Novosibirsk, Russia, May, 30 – June, 4, 2011

"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

## Moshkin N.P. Suwannasri P.## Numerical simulation of self-propelled motion of a torus rotating about its centerline in a viscous incompressible fluid## Reporter: Moshkin N.P.In the present work, the problem of the motion of self-propelled torus in a viscous incompressible fluid is investigated numerically. The surface of torus rotates with constant velocity around its centerline. The rotating boundary of a torus generates inertia in the surrounding fluid. The outer and inner portions produce inertia in opposite directions. There are two self-motion regimes. In one of them, the torus moves in the direction of the inner surface motion due to the larger production of inertia by the outer portion of the torus boundary. The direction of propulsion is the same as in the case of zero Reynolds number. In another one the torus moves in opposite direction due to the high momentum flux associated with the jet of fluid expelled from the hole. The drag coefficients and flow patterns are analyzed at Reynolds numbers Re =20, 30, 40 , (Reynolds number defined by velocity of uniform stream and smaller diameter of torus), the aspect ratios Ar=2, 3 , (aspect ratio is defined as ratio of torus diameter to cross-section diameter of torus), and a range of rotational rate -4.5< alpha < 2.5 (alpha is defined as ratio of tangential tank-treading motion of torus surface to the uniform far-field velocity).
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