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Computation 2016, 4(3), 32; doi:10.3390/computation4030032

Calculation of the Acoustic Spectrum of a Cylindrical Vortex in Viscous Heat-Conducting Gas Based on the Navier–Stokes Equations

Department of Quantum Statistics and Field Theory, Faculty of Physics, M.V. Lomonosov Moscow State University, Leninskie Gory, 1-2, 119991 Moscow, Russia
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Author to whom correspondence should be addressed.
Academic Editor: Ali Cemal Benim
Received: 6 July 2016 / Revised: 11 August 2016 / Accepted: 15 August 2016 / Published: 20 August 2016
(This article belongs to the Section Computational Engineering)
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Abstract

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. View Full-Text
Keywords: Navier–Stokes equations; cylindrical vortex; acoustic radiation; heat-conducting gas Navier–Stokes equations; cylindrical vortex; acoustic radiation; heat-conducting gas
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Petrova, T.; Shugaev, F. Calculation of the Acoustic Spectrum of a Cylindrical Vortex in Viscous Heat-Conducting Gas Based on the Navier–Stokes Equations. Computation 2016, 4, 32.

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