The flow past a freely rotating sphere

David Fabre (1) , Joël Tchoufag (2) , Vincenzo Citro (3) , Flavio Giannetti (3) , Paolo Luchini (3)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 UC Berkeley - University of California [Berkeley]
3 UNISA - Università degli Studi di Salerno = University of Salerno

We consider the flow past a sphere held at a fixed position in a uniform incoming flow but free to rotate around a transverse axis. A steady pitchfork bifurcation is reported to take place at a threshold \(Re^\mathrm{OS}=206\) leading to a state with zero torque but nonzero lift. Numerical simulations allow to characterize this state up to \(Re\approx 270\) and confirm that it substantially differs from the steady-state solution which exists in the wake of a fixed, non-rotating sphere beyond the threshold \(Re^\mathrm{SS}=212\). A weakly nonlinear analysis is carried out and is shown to successfully reproduce the results and to give substantial improvement over a previous analysis (Fabre et al. in J Fluid Mech 707:24–36, 2012). The connection between the present problem and that of a sphere in free fall following an oblique, steady (OS) path is also discussed.

Mots clés: Wakes; Flow instabilities, Fluid-structure interactions, Freely moving bodies

Domaines: Mécanique des fluides [physics.class-ph]

David Fabre, Joël Tchoufag, Vincenzo Citro, Flavio Giannetti, Paolo Luchini. The flow past a freely rotating sphere. Theoretical and Computational Fluid Dynamics, 2017, 31, pp.475-482. ⟨10.1007/s00162-016-0405-x⟩. ⟨hal-03240776⟩