Nonlinear standing wave and acoustic streaming in an exponential-shape resonator by gas-kinetic scheme simulation

Zhang, Xiaoqing; Feng, Heying; Qu, Chengwu

doi:10.1063/1.4965301

Cited by 3 publications

(4 citation statements)

References 28 publications

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“…These results also show that, for the exponential tube, the optimal shape parameter was 2.2, with which the highest value of the pressure amplitude can be produced. An earlier study [29] also revealed that the m = 2.2 exponential tube has a better energy-gathering ability and shock-suppression effect.…”

Section: Validation Of the Modelmentioning

confidence: 86%

“…In past decades, with the development of mesoscopic methods, the gas-kinetic scheme (GKS) has been widely used to study the compressible fluid flow, heat transfer, turbulent flow, hypersonic, and non-linear acoustic problems [23][24][25][26][27][28][29][30][31], etc. Xu et al [23,24] developed and continually improved the multidimensional gas-kinetic Bhatnagar-Gross-Krook (BGK) scheme to improve its favorable properties in capturing discontinuities.…”

Section: Introductionmentioning

confidence: 99%

“…Feng et al [27,28] applied the GKS method to solve the two-dimensional compressible NS equations and simulated the high-amplitude non-linear standing waves, flow fields, and streaming behavior in cylindrical resonators, with satisfactory results. Then, Zhang et al [29] extended the GKS method to simulate two-dimensional non-linear flow fields and streaming motions in exponential varying cross-section resonators. They found that the exponential resonators have the ability to suppress the shock waves, acoustic streaming, and vortices and gave an optimum index of winding for exponential resonators.…”

Section: Introductionmentioning

confidence: 99%

“…Schematic of the exponential-shaped resonator driven by a piston.An earlier study[29] describes eight different exponential resonators with m = 0, 0.6, 2.0, 2.1, 2.2, 2.3, 2.4, and 3.0; the authors revealed that the m = 2.2 exponential tube exhibits better sound-pressure amplification ability and suppression effects on shock waves, acoustic streaming, and vortices. Accordingly, in this study, the m = 2.2 exponential resonator was investigated under different acoustic vibration conditions.The initial state of the computation is unperturbed air, i.e., initial density ρ 0 = 1.226 kg/m 3 , pressure P 0 = 101,300 Pa, kinetic viscosity coefficient µ = 1.86 × 10−5 kg/(m.s), gas constant R = 287 J/(kg.K), ratio of specific heat γ = 1.4, Prandtl number P r = 0.71, and acoustic speed c 0 = 340.1 m/s.…”

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confidence: 99%

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Evolution of Flow and Streaming in Exponential Variable Cross-Section Resonators

et al. 2020

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A gas-kinetic scheme (GKS) based on an unstructured grid is applied to simulate the evolution of the fluid motions in exponential variable cross-section resonators. The effects of the acoustic field intensity on the oscillatory pressure, velocity, temperature, and flow streaming structure were investigated numerically, and the model was validated. The results demonstrate that the geometry and driving strength are the main factors affecting the final performance of the system. For the quasi-linear and moderate non-linear cases in optimum exponential tube, the periodic generation, evolution, and shedding of vortices in flow fields are associated with the storage and release of energy, which is the transmission mode of the third type of direct current (DC) flow, and its driving mechanism is attributed to the asymmetrical pressure and temperature. Meanwhile, some new physical characteristics were also discovered for the highly non-linear case, e.g., the disorder and unsteadiness of the flow direction accomplished with turbulent flow streaming structures. The secondary flow is manifested as multiscale, irregular and unsteady vortices throughout the tube. The smallest increment of pressure and velocity amplitude occurs concurrently with the biggest increment of temperature amplitude. These evidences suggest that there is an optimal driving strength, even for a good configuration tube, with which the maximum efficiency can be obtained.

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Section: Validation Of the Modelmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Evolution of Flow and Streaming in Exponential Variable Cross-Section Resonators

et al. 2020

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A novel non-linear one-dimensional unsteady model for thermoacoustic engine and its application on a looped traveling-wave thermoacoustic engine

et al. 2021

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Simulating energy cascade of shock wave formation process in a resonator by gas kinetic scheme

Zhang

Feng

2017

Journal of Applied Physics

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The temporal-spatial evolution of gas oscillation was simulated by gas kinetic scheme (GKS) in a cylindrical resonator, driven by a piston at one end and rigidly closed at the other end. Periodic shock waves propagating back and forth were observed in the resonator under finite amplitude of gas oscillation. The studied results demonstrated that the acoustic pressure is a saw-tooth waveform and the oscillatory velocity is a square waveform at the central position of the resonant tube. Moreover, it was found by harmonic analysis that there was no presence of obvious feature for pressure node in such a typical standing wave resonator, and the distribution of acoustic fields displayed a one-dimensional feature for the acoustic pressure while a quasi-one-dimensional form for oscillatory velocity, which demonstrated the nonlinear effects. The simulation results for axial distribution of acoustic intensity showed a good consistency with the published experimental data in the open literature domain, which provides a verification for the effectiveness of the GKS model proposed. The influence of displacement amplitude of the driving piston on the formation of shock wave was numerically investigated, and the simulated results revealed the cascade process of harmonic wave energy from the fundamental wave to higher harmonics. In addition, this study found that the acoustic intensity at the driving end of the resonant tube would increase linearly with the displacement amplitude of the piston due to nonlinear effects, rather than the exponential variation by linear theory. This research demonstrates that the GKS model is strongly capable of simulating nonlinear acoustic problems.

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Nonlinear standing wave and acoustic streaming in an exponential-shape resonator by gas-kinetic scheme simulation

Cited by 3 publications

References 28 publications

Evolution of Flow and Streaming in Exponential Variable Cross-Section Resonators

Evolution of Flow and Streaming in Exponential Variable Cross-Section Resonators

A novel non-linear one-dimensional unsteady model for thermoacoustic engine and its application on a looped traveling-wave thermoacoustic engine

Simulating energy cascade of shock wave formation process in a resonator by gas kinetic scheme

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