Sound propagation through a rarefied gas in rectangular channels

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.
LanguageEnglish
Article number053110
Number of pages9
JournalPhysical Review E
Volume94
DOIs
Publication statusPublished - 11 Nov 2016

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Rarefied Gas
rarefied gases
sound propagation
aspect ratio
Acoustic waves
Propagation
oscillations
Aspect Ratio
acoustics
Aspect ratio
Gases
acoustic frequencies
cavities
Oscillation
Cavity
rarefaction
gas pressure
Sound
Boltzmann equation
interference

Keywords

  • sound propagation
  • rarefied gas
  • rectangular channels
  • linearized Boltzmann equation
  • gas rarefaction
  • two-dimensional cavity
  • oscillation frequency
  • cavity aspect ratio

Cite this

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title = "Sound propagation through a rarefied gas in rectangular channels",
abstract = "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.",
keywords = "sound propagation, rarefied gas, rectangular channels, linearized Boltzmann equation, gas rarefaction, two-dimensional cavity, oscillation frequency, cavity aspect ratio",
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Sound propagation through a rarefied gas in rectangular channels. / Wu, Lei.

In: Physical Review E, Vol. 94, 053110, 11.11.2016.

Research output: Contribution to journalArticle

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AB - 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.

KW - sound propagation

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