Introduction

The Taylor vortex flow between two concentric rotating cylinders with finite lengths appears in journal bearings, a variety of fluid machinery and chemical reactors. When the flow pattern changes, unsteady variations of property values such as torque and rate of reaction arise. Therefore, the analysis and prediction of unsteady flow is important from an engineering viewpoint. In the present work, it is assumed that the inner cylinder is rotating and the outer cylinder and the end walls of the cylinders are stationary.

The main parameters which determine the mode of the Taylor vortex flow are the Reynolds number Re and the aspect ratio ${\sl\Gamma }$. When ${\sl\Gamma }$ and Re are varied, experimental evidence has shown that the Taylor vortex flow has a variety of modes (Toya et al., 1994)(Werely and Lueptow, 1998).

The Taylor vortex flow has a normal mode and an anomalous mode. When the end walls of the cylinders are fixed, the normal mode has normal cells which give an inward flow in the region adjacent to the end wall. The anomalous mode has anomalous cell on either or both end walls. The anomalous cell gives an outward flow near the end wall, which is opposite to the flow direction in the normal mode.

While the Taylor vortex flow with an infinite or moderate aspect ratio has provoked a great deal of controversy, some studies on the Taylor vortex flow with aspect ratio of about unity have been made. Benjamin and Mullin (1981) experimentally confirmed the existence of the anomalous one-cell mode. They also presented the critical loci where the steady flows become the normal two-cell mode or anomalous one-cell mode in the $(Re, {\sl \Gamma})$ plane. Cliffe (1983) used numerical bifurcation techniques with a finite-element discretization of the steady Navier-Stokes equations, to determine the bifurcation for the one and two cell interaction. Pfister et al. (1988) used unsteady equations and revealed the transition from the asymmetric one-cell mode to the symmetric two-cell mode of flows with gradually decreasing Reynolds number. Nakamura and Toya (1996) investigated these phenomena experimentally and confirmed that the anomalous one-cell mode has extra cells and that twin vortices which develop from extra vortices exist. Despite these experimental results, however, few attempts have been made at numerical investigations of the mode exchanges of the Taylor vortex flow under unsteady conditions.

In this study, the existence of experimentally observed modes, including the twin-cell mode, is numerically confirmed, and the unsteady transformation during the gradual reduction of Re is examined.

  

Figure 1: Numerically calculated mode pattern. Re is increased suddenly from rest.