Statistical models of large scale turbulent flow

J.J.H. Brouwers

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    Abstract

    The Langevin and diffusion equations for statistical velocity and displacement of marked fluid particles are formulated for turbulent flow at large Reynolds number for which Lagrangian Kolmogorov K-41 theory holds. The damping and diffusion terms in these equations are specified by the first two terms of a general expansion in powers of C −1 0
    C0−1
    where C0 is Lagrangian based universal Kolmogorov constant: 6≲C 0 ≲7
    6≲C0≲7
    . The equations enable the derivation of descriptions for transport by turbulent fluctuations of conserved scalars, momentum, kinetic energy, pressure and energy dissipation as a function of the derivative of their mean values. Except for pressure and kinetic energy, the diffusion coefficients of these relations are specified in closed-form with C −1 0
    C0−1
    as constant of proportionality. The relations are verified with DNS results of channel flow at Reτ=2000. The presented results can serve to improve or replace the diffusion models of current CFD models.
    Original languageEnglish
    Pages (from-to)369–399
    Number of pages31
    JournalFlow, Turbulence and Combustion
    Volume97
    Issue number2
    DOIs
    Publication statusPublished - 2016

    Fingerprint

    turbulent flow
    Turbulent flow
    kinetic energy
    Kinetic energy
    channel flow
    charge flow devices
    Reynolds number
    Channel flow
    derivation
    dissipation
    diffusion coefficient
    energy dissipation
    damping
    scalars
    momentum
    Energy dissipation
    Momentum
    Computational fluid dynamics
    expansion
    Damping

    Cite this

    Brouwers, J.J.H. / Statistical models of large scale turbulent flow. In: Flow, Turbulence and Combustion. 2016 ; Vol. 97, No. 2. pp. 369–399.
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    Statistical models of large scale turbulent flow. / Brouwers, J.J.H.

    In: Flow, Turbulence and Combustion, Vol. 97, No. 2, 2016, p. 369–399.

    Research output: Contribution to journalArticleAcademicpeer-review

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    AB - The Langevin and diffusion equations for statistical velocity and displacement of marked fluid particles are formulated for turbulent flow at large Reynolds number for which Lagrangian Kolmogorov K-41 theory holds. The damping and diffusion terms in these equations are specified by the first two terms of a general expansion in powers of C −1 0 C0−1 where C0 is Lagrangian based universal Kolmogorov constant: 6≲C 0 ≲7 6≲C0≲7. The equations enable the derivation of descriptions for transport by turbulent fluctuations of conserved scalars, momentum, kinetic energy, pressure and energy dissipation as a function of the derivative of their mean values. Except for pressure and kinetic energy, the diffusion coefficients of these relations are specified in closed-form with C −1 0 C0−1 as constant of proportionality. The relations are verified with DNS results of channel flow at Reτ=2000. The presented results can serve to improve or replace the diffusion models of current CFD models.

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