The influence of imperfections on the flow structure of steady vortex breakdown bubbles

Abstract

Vortex breakdown bubbles in the flow in a closed cylinder with a rotating end-cover have previously been successfully simulated by axisymmetric codes in the steady range. However, high-resolution experiments indicate a complicated open bubble structure incompatible with axisymmetry. Numerical studies with generic imperfections in the flow have revealed that the axisymmetric bubble is highly sensitive to imperfections, and that this may resolve the apparent paradox. However, little is known about the influence of specific, physical perturbations on the flow structure. We perform fully three-dimensional simulations of the flow with two independent perturbations: an inclination of the fixed cover and a displacement of the rotating cover. We show that perturbations below a realistic experimental uncertainty may give rise to flow structures resembling those obtained in experiments, that the two perturbations may interact and annihilate their effects, and that the fractal dimension associated with the emptying of the bubble can quantitatively be linked to the visual bubble structure.