The music of oil rigs

If a cylinder is placed across a flow stream, it will release (“shed”) a periodic sequence of vortices, at a frequency which depends on its diameter, the flow velocity and the fluid properties. This periodic phenomenon may lead to vibrations of the cylinder (“flow-induced vibrations”), which could have detrimental effects.

a) Perform a dimensional analysis of this problem and determine the relevant dimensionless groups.

b) To test possible vibrations of the underwater cylindrical pylons of an off-shore oil rig, due to oceanic streams, a small-scale, geometrically similar model, scaled 5:1 is tested in a wind tunnel. If the diameter of the pylons is 0.5 m and the water current maximum velocity is 1 m/s, determine the wind tunnel speed that is required in order to achieve dynamic similarity.

c) If the measured frequency of vortices in the wind tunnel tests is 150 Hz, determine the frequency of vortices shed by the pylons.

Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada. Image from Oil Rig