 0). The spatial distribution of the power spectrum at any frequency epresses the distribution of intensity of the dipole noise sources at the frequency concerning location of the observation point. Notice that computational results of only even computational steps are used to evaluate D ( o, y, t), because amount of the calculated flow data is huge. Figure 7 shows the distribution of S D,D at the frequency of 146Hz that corresponds with the peak frequency of the Aeolian tone. This figure epresses intensive noise sources are located on the separated share layer near the separation point, i.e. the region near the upstream edge of the contact strip, or the region near the upstream corner of the bottom surface of the panhead. On the contrast, Fig. 8 shows distribution of the noise source contributions defined as Equation (9) toward the dipole noise observed at the point 0. This figure shows the contributions at the frequency of 146Hz just as shown in Fig. 7. In the region where the intensive noise sources concentrates, i.e. the region near the upstream edge of the contact strip, or the region near the upstream corner of the bottom surface of the panhead, the dipole noise source contributions of the positive sign and that of the negative sign are distributed side-by-side. This means that these contribution components are cancel out each other, therefore, net of the total contributions should be lower than what they seem in Fig. 7. On the contrast, it can be found that noise source contributions are high in the region where the Karman vortees roll up. Figure 7, indicating the evaluation based on the power spectrum of the dipole noise source strength, never lead these conclusions. Fig. 7 Distribution of S D,D ( 0, y, ω) Fig. 8 Contributions of dipole noise source ( o = (2000,2000,0), 146Hz ) ( o = (2000,2000,0), 146Hz ) For more quantitative discussion, the flow field around the panhead is divided in four regions as shown in Fig. 9(a), and dipole noise source contributions at the frequency of 146Hz is integrated within each region. Figure 9(b) shows calculated results. The region 4, which corresponds to the wake region of the panhead, has larger contributions than the region 2 and the region 3, where intensive noise sources are locally-distributed as shown in Fig. 7. In particular, the region 2 has few contributions toward the dipole noise observed in the far-field, even though it includes intensive dipole noise sources. Along the shear layer near the separation points, ωu has large a value and its time derivative also has a large value, because the shear layer contains vorte sheet streaming downstream. Therefore, dipole noise source strength defined in Equation (2) takes a large value along the shear layer. However, time derivatives of ωu at both sides of the shear layer have the opposite signs because the share layer has stable spatial structure but it fluctuates periodically. Consequently, the noise source contributions on the shear layer near the separation point cancel out each other; net contributions of the noise sources toward the dipole noise do not have a large value. On the contrast, flow field is essentially unstable in the wake region of the panhead; a Karman vorte generates, convects downstream, and breaks down in the wake region. Therefore, even if the noise source strengths do not grow up significantly in the wake region, total contribution of these dipole noise sources toward the dipole noise radiating to the far-field takes a large value, because intensive mutual cancelation of noise sources does not occur. In this way, adequate evaluation of the noise source structure can be

8 performed by focusing distribution of dipole noise source contributions rather than distribution of dipole noise source strength (a) Definition of regions to estimate dipole noise source contributions D (, y, ω ) p o Summation of noise noise source contribution Region No. (b) Summations of dipole noise source contributions Fig. 9 Estimation of dipole noise source contributions on some regions ( o = (2000,2000,0), 146Hz ) 3.4 The spatial structure of dipole noise source of the panhead In this section, the spatial structure of the dipole noise generated by the panhead is evaluated by calculating widespread distribution of the dipole noise source contributions around the panhead. The noise observation point 0 in the far-field is set at the same position as in the previous sections. Figure 10(a) shows spatial distribution of the dipole noise contributions at the frequency of 146Hz, which corresponds with the primary frequency of the Aeoliane tone. In the wake of the panhead, the region with positive contributions and the region with negative contributions periodically alternate in the y 1 direction. The pitch of the periodic distribution is equal to the pitch of the Karman vorte pairs. This figure clearly indicates that the dipole noise source structure of the Aeolian tone is closely related with the spatial structure of the Karman vorte street. Figure 10(b) shows the spatial distribution of the dipole noise source contributions at the frequency of 303Hz, which corresponds with the second harmonics of the Aeolian tone. Same as in case of the frequency of 146Hz, the region with positive contributions and the region with negative contributions periodically alternate in the y 1 direction, however, the pitch of the periodic distribution is not equal to the pitch of the Karman vorte pairs but equal to the pitch of each Karman vorte. This is because the dipole noise at the frequency of 303Hz coincides with the shedding of each Karman vorte. The periodic stripe pattern of the noise source contributions shown in Fig. 10(b) leans to y 1 ais. This is because the observation point 0 is located at the diagonal downstream direction of the panhead. Figure 10(c) epresses the spatial distribution of the dipole noise source contribution at the frequency of 517Hz, at which the dominant peak of the aeroacoustic noise can not be observed. This figure indicates that noise sources near the panhead intensively cancel out each other, therefore, any ordered structures of the noise source can not be detected. Figure 11 is a close-up of the dipole noise source contributions near the panhead. It is proven that the dipole noise sources with significant contributions are localized near the trailing edge of the panhead. As mentioned above, evaluation of the spatial distribution of dipole noise source contributions is very helpful to identify the spatial noise source structure; it can be a powerful tool to investigate the mechanism of dipole noise generation.

9 Fig. 10 Distribution of dipole noise source contributions around the panhead ( o = (2000,2000,0) ) Fig.11 Close-up of distribution of dipole noise source contributions near the panhead ( 517Hz ) ( o = (2000,2000,0) )

10 4. Concluding remarks In order to identify noise source structure of dipole noise, the new method evaluating net contribution of the dipole noise source toward the aeroacoustic noise observed in the far-field is proposed. This method calculates the cross-correlation between the local dipole noise source strength in the flow field and the dipole noise observed in the far-field. In this study, the spatial structure of the dipole noise source around the panhead of the high-speed pantograph is identified, and mechanism of dipole noise generation by the panhead is discussed. This method is a powerful tool for design and modification of the panhead shape that generates less aeroacoustic noise. Acknowledgments This study was supported by Mr. TAKAIWA, a former graduate student of Tokyo University of Agriculture and Technology (currently belong to HONDA). The authors would like to epress their appreciation for his cooperation. References [1] N. Curle. The influence of solid boundaries upon aerodynamic sound, Proc. Roy. Soc., A 231, pp , (1955) [2] J.C. Hardin, and S.L. Lamkin. Aeroacoustic Computation of Cylinder Wake Flow, AIAA Journal, Vol.22, No.1, pp.51-57, (1984) [3] M.S. Howe. Acoustics of Fluid-Structure Interactions, Cambridge Univ. Press, UK, pp , (1998) [4] M.J. Lighthill. On sound generated aerodynamically. 1 General theory, Proc. Roy. Soc., A 211, pp , (1952) [5] T.E. Siddon. Surface dipole strength by cross-correlation method, J. Acoust. Soc. Amer., 53-2, pp , (1973) [6] T. Takaishi, M. Ikeda, and C. Kato. "Method of evaluating dipole sound sources in a finite computational domain", J. Acoust. Soc. Amer., 116-3, pp , (2004)