Turbulent energy redistribution in spanwise rotating channel flows

Karuna S. Koppula, André Bénard, Charles A. Petty

    Research output: Contribution to journalArticle

    • 1 Citations

    Abstract

    For fully developed turbulent flows of a Newtonian fluid in a nonrotating channel with a large aspect ratio (i.e., spanwise length scale ≫ transverse length scale), the longitudinal component of the mean velocity and the mean pressure are symmetrical functions of the transverse coordinate. The three unequal normal components of the Reynolds stress are also symmetrical functions about the midplane whereas the shear component of the Reynolds stress is spatially antisymmetric. However, if the channel rotates around the spanwise axis, the Coriolis acceleration breaks the spatial symmetry of the flow field. This phenomenon occurs because the angular velocity of the frame directly couples with the linear momentum of the flow field to redistribute the turbulent kinetic energy. Consequently, rotating channel flows are ideal for testing the efficacy of closure models for the Reynolds averaged Navier-Stokes (RANS) equation. It is noteworthy that none of the classical "eddy" viscosity models are able to predict the Coriolis symmetry breaking phenomenon in spanwise rotating fully developed channel flows. This fundamental deficiency occurs because the "eddy" viscosity hypothesis assumes that the Reynolds stress is a frame-indifferent dyadic-valued operator (i.e., objective). Unlike the viscous transport of momentum, the transport of momentum by turbulent fluctuations is directly influenced by the angular velocity of the reference frame. In this paper, a recently developed algebraic closure for the Reynolds stress [see Koppula, K.; Bénard, A.; Petty, C. Realizable Algebraic Reynolds Stress Closure. Chem. Eng. Sci.2009, 64, 4611], referred to hereinafter as the universal realizable anisotropic prestress (URAPS) closure, is used to predict the spatial distribution of the normalized Reynolds (NR) stress (i.e., R≡ /tr() for rotating and for nonrotating fully developed channel flows. The new closure is formulated as an algebraic mapping of the NR stress into itself and is, thereby, realizable for all turbulent flows regardless of the specific benchmark flows used to estimate model parameters. The fixed points of the non-negative mapping depend explicitly on three specific time scales associated with the local statistical state of turbulence. The a priori predictions of the NR stress are consistent with previously published direct numerical simulations of the Navier-Stokes equation.

    Original languageEnglish (US)
    Pages (from-to)8905-8916
    Number of pages12
    JournalIndustrial and Engineering Chemistry Research
    Volume50
    Issue number15
    DOIs
    StatePublished - Aug 3 2011

    Profile

    Addison Disease
    Viscosity
    Channel flow
    Coriolis Force
    Anthralin
    Momentum
    Aurovertins
    Focal Dermal Hypoplasia
    Hereditary Corneal Dystrophies
    Artificial Heart
    Alternaria
    Hydrocortisone
    Angular velocity
    Navier Stokes equations
    Turbulent flow
    Flow fields
    Acetyl-CoA Hydrolase
    Benzyl Compounds
    Blood Stains
    Auscultation

    ASJC Scopus subject areas

    • Chemical Engineering(all)
    • Chemistry(all)
    • Industrial and Manufacturing Engineering

    Cite this

    Turbulent energy redistribution in spanwise rotating channel flows. / Koppula, Karuna S.; Bénard, André; Petty, Charles A.

    In: Industrial and Engineering Chemistry Research, Vol. 50, No. 15, 03.08.2011, p. 8905-8916.

    Research output: Contribution to journalArticle

    Koppula, Karuna S.; Bénard, André; Petty, Charles A. / Turbulent energy redistribution in spanwise rotating channel flows.

    In: Industrial and Engineering Chemistry Research, Vol. 50, No. 15, 03.08.2011, p. 8905-8916.

    Research output: Contribution to journalArticle

    @article{3d96cf656d7f4634813802700092e9fe,
    title = "Turbulent energy redistribution in spanwise rotating channel flows",
    abstract = "For fully developed turbulent flows of a Newtonian fluid in a nonrotating channel with a large aspect ratio (i.e., spanwise length scale ≫ transverse length scale), the longitudinal component of the mean velocity and the mean pressure are symmetrical functions of the transverse coordinate. The three unequal normal components of the Reynolds stress are also symmetrical functions about the midplane whereas the shear component of the Reynolds stress is spatially antisymmetric. However, if the channel rotates around the spanwise axis, the Coriolis acceleration breaks the spatial symmetry of the flow field. This phenomenon occurs because the angular velocity of the frame directly couples with the linear momentum of the flow field to redistribute the turbulent kinetic energy. Consequently, rotating channel flows are ideal for testing the efficacy of closure models for the Reynolds averaged Navier-Stokes (RANS) equation. It is noteworthy that none of the classical {"}eddy{"} viscosity models are able to predict the Coriolis symmetry breaking phenomenon in spanwise rotating fully developed channel flows. This fundamental deficiency occurs because the {"}eddy{"} viscosity hypothesis assumes that the Reynolds stress is a frame-indifferent dyadic-valued operator (i.e., objective). Unlike the viscous transport of momentum, the transport of momentum by turbulent fluctuations is directly influenced by the angular velocity of the reference frame. In this paper, a recently developed algebraic closure for the Reynolds stress [see Koppula, K.; Bénard, A.; Petty, C. Realizable Algebraic Reynolds Stress Closure. Chem. Eng. Sci.2009, 64, 4611], referred to hereinafter as the universal realizable anisotropic prestress (URAPS) closure, is used to predict the spatial distribution of the normalized Reynolds (NR) stress (i.e., R≡ /tr() for rotating and for nonrotating fully developed channel flows. The new closure is formulated as an algebraic mapping of the NR stress into itself and is, thereby, realizable for all turbulent flows regardless of the specific benchmark flows used to estimate model parameters. The fixed points of the non-negative mapping depend explicitly on three specific time scales associated with the local statistical state of turbulence. The a priori predictions of the NR stress are consistent with previously published direct numerical simulations of the Navier-Stokes equation.",
    author = "Koppula, {Karuna S.} and André Bénard and Petty, {Charles A.}",
    year = "2011",
    month = "8",
    doi = "10.1021/ie1020409",
    volume = "50",
    pages = "8905--8916",
    journal = "Industrial & Engineering Chemistry Product Research and Development",
    issn = "0888-5885",
    publisher = "American Chemical Society",
    number = "15",

    }

    TY - JOUR

    T1 - Turbulent energy redistribution in spanwise rotating channel flows

    AU - Koppula,Karuna S.

    AU - Bénard,André

    AU - Petty,Charles A.

    PY - 2011/8/3

    Y1 - 2011/8/3

    N2 - For fully developed turbulent flows of a Newtonian fluid in a nonrotating channel with a large aspect ratio (i.e., spanwise length scale ≫ transverse length scale), the longitudinal component of the mean velocity and the mean pressure are symmetrical functions of the transverse coordinate. The three unequal normal components of the Reynolds stress are also symmetrical functions about the midplane whereas the shear component of the Reynolds stress is spatially antisymmetric. However, if the channel rotates around the spanwise axis, the Coriolis acceleration breaks the spatial symmetry of the flow field. This phenomenon occurs because the angular velocity of the frame directly couples with the linear momentum of the flow field to redistribute the turbulent kinetic energy. Consequently, rotating channel flows are ideal for testing the efficacy of closure models for the Reynolds averaged Navier-Stokes (RANS) equation. It is noteworthy that none of the classical "eddy" viscosity models are able to predict the Coriolis symmetry breaking phenomenon in spanwise rotating fully developed channel flows. This fundamental deficiency occurs because the "eddy" viscosity hypothesis assumes that the Reynolds stress is a frame-indifferent dyadic-valued operator (i.e., objective). Unlike the viscous transport of momentum, the transport of momentum by turbulent fluctuations is directly influenced by the angular velocity of the reference frame. In this paper, a recently developed algebraic closure for the Reynolds stress [see Koppula, K.; Bénard, A.; Petty, C. Realizable Algebraic Reynolds Stress Closure. Chem. Eng. Sci.2009, 64, 4611], referred to hereinafter as the universal realizable anisotropic prestress (URAPS) closure, is used to predict the spatial distribution of the normalized Reynolds (NR) stress (i.e., R≡ /tr() for rotating and for nonrotating fully developed channel flows. The new closure is formulated as an algebraic mapping of the NR stress into itself and is, thereby, realizable for all turbulent flows regardless of the specific benchmark flows used to estimate model parameters. The fixed points of the non-negative mapping depend explicitly on three specific time scales associated with the local statistical state of turbulence. The a priori predictions of the NR stress are consistent with previously published direct numerical simulations of the Navier-Stokes equation.

    AB - For fully developed turbulent flows of a Newtonian fluid in a nonrotating channel with a large aspect ratio (i.e., spanwise length scale ≫ transverse length scale), the longitudinal component of the mean velocity and the mean pressure are symmetrical functions of the transverse coordinate. The three unequal normal components of the Reynolds stress are also symmetrical functions about the midplane whereas the shear component of the Reynolds stress is spatially antisymmetric. However, if the channel rotates around the spanwise axis, the Coriolis acceleration breaks the spatial symmetry of the flow field. This phenomenon occurs because the angular velocity of the frame directly couples with the linear momentum of the flow field to redistribute the turbulent kinetic energy. Consequently, rotating channel flows are ideal for testing the efficacy of closure models for the Reynolds averaged Navier-Stokes (RANS) equation. It is noteworthy that none of the classical "eddy" viscosity models are able to predict the Coriolis symmetry breaking phenomenon in spanwise rotating fully developed channel flows. This fundamental deficiency occurs because the "eddy" viscosity hypothesis assumes that the Reynolds stress is a frame-indifferent dyadic-valued operator (i.e., objective). Unlike the viscous transport of momentum, the transport of momentum by turbulent fluctuations is directly influenced by the angular velocity of the reference frame. In this paper, a recently developed algebraic closure for the Reynolds stress [see Koppula, K.; Bénard, A.; Petty, C. Realizable Algebraic Reynolds Stress Closure. Chem. Eng. Sci.2009, 64, 4611], referred to hereinafter as the universal realizable anisotropic prestress (URAPS) closure, is used to predict the spatial distribution of the normalized Reynolds (NR) stress (i.e., R≡ /tr() for rotating and for nonrotating fully developed channel flows. The new closure is formulated as an algebraic mapping of the NR stress into itself and is, thereby, realizable for all turbulent flows regardless of the specific benchmark flows used to estimate model parameters. The fixed points of the non-negative mapping depend explicitly on three specific time scales associated with the local statistical state of turbulence. The a priori predictions of the NR stress are consistent with previously published direct numerical simulations of the Navier-Stokes equation.

    UR - http://www.scopus.com/inward/record.url?scp=79960870525&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=79960870525&partnerID=8YFLogxK

    U2 - 10.1021/ie1020409

    DO - 10.1021/ie1020409

    M3 - Article

    VL - 50

    SP - 8905

    EP - 8916

    JO - Industrial & Engineering Chemistry Product Research and Development

    T2 - Industrial & Engineering Chemistry Product Research and Development

    JF - Industrial & Engineering Chemistry Product Research and Development

    SN - 0888-5885

    IS - 15

    ER -