Time domain modelling of a Helmholtz resonator analogue for water waves

Euvé, Leo-Paul; Pham, Kim; Petitjeans, Philippe; Pagneux, Vincent; Maurel, Agnès

doi:10.1017/jfm.2021.450

Cited by 9 publications

(10 citation statements)

References 38 publications

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“…In Euvé et al. (2021 a , b ), we pointed out the analogy between an underwater resonant cavity for water waves and an acoustic Helmholtz resonator in two dimensions. Here, the geometry of the cavity is three-dimensional, and we will see that, mutatis mutandis , the analogy still holds.…”

mentioning

confidence: 89%

“…The dynamics of a resonator are captured through the separation of three scales similar to that used in Euvé et al. (2021 a ). The smallest, microscopic scale is associated with the dimensions of the hole: its width , which is also the width of the vertical walls, and , with its cross-section.…”

Section: Preliminariesmentioning

confidence: 99%

“…We consider resonant cavities whose vertical walls extend through the entire depth h of the fluid, with completely submerged holes drilled on two opposite walls. The dynamics of a resonator are captured through the separation of three scales similar to that used in Euvé et al (2021a). The smallest, microscopic scale is associated with the dimensions of the hole: its width e, which is also the width of the vertical walls, and √ s, with s its cross-section.…”

Section: Separation Of the Scalesmentioning

confidence: 99%

“…In the present study, we analyse the dispersion of a periodic medium with subwavelength resonators inspired by the recent works of Euvé et al. (2021 a , b ). The medium is composed of alternating open canals and resonant canals formed by one or two resonators; see figure 1.…”

Section: Introductionmentioning

confidence: 99%

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Negative refraction of water waves by hyperbolic metamaterials

2023

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We study the propagation of water waves in a three-dimensional device alternating open canals and resonant canals with subwavelength resonances. The dispersion of water waves in such a medium is obtained by analysing the full three-dimensional problem and combining Bloch–Floquet analysis with an asymptotic technique. We obtain the closed forms of the dispersions for resonant canals containing one or two resonators, which depend on only two functions associated with symmetric and antisymmetric modes, and on a geometric parameter analogous to the hopping parameter in topological systems. The analysis of the complete band structure reveals frequency ranges alternating between elliptical and hyperbolic dispersions; in particular, the hyperbolic regime gives rise to a negative effective water depth with a consequent negative refraction. Throughout the course of our study, our theoretical results are validated by comparison with numerical calculations of the full three-dimensional problem.

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mentioning

confidence: 89%

Section: Preliminariesmentioning

confidence: 99%

Section: Separation Of the Scalesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Negative refraction of water waves by hyperbolic metamaterials

2023

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“…The Reynolds stress depends on the crossproduct terms between fluctuating velocities in different directions. [37][38][39][40] Thus, the turbulence and turbulence stress need to be modeled. In the literature, LES (large eddy simulation) or DNS (direct numerical simulations) could be conducted.…”

Section: Description Of the Structure-modified Helmholtz Resonator An...mentioning

confidence: 99%

Numerical optimizing noise damping performances of Helmholtz resonators with a rigid baffle implemented at neck in presence of a grazing flow

Guan

2022

Journal of Low Frequency Noise, Vibration and Active Control

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As an applicable noise attenuator, Helmholtz resonator is mainly used to dampen acoustic noise at low- and medium-frequency ranges. It is typically implemented in combustion-engines and gas turbines to dampen thermoacoustic instabilities. However, it has a narrow effective frequency range and does not work effectively at off-design conditions. In this work, we consider a modified structured Helmholtz resonator (HR) at its neck by applying a rigid baffle in order to maximize its’ noise damping effect and to broaden its frequency bands. The resonator is attached to a cylindrical duct/pipe in presence of a mean flow (grazing flow), aiming to simulate the practical engines flow configuration. For this, a two-dimensional frequency domain numerical model is developed by using COMSOL V5.3. The numerical simulations are carried out by solving the linearized Navier–Stokes equation in frequency domain with low computational cost and time. In order to obtain an optimum design in terms of the maximum noise damping performances, 10 new different configurations/designs are proposed. The effects of 1) the single baffle attached to the upstream or downstream sidewall of the neck ends, that is, Design A, B, C, and D or double baffles, that is, Design E, F, G, and H), 2) the baffle implementation location, 3) the length of the rigid baffle, and 4) the grazing flow low Mach number are evaluated and compared. It is found that Design C is associated with improved TL by 50% and decreased resonant frequency by 20% comparing with the conventional HR. The present preliminary study shows that Design C is the better design. Further experimental and optimization researches are needed to sheds light on the optimum design of a Helmholtz resonator with neck structure being modified, as there is a low Mach number grazing flow.

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