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Spiral Vortices and Taylor Vortices in the Annulus between Rotating Cylinders and the Effect of an Axial Flow

Ch. Hoffmann·M. Lücke·A. Pinter
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Abstract

We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter-rotating as well as with co-rotating cylinders. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method for a fixed axial periodicity length of the vortex patterns and for a finite system of aspect ratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5. Differences in structure, dynamics, symmetry properties, bifurcation and stability behavior between spiral vortices with azimuthal wave numbers M=+-1 and M=0 Taylor vortices are elucidated and compared in quantitative detail. Simulations in axially periodic systems and in finite systems with stationary rigid ends are compared with experimental spiral data. In a second part of the paper we determine how the above listed properties of the M=-1,0,1 vortex structures are changed by an externally imposed axial through-flow with Reynolds numbers in the range -40 <= Re <= 40. Among others we investigate when left handed or right handed spirals or toroidally closed vortices are preferred.

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Ch. Hoffmann, M. Lücke, A. Pinter. 2005-05-24. Spiral Vortices and Taylor Vortices in the Annulus between Rotating Cylinders and the Effect of an Axial Flow. https://doi.org/10.1103/physreve.69.056309

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