Vortex Element Analysis of Selected Time-Dependent Flows

摘要

Previous investigations of oscillating (harmonic) flow past circular cylindersvia the discrete vortex method have met with limited success due to a variety of reasons. These assumptions have proven to be too severe, and cannot allow the prediction of the kinematics and dynamics of the oscillating flow about bluff bodies in general and about a circular cylinder in particular. In the current analysis, the ambient velocity was given by U = Um sin wt, and the velocity distribution and the boundary layer were calculated about the cylinder at suitable time intervals. Several methods were implemented to predict separation, all of which required a minimum of arbitrary assumptions. Nascent vortices were placed at the separation points in such a manner that the Kutta condition was satisfied. Several functional forms of dissipation were investigated, but it was found not to be of overriding influence in the flow kinematics. Counter vortices were found to be a necessary aspect of the analysis, providing continuity from one half cycle to the next. Flow visualization experiments were conducted for a Keulegan-Carpenter number of 10 as a basis for comparison. The kinematics obtained from the numerical model produced a vortex shedding pattern which was typical of those observed experimentally for higher Keulegan-Carpenter numbers. Significant problems were encountered in the prediction of boundary layer separation. At this point, it was obvious that the interaction of a vortex with a boundary layer warranted analysis in a much simpler flow situation; the blade-vortex interaction (BVI) problem proved to be ideal. A boundary layer code which predicted separation on an infinite flat plate under the influence of a line vortex was adapted to the BVI problem, so that it could be used with a semi-infinite plate in a flow field comprised of a free stream and numerous discrete vortices.