Sound propagation through a rarefied gas. Influence of the gas–surface interaction

Kalempa, Denize; Sharipov, Felix

doi:10.1016/j.ijheatfluidflow.2012.09.003

Cited by 18 publications

(10 citation statements)

References 36 publications

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“…12a and d. This is actually consistent with the discovery in Ref. [36] that in some parameter regions the pressure is sensitive to gas-surface boundary condition while in other regions it is not. Therefore, in the following, the accuracy of macroscopic equations will be assessed only by comparing with solutions of the kinetic model (44) using the equivalent diffuse boundary condition.…”

Section: Sound Propagation Between the Transducer And Receiversupporting

confidence: 92%

“…In fact, some macroscopic equations have already been used to calculate the speed and attenuation of sound under the periodic boundary condition, which are compared to experiments conducted between the transducer and receiver; since the gas-wall boundary condition (i.e. the energy accommodation coefficient) may strongly affect the pressure tensor [36], this kind of comparison cannot be used to validate the accuracy of macroscopic equations rigorously. Instead, we will compare directly with LBE solutions under the gas-kinetic boundary condition and the corresponding slip and jump boundary conditions for macroscopic equations.…”

Section: Methods To Test the Accuracy Of Macroscopic Equationsmentioning

confidence: 99%

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On the accuracy of macroscopic equations for linearized rarefied gas flows

2020

Adv. Aerodyn.

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Many macroscopic equations are proposed to describe the rarefied gas dynamics beyond the Navier-Stokes level, either from the mesoscopic Boltzmann equation or some physical arguments, including (i) Burnett, Woods, super-Burnett, augmented Burnett equations derived from the Chapman-Enskog expansion of the Boltzmann equation, (ii) Grad 13, regularized 13/26 moment equations, rational extended thermodynamics equations, and generalized hydrodynamic equations, where the velocity distribution function is expressed in terms of low-order moments and Hermite polynomials, and (iii) bi-velocity equations and "thermo-mechanically consistent" Burnett equations based on the argument of "volume diffusion". This paper is dedicated to assess the accuracy of these macroscopic equations. We first consider the Rayleigh-Brillouin scattering, where light is scattered by the density fluctuation in gas. In this specific problem macroscopic equations can be linearized and solutions can always be obtained, no matter whether they are stable or not. Moreover, the accuracy assessment is not contaminated by the gas-wall boundary condition in this periodic problem. Rayleigh-Brillouin spectra of the scattered light are calculated by solving the linearized macroscopic equations and compared to those from the linearized Boltzmann equation. We find that (i) the accuracy of Chapman-Enskog expansion does not always increase with the order of expansion, (ii) for the moment method, the more moments are included, the more accurate the results are, and (iii) macroscopic equations based on "volume diffusion" do not work well even when the Knudsen number is very small. Therefore, among about a dozen tested equations, the regularized 26 moment equations are the most accurate. However, for moderate and highly rarefied gas flows, huge number of moments should be included, as the convergence to true solutions is rather slow. The same conclusion is drawn from the problem of sound propagation between the transducer and receiver. This slow convergence of moment equations is due to the incapability of Hermite polynomials in the capturing of large discontinuities and rapid variations of the velocity distribution function. This study sheds some light on how to choose/develop macroscopic equations for rarefied gas dynamics.

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Section: Sound Propagation Between the Transducer And Receiversupporting

confidence: 92%

Section: Methods To Test the Accuracy Of Macroscopic Equationsmentioning

confidence: 99%

On the accuracy of macroscopic equations for linearized rarefied gas flows

2020

Adv. Aerodyn.

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“…In this case, the integral phase speed, defined by Eqs. (19) and (21) in Ref. [12], is introduced to calculate the sound speed at the receptor.…”

Section: B the Sound Speed Near The Sourcementioning

confidence: 99%

“…In the past decade, oscillatory gas flows have been extensively studied [11][12][13][14][15][16][17][18][19][20], most of which, however, are for flows between two parallel plates. While the viscous damping is dominate at low oscillation frequencies, at relatively high oscillation frequencies, inertial force leads to the interference of sound waves along the oscillating direction of the plate, so that the magnitude of the damping force on the oscillating plate oscillates when the oscillation frequency varies [18].…”

Section: Introductionmentioning

confidence: 99%

Sound propagation through a rarefied gas in rectangular channels

2016

Phys. Rev. E

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This version is available at https://strathprints.strath.ac.uk/58309/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Sound propagation through a rarefied gas in rectangular channels A sound propagation through a rarefied gas inside a two-dimensional cavity is investigated on the basis of the linearized Boltzmann equation, where one of the cavity wall oscillates harmonically in the normal direction to its own surface and is considered as a sound source. An analytical solution at high oscillation frequencies is obtained, and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillation frequency on the average gas pressure exerted on the oscillating plate is studied. It is found that, at large values of the aspect ratio, the average pressure oscillates when the sound frequency varies, due to the sound resonance and anti-resonance along the oscillation direction of the plate. However, at small values of the aspect ratio, the average pressure is a monotonically decreasing function of the sound frequency, which cannot be observed in the corresponding one-dimensional counterpart. This is explained by the sound interference in the direction parallel to the oscillating plate. The influence of both the cavity aspect ratio and oscillation frequency on the sound speed is also investigated: again it is found that different aspect ratio leads to the different behavior of the sound speed as a function of the oscillation frequency.

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“…In the past decade, in order to investigate the damping due to the normal pressure, the propagation of sound waves (Hadjiconstantinou 2002;Sharipov & Kalempa 2008a;Kalempa & Sharipov 2009;Gu & Emerson 2011;Struchtrup 2011;Desvillettes & Lorenzani 2012;Kalempa & Sharipov 2012) between two parallel plates or in a semi-infinite space has been extensively studied; to investigate the damping caused by the shear force, oscillatory Couette flows both in planar (Park, Bahukudumbi & Beskok 2004;Tang et al 2008;Sharipov & Kalempa 2008b;Doi 2009;Taheri et al 2009;Yap & Sader 2012) and cylindrical geometries (Emerson et al 2007;Shi & Sader 2010;Gospodinov, Roussinov & Stefan 2012) have been studied. For these investigations the adopted methods have included the direct simulation Monte Carlo (DSMC) method (Bird 1994), the discrete velocity method for the linearized Bhatnagar-Gross-Krook (BGK), ellipsoidal statistical BGK, and Shakhov kinetic model equations (Bhatnagar, Gross & Krook 1954;Holway 1966;Shakhov 1968), the numerical kernel method for the linearized Boltzmann equation of hard-sphere gases (Doi 2009), the regularized 13-and 26-moment equations (Struchtrup 2005;Gu & Emerson 2011), and the lattice Boltzmann method (Tang et al 2008;Meng & Zhang 2011).…”

Section: Introductionmentioning

confidence: 99%

Oscillatory rarefied gas flow inside rectangular cavities

Reese

Zhang

2014

J. Fluid Mech.

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Two-dimensional oscillatory lid-driven cavity flow of a rarefied gas at arbitrary oscillation frequency is investigated using the linearized Boltzmann equation. An analytical solution at high oscillation frequencies is obtained, and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillating frequency on the damping force exerted on the moving lid is studied. Surprisingly, it is found that, over a certain frequency range, the damping is smaller than that in an oscillatory Couette flow. This reduction in damping is due to the anti-resonance of the rarefied gas. A scaling law between the anti-resonant frequency and the aspect ratio is established, which would enable the control of the damping through choosing an appropriate cavity geometry

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Sound propagation through a rarefied gas. Influence of the gas–surface interaction

Cited by 18 publications

References 36 publications

On the accuracy of macroscopic equations for linearized rarefied gas flows

On the accuracy of macroscopic equations for linearized rarefied gas flows

Sound propagation through a rarefied gas in rectangular channels

Oscillatory rarefied gas flow inside rectangular cavities

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