Mixing enhancement by dual speed rotating stirrer

Stirring is a well-known means of fluid mixing due to the emergence of complex patterns in the flow, even at low Reynolds numbers. In this work, we consider a stirrer rotating along a circular trajectory at constant speed. The fluid flow, considered incompressible, inviscid and two dimensional (in a circular container), is modeled by a point vortex model consisting of a vortex rotating in a circular container at constant angular speed. The mixing problem is addressed by considering the Hamiltonian form of the advection equations formulated in a frame of reference moving with the vortex. The dynamics of passive fluid particles is considered using dynamical systems theory. The bifurcation diagram reveals the presence of degenerate fixed points and homoclinic/heteroclinic orbits, whose nature varies for different parameter values. By considering an initially concentrated set of marker particles and using the various structures of the phase space in the bifurcation diagram, we produce a complex dynamics which, in turn, can generate efficient mixing. The latter is studied using both numerical simulations and physical experiments. A perturbation study for one particular structure for the phase space shows the presence of a transverse homoclinic orbit as well as resonances, or a set of closed trajectories

Control of chaotic advection

A method of chaos reduction for Hamiltonian systems is applied to control chaotic advection. By adding a small and simple term to the stream function of the system, the construction of invariant tori has a stabilization effect in the sense that these tori act as barriers to diffusion in phase space and the controlled Hamiltonian system exhibits a more regular behaviour

A Coaxial Vortex Ring Model for Vortex Breakdown

A simple - yet plausible - model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the rings. It is shown that this model exhibits in the advection of passive fluid particles (kinematics) just about all of the characteristics that have been observed in what is now a substantial body of published research on the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very nature of the fluid dynamics in axisymmetric breakdown flows can be predicted and controlled by the choice of the initial ring configurations and their vortex strengths. The dynamic intricacies produced by the two ring + swirl model are illustrated with several numerical experiments.Comment: 40 pages, 9 figures, submitted to Physica

Les Enjeux de la sécurité d'utilisation des dispositifs médicaux réutilisables ou à usage multiple en orthopédie et traumatologie

LYON1-BU Santé (693882101) / SudocSudocFranceF

TWO-VORTEX MODELS FOR VORTEX BREAKDOWN

ABSTRACT A simple Hamiltonian dynamical systems model for vortex breakdown of the bubble-type (B-type) is developed and analyzed. This model is constructed using the flow induced by two point vortices moving in a half-plane immersed in an ideal INTRODUCTION The first recorded study of vortex breakdown phenomena appears to be that in the experimental paper of Peckham & Atkinson [1]. This was followed by the more focused investigations of Elle The early work on vortex breakdown quickly captured the attention of several talented fluid mechanicians, and numerous investigations were initiated to explain the phenomenon. With this intense level of scrutiny, it was soon realized that there were at least two types of vortex breakdown regimes: an axisymmetric bubble type (B-type) configuration; and a definitely asymmetric spiral type (S-type) structure often observed at the trailing edg