TY - JOUR

T1 - Sound propagation through a rarefied gas in rectangular channels

AU - Wu, Lei

PY - 2016/11/11

Y1 - 2016/11/11

N2 - 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.

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

KW - rarefied gas

KW - rectangular channels

KW - linearized Boltzmann equation

KW - gas rarefaction

KW - two-dimensional cavity

KW - oscillation frequency

KW - cavity aspect ratio

UR - http://journals.aps.org/pre/

U2 - 10.1103/PhysRevE.94.053110

DO - 10.1103/PhysRevE.94.053110

M3 - Article

VL - 94

JO - Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1539-3755

M1 - 053110

ER -