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Computational analysis and design optimization for acoustic devices
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Design Optimization Group)
2023 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis focuses on material distribution topology optimization for acoustic waveguides. The limitations of the material distribution approach are discussed in the context of acoustic waveguides with extensive viscous and thermal boundary losses. An extension of the material distribution method is introduced which is capable of incorporating these boundary losses in the optimization process. Furthermore, a computational analysis of waveguide acoustic black holes (WABs) is also provided followed by a topology optimization approach for the conceptual design of a WAB with enhanced wave-focusing capabilities, utilizing the novel method introduced in the first part of the thesis.  The thesis commences with a comprehensive literature review to set the context for the subsequent research. The material distribution topology optimization is then discussed in detail, focusing on the design of a transition section for impedance matching between two cylindrical waveguides with different radii to maximize planar wave transmission. The linear wave propagation in the device is modeled using the Helmholtz equation and solved utilizing the finite element method to obtain acoustic pressure distribution. Nonlinear density filters are used to impose a size control on the design, and the design optimization problem is formulated and solved utilizing the method of moving asymptotes (MMA) with the sensitivity information provided through an ad-joint method. Selected results are provided for the considered design optimization problem. We expanded the analysis to encompass viscothermal acoustics and introduced a novel material distribution method capable of incorporating complex interface conditions. The new method is then applied to design acoustic absorbers with the aim of maximizing boundary losses in a targeted frequency range. The selected results represent the effectiveness of the proposed method.  The thesis further explores the limitations of the classical ribbed design of WABs in achieving true wave-focusing capabilities. To address this, a design optimization problem is formulated to obtain a conceptual design of a WAB. Utilizing the novel material distribution method for viscothermal acoustics introduced in this thesis, the optimization problem is solved, and the optimized design is compared with the results of a classical lossless approach and the ribbed design WAB. The numerical simulations demonstrate the superior wave-focusing capabilities of the optimized design, especially when incorporating boundary losses in the optimization process.   

Place, publisher, year, edition, pages
Umeå: Umeå University , 2023. , p. 57
Series
Report / UMINF, ISSN 0348-0542 ; 23.05
Keywords [en]
Design optimization, computational analysis, viscothermal acoustics, material distribution topology optimization, acoustic black holes, finite element method
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:umu:diva-214089ISBN: 978-91-8070-146-4 (print)ISBN: 978-91-8070-147-1 (electronic)OAI: oai:DiVA.org:umu-214089DiVA, id: diva2:1793940
Public defence
2023-09-29, NAT.D 300, Naturvetarhuset, Umeå, 09:15 (English)
Opponent
Supervisors
Available from: 2023-09-08 Created: 2023-09-04 Last updated: 2023-09-05Bibliographically approved
List of papers
1. Topology optimization of an acoustic diode?
Open this publication in new window or tab >>Topology optimization of an acoustic diode?
2021 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 63, no 6, p. 2739-2749Article in journal (Refereed) Published
Abstract [en]

By using topology optimization, we consider the problem of designing a passive acoustic device that allows for one-way flow of sound waves; such a device is often colloquially referred to as an acoustic diode. The Helmholtz equation is used to model the time harmonic linear wave propagation together with a Dirichlet-to-Neumann (DtN) type boundary condition, and the finite element method is used for discretization. The objective of this study is to maximize the wave propagation in one direction (from left to right) and minimize the wave propagation in the reverse direction (from right to left) for planar incoming waves. The method of moving asymptotes (MMA) solves the optimization problem, and a continuation approach is used for the penalizing intermediate design variables. The results for the optimized waveguide show that more than 99.8% of the power of planar incoming waves get transmitted from left to right while less than 0.3% gets transmitted in the reverse direction for planar incoming waves in the specified frequency range. Since a true diode is a non-reciprocal device and here we used a linear acoustic wave model, which is basically reciprocal, we discuss details about how it appears to be possible to obtain a one-way waveguiding effect using this linear model.

Place, publisher, year, edition, pages
Springer, 2021
Keywords
Helmholtz equation, topology optimization, acoustic diode
National Category
Computational Mathematics
Research subject
Numerical Analysis
Identifiers
urn:nbn:se:umu:diva-179740 (URN)10.1007/s00158-020-02832-9 (DOI)000615764500003 ()2-s2.0-85100577809 (Scopus ID)
Available from: 2021-02-09 Created: 2021-02-09 Last updated: 2023-09-05Bibliographically approved
2. How the waveguide acoustic black hole works: A study of possible damping mechanisms
Open this publication in new window or tab >>How the waveguide acoustic black hole works: A study of possible damping mechanisms
2022 (English)In: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 151, no 6, p. 4279-4290Article in journal (Refereed) Published
Abstract [en]

The acoustic black hole (ABH) effect in waveguides is studied using frequency-domain finite element simulations of a cylindrical waveguide with an embedded ABH termination composed of retarding rings. This design is adopted from an experimental study in the literature, which surprisingly showed, contrary to the structural counterpart, that the addition of damping material to the end of the waveguide does not significantly reduce the reflection coefficient any further. To investigate this unexpected behavior, we model different damping mechanisms involved in the attenuation of sound waves in this setup. A sequence of computed pressure distributions indicates occurrences of frequency-dependent resonances in the device. The axial position of the cavity where the resonance occurs can be predicted by a more elaborate wall admittance model than the one that was initially used to study and design ABHs. The results of our simulations show that at higher frequencies, the visco-thermal losses and the damping material added to the end of the setup do not contribute significantly to the performance of the device. Our results suggest that the primary source of damping, responsible for the low reflection coefficients at higher frequencies, is local absorption effects at the outer surface of the cylinder.

Keywords
Acoustic black hole, Finite element method, Helmholtz equation
National Category
Fluid Mechanics and Acoustics Applied Mechanics Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-198676 (URN)10.1121/10.0011788 (DOI)000818623100001 ()35778217 (PubMedID)2-s2.0-85133707077 (Scopus ID)
Funder
Swedish Research Council, Swedish Research Council
Available from: 2022-08-17 Created: 2022-08-17 Last updated: 2023-09-05Bibliographically approved
3. Extending material distribution topology optimization to boundary-effect-dominated problems with applications in viscothermal acoustics
Open this publication in new window or tab >>Extending material distribution topology optimization to boundary-effect-dominated problems with applications in viscothermal acoustics
2023 (English)In: Materials & design, ISSN 0264-1275, E-ISSN 1873-4197, Vol. 234, article id 112302Article in journal (Other academic) Published
Abstract [en]

A new formulation is presented that extends the material distribution topology optimization method to address boundary-effect-dominated problems, where specific boundary conditions need to be imposed at solid–fluid interfaces. As an example of such a problem, we focus on the design of acoustic structures with significant viscous and thermal boundary losses. In various acoustic applications, especially for acoustically small devices, the main portion of viscothermal dissipation occurs in the so-called acoustic boundary layer. One way of accounting for these losses is through a generalized acoustic impedance boundary condition. This boundary condition has previously been proven to provide accurate results with significantly less computational effort compared to Navier–Stokes simulations. To incorporate this boundary condition into the optimization process at the solid–fluid interface, we introduce a mapping of jumps in densities between neighboring elements to an edge-based boundary indicator function. Two axisymmetric case studies demonstrate the effectiveness of the proposed design optimization method. In the first case, we enhance the absorption performance of a Helmholtz resonator in a narrow range of frequencies. In the second case, we consider an acoustically larger problem and achieve an almost-perfect broadband absorption. Our findings underscore the potential of our approach for the design optimization of boundary-effect-dominated problems.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Design optimization, Topology optimization, Helmholtz equation, Acoustic boundary layer, Absorption coefficient, Broadband absorption
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-214109 (URN)10.1016/j.matdes.2023.112302 (DOI)2-s2.0-85171333478 (Scopus ID)
Funder
eSSENCE - An eScience CollaborationSwedish Research Council, 2018-03546Swedish Research Council, 2022-03783
Note

Originally included in thesis in manuscript form. 

Available from: 2023-09-05 Created: 2023-09-05 Last updated: 2023-09-28Bibliographically approved
4. Topology optimization of a waveguide acoustic black hole for enhanced wave focusing
Open this publication in new window or tab >>Topology optimization of a waveguide acoustic black hole for enhanced wave focusing
2024 (English)In: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 155, no 1, p. 742-756Article in journal (Refereed) Published
Abstract [en]

The waveguide acoustic black hole (WAB) effect is a promising approach for controlling wave propagation in various applications, especially for attenuating sound waves. While the wave-focusing effect of structural acoustic black holes has found widespread applications, the classical ribbed design of waveguide acoustic black holes (WABs) acts more as a resonance absorber than a true wave-focusing device. In this study, we employ a computational design optimization approach to achieve a conceptual design of a WAB with enhanced wave-focusing properties. We investigate the influence of viscothermal boundary losses on the optimization process by formulating two distinct cases: one neglecting viscothermal losses and the other incorporating these losses using a recently developed material distribution topology optimization technique. We compare the performance of optimized designs in these two cases with that of the classical ribbed design. Simulations using linearized compressible Navier–Stokes equations are conducted to evaluate the wave-focusing performance of these different designs. The results reveal that considering viscothermal losses in the design optimization process leads to superior wave-focusing capabilities, highlighting the significance of incorporating these losses in the design approach. This study contributes to the advancement of WAB design and opens up new possibilities for its applications in various fields.

Place, publisher, year, edition, pages
Acoustical Society of America, 2024
Keywords
Acoustical properties, Acoustic phenomena, Acoustic waves, Black holes, Finite-element analysis, Mathematical optimization, Boundary integral methods, Optimization problems, Liquid solid interfaces, Navier Stokes equations
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-214110 (URN)10.1121/10.0024470 (DOI)001153140300001 ()38284824 (PubMedID)2-s2.0-85183806282 (Scopus ID)
Funder
eSSENCE - An eScience CollaborationSwedish Research Council, 2018-03546Swedish Research Council, 2022-03783
Note

Originally included in thesis in manuscript form. 

Available from: 2023-09-05 Created: 2023-09-05 Last updated: 2024-02-14Bibliographically approved
5. Topology optimization of a broadband acoustic transition section using deterministic and stochastic approaches
Open this publication in new window or tab >>Topology optimization of a broadband acoustic transition section using deterministic and stochastic approaches
(English)Manuscript (preprint) (Other academic)
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-214112 (URN)
Available from: 2023-09-05 Created: 2023-09-05 Last updated: 2023-09-05

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