Calculation of the dynamic air flow resistivity of fibre materials

Viggo Tarnow

    Research output: Contribution to journalJournal articleResearchpeer-review

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    Abstract

    The acoustic attenuation of acoustic fiber materials is mainly determined by the dynamic resistivity to an oscillating air flow. The dynamic resistance is calculated for a model with geometry close to the geometry of real fibre material. The model constists of parallel cylinders placed randomly. Two case are treated: flow perpendicular to the cylinder axes, and flow parallel to the axes. In each case two new approximate procedures were used. In the first procedure, one solves the equation of flow in a Voronoi cell around the fiber, and averages over the distribution of the Voronoi cells.The second procedure is an extension to oscillating air flow of the Brinkman self-consistent procedure for dc flow. The procedures are valid for volume concentrations of cylinders less than 0.1. The calculations show that for the density of fibers of interest for acoustic fibre materials the simple self-consistent procedure gives the same results as the more complicated procedure based on average over Voronoi cells. Graphs of the dynamic resistivity versus frequency are given for fiber densities and diameters typical for acoustic fiber materials.
    Original languageEnglish
    JournalAcoustical Society of America. Journal
    Volume102
    Issue number3
    Pages (from-to)1680-1688
    ISSN0001-4966
    DOIs
    Publication statusPublished - 1997

    Bibliographical note

    Copyright (1997) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.

    Cite this

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    title = "Calculation of the dynamic air flow resistivity of fibre materials",
    abstract = "The acoustic attenuation of acoustic fiber materials is mainly determined by the dynamic resistivity to an oscillating air flow. The dynamic resistance is calculated for a model with geometry close to the geometry of real fibre material. The model constists of parallel cylinders placed randomly. Two case are treated: flow perpendicular to the cylinder axes, and flow parallel to the axes. In each case two new approximate procedures were used. In the first procedure, one solves the equation of flow in a Voronoi cell around the fiber, and averages over the distribution of the Voronoi cells.The second procedure is an extension to oscillating air flow of the Brinkman self-consistent procedure for dc flow. The procedures are valid for volume concentrations of cylinders less than 0.1. The calculations show that for the density of fibers of interest for acoustic fibre materials the simple self-consistent procedure gives the same results as the more complicated procedure based on average over Voronoi cells. Graphs of the dynamic resistivity versus frequency are given for fiber densities and diameters typical for acoustic fiber materials.",
    author = "Viggo Tarnow",
    note = "Copyright (1997) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.",
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    Calculation of the dynamic air flow resistivity of fibre materials. / Tarnow, Viggo.

    In: Acoustical Society of America. Journal, Vol. 102, No. 3, 1997, p. 1680-1688.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Calculation of the dynamic air flow resistivity of fibre materials

    AU - Tarnow, Viggo

    N1 - Copyright (1997) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.

    PY - 1997

    Y1 - 1997

    N2 - The acoustic attenuation of acoustic fiber materials is mainly determined by the dynamic resistivity to an oscillating air flow. The dynamic resistance is calculated for a model with geometry close to the geometry of real fibre material. The model constists of parallel cylinders placed randomly. Two case are treated: flow perpendicular to the cylinder axes, and flow parallel to the axes. In each case two new approximate procedures were used. In the first procedure, one solves the equation of flow in a Voronoi cell around the fiber, and averages over the distribution of the Voronoi cells.The second procedure is an extension to oscillating air flow of the Brinkman self-consistent procedure for dc flow. The procedures are valid for volume concentrations of cylinders less than 0.1. The calculations show that for the density of fibers of interest for acoustic fibre materials the simple self-consistent procedure gives the same results as the more complicated procedure based on average over Voronoi cells. Graphs of the dynamic resistivity versus frequency are given for fiber densities and diameters typical for acoustic fiber materials.

    AB - The acoustic attenuation of acoustic fiber materials is mainly determined by the dynamic resistivity to an oscillating air flow. The dynamic resistance is calculated for a model with geometry close to the geometry of real fibre material. The model constists of parallel cylinders placed randomly. Two case are treated: flow perpendicular to the cylinder axes, and flow parallel to the axes. In each case two new approximate procedures were used. In the first procedure, one solves the equation of flow in a Voronoi cell around the fiber, and averages over the distribution of the Voronoi cells.The second procedure is an extension to oscillating air flow of the Brinkman self-consistent procedure for dc flow. The procedures are valid for volume concentrations of cylinders less than 0.1. The calculations show that for the density of fibers of interest for acoustic fibre materials the simple self-consistent procedure gives the same results as the more complicated procedure based on average over Voronoi cells. Graphs of the dynamic resistivity versus frequency are given for fiber densities and diameters typical for acoustic fiber materials.

    U2 - 10.1121/1.420079

    DO - 10.1121/1.420079

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    JO - Acoustical Society of America. Journal

    JF - Acoustical Society of America. Journal

    SN - 0001-4966

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    ER -