Atlantis Press Paper Details: Sound Attenuation in a Circular Duct of a Viscous Medium in the Absence of Mean Flow

An analytical method to study the effect of viscosity of a medium and the wave number on sound propagation and sound attenuation numbers in circular ducts has been presented. The method is based on the variation of parameters of the solution corresponding to the case of inviscid acoustic waves in circular ducts and axisymmetric modes. A mathematical model is constructed to describe the physical problem in general. Three basic assumptions have been considered, namely, each flow quantity has been written as the sum of a steady mean flow and an unsteady acoustic flow quantity. The effect of thermal conductivity of the gas has been neglected as well as no mean flow. The results for a wide range of wave numbers and Reynolds numbers show that for a viscous medium, the propagation number is a weak function of the Reynolds number, and as the Reynolds number increases, the propagation number approaches its inviscid value. Also the propagation number is independent of the wave number. For the attenuation number, it decreases monotonically with the increase of the Reynolds number and it vanishes when Reynolds number exceeds 104.

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title:		Sound Attenuation in a Circular Duct of a Viscous Medium in the Absence of Mean Flow
publication:		JNMP
volume-issue:		4 - 1-2
pages:		231 - 240
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.1997.4.1-2.37 (how to use a DOI)
author(s):		Mina B. ABD-EL-MALEK, Sarwat N. HANNA
publication date:		May 1997
abstract:		An analytical method to study the effect of viscosity of a medium and the wave number on sound propagation and sound attenuation numbers in circular ducts has been presented. The method is based on the variation of parameters of the solution corresponding to the case of inviscid acoustic waves in circular ducts and axisymmetric modes. A mathematical model is constructed to describe the physical problem in general. Three basic assumptions have been considered, namely, each flow quantity has been written as the sum of a steady mean flow and an unsteady acoustic flow quantity. The effect of thermal conductivity of the gas has been neglected as well as no mean flow. The results for a wide range of wave numbers and Reynolds numbers show that for a viscous medium, the propagation number is a weak function of the Reynolds number, and as the Reynolds number increases, the propagation number approaches its inviscid value. Also the propagation number is independent of the wave number. For the attenuation number, it decreases monotonically with the increase of the Reynolds number and it vanishes when Reynolds number exceeds 104.
copyright:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		4-1_2art37.pdf (156 K)