Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-17T04:18:02.008Z Has data issue: false hasContentIssue false
  • English
  • Français

Application of Fast Multipole Method for Parallel Mufflers

Published online by Cambridge University Press:  22 March 2012

C.-H. Wu  and
C.-N. Wang
C.-H. Wu*
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
C.-N. Wang
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Corresponding author ([email protected])
Get access

Abstract

The purpose of this study is to examine the acoustic performance of parallel simple expansion mufflers by a new approach for an acceleration of computational time required. The fast multipole method separated the field points and source points into two terms by means of addition theorem. When the boundary is divided into uniform meshes, the integration of source element can be calculated fast. Therefore, the fast multipole method, when compared with the boundary element method, reduces CPU time from an order of N2 to NlogγN, where N is the number of unknowns and γ is a constant. The numerical results have been compared with experiments and analytical approaches based on pressure and velocity continuity, as well as the modal meshing approach; the results clearly show that the agreements are good.

Keywords

FMMBEMTransfer functionMufflers
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. 153 - 162
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Young, C. I. J. and Crocker, M. J., “Prediction of Transmission Loss in Mufflers by the Finite-Element Method,” Journal of the Acoustical Society of America, 57, pp. 144–148 (1975).CrossRefGoogle Scholar
2. Mehdizadeh, O. Z. and Paraschivoiu, M., “A Three-Dimensional Finite Element Approach for Predicting the Transmission Loss in Mufflers and Silencers with No Mean Flow,” Applied Acoustics, 66, pp. 902–918 (2005).CrossRefGoogle Scholar
3. Barbieri, R. and Barbieri, N., “Finite Element Acoustic Simulation Based Shape Optimization of a Muffler, Applied Acoustics, 67, pp. 346–357 (2006).CrossRefGoogle Scholar
4. Tanaka, T., Fujikawa, T., Abe, T. and Utsuno, H., “A Method for the Analytical Prediction of Insertion Loss of a Two-Dimensional Muffler Model Based on the Transfer Matrix Derived from the Boundary Element Method,” Journal of Vibration, Acoustics, Stress, and Reliability in Design, 107, pp. 86–91 (1985).CrossRefGoogle Scholar
5. Wang, C. N., “A Boundary Element Analysis for Simple Expansion Silencers with Mean Flow,” Journal of the Chinese Institute of Engineers, 23, pp. 529–536 (2000).CrossRefGoogle Scholar
6. Wang, C. N., “A Numerical Analysis for Perforated Muffler Components with Mean Flow,” Journal of Vibration and Acoustics, 121, pp. 231–236 (1999).CrossRefGoogle Scholar
7. Wang, C. N., “Numerical Decoupling Analysis of a Resonator with Absorbent Material,” Applied Acoustics, 58, pp. 109–122 (1999).CrossRefGoogle Scholar
8. Wang, C. N. and Liao, C. Y., “Boundary Integral Equation Method for Evaluating the Performance of Straight-Through Resonator with Mean Flow,” Journal of Sound and Vibration, 216, pp. 281–294 (1998).CrossRefGoogle Scholar
9. Panigrahi, S. N. and Munjal, M. L., “Plane Wave Propagation in Generalized Multiply Connected Acoustic Filters,” Journal of the Acoustical Society of America, 118, pp. 2860–2868 (2005).CrossRefGoogle Scholar
10. Kar, T. and Munjal, M. L., “Plane Wave Analysis of Acoustic Wedges Using the Boundary-Condition-Transfer Algorithm,” Applied Acoustics, 67, pp. 901–917 (2006).CrossRefGoogle Scholar
11. Munjal, M. L., “Plane Wave Analysis of Side Inlet/Outlet Chamber Mufflers with Mean Flow,” Applied Acoustics, 52, pp. 165–175 (1997).CrossRefGoogle Scholar
12. Wang, C. N., Wu, C. H. and Wu, T. D., “A Network Approach for Analysis of Silencers with/without Absorbent Material,” Applied Acoustics, 70, pp. 208–214 (2009).CrossRefGoogle Scholar
13. Rokhlin, V., “Rapid Solution of Integral Equations of Classical Potential Theory,” Journal of Computational Physics, 60, pp. 187–207 (1985).CrossRefGoogle Scholar
14. Greengard, L. and Rokhlin, V., “A Fast Algorithm for Particle Simulations,” Journal of Computational Physics, 73, pp. 325–348 (1987).CrossRefGoogle Scholar
15. Chen, J. T. and Chen, K. H., “Applications of the Dual Integral Formulation in Conjunction with Fast Multipole Method in Large-Scale Problems for 2D Exterior Acoustics,” Engineering Analysis with Boundary Elements, 28, pp. 685–709 (2004).CrossRefGoogle Scholar
16. Chen, K. H., Chen, J. T., Kao, J. H. and Lee, Y. T., “Applications of Dual Integral Formulation in Conjunction with Fast Mutipole Method to Oblique Incident Wave Problem,” International Journal for Numerical Methods in Fluids, 59, pp. 711–751 (2009).CrossRefGoogle Scholar
17. Chen, J. T. and Hong, H. K., “Review of Dual Boundary Element Methods with Emphasis on Hypersingular Integrals and Divergent Series,” Applied Mechanics Reviews, American Society of Mechanical Engineers, 52, pp. 17–33 (1999).Google Scholar
18. Fujiwara, H., “The Fast Multipole Method for Integral Equation of Seismic Scattering Problems,” Geophysical Journal International, 133, pp. 773–782 (1998).CrossRefGoogle Scholar
19. Fujiwara, H., “The Fast Multipole Method for Solving Integral Equation of Three-Dimensional Topography and Basin Problems,” Geophysical Journal International, 140, pp. 198–210 (2000).CrossRefGoogle Scholar
20. Nishimura, N., “Fast Multipole Accelerated Boundary Integral Equation Methods,” Applied Mechanics Review, American Society of Mechanical Engineers, 55, pp. 299–324 (2002).Google Scholar
21. Gomez, J. E. and Power, H., “A Multipole Direct and Indirect BEM for 2D Cavity Flow at Low Reynolds Number,” Engineering Analysis with Boundary Elements, 19, pp. 17–31 (1997).CrossRefGoogle Scholar
22. Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, NY, USA (1965).Google Scholar
23. Wu, C. J., Wang, X. J. and Tang, H. B., “Transmis- sion Loss Prediction on a Single-inlet/Doubleoutlet Cylindrical Expansion-Chamber Muffler by using the Modal Meshing Approach,” Applied Acoustics, 69, pp. 173–178 (2007).CrossRefGoogle Scholar
24. Denia, F. D. and Selamet, A., “Letter to Editor ‘Transmission Loss Prediction on a singleinlet/double-outlet Cylindrical Expansion-Chamber Muffler by using the Modal Meshing Approach’ by C.J. Wu X.J. Wang H.B. Tang,” Applied Acoustics, 69, pp. 280–281 (2008).CrossRefGoogle Scholar
25. Tang, H. B., “Reply to Comments on ‘Transmission Loss Prediction on a single-inlet/double-outlet Cylindrical Expansion-Chamber Muffler by Using the Modal Meshing Approach’,” Applied Acoustics, 69, p. 282 (2008).CrossRefGoogle Scholar
26. Denia, F. D. and Selamet, A., “Remark on Reply to Comments on ‘Transmission Loss Prediction on a Single-inlet/double-outlet Cylindrical ExpansionChamber Muffler by Using the Modal Meshing Approach’, Applied Acoustics, 69, pp. 283–284 (2008).CrossRefGoogle Scholar
27. Munjal, M. L., “A Simple Numerical Method for Three-Dimensional Analysis of Simple Expansion Chamber Mufflers of Rectangular as Well as Circular Cross-Section with a Stationary Medium,” Journal of Sound and Vibration, 116, pp. 71–88 (1987).CrossRefGoogle Scholar
28. Chung, J. Y. and Blaser, D. A., “Transfer Function Method of Measuring In-Duct Acoustic Properties, I. Theory,” Journal of the Acoustical Society of America, 68, pp. 907–913 (1980).CrossRefGoogle Scholar
29. Chung, J. Y. and Blaser, D. A., “Transfer Function Method of Measuring In-Duct Acoustic Properties, II. Experiment,” Journal of the Acoustical Society of America, 68, pp. 914–921 (1980).CrossRefGoogle Scholar
30. Wu, C. H. and Wang, C. N., “An Application of Fast Multipole Method in Analyzing Acoustic Filters,” Journal of the Chinese Institute of Engineers, 32, pp. 779–787 (2009).CrossRefGoogle Scholar