The Self-Induction Theory of Vortex Breakdown
WASHINGTON UNIV SEATTLE DEPT OF AERONAUTICS AND ASTRONAUTICS
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A new study of the transient stages leading to the formation of vortex breakdown shows that vortex breakdown is initiated by a negative vorticity gradient that causes an inviscid self-induction feedback mechanism resulting in steady state vortex breakdown. We call this the self-induction theory of vortex breakdown. The vortex filament method captures the evolution of this transient formation of vortex breakdown. An axial vorticity gradient is introduced into the vortex tube by changing the circulation along the tube. Thereafter, the self-induction process starts on its own as the axial vorticity induces azimuthal velocity, which in turn tilts the vorticity vector in the azimuthal direction. Due to the gradient in azimuthal vorticity caused by the increase in circulation, the vortex tube radially expands and the vortex filaments contract in an action we call pile-up. This is followed by a sign switch in the azimuthal vorticity caused by the region downstream of the vorticity gradient rotating slower than the upstream region. These actions proceed together until they form what we call the turning point where the vortex filaments turn inward on themselves causing a sign switch in the axial vorticity. Vorticity and velocity data produced from this simulation compare well to experimental data. In conjunction with the computer simulation, we have verified these results experimentally with a delta wing model in a water tunnel using dye flow visualization, laser-induced fluorescence, and particle image velocimetry. These results, combined with comparisons with previous experiments agree with one another and support the self-induction theory of vortex breakdown.
- Fluid Mechanics