Nonlinear resonance and viscous dissipation in an acoustic chamber

Lee, Chun P.; Wang, Taylor G.

doi:10.1121/1.405214

Cited by 10 publications

(3 citation statements)

References 1 publication

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“…Some publications can be found in the time domain. 20,21 They treat a nonlinear resonance problem in an acoustic chamber by using existing numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Numerical model for nonlinear standing waves and weak shocks in thermoviscous fluids

Vanhille

Campos-Pozuelo²

2001

The Journal of the Acoustical Society of America

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Nonlinear standing waves in a one-dimensional tube are studied numerically by using a finite-difference algorithm. The numerical code models the acoustic field in resonators for homogeneous, thermoviscous fluids. Calculations are performed exclusively in the time domain, and all harmonic components are obtained by one resolution. The fully nonlinear differential equation is written in Lagrangian coordinates. It is solved without truncation. Effects of absorption are included. Displacement and pressure wave forms are calculated at different locations and results are shown for different excitation levels and tube lengths. Amplitude distributions along the resonator axis for every harmonic component are also evaluated. Simulations are performed for amplitudes ranging from linear to strongly nonlinear and weak shock. A very good concordance with classic experimental and analytical results is obtained.

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“…Some publications can be found in the time domain. 20,21 They treat a nonlinear resonance problem in an acoustic chamber by using existing numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Numerical model for nonlinear standing waves and weak shocks in thermoviscous fluids

Vanhille

Campos-Pozuelo²

2001

The Journal of the Acoustical Society of America

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“…This is because the appearance of the non-linear shock waves in resonant oscillations and the small Ma number of the gas flow require a high-resolution numerical scheme and a large computing resource. Moreover, most of these conventional simulations are restricted to solve just one-dimensional non-linear wave equations [5][6][7][8]. Recently, enumerable progresses with two-dimensional simulations are carried out.…”

Section: Introductionmentioning

confidence: 99%

Implicit–explicit finite‐difference lattice Boltzmann method with viscid compressible model for gas oscillating patterns in a resonator

Wang

Huang

et al. 2008

Numerical Methods in Fluids

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SUMMARYDifficulties for the conventional computational fluid dynamics and the standard lattice Boltzmann method (LBM) to study the gas oscillating patterns in a resonator have been discussed. In light of the recent progresses in the LBM world, we are now able to deal with the compressibility and non-linear shock wave effects in the resonator. A lattice Boltzmann model for viscid compressible flows is introduced firstly. Then, the Boltzmann equation with the Bhatnagar-Gross-Krook approximation is solved by the finite-difference method with a third-order implicit-explicit (IMEX) Runge-Kutta scheme for time discretization, and a fifth-order weighted essentially non-oscillatory (WENO) scheme for space discretization. Numerical results obtained in this study agree quantitatively with both experimental data available and those using conventional numerical methods. Moreover, with the IMEX finite-difference LBM (FDLBM), the computational convergence rate can be significantly improved compared with the previous FDLBM and standard LBM. This study can also be applied for simulating some more complex phenomena in a thermoacoustics engine.

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“…Gaitan and Atchley (1993) used the perturbation model developed by Coppens and Sanders (1968) to study finite-amplitude standing waves in harmonic and inharmonic resonators. The harmonic resonator was a uniform cylinder ( Other than the piston driving, Lee and Wang (1992) numerically analyzed the nonlinear resonance of a closed rigid tube, in which the gas was assumed to be excited by an external body force. The nonlinear resonance of an air-filled acoustic resonator with rigid walls was studied numerically using the fully nonlinear Lagrangian wave equation.…”

Section: Resonatorsmentioning

confidence: 99%

Nonlinear standing waves in miniature acoustic resonators

Luo¹

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The research on both fundamental mechanisms and applications in nonlinear acoustic resonances has recently become active. By using shaped resonators, the acoustic saturations occurred in straight cylindrical resonators have been removed and large amplitude pressure oscillations have been obtained. Acoustic compressors have been developed following this technology. It is of interests to investigate if the nonlinear resonance can be used to produce high pressure gas oscillations in miniature/micro scales, which would be useful in microfluidics and bio-engineering applications. In order to have nonlinear resonances in small resonators, some issues, such as viscosity effects, resonator configurations and actuating methods, need to be studied. This thesis presents a study on nonlinear resonance oscillations in shaped resonators. The main objective of the study is to investigate acoustic characteristics of nonlinear standing waves in small-size and miniature resonators. This is achieved by studying the effect of resonator geometry and driving methods on the resonance pressures theoretically and experimentally. At the end of the study, a novel design for miniature resonators is demonstrated. The theoretical study in this dissertation mainly comprises three aspects. Firstly, resonance pressures in shaped resonators driven by a shaking force are studied. The resonators are of two types of configurations: one is axisymmetric with cross sectional area being exponentially expanded; another is of a low-aspect-ratio rectangular cross section whose width is exponentially expanded. One-dimensional nonlinear wave equations are obtained by modifying equations developed by Ilinskii et al. (1998), taking into account of shear viscosity and bulk viscosity terms which are derived from I

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Nonlinear resonance and viscous dissipation in an acoustic chamber

Cited by 10 publications

References 1 publication

Numerical model for nonlinear standing waves and weak shocks in thermoviscous fluids

Numerical model for nonlinear standing waves and weak shocks in thermoviscous fluids

Implicit–explicit finite‐difference lattice Boltzmann method with viscid compressible model for gas oscillating patterns in a resonator

Nonlinear standing waves in miniature acoustic resonators

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