Transition to Taylor vortex flow between combinations of circular and conical cylinders

The stability and flow transitions in the annular gap between two coaxial rotating bodies, termed Taylor-Couette flow, presents a great importance in the field of fluid dynamics. In this paper, the fluid motion in an annulus between cylinder-cone combinations is investigated numerically using CFD simulations for a three dimensional viscous and incompressible flow. The transitional phenomena occurring in this flow are discussed under the effect of opening angles of the outer cylinder. The main goal it is to show how operates the change in the structure of the movement when changing the geometry of the flow through angular deviation, i.e., from coaxial rotating cylinders to an inner cylinder rotating in a conical container. Particular attention is given to the transitional regime and the onset of Taylor vortices when the outer cylinder is replaced with a cone. The numerical calculations are carried out over a range of apex angle α from 0 (classical case) up to 12°. The critical Taylor number, Tac1, characterizing the occurrence of Taylor vortices in the flow, decreases drastically: the first instability mode of transition changes from Tac1 = 41.6, corresponding to the classical case to Tac1 = 20.3 when the apex angle reaches 12°. The velocity distribution and the wavelengths are also presented. It is established that the number of vortices occurring in the gap between rotating cylinder in a cone is inversely proportional to the apex angles