Numerical investigation of the effect of different working fluids on the pattern formation in a narrow rotating annulus

Abstract

Fluid evolving in an annular gap between two coaxial cylinders, well known as Taylor–Couette flow, is one of the fundamental problems in fluid mechanics for the study of instabilities and the transition to turbulence. This flow system is typically a closed environment, where the working fluid is confined axially by end-plates and radially between the cylinders. In this work, we investigate, via CFD simulation, the influence of the working fluids confined inside an infinite aspect ratio Taylor–Couette system on the onset of cellular pattern. The inner cylinder rotates freely about a vertical axis through its centre, while the outer one, the upper and bottom end-caps are held at rest. The basic system is characterized by a height H = 150 mm, an annular gap d = 5 mm, a ratio of the inner to the outer cylinders radii η = 0.909, an aspect ratio corresponding to the cylinders height reported to the gap length Γ = 30 and a ratio of the gap to the radius of the inner cylinder δ = 0.1. The flow behaviour and the time-independent formation of axisymmetric vortices are investigated under steady-state condition. The main goal of this work is to show how the change in cellular pattern operates when changing the working fluid by simulating and comparing four different liquids, namely hydrogen, helium, lithium and water. Particular attention is given to the onset of Taylor vortices in the vicinity of the threshold of transition, i.e. from the laminar Couette flow to the occurrence of Taylor vortex flow. In addition, the flow patterns are presented in terms of distributions of wall shear stress, skin friction coefficient, streamlines and velocity components. The computed results show that the critical Taylor number for the different liquids is the same, Tac1 = 42.4. Interestingly, lithium and hydrogen exhibit quite different behaviours than other liquids. The shape and wavelength of Ekman cells and the Taylor vortices for lithium and hydrogen show significant changes compared to water and helium.