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Quantitative analysis of the angular dynamics of a single spheroid in simple shear flow at moderate Reynolds numbers

Tomas Rosén1,2,*, Arne Nordmark1, Cyrus K. Aidun3, Minh Do-Quang1, and Fredrik Lundell1,2

  • 1KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
  • 2Wallenberg Wood Science Center, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
  • 3G. W. Woodruff School of Mechanical Engineering and Parker H. Petit Institute for Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, Georgia 30332-0405, USA

  • *rosen@mech.kth.se
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Phys. Rev. Fluids 1, 044201 – Published 1 August, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.044201

Abstract

A spheroidal particle in simple shear flow shows surprisingly complicated angular dynamics; caused by effects of fluid inertia (characterized by the particle Reynolds number Rep) and particle inertia (characterized by the Stokes number St). Understanding this behavior can provide important fundamental knowledge of suspension flows with spheroidal particles. Up to now only qualitative analysis has been available at moderate Rep. Rigorous analytical methods apply only to very small Rep and numerical results lack accuracy due to the difficulty in treating the moving boundary of the particle. Here we show that the dynamics of the rotational motion of a prolate spheroidal particle in a linear shear flow can be quantitatively analyzed through the eigenvalues of the log-rolling particle (particle aligned with vorticity). This analysis provides an accurate description of stable rotational states in terms of Rep,St, and particle aspect ratio (rp). Furthermore we find that the effect on the orientational dynamics from fluid inertia can be modeled with a Duffing-Van der Pol oscillator. This opens up the possibility of developing a reduced-order model that takes into account effects from both fluid and particle inertia.

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Phys. Rev. Fluids 1, 044201– Published 1 August, 2016
  • Received 16 February 2016

©2016 American Physical Society

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