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Sound wave propagation in rarefied molecular gases

Published online by Cambridge University Press:  20 October 2023

Shaokang Li Open the ORCID record for Shaokang Li [Opens in a new window] ,
Wei Su Open the ORCID record for Wei Su [Opens in a new window]  and
Yonghao Zhang Open the ORCID record for Yonghao Zhang [Opens in a new window]
Shaokang Li
Affiliation:
Institute of Multiscale Thermofluids, School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, UK
Wei Su
Affiliation:
Division of Emerging Interdisciplinary Areas, The Hong Kong University of Science and Technology, Hong Kong, PR China Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, PR China
Yonghao Zhang*
Affiliation:
Centre for Interdisciplinary Research in Fluids, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
*
†Email address for correspondence: yonghao.zhang@imech.ac.cn
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Abstract

Sound wave propagation in rarefied flows of molecular gases confined in micro-channels is investigated numerically. We first validate the employed kinetic model against the experimental results and then systematically study the gas damping and surface force on the transducer as well as the resonance/anti-resonance in confined space. To quantify the impact of the finite relaxation rates of the translational and internal energies on wave propagation, we examine the roles of bulk viscosity and thermal conductivity in depth over a wide range of rarefactions and oscillation frequencies. It is found that the bulk viscosity only exerts influence on the pressure amplitude and its resonance frequency in the slip regime in high oscillations. In addition, the internal degree of freedom is frozen when the bulk viscosity of a molecular gas is large, resulting in the pressure amplitude of sound waves in the molecular gas being the same as in a monatomic gas. Meanwhile, the thermal conductivity has a limited influence on the pressure amplitude in all the simulated flows. In the case of the thermoacoustic wave, we prove that the Onsager–Casimir reciprocal relation also holds for molecular gases, i.e. the pressure deviation induced by the temperature variation is equal to the heat flux induced by the plate oscillation. Our findings enable an enhanced understanding of sound wave propagation in molecular gases, which may facilitate the design of nano-/micro-scale devices.

JFM classification

Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , A35
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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