Bingham Fluids: Deformation and Energy Dissipation in Triangular Cross Section Tube Flow

Mario F. Letelier, Cristian Barrera, Siginer Dennis, Juan S. Stockle, Felipe Godoy, C. Rosas

    Research output: Contribution to journalArticle

    Abstract

    Flow of Bingham plastics through straight, long tubes with non-circular cross-sections is studied by means of an analytical method that allows to model a wide spectrum of tube geometries. Shear stress normal to equal velocity lines, velocity field and plug zones are explored, in particular in a tube with equilateral triangular cross-section for small values of the Bingham number Bi, and they are compared with corresponding numerical solutions. We show that a circular plug is present at the center of the triangular tube cross-section, consistent with numerical simulations as well as with previous results in the literature, if calculations up to and including first order in the shape perturbation parameter ϵ are taken into account. However with the inclusion of the second order terms in the algorithm this structure is no longer present and no plug zone is predicted for the same pressure drop. We find that in that case normal shear stresses are always greater than the yield stress of the fluid. As a result, the central region becomes a pseudo-plug since it presents small but non-vanishing relative deformations and does not move as a rigid core. The energy dissipation function for the Bingham fluid flow is written in terms of natural coordinates. Its distribution depends only on the normal shear stress at any point with Bingham number as a parameter.
    Original languageEnglish
    Pages (from-to)161-173
    JournalMeccanica
    Volume53
    Issue number1-2
    DOIs
    Publication statusPublished - 2016

    Fingerprint

    Pipe flow
    plugs
    Shear stress
    Energy dissipation
    dissipation
    energy dissipation
    shear stress
    tubes
    Fluids
    fluids
    cross sections
    Pressure drop
    Yield stress
    Flow of fluids
    pressure drop
    Plastics
    fluid flow
    plastics
    Geometry
    velocity distribution

    Cite this

    Letelier, Mario F. ; Barrera, Cristian ; Dennis, Siginer ; Stockle, Juan S. ; Godoy, Felipe ; Rosas, C. / Bingham Fluids: Deformation and Energy Dissipation in Triangular Cross Section Tube Flow. In: Meccanica. 2016 ; Vol. 53, No. 1-2. pp. 161-173.
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    title = "Bingham Fluids: Deformation and Energy Dissipation in Triangular Cross Section Tube Flow",
    abstract = "Flow of Bingham plastics through straight, long tubes with non-circular cross-sections is studied by means of an analytical method that allows to model a wide spectrum of tube geometries. Shear stress normal to equal velocity lines, velocity field and plug zones are explored, in particular in a tube with equilateral triangular cross-section for small values of the Bingham number Bi, and they are compared with corresponding numerical solutions. We show that a circular plug is present at the center of the triangular tube cross-section, consistent with numerical simulations as well as with previous results in the literature, if calculations up to and including first order in the shape perturbation parameter ϵ are taken into account. However with the inclusion of the second order terms in the algorithm this structure is no longer present and no plug zone is predicted for the same pressure drop. We find that in that case normal shear stresses are always greater than the yield stress of the fluid. As a result, the central region becomes a pseudo-plug since it presents small but non-vanishing relative deformations and does not move as a rigid core. The energy dissipation function for the Bingham fluid flow is written in terms of natural coordinates. Its distribution depends only on the normal shear stress at any point with Bingham number as a parameter.",
    author = "Letelier, {Mario F.} and Cristian Barrera and Siginer Dennis and Stockle, {Juan S.} and Felipe Godoy and C. Rosas",
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    Letelier, MF, Barrera, C, Dennis, S, Stockle, JS, Godoy, F & Rosas, C 2016, 'Bingham Fluids: Deformation and Energy Dissipation in Triangular Cross Section Tube Flow', Meccanica, vol. 53, no. 1-2, pp. 161-173. https://doi.org/10.1007/s11012-017-0716-z

    Bingham Fluids: Deformation and Energy Dissipation in Triangular Cross Section Tube Flow. / Letelier, Mario F.; Barrera, Cristian; Dennis, Siginer; Stockle, Juan S.; Godoy, Felipe; Rosas, C.

    In: Meccanica, Vol. 53, No. 1-2, 2016, p. 161-173.

    Research output: Contribution to journalArticle

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    T1 - Bingham Fluids: Deformation and Energy Dissipation in Triangular Cross Section Tube Flow

    AU - Letelier, Mario F.

    AU - Barrera, Cristian

    AU - Dennis, Siginer

    AU - Stockle, Juan S.

    AU - Godoy, Felipe

    AU - Rosas, C.

    PY - 2016

    Y1 - 2016

    N2 - Flow of Bingham plastics through straight, long tubes with non-circular cross-sections is studied by means of an analytical method that allows to model a wide spectrum of tube geometries. Shear stress normal to equal velocity lines, velocity field and plug zones are explored, in particular in a tube with equilateral triangular cross-section for small values of the Bingham number Bi, and they are compared with corresponding numerical solutions. We show that a circular plug is present at the center of the triangular tube cross-section, consistent with numerical simulations as well as with previous results in the literature, if calculations up to and including first order in the shape perturbation parameter ϵ are taken into account. However with the inclusion of the second order terms in the algorithm this structure is no longer present and no plug zone is predicted for the same pressure drop. We find that in that case normal shear stresses are always greater than the yield stress of the fluid. As a result, the central region becomes a pseudo-plug since it presents small but non-vanishing relative deformations and does not move as a rigid core. The energy dissipation function for the Bingham fluid flow is written in terms of natural coordinates. Its distribution depends only on the normal shear stress at any point with Bingham number as a parameter.

    AB - Flow of Bingham plastics through straight, long tubes with non-circular cross-sections is studied by means of an analytical method that allows to model a wide spectrum of tube geometries. Shear stress normal to equal velocity lines, velocity field and plug zones are explored, in particular in a tube with equilateral triangular cross-section for small values of the Bingham number Bi, and they are compared with corresponding numerical solutions. We show that a circular plug is present at the center of the triangular tube cross-section, consistent with numerical simulations as well as with previous results in the literature, if calculations up to and including first order in the shape perturbation parameter ϵ are taken into account. However with the inclusion of the second order terms in the algorithm this structure is no longer present and no plug zone is predicted for the same pressure drop. We find that in that case normal shear stresses are always greater than the yield stress of the fluid. As a result, the central region becomes a pseudo-plug since it presents small but non-vanishing relative deformations and does not move as a rigid core. The energy dissipation function for the Bingham fluid flow is written in terms of natural coordinates. Its distribution depends only on the normal shear stress at any point with Bingham number as a parameter.

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