Inertial torque on a small spheroid in a stationary uniform flow

Abstract

How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. Here we compute the torque acting on a small spheroid in a uniform flow by numerically solving the Navier-Stokes equations. Particle shape is varied from oblate (aspect ratio $\lambda =1/6$) to prolate ($\lambda =6$), and we consider low and moderate particle Reynolds numbers ($\mathrm{Re}\le 50$). We demonstrate that the angular dependence of the torque, predicted theoretically for small particle Reynolds numbers remains qualitatively correct for Reynolds numbers up to $\mathrm{Re}\sim 10$. The amplitude of the torque, however, is smaller than the theoretical prediction, the more so as $\mathrm{Re}$ increases. For Re larger than $10$, the flow past oblate spheroids acquires a more complicated structure, resulting in systematic deviations from the theoretical predictions. Overall, our numerical results provide a justification of recent theories for the orientation statistics of ice-crystals settling in a turbulent flow.

arXiv comment11 pages, 4 figures

References in corpus (8)

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• Theory for the effect of fluid inertia on the orientation of a small particle settling in turbulence
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Cited by in corpus (6)

• Effect of particle inertia on the alignment of small ice crystals in turbulent clouds
• Inertia induces strong orientation fluctuations of non-spherical atmospheric particles
• Experimental validation of fluid inertia models for a cylinder settling in a quiescent flow
• The rotation of a sedimenting anisotropic particle in a linearly stratified ambient
• Torques on curved atmospheric fibres
• Inertial torque on a squirmer