Modal Acoustic Impedance of an Infinite Cylindrical Source Immersed in an Unbounded Thermoviscous Fluid

Farnaz Bagheri, Seyyed Mohammad Hasheminejad, Mohammad Esmail Aryaee Panah

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Abstract

A modal impedance matrix is formulated for an infinite cylindrical source undergoing axisymmetric oscillations in a thermoviscous acoustic medium. The formulation utilizes the governing equations of Hasheminejad and Alibakhshi and the analysis method of Hasheminejad and Geers. A matrix based method is used to generate the impedance curves. At first governing equations of the acoustic fields in the thermoviscous fluid are manipulated to yield the well-known Helmholtz equations and corresponding wave numbers. Equations of radial and meridional velocities and the excess temperature are also derived. In addition, the classical relations for radial and meridional stresses and the heat flux are employed as potential based equations. Velocities and the excess temperature as well as the stresses and the heat flux are expressed as Hankel series with unknown coefficients at the surface of the source. Eventually the modal impedances for three first modes are calculated and plotted as a function of distance from the source surface. Numerical results for immersion in glycerol and olive oil are obtained as examples. Considering the thermoviscous effects in cylindrical coordinates can be regarded as the main contribution of the present work to the previous ones.
Original languageEnglish
Title of host publicationProceedings of 20th Annual International Conference on Mechanical Engineering-ISME2012
Number of pages4
Publication date2012
Publication statusPublished - 2012
Externally publishedYes
Event20th Annual International Conference on Mechanical Engineering - Shiraz University, Shiraz, Iran, Islamic Republic of
Duration: 16 May 201218 May 2012
Conference number: 20

Conference

Conference20th Annual International Conference on Mechanical Engineering
Number20
LocationShiraz University
CountryIran, Islamic Republic of
CityShiraz
Period16/05/201218/05/2012

Keywords

  • Thermoviscous fluid
  • Acoustic impedance
  • Cylindrical source

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