This purpose is about a computational fluid dynamics investigation of a step varying in annular space effect on Taylor vortices flow and velocity in cylindrical Taylor-Couette system. Three cases are considered, the first geometric configuration GCi where the change in radius of the outer cylinder, and the half endplate is replaced by fluid close to the inner cylinder. The second geometrical configuration GCo with a step change in radius of inner cylinder and the half end-plate is replaced by a fluid close to outer cylinder. The last case CGb, the system has a change in both cylinders. The bottom endplate is attached to the outer cylinder, which are held fixed, the inner one is rotating, and a cylinder radius ratio of η = 0.66. Hence, the Taylor vortices flow development in geometrical configuration GCo for different Reynolds number values and Axial profile of dimensionless tangential velocity component midway across the gap for Τa = = 59.42, a numerical method based on the finite volume method is employed in simulations.

The Taylor Couette problem, which is the fluid motion in an annulus between two concentric rotating bodies, is a convenient flow system to study the laminar-turbulent transition and has a fundamental interest in the wavenumber selection processes. This paper presents a numerical study of conical Taylor-Couette flows when the inner cylinder is a regular straight cylinder, but the outer cylinder has a tilted, conical shape. The apex angle between the inner cylinder and the outer cone is varied between 0 and 12 degrees. The parameter that determines the flow regimes is the Taylor number based on the angular velocity of the inner cylinder. The calculations are carried out using a three-dimensional CFD of incompressible viscous flow. Computations for the onset of Taylor vortices in the classical configuration with straight cylinders show good agreement with experimental data. For the case of a conical outer cylinder, calculations show a decrease in the critical Taylor number for the onset of the first instability along with the number of rolls with the apex angle. The main result of this geometrical modification is that the gap width varies in height, and the Taylor vortices then vary in size, being large where the gap is wide, and small where the gap is narrow. Pressure distribution is also computed.