Near Field and Far Field Prediction of Noise in and around a Loudspeaker: A Numerical and Experimental Investigation M. Younsi, V. Morgenthaler ANSYS France SAS, France G. Kergourlay Canon CRF, France Summary This paper aims at studying the acoustic behavior and the noise propagation in and around a loudspeaker Bass-Reflex type when its membrane is excited at low frequency with a harmonic signal. Both numerical simulations and experimental tests have been performed. The near field noise has been predicted on the basis of a direct approach: LES (Large Eddy Simulation) calculation in which acoustic sources and coupling with turbulence are fully represented. For the far field noise, the acoustic analogy method from Ffowcs-Williams and Hawkings (FW-H) has been used. In parallel with this calculation, acoustic measurements at different distances and directions from the loudspeaker have been run in an anechoic environment. The numerical results are compared with the experimental data and a good match is obtained both in behavior and intensity. 1. Introduction 1 In order to enhance low frequency performances of loudspeakers, bass reflex ports are commonly used. The objective of this technique is to extend the low frequency response of loudspeaker systems by creating a Helmholtz resonator. The movement of the air caused by the loudspeaker driver is characterized by a pumping phenomenon through the port. The flow behavior within the port has a significant influence on the system efficiency. At high pressure level, the air velocity within the port increases and creates turbulence structures and vortex shedding which are responsible for the aerodynamic noise generation. For these reasons, the port design optimization is considered as an important step by high quality loudspeakers manufacturers. In an industrial environment, the recent development of Computational Fluid Dynamics (CFD) for 3D viscous flow fields provides an efficient tool for flows analysis and design. There is a continuously increasing demand in all areas of CFD for unsteady flow simulations. Several researchers have made significant contributions to study loudspeakers using different methods. However, little work is available in the literature 1 (c) European Acoustics Association ISSN 2226-5147 ISBN 978-80-01-05013-2 concerning the application of CFD techniques in this field. Z. Rapoport and A. Devantier [1] used a 2D axisymmetric model in order to study the unsteady fluid flow in loudspeaker ports. In their work, a commercial code (ANSYS Fluent) was used where the turbulent flow was modeled using LES technique. They studied the effect of the port entrance angle on the flow behavior. By varying this parameter, six geometries were created and their acoustic efficiency were studied and analyzed. The numerical results showed the influence of the entrance angle of the port on the flow. In addition to this, the evidence of vortex shedding was clearly observed. Finally, experimental work based on listening tests was performed in order to confirm the numerical study. N.B Roozen et. al. [2] studied a method to reduce bass-reflex port nonlinearties by optimizing the port geometry. In their study, 2D axisymmetric calculations and measurements are presented for a number of ports geometries. The effect of rounding the port lips and the effect of nozzle in the port on the production of blowing sounds was investigated. Their results showed that the intensity of the unsteady flow separation, as well as the radiation efficiency of the port and the quality factor of the port resonances, altogether determine the level of blowing noise. They concluded that the port contour geometry has an important impact on the blowing sounds intensity. 504
Thus, the acoustic losses can be reduced by using a port contour geometry that slowly diverges. In an additional work, N.B Roozen et. al. [3] [4] were interested in observing the response to harmonic excitation using experimental investigations. In the first part of their study, they summarized the dominant physical phenomena and presented the port geometry alterations for minimizing the blowing sound. In the second part, a method to estimate the time-averaged point of separation was performed. Analytic method based on the unsteady Bernoulli equation was used. A direct method for determining the velocity of the air particles in the port was also performed using Laser Doppler Anemometry. 2. 3D Flow Simulation In the present work, a box loudspeaker equipped with a bass-reflex port has been studied. The Computer Aided Design (CAD) and the mesh generation are first performed (section 2.1), along with choice of simulations parameters and boundary conditions. Then the CFD analysis leading to the flow behavior and the acoustic prediction is performed using Ansys Fluent 12 [5] software (sections 2.2, 2.3, 2.4). The flow morphology analysis is detailed (section 2.5). Finally, the pressure signals in and around the loudspeaker are analyzed (section 2.6). 2.1. Geometry, Mesh and Boundary Conditions Using the initial CAD of the loudspeaker, 3D fluid volume geometry and mesh have been generated with ANSYS Design Modeler and ANSYS Meshing respectively. Figure 1 shows the loudspeaker geometry and the corresponding fluid volume. Due to the geometry complexity, this calculation domain has been divided in several blocks in order to generate a good quality hexahedral mesh. The grid refinement has been studied and adapted to the flow morphology. Thus, a particular attention has been paid to the boundary layer resolution and the mean cell size in the calculation domain has been estimated in order to capture a maximal frequency of 6 khz. For numerical stability reasons, and to minimize edges effects, the computational domain has been extended downstream. Based on these considerations, 2.6 millions cells have been created in the calculation domain. Figure 1 shows the resulting mesh which is considered to be fine enough to capture the desired flow instabilities and therefore capture the acoustic behavior. The driver geometry has been isolated from the complete domain in order to apply a Moving and Deforming Mesh (MDM) model in ANSYS Fluent solver. Thus, a spring analogy method based on the smoothing algorithm has been applied on this region which allows simulating the sinusoidal movement of the driver. Pressure outlet boundary condition has been applied at the external surfaces of the downstream domain and wall boundary conditions elsewhere. In addition to this, enclosure surfaces have been placed at the port outlet in order to use them as integration surfaces for quadrupole sources calculation in the FW-H model. 2.2. Numerical Modeling Ideal gas state equation has been used in order to describe the thermodynamic behavior of the air in the loudspeaker enclosure. Thus the compressible unsteady flow is generated by the sinusoidal movement of the driver whose velocity is given by the following harmonic equation: X (t) = 0.58 cos (2 π.50.t) (1) The frequency of the driver oscillation is set to 50 Hz and the equation (1) has been implemented in the MDM model using a User Defined Function (UDF) in ANSYS Fluent. As mentioned previously, a smoothing algorithm has been applied in this study particularly because of the driver amplitude displacement which is very small (3.692 mm). Consequently, deleting and creating cells in the domain is not necessary and morphing them is enough. Moreover, this method is less computer time consuming. According to numerical considerations for this simulation, such as Courant number taken in between 1 and 10, a time step of 8 µs has been used. This value is small enough to capture the pressure signal due to the driver excitation and ensure solver stability. Figure 2 illustrates near field and far field sensors locations where the acoustic pressures have been computed. 505
2.3.1 The Large Eddy Simulation Model It is possible, in theory, to directly resolve the whole spectrum of turbulent scales using an approach known as Direct Numerical Simulation (DNS). No modeling is required in DNS and might have been successfully used if the solver numerical schemes were accurate enough to generate very limited numerical noises which will not affect the smaller eddies formation. Moreover, the resolution of the whole spectrum eddies requires a finer mesh which would increase the calculation cost dramatically. Figure 1. Geometry and Mesh. P1 14cm 7cm Figure 2. Pressure sensors location 2.3. Turbulence Modeling The flow generated by the loudspeaker is laminar in most of the domain except in the loudspeaker s port were the flow restriction increase the fluid velocity and transition the fluid from a laminar state to a turbulent one. In order to capture correctly all the physics and especially the broadband noise generated by the turbulent part of the flow, a turbulence modeling approach which can work both in laminar and turbulent situation has to be chosen. The largest eddies will be generated here by the jet instability triggered by the port. Large eddies will also be generated inside the boundary layer attached to the port wall. These eddies are responsible for the tonal noise and should be described very precisely as they are bringing energy to turbulence. Turbulence is breaking this large eddies into smaller ones until viscosity dissipate them at the smallest scales. Those intermediaries eddies form the broadband noise. We choose to use the Large Eddy Simulation (LES) approach as often used for aero-acoustic calculations [6]. In this approach, large eddies are resolved directly, while small eddies effects on momentum and mass transport are modeled. As the smaller eddies are modeled, the need of an extremely precise numerical scheme is lessen. Moreover, in this study, only the lower frequencies of the spectrum are considered, which relieves the need for carefully modeling the smaller scales. Several subgrid-scale turbulence models can be used in ANSYS Fluent. We choose the model proposed by Smagorinsky [7]. In the Smagorinsky model is a mixing length model where the mixing length is taken as the filter width. This model suffers from two main drawbacks: the lack of universality of the Smagorinsky constant and the impossibility of treating relaminarization and thus boundary layer. To try and avoid the problem of the classical Smagorinsky model Germano et al. [8] and subsequently Lilly [9] conceived a procedure in which the Smagorinsky model constant, is dynamically computed based on the information provided by the resolved scales of motion. The dynamic procedure thus obviates the need for users to specify the Smagorinsky constant in advance. The obtained constant varies in time and space over a fairly wide range. To avoid numerical instability, in ANSYS Fluent, the result is clipped at zero and 0.23 by default. This approach enables also the Smagorinsky model to reproduce relaminarization with a Smagorinsky constant which naturally soften with a decreasing Reynolds number. 506
2.4. Far Field Noise Prediction Acoustic analogy based on the FW-H model has been used in this simulation in order to predict the acoustic pressures in far field region (P10 and P11 in Figure 2). The FW-H model [10, 11] is essentially an inhomogeneous wave equation that can be derived by manipulating the continuity equation and the Navier-Stokes equation. Based on its mathematical structure, this equation takes into account the source terms which are monopole (thickness), dipole (loading) and quadrupole sources. The monopole source term models the noise generated by the displacement of fluid as the body passes. The dipole or loading source term models the noise that results from the unsteady motion of the force distribution on the body surface. Both of these sources are surface sources. The quadrupole represent volume sources in the region outside the source surface. The contribution of the volume integrals becomes small when the flow is low subsonic. Once the statistical stability is reached on the variables provided by the LES calculation, the fluctuating pressure and velocity upon the integration surfaces can be extracted for 21500 time steps. Then, the sound pressure signals are computed at the receiver locations using the source data collected during the unsteady aerodynamic computations. 2.5. CFD Results and Discussion Figure 3 shows the instantaneous velocity field at the middle plan. By analyzing this result, a complex flow can be observed at the port inlet and outlet. It is shown clearly that the driver sinusoidal movement combined with the contraction of the flow sections induces a vortex shedding phenomenon. Thus, turbulent structures are generated at each mid-period at upstream and downstream alternately. In the pressure field, a non homogenous pressure distribution is observed, particularly around the port outlet. Using an animation, a pumping phenomenon occurring at 50 Hz can be observed between the driver zone and the enclosure zone. 2.6. Pressure Signals Analysis The fluctuating pressures post-processing has been done after the stability of the unsteady variables. The time histories of the pressure fluctuations at point P10 is shown in Figure 4. All the obtained signals are regular and a period of 0.02 s can be observed clearly. Compared to the far field region, the signal amplitude is higher at sensor P1, which is closer to the driver. Figure 3. Instantaneous velocity (a), pressure fields (b) Pressure [Pa] (ms -1 ) Pa (b) (a) Figure 4. Computed fluctuating pressure signal at P10 3. Experimental Work Time [s] Figure 5 shows the test bench which has been realized accordingly to the simulated system: a 25 cm- driver is placed in the front plate of a ventedbox of 48 liters equipped with an 11cm-length vent of diameter 18mm located at its back plate. Free-field acoustic measurements have been performed in an anechoic room. The driver is excited by a constant voltage signal of intensity U=8.55V at a frequency of 50 Hz. This voltage enables getting a driver membrane velocity of 580 mm/s, which has been carefully measured by laser vibrometry. 507
Figure 5. Test facility in anechoic room 4. Test Analysis Correlation Figures 6 and 7 give the test-analysis correlation performed on the simulated and measured data for points 7 and 10 respectively. The upper part of the Figures corresponds to the superposition of the pressure fluctuations in the temporal domain. The lower part corresponds to the spectral analysis of the signals: a fast Fourier transform has been done on 8.65 periods of the windowed time signals for both numerical and experimental data. The four experimental data superimposed rather well, which shows the reproducibility and repeatability of the test. Figure 7. Test-analysis correlation at Point 10 Up: Fluctuations of pressure (Pa) as function of time Bottom: spectral analysis 20Hz-20 khz 5. Discussion and Conclusion Good qualitative and quantitative results have been found with the chosen CFD approach compared to measurements. The comparison between the computed and measured temporal signals both in near and far fields region shows a good agreement in frequency. Moreover, in the far field the amplitude is also the same. At this location, the signal is obtained using the FW-H acoustic analogy. This result illustrates the quality of the noise sources prediction provided by the LES calculation. However, a 30% discrepancy in the near field signals amplitude can be observed. This difference may be explained by an experimental bias due to the microphone intrusion which interacts frontally with the air flow. In the spectral analysis, the measured and computed results show similar overall behavior for low frequencies until 200 Hz. At higher frequencies, the spectra are different. This discrepancy could be justified by: - The numerical dissipation which becomes predominant at very low pressure levels. - The mesh coarsening far from the source which has an impact on the frequencies interval modeled. Figure 6. Test-analysis correlation at Point 7 Up: Fluctuations of pressure (Pa) as function of time Bottom: spectral analysis 20Hz-20 khz - The acoustic reflections at far field location which are not taken into account in the FW- H model. 508
- The quality and the size of the microphone dynamics: The 1/f noise level should be decreased. The analyses performed at the different control points in near-field and in far-field give first conclusions. The following ways to improve the correlation were suggested: - Finer grid mesh should be used in order to reduce the numerical dissipation. - A stronger excitation should be used in order to increase the signal to noise ratio. The limitation is to change the turbulence regime (Mach and Reynolds number). The velocity of the membrane was chosen in order to be close to the turbulence regime observed with the analyzed high-quality speaker in usual listening conditions. - The sensor appears to be intrusive in nearfield: use of a ¼ or even 1/8 one instead of a ½ microphone. Hot-wire probes that are less intrusive could also be used to correlate non-stationary velocity simulations and experimental data. In this case, transient non-stationary velocities [m/s] have to be saved in addition to static pressure [Pa] for near-field points (all points except points 10 and 12). Harmonic Excitation and remedial Measures, J. Acoust. Soc. Am. 1998 [4] N. B. Roozen, M. Bockholts, P. V. Eck, A. Hirschberg, Vortex Sound in Bass-reflex Ports of Loudspeakers. Part II. A Method to Estimate the Point of Separation, J. Acoust. Soc. Am. 1998 [5] Ansys Inc. Copyright 2008. [6] C. Wagner, T. Hüttl, P. Sagaut, Large-Eddy Simulation for Acoustics, Cambridge University Press, 2007. [7] Smagorinsky, J., 1963. General circulation experiments with the primitive equations. The Basic Experimental Monthly Weather Revision, Vol. 91, pp 99-164. [8] Germano, M., Piomelli, U., Moin, P. and Cabot, W. H., 1991. A Dynamic Subgrid-Scale Eddy Viscosity Model, Physics of Fluids A, Vol. 3, No. 7, pp. 1760-1765. [9] Lilly, D. K., 1991. A Proposed Modification of the Germano Subgrid-Scale Closure Method, Physics of Fluids A, Vol. 4, No. 3, pp. 633-635. [10] J. E. Ffowcs Williams and D.L. Hawkings, Sound generation by turbulence and surfaces in arbitrary motion, Philosophical Transactions of the Royal Society of London. Series A, vol. 264, no. 1151, pp. 321 342, 1969 [11] K. S. Brentner and F. Farassat, Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces, AIAA Journal, vol. 36, no. 8, pp. 1379 1386, 1998 6. Acknowledgement The authors wish to thank Mr. Pierre-Yves Diquelou from Cabasse company located in Brest (France) for his help doing acoustic measurements. 7. References [1] Z. Rapoport, A. Devantier, Method for Predicting Loudspeaker Port Performance and Optimizing Loudspeaker Port Designs Utilizing Bi-directional Fluid Flow Principles, PCT, 2006 [2]N.B. Roozen, J.E.M. Vael, J.A.M, Reduction of Bass-Reflex Port Nonlinearities by Optimizing the Port Geometry, Audio Engineering Society, 1998 [3]N. B. Roozen, M. Bockholts, P. V. Eck, A. Hirschberg, Vortex Sound in Bass-reflex Ports of Loudspeakers. Part I. Observation of Response to 509