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
λ
=
1
/
6
) to prolate
(
λ
=
6
)
, and we consider low and moderate particle Reynolds numbers
(
Re
≤
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
Re
∼
10
. The amplitude of the torque, however, is smaller than the theoretical prediction, the more so as
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.
λ
=
1
/
6
) to prolate
(
λ
=
6
)
, and we consider low and moderate particle Reynolds numbers
(
Re
≤
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
Re
∼
10
. The amplitude of the torque, however, is smaller than the theoretical prediction, the more so as
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.