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Extending material distribution topology optimization to boundary-effect-dominated problems with applications in viscothermal acoustics
Umeå University, Faculty of Science and Technology, Department of Computing Science.
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0003-0473-3263
Umeå University, Faculty of Science and Technology, Department of Computing Science. Department of Mathematics and Computer Science, Karlstad University, Karlstad, Sweden.ORCID iD: 0000-0001-8704-9584
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. Vol. 234, article id 112302
Keywords [en]
Design optimization, Topology optimization, Helmholtz equation, Acoustic boundary layer, Absorption coefficient, Broadband absorption
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:umu:diva-214109DOI: 10.1016/j.matdes.2023.112302Scopus ID: 2-s2.0-85171333478OAI: oai:DiVA.org:umu-214109DiVA, id: diva2:1794206
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
In thesis
1. Computational analysis and design optimization for acoustic devices
Open this publication in new window or tab >>Computational analysis and design optimization for acoustic devices
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
Design optimization, computational analysis, viscothermal acoustics, material distribution topology optimization, acoustic black holes, finite element method
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:umu:diva-214089 (URN)978-91-8070-146-4 (ISBN)978-91-8070-147-1 (ISBN)
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

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Mousavi, AbbasBerggren, MartinWadbro, Eddie

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