The stability of a slightly eccentric straight vortex filament in a circular tube
Abstract
The threedimensional stability of a straight vortex that runs down a circular tube, parallel with its axis but slightly displaced from it, was investigated experimentally. The vortex flow was modelled by an infinitely long concentrated potential vortex filament. The interaction of the vortex flow field with the tube walls, because of its small initial eccentricity, makes the vortex autorotate about the axis of the tube at a constant angular velocity. The walls of the tube are modelled by a surface distribution of potential sources. Small threedimensional waves are imposed on the vortex filament, concurrently with fluctuations in the intensity of the surface distribution of the sources over the tube walls. A prescribed unsteady longitudinal perturbation to the radius of the tube is also considered. A linearization of the flowfield equations results in a system of firstorder linear differential equations for the time history of the vortex perturbations. The development of the perturbations is shown to be analogous to the motion of a mass on a springdamper combination. The 'generalized damping' of the offcenter vortextube system governs the dynamic stability of the vortex, whereas its 'rigidity' governs its static stability. It is shown that the vortex develops a dynamic instability in a narrow range of wave numbers, as a direct result of its small eccentricity. Unexplained oscillations, which were previously observed in vortex flows in tubes, can be attributed to this dynamic instability of the vortex.
 Publication:

Israel Society of Aeronautics and Astronautics, 31st Israel Annual Conference on Aviation and Astronautics
 Pub Date:
 February 1990
 Bibcode:
 1990isaa.conf..197R
 Keywords:

 Autorotation;
 Eccentricity;
 Flow Stability;
 Tubes;
 Vortex Breakdown;
 Vortex Filaments;
 Vortices;
 Damping;
 Flow Distribution;
 Mathematical Models;
 Perturbation;
 Waves;
 Fluid Mechanics and Heat Transfer