Dynamics of Bilaterally Symmetric Vortex Rings

摘要

The purpose of the investigation is to predict the dynamics of vortex rings of bilaterally symmetric shape. Such rings are of interest in the study of velocity and temperature irregularities in jets and wakes as well as in combustion chambers, and in air pollution and airport turbulence problems. The induced velocity at each point on the vortex ring is found by the Biot-Savart Law with an averaging procedure to eliminate the infinite velocity discontinuity which arises due to the application of the law. Once the induced velocity has been found, it is related to the motion of the ring by two different methods: (1) hydrodynamic vortex-the ring moves with the same velocity as the local and (2) rankine vortex-the induced velocity gives rise to a relative velocity on the ring and thus results in lift and drag forces on the ring. The ring then distorts under the influence of these forces. Experiments are performed utilizing the starting vortex behind an airfoil and the vortex formed by impulsive flow through an orifice. The qualitative agreement between the theory and experiment is excellent. However quantitative comparison is not as yet possible because the core size of the vortex and the strength of the circulation are unknown. The main difference between the two methods of treating the vortex motion appears to be the time scale of the problem. However, the time scale also depends upon the choice of the numerical value of the circulation. (Author)