Confined vortex breakdown generated by a rotating cone

Abstract

Confined vortex breakdown generated by a rotating cone within a closed cylindrical container has been studied both by numerical simulation and by experimental techniques. A comprehensive investigation of the various flow regimes has been carried out by flow visualization. From laser–Doppler measurements of the entire flow field (three velocity components) detailed maps of the time-averaged flow structures for single and double breakdown have been constructed. Three-dimensional time-dependent simulations of steady and unsteady breakdown have been performed. Steady numerical and experimental flow fields obtained at Reynolds number 2200 for a gap ratio of 2 show notable agreement. At critical Reynolds numbers of approximately 3095, for a gap ratio of 2, and 2435, for a gap ratio of 3, the flow was observed becoming unsteady. The periodic behaviour exhibited by the unsteady flow suggested the occurrence of a supercritical Hopf bifurcation. This conjecture was confirmed by the evolution of the oscillation amplitude as a function of criticality, measured for a gap ratio of 3. The dynamical behaviour of unsteady vortex breakdown structures is depicted by numerical simulation of two distinct oscillatory regimes, at Reynolds numbers 2700 and 3100. A thorough analysis of the numerical results has shown that whereas the former regime is characterized by the steady oscillation of closely axisymmetric breakdowns, the latter displays precession of breakdown structures about the central axis. Additionally, it was observed that the mode bringing about the Hopf bifurcation is non-axisymmetric, with azimuthal periodicity of π/2 radians. From examination of measured velocity power spectra at higher Reynolds numbers, a transition scenario was also educed. In the present case, the Ruelle–Takens–Newhouse theorem has been shown to apply.