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Rotation statistics of fibers in wall shear turbulence

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Abstract

In this paper, the rotation of rigid fibers is investigated for the reference case of turbulent channel flow. The aim of the study is to examine the effect of local shear and turbulence anisotropy on the rotational dynamics of fibers with different elongation and inertia. To this aim, statistics of the fiber angular velocity, Ω, are extracted from direct numerical simulation of turbulence at shear Reynolds number Re τ = 150 coupled with Lagrangian tracking of prolate ellipsoidal fibers with Stokes number, St, ranging from 3 to 100 and aspect ratio, λ, ranging from 1 to 50. Accordingly, the fiber-to-fluid density ratio ranges from \({S \simeq 7}\) (for St = 1, λ = 50) to \({S \simeq 3, 470}\) (for St = 100, λ = 1). Statistics are compared one to one with those obtained for spherical particles to highlight effects due to elongation. Results for mean and fluctuating angular velocities show that elongation is important for fibers with small inertia (St ≤  5 in the present flow-fiber combination). For fibers with larger inertia, elongation has an impact on fiber rotation only in the streamwise and wall-normal directions, where mean values of Ω are zero. It is also shown that, in the center of the channel, the Lagrangian autocorrelation coefficients of Ω and corresponding rotational turbulent diffusivities match the exponential behavior predicted by the theory of homogeneous dispersion. In this region of the channel, the probability density function of fiber angular velocities is generally close to Gaussian, indicating that particle rotation away from solid walls can be modeled as a diffusion process of the Ornstein–Uhlenbeck type at stationary state. In the strong shear region (comprised within a distance of 50 viscous units from the wall in the present simulations), fiber anisotropy adds to flow anisotropy to induce strong deviations on fiber rotational dynamics with respect to spherical particles. The database produced in this study is available to all interested users at https://www.fp1005.cism.it.

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Authors and Affiliations

  1. Department of Fluid Mechanics, CISM, Piazza Garibaldi 18, 33100, Udine, Italy

    Cristian Marchioli & Alfredo Soldati

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  1. Cristian Marchioli
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  2. Alfredo Soldati
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Correspondence to Cristian Marchioli.

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Marchioli, C., Soldati, A. Rotation statistics of fibers in wall shear turbulence. Acta Mech 224, 2311–2329 (2013). https://doi.org/10.1007/s00707-013-0933-z

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  • DOI: https://doi.org/10.1007/s00707-013-0933-z

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