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Numerical Modeling of Internal Helmholtz Resonators Created by Punching Small Holes on a Thin-Walled Tube
ISSN: 0148-7191, e-ISSN: 2688-3627
Published June 05, 2019 by SAE International in United States
This content contains downloadable datasetsAnnotation ability available
Helmholtz resonators are normally an afterthought in the design of mufflers to target a very specific low frequency, usually the fundamental firing frequency of the engine. Due to space limitations in a complex muffler design, a resonator may have to be built by punching a few small holes on a thin-walled tube to create a neck passage into a small, enclosed volume outside the tube. The short neck passage created by punching a few small holes on a thin-walled tube can pose a great challenge in numerical modeling, especially when the boundary element method (BEM) is used. In this paper, a few different BEM modeling approaches are compared to one another and to the finite element method (FEM). These include the multi-domain BEM implemented in a substructure BEM framework, modeling both sides of the thin-walled tube and the details of each small hole using the Helmholtz integral equation and the hypersingular integral equation, and modeling just the mid surface of the thin-walled tube. The FEM and BEM solutions are used to estimate the effective neck length commonly used in an analytical solution. The effect of changing the locations of the holes is also investigated.
CitationZhou, H. and Wu, T., "Numerical Modeling of Internal Helmholtz Resonators Created by Punching Small Holes on a Thin-Walled Tube," SAE Technical Paper 2019-01-1486, 2019, https://doi.org/10.4271/2019-01-1486.
Data Sets - Support Documents
|[Unnamed Dataset 1]|
- Wu, T.W. and Wan, G.C. , “Muffler Performance Studies Using a Direct Mixed-Body Boundary Element Method and a Three-Point Method for Evaluating Transmission Loss,” Journal of Vibration and Acoustics, ASME Transactions 118:479-484, 1996.
- Wu, T.W., Cheng, C.Y.R., and Zhang, P. , “A Direct Mixed-Body Boundary Element Method for Packed Silencers,” Journal of Acoustical Society of America 111:2566-2572, 2002.
- Lou, G., Wu, T.W., and Cheng, C.Y.R. , “Boundary Element Analysis of Packed Silencers with a Substructuring Technique,” Engineering Analysis with Boundary Elements 27:643-653, 2003.
- Cheng, C.Y.R., Seybert, A.F., and Wu, T.W. , “A Multidomain Boundary Element Solution for Silencer and Muffler Performance Prediction,” Journal of Sound and Vibration 151:119-129, 1991.
- Wang, C.N., Tse, C.C., and Chen, Y.N. , “A Boundary Element Analysis of a Concentric-tube Resonator,” Engineering Analysis with Boundary Elements 12:21-27, 1993.
- Wang, P. and Wu, T.W. , “Impedance-to-Scattering Matrix Method for Large Silencer Analysis Using Direct Collocation,” Engineering Analysis with Boundary Elements 73:191-199, 2016.
- Wu, T.W. , editor, Boundary Element Acoustics Fundamentals and Computer Codes (Southampton: WIT Press, 2000).
- Krishnasamy, G., Rizzo, F.J., and Liu, Y. , “Boundary Integral Equations for Thin Bodies,” International Journal for Numerical Methods in Engineering 37:107-121, 1994.
- Liu, Y. and Rizzo, F.J. , “Scattering of Elastic Waves From Thin Shapes in Three Dimensions Using the Composite Boundary Integral Equation Formulation,” Journal of Acoustical Society of America 102:926-932, 1997.
- Kinsler, L.E., Frey, A.R., Coppens, A.B., and Sanders, J.V. , Fundamentals of Acoustics Third Edition (Wiley, 1982).
- LMS Virtual.Lab, Siemens.