Theoretical Approach of the Mean Hydrodynamic Field in the Conical Taylor-Couette Flow

Abstract

The flow between rotating cones have been investigated experimentally and numerically by several authors. There are a few analytical studies concerning the so called flow system. The flow is defined by an incompressible viscous fluid characterized by constant physical properties (density and kinematic viscosity) between two coaxial cones. The cones have the same apex angle, giving a constant radial gap. The inner cone rotates with an angular velocity Ω and the outer one is maintained at rest. Furthermore, the basic flow between rotating coaxial cones is fully three-dimensional resulting from the balance between centrifugal and viscous forces. The present work focuses in analytical and numerical approach to establish the mean velocity profiles characterizing the basic flow. For that purpose, a particular curvilinear coordinate system is used to establish the governing equation corresponding to the conical Taylor-Couette flow system. The obtained results indicate that the flow is dominated mainly by the tangential velocity component.

Occurrence of Taylor-Dean Instability in Flow Between Horizontal Coaxial Rotating Cones

“…Both cones have the same apex angle Ф = 12° giving a constant annular gap δ = d/R 1max where d = (9.68± 0.2) mm. The inner cone can rotate and the outer cone is maintained at rest [15].…”