Study of vortex breakdown by particle tracking velocimetry (PTV) Part 3: Time-dependent structure and development of breakdown-modes

Abstract

This third part of the study deals with the time-dependent nature of vortex breakdown. The results show the unsteady velocity and vorticity field of the initiation and development of breakdown and transition between both predominant breakdown modes, the bubble and the spiral. During the development to breakdown, the generated amount of circumferential vorticity follows the theoretical prediction by Brown and Lopez (1990). This confirms the idea of positive feedback as the key-mechanism leading to vortex breakdown. We regard the bubble-type as the fundamental breakdown type, that is stationary and nearly axisymmetric. The circumferential vorticity is distributed in a form of an elliptical vortex-ring-like structure. Starting from this stage, an increase of volume flux to a higher Reynolds number leads to the transition to the spiral-type with an initial stretching of the vortex ring-like structure and a subsequent change to an asymmetric circumferential vorticity distribution. This in combination with the inductive effect causes the front stagnation point to be deflected radially away and later to rotate around the centerline. Consequently the approaching vortex core is radially deflected in opposite direction and evolves in a spiral path. The idea of a second positive feedback-mechanism gives a possible explanation for the transition. Following this theory the asymmetry of circumferential vorticity will trigger itself at a certain degree by the interaction with the inductively affected stagnation point and its influence on the approaching vortex core. This self-enhancing process will finally lead to the spiral-type breakdown in which the radial distance between rotating stagnation point and deflected vortex core is of the order of the characteristic vortex core radius. The reversed transition from the spiral to a stable bubble-type can be regenerated by decreasing the Reynolds number down to the value that corresponds to the stable bubble state. The flow structure evolves nearly in the time-reversed way as during transition from bubble towards the spiral.