Simulation of Flow Induced Noise in Exhaust Silencers

Transcription

1 Simulation of Flow Induced Noise in Exhaust Silencers Barbara NEUHIERL 1 ; 1 Exa GmbH, Germany ABSTRACT This paper deals with the simulation of flow generated noise in exhaust systems. Exhaust noise typically has two components: Charge cycle fluctuations and additional noise caused by exhaust gas flow through the ducts, passing bends and small openings. The latter cannot be captured by the usually applied 1D simulation tools, but contributes nevertheless significantly to the pass by sound. Therefore the Lattice-Boltzmann Method, a transient and compressible scheme describing the evolution of particle distributions in time, was applied, predicting the flow through the system and the generation and propagation of acoustic phenomena at the same time without the need for acoustic analogies of any kind. A study of two slightly different end silencer outlet pipes was performed in order to demonstrate the method s ability to predict correct trends and obtain good correlation with experiments. Experiments have shown that one of the mufflers is significantly quieter in terms of the broadband flow noise, but also shows a very annoying tonal sound. The other pipe, though louder over most of the frequency range, does not show such narrowband effects. Both tonal and broadband effects could be captured by the simulation, and the mechanism leading to the unwanted sound generation could be investigated. Keywords: Exhaust System, Exhaust Noise, Muffler, Aeroacoustics, Flow Noise, Computational Aeroacoustics 1. INTRODUCTION Exhaust systems in general are designed to reduce the order-based noise caused from the orderbased fluctuations coming from the engine load cycle. To do so, a muffler typically exists of pipes and chambers, connected by openings and perforations, which serve to reduce the fluctuations by acting e.g. as resonators or behave similar to acoustic liners. At the same time, significant mass flow needs to pass small geometry features as pipes or small openings to finally leave the system at the orifice. This fluid flow leads to the generation of additional noise sources. This additional noise is usually of broadband nature and in the mid-to high frequency range, here 500 Hz Hz and above. Sometimes extreme, unwanted noise effects can be observed, e.g. tonal components. These are usually perceived as extremely annoying and can lead to acoustic failure of the system. Thus, they need to be prevented in any case. It is therefore advantageous to have a method that can predict acoustics reliable in early design phases. Here, it was shown that it is indeed possible to predict this kind of noise generation during a virtual product development phase. 2. THE LATTICE-BOLTZMANN METHOD FOR COMPUTATIONAL AEROACOUSTICS Aeroacoustic phenomena are transient in nature, so it seems appropriate to use also a transient approach when performing computational aeroacoustics. Therefore the Lattice-Boltzmann Method, which has its origin in statistical physics, was chosen for the simulations presented in this paper. The flow is basically described by the Lattice-Boltzmann equation, a discrete kinetic equation modeling the dynamics of particle distribution functions. The particle functions are defined on a regular cartesian grid. During an incremental time interval, they jump from one grid cell to the next, according 1 bneuhierl@exa.com 4304

2 to a set of discrete particle velocities, where they collide with other particle distributions or solid structures, changing their velocity and momentum. This interaction is modeled by the collision operator, ensuring meaningful physical behavior in order to approximate the Navier-Stokes equations. Evolving over time, the particle distribution movement thus represents inherently the transient and compressible flow behavior. Macroscopic flow results, like e.g. pressure, density, velocity, are derived via a spatial integration of the particle distributions. The approach allows an exact representation of the boundary geometry in combination with local refinement of the grid, thus enabling detailed representation of both geometry details and flow structures. In order to take into account also high-reynolds number boundary layers and small fluctuations in the flow field not resolved by the grid, the Lattice-Boltzmannn equation is extended by a turbulence model. Hence the Lattice-Boltzmann method allows to simulate very efficiently transient, compressible, fluid flows without significant numerical dissipation. The flow itself, as well as the flow-generated acoustic sources and propagation of the resulting acoustic waves are represented at the same time, making the use of any acoustic analogy unnecessary. 3. PROBLEM DESCRIPTION In this study, the two exemplary exhaust silencers shown in Figure 1 were examined. They both consist of a pipe with perforations, enclosed by a chamber. The perforation holes connect the volumes of the pipe and chamber. The chamber is originally meant to be filled with acoustically absorbing material, but was left empty for the cases examined within this study. The air is flowing through the pipe, leaving the system at the orifice. In one case, the perforations were shaped as round holes with a diameter of 3.5 mm, while in the other case, there were slots with a length of 19 mm and a width of 3 mm. The silencer with the hole-shaped openings shall be referred to as silencer 1, the one with the slots as silencer 2. Figure 1 Silencer 1 with hole-shaped (left) and silencer 2 with slot-shaped openings (right) It has been observed that both silencers show significantly different aeroacoustic behavior. Figure 3 below, a Campbell-diagram, documents the results of measurements on a test bench, where a continually increasing mass flow was imposed at the inlet. The system was placed in an anechoic environment. Both incoming flow and environment were at room temperature (20 C). The diagram shows the acoustic answer measured in a microphone point outside the orifice, see Figure

3 INTER-NOISE 2016 microphone Figure 2 Microphone position defined relatively to orifice Silencer 1 shows a rather narrow-banded phenomenon, a tonal noise at a certain frequency. The frequency of this tonal noise is constant and independent of the mass flow, until a certain mass flow rate (around 430 kg/h) is reached. Then all of a sudden the tonal phenomenon changes its frequency. This can be seen clearly in Figure 3 on the left hand side. Figure 3 Sound pressure level over mass flow, silencer 1 with hole-shaped openings (left), silencer 2 with slot-shaped openings (right) Silencer 2 does not cause such significant effect, here the resulting sound level increases 6 khz, but no extremely prominent peak like in the case of silencer 1 can be identified. The broadband level on the other side is higher for almost the complete frequency range, though. 4. SIMULATION SETUP The simulation environment was modeled according to the experiment, in order to represent the same environment. To do so, an extended inlet with anechoic termination to avoid reflections was added. Unlike in the experiment, a constant mass flow was applied. Two mass flows (350 kg/h and 550 kg/h) were examined, in order to capture the two different characteristic acoustic behaviors of the flow. Similar to experiment, the flow leaves the system into an anechoic chamber, realizing a Sommerfeld radiation condition. The transient pressure was recorded in probe points outside the orifice, at the position of the microphones in the experiment (Figure 2 above). 5. RESULTS 5.1 Flow structures To examine the system in principle first, flow structures were analyzed. This kind of representation of flow structures allows demonstrative visualization of turbulent flow structures. Figure 4 shows instantaneous pictures of lambda2 isosurfaces, lambda2 being a vortex criterion as documented in [5]. The isosurfaces are colored by vorticity (rot v, v being the velocity vector.) The chosen viewpoint emphasizes the flow structures leaking through the openings into the surrounding 4306

4 chamber. In case of silencer 1, small fluctuation vortex structures can be observed directly in the round holeshaped openings. The long slot openings in silencer 2 lead to the development of small wakes at each opening, resulting in stronger fluctuations and more turbulent structures. This fact corresponds well with the higher broadband acoustic levels found in the spectra for silencer 2. Figure 4 Lambda2 isosurfaces, colored by vorticity: silencer 1 with holes (left), silencer 2 with slots (right) A closer look at the openings both for silencer 1 and silencer 2 is shown in Figure 5. Here, instantaneous pictures of the transient velocity magnitude in a plane cutting through the middle of the muffler are visualized. In case of silencer 1, only a small fluid flow is observed at the hole-shaped openings, leaking into the surrounding chamber. For silencer 2, the flow is disturbed to a larger extend, the small vortex streets with a wake that were visualized by plotting the lambda2 isosurfaces already in Figure 4 can be seen clearly also in this illustration. Figure 5 Instantaneous pictures of transient velocity magnitude, silencer 1 (left), silencer 2 (right) 5.2 Comparison of simulation and experiment The spectra in Figure 6 show acoustic results gained by simulation at the microphone point described in Figure 2, both for silencer 1 and silencer 2. Two mass flow rates are shown in each diagram, 350 kg/h (blue curves) and 550 kg/h (red curves). A timesignal with the length of 0.4 seconds was written out during the simulation. The curves for silencer 1 clearly show high values for frequencies around 6-7 khz (350 kg/h) respective 9-10 khz (550 kg/h), which corresponds to the characteristic ridges observed in the 4307

5 Campbell diagram (Figure 3). Figure 6 Simulation results: sound pressure level at microphone points, comparison of two mass flows, silencer 1 with holes (left), silencer 2 with slots (right); f=10 Hz In contrast, the results for silencer 2 do have also some peaks, but these are narrower, and the broad-band level has a more constant gradient. Figure 7 shows experimental results generated with a constant mass flow for the two operating points also examined in the simulations. The characteristics seen in the simulation spectra are in principle also visible here, e.g the typical increase of sound pressure level in case of silencer 1, which shifts with mass flow rate. It must also be emphasized that the time signal length from experiments is typically much longer (e.g seconds) than that written out from simulations. Figure 7 Experimental results: sound pressure level at microphone points, comparison of two mass flows, silencer 1 with holes (left), silencer 2 with slots (right); f=10hz 4308

6 5.3 Resonances in the system So-called dbmaps are gathered by performing a Fast-Fourier transformation (FFT) for every fluid cell, enabling the visualization of the pressure fluctuations in the frequency domain. Such analysis can be done for any frequency band of interest. Figure 8 shows 1/3 rd octave dbmaps in a plane cutting through the chamber for silencer 1 and two different mass flows (350 kg/h and 550 kg/h). For the frequency bands where the peak is observed in Figure 6 above (5 khz 1/3 rd octave band and 6.3 khz 1/3 rd octave band in case of mass flow 350 kg/h and 12.5 khz 1/3 rd octave band in case of mass flow 550 kg/h), it can be clearly seen that the pressure fluctuations are much higher than in the neighboring frequency bands. This is strong evidence that resonances occur. The dbmaps also give a hint about the shape of the excited eigenfrequencies of the system. Figure 8 dbmaps, comparison of 2 mass flow results, silencer with holes, 1/3 rd - octave band spectra The mechanism of the generated tonal noise thus seems to be clear: Every cavity, or system of cavities - like connected pipes and chambers - has certain acoustic eigenmodes with corresponding eigenfrequencies. These are patterns the system tends to answer with when excited, analogous to eigenmodes of structures. The flow going through the silencer causes turbulent structures, vortices, 4309

7 separations. This can mean that acoustic sources are generated, which directly emit sound that is propagated within the system and into the environment (for more details of the sound generating mechanisms, see e.g. [7]). But apart from that it can also mean that the eigenmodes of the system are excited by the flow structures, leading to an amplification of the eigenfrequencies and resulting in tonal components visible in the spectrum. The exciting mechanism in principle can be both of broadbanded nature, or tonal with a frequency changing due to flow speed according to the strouhal number of the flow structure causing the excitation. In case of silencer 1, an eigenmode at around 6 khz is excited by the turbulent structures caused by the flow. The fact that the answer of the system is at the same constant frequency, regardless of the changing speed of the flow, means that it is excited by broadbanded structures. If the mass flow is steadily increased, the flow fluctuations forming the excitation accelerate. At a certain point the next eigenmode, with an eigenfrequency increased by a factor of two, is then excited. This leads to the resonance visible in the 1/3 rd octave band around 12.5 khz in Figure 8 at the right side. As an attempt of making the excited eigenmodes better visible, isosurfaces of the dbmaps have been generated, see Figure 9. This gives a 3D impression of the eigenmode structures. For the higher mass flow, the excited structures are smaller (Figure 9, bottom right) and correspond to higher frequencies. Mass flow 350 kg/h: 5 khz Mass flow 550 kg/h: 10 khz Mass flow 350 kg/h: 6.3 khz Mass flow 550 kg/h: 12.5 khz Figure 9 dbmap isosurfaces for 1/3 rd octave bands silencer 1 Similar dbmaps as in Figure 8 are shown for silencer 2 in Figure 10. The fluctuations due to the small wakes caused by the slots are obvious for all frequencies. One resonance can be observed for the higher mass flow rate, between 5 khz and 6 khz. This corresponds to the narrow peak at the same frequency visible in the simulation and experimental spectra (Figure 6, Figure 7). The resonance is much weaker, though, and the pattern also is different from silencer 1, which is to be expected as the geometry of the connection between pipe and chamber influences the characteristic eigenmode behavior. 4310

8 Figure 10 dbmaps, comparison of 2 mass flow results, silencer with slots, 1/3 rd -octave band spectra 6. CONCLUSIONS In this study, it has been demonstrated that flow induced noise phenomena in exhaust systems can be predicted numerically by performing a one-field, transient, compressible CFD simulation. Experiments on a test bench confirm that the simulation result capture the correct trend. CFD simulation thus enables developers not only to find problematic behavior of exhaust silencers in early phases of the product development process, but also can be used to gain better understanding of noise generating mechanisms, and find and test solutions in order to avoid acoustic failure. 4311

9 REFERENCES 1. P. Bhatnagar, E. Gross, M. Krook A model for collision processes in gases. I. small amplitude processes in charged and neutral lone-component system, Pys. Rev., vol.94, pp , U. Frisch, B. Hasslacher, and Y. Pomeau Lattice-gas Automata for the Navier-Stokes Equations [J], Phys. Rev. Lett., Vol. 56, pp , H. Chen, S. Chen, and W. H. Matthaeus Recovery of the Navier-Stokes equations through a lattice gas Boltzmann equation method. Physical Review A, vol.45, 5339, Y. Qian, D. d'humieres, P. Lallemand Lattice BGK Models for Navier-Stokes Equation, Europhys. Lett., 17, pp , J. Jeong, F. Hussain On the identification of a vortex, Journal of Fluid Mechanics, Volume 285, pp 69-94, H. Chen, C. Teixeira, K. Molvig Digital Physics Approach to Computational Fluid Dynamics, Some Theoretical Features, Int. J. Mod. Phys. C, 8 (4), p. 675, H. Chen, I. Goldhirsh, S. Orszag Discrete rotational symmetry, moment isotropy, and higher order lattice Boltzmann models [J], J. Sci. Computing, S. Chen, S. G. Doolen Lattice Boltzmann Method for Fluid Flows, Ann. Rev.Fluid n. Mech., Vol.30: p , Chen, H., Teixeira, C. and Molvig, K. Realization of Fluid Boundary Conditions via Discrete Boltzmann Dynamics [J], Intl J. Mod. Phys. C, Vol. 9 (8), pp , H. Chen Volumetric Formulation of the Lattice Boltzmann Method for Fluid Dynamics: Basic Concept [J], Phys. Rev. E, Vol. 58, pp , H. Chen, S. Kandasamy, S. Orszag, R. Shock, S. Succi, V. Yakhot Extended Boltmann Kinetic equation for Turbulent Flows, Science, Vol.301, pp , Y. Li, R. Shock, R. Zhang, H. Chen Numerical Study of Flow Past an Impulsively Started Cylinder by Lattice Boltzmann Method [J], J. Fluid Mech., Vol. 519, pp , H. Chen, S. Orszag, I Staroselsky, S. Succi Expanded Analogy between Boltzmann Kinetic Theory of Fluid and Turbulence [J], J. Fluid Mech., Vol. 519, pp , R. Zhang, X. Shan, H. Chen Efficient Kinetic Method for fluid simulation beyond Navier-Stokes equation, Phys. Rev. E, 74, , X. Shan, H. Chen A general multiple-relaxation-time Boltzmann collision model [J], International Journal of Modern Physics C 18, 635, G. A. Brès, F. Pérot, D. Freed Properties of the Lattice-Boltzmann Method for Acoustics [M], AIAA , 13th AIAA/CEAS aeroacoustics conference, Miami, Florida, R. Zhang, H. Fan, H. Chen A lattice Boltzmann approach for solving scalar transport equations."[j], Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 369(1944), , Th. Rose, J. Krüger, B. Neuhierl Strömungsakustische Simulation von Abgasanlagen, Symposium für Motor- und Aggregate-Akustik, Magdeburg, A. Mann, F. Perot, M. Meskine, M.-S. Kim Designing quieter HVAC systems coupling LBM and flowinduced noise source identification methods, 10th FKFS conference, Stuttgart, A. Mann, M.-S.Kim, F. Perot, B. Neuhierl, R. Powell, Th. Rose, J. Krüger Exhaust and Muffler Aeroacoustics Predictions using Lattice Boltzmann Method, SAE ,