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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.

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.

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.

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.