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标题：Calculation of the Acoustic Spectrum of a Cylindrical Vortex in Viscous Heat-Conducting Gas Based on the Navier–Stokes Equations
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作者：Tatiana Petrova ; Fedor Shugaev
期刊名称：Computation
电子版ISSN：2079-3197
出版年度：2016
卷号：4
期号：3
页码：32-43
DOI：10.3390/computation4030032
出版社：MDPI Publishing
摘要：An extremely interesting problem in aero-hydrodynamics is the sound radiation of a single vortical structure. Currently, this type of problem is mainly considered for an incompressible medium. In this paper a method was developed to take into account the viscosity and thermal conductivity of gas. The acoustic radiation frequency of a cylindrical vortex on a flat wall in viscous heat-conducting gas (air) has been investigated. The problem is solved on the basis of the Navier–Stokes equations using the small initial vorticity approach. The power expansion of unknown functions in a series with a small parameter (vorticity) is used. It is shown that there are high-frequency oscillations modulated by a low-frequency signal. The value of the high frequency remains constant for a long period of time. Thus the high frequency can be considered a natural frequency of the vortex radiation. The value of the natural frequency depends only on the initial radius of the cylindrical vortex, and does not depend on the intensity of the initial vorticity. As expected from physical considerations, the natural frequency decreases exponentially as the initial radius of the cylinder increases. Furthermore, the natural frequency differs from that of the oscillations inside the initial cylinder and in the outer domain. The results of the paper may be of interest for aeroacoustics and tornado modeling.
关键词：Navier–Stokes equations; cylindrical vortex; acoustic radiation; heat-conducting gas Navier–Stokes equations ; cylindrical vortex ; acoustic radiation ; heat-conducting gas