Early bifurcation in rotating fluid flow with free surface studied by axisymmetric numerical simulations

Abstract

Simulations of a fluid rotating inside a partially open cylindrical cavity, performed by numerical solution of the unsteady axisymmetric Navier-Stokes equations, are presented. The configuration consists of a cylindrical vessel holding the fluid, which is entrained into motion by a rotating lid. This one is a coaxial disk in contact with the fluid surface but without covering it entirely. The study focuses on the occurrence of time-dependent flow, more specifically, the first transition to unsteadiness, by considering cavity cases with different amounts of free surface, for a fixed aspect ratio. By following the time evolution of a few arbitrarily chosen dynamical variables as a function of the Reynolds number, the location of this first Hopf bifurcation is obtained for a collection of cavity cases. Results show a rather strong influence of the free surface both on the onset of the unsteadiness and on the dynamical features of the flow.

Shear viscosity and rheology of ternary and quaternary lyotropic liquid crystals in discotic and calamitic nematic phases

“…Firstly, assuming no-slip condition on all solid boundaries, it is reasonable to expect a secondary flow velocity field profile as sketched (for a discussion and computer simulations on the flow of rotating ordinary fluids, see for instance (Santos and Sørensen 1996) and references there in). Secondly, typically one expects that the primary flow (tangential velocity component) remains confined to a boundary layer region of thickness δ of the order of Landau and Lifshitz (1988), Slichting (1979), and Tritton (1987),…”