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Hydrodynamic torque on a slender cylinder rotating perpendicularly to its symmetry axis

Pierson, Jean-Lou and Kharrouba, Mohammed and Magnaudet, Jacques Hydrodynamic torque on a slender cylinder rotating perpendicularly to its symmetry axis. (2021) Physical Review Fluids. ISSN 2469-990X

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Official URL: https://doi.org/10.1103/PhysRevFluids.6.094303

Abstract

Using fully-resolved simulations, we examine the torque experienced by a finite-length circular cylinder rotating steadily perpendicularly to its symmetry axis. The aspect ratio χ, i.e., the ratio of the length of the cylinder to its diameter, is varied from 1 to 15. In the creeping-flow regime, we employ the slender-body theory to derive the expression of the torque up to order 4 with respect to the small parameter 1/ ln(2χ). Numerical results agree well with the corresponding predictions for χ = 3. We introduce an ad hoc modification in the theoretical prediction to fit the numerical results obtained with shorter cylinders, and a second modification to account for the increase of the torque resulting from finite inertial effects. In strongly inertial regimes, a prominent wake pattern made of two pairs of counter-rotating vortices takes place. Nevertheless the flow remains stationary and exhibits two distinct symmetries, one of which implies that the contributions to the torque arising from the two cylinder ends are identical. We build separate empirical formulas for the contributions of pressure and viscous stress to the torque provided by the lateral surface and the cylinder ends.We show that, in each contribution, the dominant scaling law may be inferred from simple physical arguments. This approach eventually results in an empirical formula for the rotation-induced torque valid throughout the range of inertial regimes and aspect ratios considered in the simulations.

Item Type:Article
HAL Id:hal-03356843
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > IFP Energies Nouvelles - IFPEN (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Deposited On:28 Sep 2021 12:36

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