Journal of Fluid Science and Technology

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1 Science and Technology Direct Numerical Prediction of Aerodynamic Noise Emitted from a Generic Automobile Rear-View Mirror* Katsunori DOI**, Masaya MIYOSHI***, Naoki HAMAMOTO**** and Yoshiaki NAKAMURA***** **Department of Aerospace Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan doi@nuae.nagoya-u.ac.jp ***Mitsubishi Heavy Industries, Ltd., 10, Oye-cho, Minato-ku, Nagoya, Japan ****Mitsubishi Motors Corporation, 1, Nakashinkiri, hashime-cho, Okazaki, Aichi Pref., Japan *****Department of Aerospace Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan Abstract We numerically simulated the aerodynamic noise generated from the unsteady flow around a generic model of automobile rear-view mirrors in this study. This generic model is made by cutting a hemispherical cylinder into half lengthwise, and placed on a flat plate. The governing equations employed in the present numerical simulation are the compressible Navier-Stokes equations, where no additional models of sound generation and propagation are used. Results show that acoustic pressure waves are generated from the disturbed wake of the mirror model and propagate into the far field. In addition, the spatial distribution of the sound pressure level (SPL) in the far field has a similar tendency to that of the experimental data. These results show that useful data on aerodynamic noise can be obtained by the simple computational method presented in this study, and utilized to make a preliminary design to reduce the aerodynamic noise. Key words: Aerodynamic Noise, Automobile Mirror, Numerical Prediction 1. Introduction *Received 14 Sep., 2011 (No ) [DOI: /jfst.7.290] Copyright 2012 by JSME Automobile noise is composed of engine noise, road noise, and aerodynamic noise. In recent years, the aerodynamic noise becomes more pronounced with improvements of some vibration reduction technologies and popularization of hybrid or all electric vehicles. The aerodynamic noise is generated from various parts such as rear-view mirrors, A-pillars, windshield wipers, radiator grilles, and wheel housings. In general, the broadband noise generated from rear-view mirrors is dominant among the noises mentioned above because the rear-view mirrors are protruding into the air flow passing the vehicle and disturb it extremely. Many researchers have investigated the characteristics and generation mechanism of rear-view mirror noise by experimental measurements and numerical simulations. Hold et al. (1) computed the unsteady flow around a generic body on a plate such as rear-view 290

2 mirrors, and showed a complex structure of the flow, where the body's wake is interacted with the plate. In addition, they measured the unsteady pressure distribution on the body and plate surfaces to validate their computational results. Siegert et al. (2) followed their study, and computed the aerodynamic noise generation and propagation from a generic body by the decoupling approach of acoustic and flow fields, in which the computed fluctuating pressure distribution was applied to the Ffowcs Williams and Hawkings analogy (3). Moreover, they also measured the sound pressure level at several locations in the far field to validate their computational results. Lokhande et al. (4) and Ask et al. (5) computed the aerodynamic noise from the generic body by a similar decoupling approach. Kato et al. (6) computed the aerodynamic noise from rear-view mirrors with real shapes by the different decoupling approach, in which the acoustic equations were derived by the difference between the compressible and the incompressible flow equations. Kato et al. (7) measured the fluctuating surface pressure on a generic body and the far-field sound pressure in detail, and clarified the characteristics of a large-scale flow structure. Chen et al. (8) also measured the surface pressure on real mirrors and the far-field sound pressure. Iida et al. (9) noticed a tonal noise generated from mirrors of real shapes with a bump, and the feedback mechanism of noise generation was made clear by experimental measurements. Nouzawa et al. (10) noticed the upwind flow influenced by front pillars, and the flow field near the front pillar and a rear-view mirror is investigated by numerical flow simulations. In general, there are two approaches to predict generation and propagation of the aerodynamic noise by numerical simulations. The first approach is the decoupling method as mentioned above. In this approach, the unsteady flow field is first computed by a flow solver, and then the acoustic field or sound sources is estimated from the computational result of flow field with some acoustic model based on Lighthill s analogy (11). Curle's equation (12) can be applied for aerodynamic noise emitted from a low-mach number flow around a stationary solid body, which is computed from the fluctuating pressure distribution on the body. Ffowcs Williams-Hawkings' equation (5) can be applied for a moving solid body. Powell s model (13) based on theory of vortex sound can be applied to investigate a distribution of aeroacoustic sources in flow field, which is estimated from vorticity and velocity distribution in the flow. Lighthill's stress tensor (11) can be also used to investigate it, which is a more general model. However, these acoustic models cannot take into account feedback effects of acoustics on flow in this approach. In addition, they usually include some assumptions, and it may be difficult to understand the mechanism of aerodynamic noise generations. The second approach is the direct simulation. In this approach, both flow and acoustic fields governed by the compressible Navier-Stokes equations are solved directly. This approach usually includes less assumption for the acoustic generation and propagation than the first one, and it may be easier to understand the mechanism of aerodynamic noise generation. However, this approach requires huge computational regions and fine computational grids in the far field, which are small enough to capture propagating waves without artificial damping. In other words, it needs a high computational cost. In addition, computational schemes with high order of accuracy are often used. In the present study, we compute aerodynamic noise generation and propagation around a generic body placed on a flat plate like automobile rear-view mirrors by direct simulation without using a high order of accuracy. Especially in the direct simulation for aerodynamic sound sources and propagating acoustic waves, it is better to use some special computational scheme with high order of accuracy or extremely fine computational grid to obtain quantitatively more accurate results. However, it is expected that a mechanism of the aerodynamic sound generation and propagation can be qualitatively simulated even without them. And, it may be more favorable in terms of the industrial usability and availability. In addition, it is expected that the disadvantage of the direct simulation, the need for scheme 291

3 Fig. 1 The shape of generic automobile rear-view mirror on flat plate. (a) x-y plane (b) x-z plane Fig. 2 Computational domain and coordinate system. with high order of accuracy or fine grid, will become insignificant by rapid improvements of computer performance in the near future. Our computational results of the fluctuating pressure distribution on the body surface and the sound pressure distribution in the far field are compared with experimental data measured by Hold et al. (1) and Siegert et al. (2) to validate the computational method and its results. 2. Computational Method The governing equations are the compressible Navier-Stokes equations. The fluid is assumed to be calorically perfect gas. The molecular viscosity is estimated by Sutherland's equation. Turbulent model is not applied. The value of variables at the cell interface is calculated by the MUSCL scheme with van Albada's limiter (14), the spatial accuracy of which is up to 3rd-order. The value of convective fluxes is calculated from Roe s approximate Riemann solver, while the value of viscous fluxes by the 2nd-order central differential scheme. The LU-SGS method, which has been extended for unstructured grids (15), is employed for time integration. The temporal accuracy of the method is 2nd-order with a backward difference scheme. 292

4 3. Computational Conditions The shape of the generic body placed on the flat plate is shown in Fig. 1. This is a simplified model of automobile rear-view mirrors, which is a longitudinal half of a circular cylinder capped by a hemisphere with the same diameter. The width of the body, which is equal to the diameter of the cylinder, is D = 200mm, while the height of the body is H=1.5D. The fluid is air, and the velocity of the uniform flow over the flat plate is U inf = 56m/s, which corresponds to a cruising speed of about 200km/h. The Reynolds number based on the body width is Re D = These conditions are the same as those in the experiments by Hold et al. (1) and Siegert et al. (2) The computational domain and the coordinate system employed in this study are shown in Fig. 2. The outer boundary is far away from the mirror the distance of which is about 10D. This distance corresponds to the acoustic wavelength of 170Hz. The non-reflecting boundary condition based on the characteristic variables, entropy and Riemann invariants (16), is applied at the outer boundary. On the surfaces of the body and the flat plate, the adiabatic wall condition is imposed. The computational grid is generated with the multi-block method, which is treated as an unstructured grid. The grid near the mirror is shown in Fig. 1. The total number of computational cells is about 22 million. 4. Results and Discussion An instantaneous distribution of streamlines behind the mirror is shown in Fig. 3. The side view is Fig. 3(a) and the top view is Fig. 3(b). The color arrangement of the lines is based on where the streamlines come from near the edge of the mirror, as shown in the left auxiliary figure. The flow is separated from the top and side edge of the mirror, and makes unstable shear layers behind the mirror. The complicated three-dimensional interaction of the separated flow produces the unsteady disturbed wake of the mirror. A part of the separated flow from the top edge reattaches on the plate. The time-averaged reattachment point is located at about 1.8H downstream of the mirror. An instantaneous distribution of pressure isosurfaces and the pressure on the plate are shown in Fig. 4. The side view is Fig. 4(a) and the top view is Fig. 4(b). Each color of the isosurfaces indicates a constant value, where the white surface corresponds to a pressure coefficient of -0.5 (Cp = -0.5) and the pink surface to Cp = In addition, the color bars in these figures indicate values of the pressure coefficient on the plate. There are low pressure regions in the shape of a pillar just behind the mirror and along its side edge, which is a vertical column of vortex. Moreover, there are low pressure regions along the plate at some distance from the mirror, which extend diagonally downstream. They form a longitudinal vortex. These regions appear either rightward or leftward alternately and periodically, which produces pressure fluctuations on the plate. Distributions of pressure isosurfaces and the pressure on the plate at several moments in this periodic phenomenon are shown in Fig. 5. The period T is about 10 msec. Isosurfaces of pressure fluctuation level behind the mirror are shown in Fig. 6. The side view is Fig. 6(a) and the top view Fig. 6(b). The pressure fluctuation level is computed based on the ratio of the difference between the unsteady pressure and the time-averaged pressure to the same reference value as in the sound pressure level. The pressure fluctuation level is the highest in regions at some distance from the mirror and behind its side edge. In these regions, change in the vortex structure from vortex lines to a longitudinal vortex occurs by the interaction with the flow separated from the top edge of the mirror. This change causes aerodynamic noise generation. However, the pressure fluctuation and generated acoustic noise are not discrete in frequency space. The large vortex structures are broken into the multi-scaled vortices at the deformation and interaction between themselves, and then the deformation, generation, dissipation, and acceleration of the 293

5 (a) Side view. (b) Top view. Fig. 3 Instantaneous streamlines behind mirror. (a) Side View. (b) Top view. Fig. 4 Instantaneous isosurfaces of pressure along with pressure distribution on plate. 294

6 (a) t = 0/4T. (b) t = 1/4T. (c) t = 2/4T. (d) t = 3/4T. (e) t = 4/4T. Fig. 5 Distributions of pressure isosurfaces along with pressure distribution on plate at several moments in a period, where T is about 10 msec. 295

7 (a) Side view. (b) Top view. Fig. 6 Isosurfaces of pressure fluctuation level behind mirror. Fig.7 Time-averaged pressure distribution on mirror. 296

8 (a) At the side edge of the rear surface. (a) On back surface of mirror. (b) On plate in wake region. Fig. 8 Spectra of Pressure Fluctuation. Fig. 9 Instantaneous pressure fluctuations on plate and symmetry plane at y=0. 297

9 multi-scale vortices generate aerodynamic broadband noise. There is no characteristic self-amplified mechanism with a feedback loop which generates discrete frequency aerodynamic noise in this phenomenon. A time-averaged pressure distribution on the surface of the mirror is shown in Fig. 7, along with the experimental data by Hold et al. (1) to validate the present computational results. The position of measurement points is roughly shown in the supplementary figure (refer to Hold et al. (1) for details). The computational results are very close to the experimental data except at the front surface near the edge. This is because the separation line in the experiment is located more downstream side than that from the computational result due to the effect of turbulence. Frequency spectra of pressure fluctuation level on the surfaces are shown in Fig. 8, along with the experimental data by Hold et al. (1). As shown in each inset, the pressure on the back surface near the side edge of the mirror is shown in Fig. 8(a) and the pressure on the plate near the edge of the wake in Fig. 8(b). The pressure fluctuation level at the both points in the computational results is lower than the experimental data. The differences are less than about 10dB except for the high frequency components, as shown in Fig. 8(b). This difference in high frequencies is attributed to lack of grid resolution, where high frequency flow fluctuations cannot be captured by the present method. Furthermore, the magnitude of the pressure fluctuation at this point on the plate is sensitive to the location of the separation point on the mirror which affects the boundary of the wake region. An instantaneous distribution of pressure fluctuations around the mirror is shown in Fig. 9. The pressure fluctuation is defined as the difference between the instantaneous pressure and the time-averaged pressure. The acoustic pressure waves with various wave lengths propagate to the far field. It can be confirmed from the shape of the acoustic waves that the source of the acoustic waves exists in the region where the pressure fluctuation level becomes the highest in the wake region, as shown in Fig. 6. Frequency spectra of the acoustic pressure level in the far field are shown in Fig. 10, along with the experimental data by Siegert et al. (2). The measurement points are located on a hemispheric surface. The radius of the surface is 0.5m and its center is located at the mirror. The location of the measurement points is shown roughly in each inset. The sound pressure levels at all the measurement points in the computational results are higher than the experimental data by about 10dB. In this paper, the pressure fluctuations are evaluated at the measurement points which are 0.5m away from the mirror, and they are treated as the sound pressure fluctuations. This is similar to that in the experiment by Siegert et al. (2) However, it is possible that the pressure fluctuations at these points include not only acoustic fluctuations but also significant flow fluctuations. A theoretical estimation of flow fluctuations compared with acoustic fluctuations radiated from an aerodynamic sound source was derived by Fujita et al. (17) and Yokono et al. (18) They showed that the amplitude ratio of the flow fluctuation to the acoustic fluctuation can be estimated as follows. λ r = (1) 2π where λ is the wave length, and is the distance from the source. The amplitude of the flow fluctuation decreases more than the acoustic fluctuation for higher frequency or longer distance. The flow fluctuation may be neglected if the amplitude of flow fluctuation is much smaller than that of acoustic fluctuation. If the threshold value of the difference between them is 10dB, then the pressure fluctuation at = 0.5m includes significant flow fluctuation for more than about 350Hz. Thus the computed pressure fluctuations shown in this paper probably include some flow fluctuation. In order to predict amplitude of only acoustic fluctuations more accurately, it is better to increase the distance from the mirror to the measurement points, or to distinguish 298

10 (a) At sensor No.3 (diagonally in front of mirror.) (b) At sensor No.4 (lateral of mirror.) Fig. 10 Sound pressure level in the far field. acoustic fluctuations from flow fluctuations by some decoupling method such as Kato et al. (6) However, it needs more computational cost, and it is contrary to the intention of this study. In addition, in the comparison between our computational result and the experimental result by Siegert et al. (2) as shown in Fig.10, it cannot be expected that amplitude of acoustic fluctuations computed and distinguished by some decoupling method agrees well with the experimental result, for following two reasons. Firstly, the distance from the mirror to the measurement points in the experiment is the same as in the computation, so that pressure fluctuations measured in the experiment may also include some influence of flow fluctuations. Secondly, the difference between the computational results and the experimental results for low frequency is approximately the same as for high frequency as shown in Fig.10, whereas the difference for low frequency must be larger than for high frequency provided that the difference is only due to flow fluctuations, because the amplitude of flow fluctuations decreases more than acoustic fluctuations for higher frequency at a distance, as shown in Eq. (1). This implies that the difference is not only due to flow fluctuations. Furthermore, even if the computational results of pressure fluctuations include some influence of flow fluctuation, the results may show some qualitative characteristics of the aerodynamic noise and they may be applied to analyses and measures for reduction of aerodynamic noise. This is because there is the correlation between acoustic fluctuations and flow fluctuations as shown by Eq. (1) unless measurement points are very close to aerodynamic sound sources. From the reasons mentioned above, we do not necessarily need to distinguish acoustic fluctuations from flow fluctuations in this study. 299

11 (c) At sensor No.5 (laterally above mirror.) (d) At sensor No.6 (above mirror.) (e) At sensor No.10 (behind mirror.) (f) At sensor No.11 (diagonally behind mirror.) Fig. 10 Sound pressure level in the far field (continued.) 300

12 (a) Side view. (b) Top view. Fig. 11 Overall sound pressure level distribution in the far field. Fig. 12 Overall sound pressure level at each measurement point. A distribution of the overall acoustic pressure levels on the hemispheric surface evaluated from the computational results is shown as the side view in Fig. 11(a) and as the top view Fig. 11(b). In addition, the overall acoustic pressure levels at the measurement points evaluated from the computational result and the experimental data are shown in Fig. 12. The overall sound pressure levels are calculated from the frequency spectra shown in Fig.10. The distribution of sound pressure level in the computational results has a slight anisotropy, as shown in Fig. 11(a) and Fig. 11(b), and the sound pressure level in front of the mirror is lower than that behind the mirror. This tendency can also be confirmed by the experimental data. Thus, the computational results can be qualitatively validated, although each value in the overall sound pressure is different from that of the experimental data by about 10 db, as shown in Fig Conclusion The numerical simulation of the aerodynamic noise generated from unsteady flow around a generic model of automobile rear-view mirrors was conducted in this study. The generic model is a longitudinal half of a hemispherical cylinder placed on a flat plate. The governing equations in this numerical simulation are the compressible Navier-Stokes equations, where any additional models of sound generation and propagation are not used. 301

13 The results obtained from this simulation are summarized as follows: 1. The sound source exists at some distance from the mirror and behind its side edge, where change in the vortex structure from vortex lines to a longitudinal vortex occurs by the interaction with the flow separated from the top edge of the mirror. 2. The spatial distribution of sound pressure level in the far field has a slight anisotropy, and the sound pressure level in front of the mirror is lower than that behind the mirror. 3. This tendency is similar to that of the experimental data. Thus, useful data on aerodynamic noise can be obtained by the present simple method. References (1) Hold, R., Brenneis, A., Eberle, A., Schwarz, V. and Siegert, R., Numerical Simulation of Aeroacoustic Sound Generated by Generic Bodies Placed on a Plate: Part I - Prediction of Aeroacoustic Sources, AIAA Paper, (1999). (2) Siegert, R., Schwarz, V. and Reichenberger, J., Numerical Simulation of Aeroacoustic Sound Generated by Generic Bodies Placed on a Plane: Part II - Prediction of Radiated Sound Pressure, AIAA Paper, (1999). (3) Ffowcs Williams, J. E. and Hawkings, D. L., Sound generated by turbulence and surfaces in arbitrary motion, Philosophical Transactions of the Royal Society of London, Series A, Vol.264 (1969), pp (4) Lokhande, B., Sovani, S. and Xu, J., Computational Aeroacoustic Analysis of a Generic Side View Mirror, SAE Paper, (2003). (5) Ask, J. and Davidson, L., The Sub-critical Flow past a Generic Side Mirror and its Impact on Sound Generation and Propagation, AIAA Paper, (2006). (6) Kato, Y., Men'shov, I., and Nakamura, Y., Aeroacoustics Simulations around Automobile Rear-View Mirrors, Journal of Fluid, Vol.3, No.7 (2008), pp (7) Kato, C., Murata, O., Kokubo, A., Ichinose, K., Kijima, T., Horinouchi, N. and Iida, A., Measurements of Aeroacoustic Noise and Pressure Fluctuation Generated by Door-Mirror Model Placed on a Flat Plate, Journal of Environment and Engineering, Vol.2, No.2 (2007), pp (8) Chen, K. H., Johnson, J., Dietschi, U. and Khalighi, B., Wind Noise Measurements for Automotive Mirrors, SAE Paper, (2009). (9) Iida, A., Kokubo, A., Tsukamoto, Y., Honda, T., Yokoyama, H., Kijima, T. and Kato, C., Generation Conditions of Aero-Acoustic Feedback Noise Radiated from a Rear-view Mirror, Transactions of the Japan Society of Mechanical Engineers, Series B, Vol.73, No.732 (2007), pp (10) Nouzawa, T., Li, Y., Kasaki, N. and Nakamura, T., Mechanism of Aerodynamic Noise Generated from Front-Pillar and Door Mirror of Automobile, Journal of Environment and Engineering, Vol.6, No.3 (2011), pp (11) Lighthill, M. J., On Sound Generated Aero-dynamically. I. General Theory, Proceedings of Royal Society of London, A211 (1952), pp (12) Curle N., The Influence of Solid Boundaries upon Aerodynamics Sound, Proceedings of Royal Society of London, A231 (1955), pp (13) Powell A., Theory of vortex sound, Journal of the Acoustical Society of America, Vol.36, No.1 (1964), pp

14 (14) Luo, H. and Baum, J. D., Edge-Based Finite Element Scheme for the Euler Equations, AIAA Journal, Vol.32 (1994), pp (15) Men'shov, I. S. and Nakamura, Y., Implementation of the LU-SGS Method for an Arbitrary Finite Volume Discretization, Proceedings of 9th Computational Fluid Dynamics Symposium, A10-2 (1995), pp (16) Jameson, A. and Baker, T. J., Solution of the Euler Equations for Complex Configurations, AIAA Paper, (1983). (17) Fujita, H. and Kovasznay, L. S. G., Unsteady Lift and Radiated Sound from a Wake Cutting Airfoil, AIAA Journal, Vol.12, No.9 (1974), pp (18) Yokono, Y. and Fujita, H., Interactive Steering of Supercomputing Simulation for Aerodynamic Noise Radiated from Square Cylinder, Transactions of the Japan Society of Mechanical Engineers, Series B, Vol.61, No.583 (1995), pp