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Görtler vortex formation at the inner cylinder in Taylor–Couette flow

Published online by Cambridge University Press:  26 April 2006

T. Wei ,
E. M. Kline ,
S. H.-K. Lee  and
S. Woodruff
T. Wei
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08855-0909, USA
E. M. Kline
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08855-0909, USA
S. H.-K. Lee
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08855-0909, USA
S. Woodruff
Affiliation:
Engineering Division, Brown University, Providence, RI 02912, USA
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Abstract

The evolution of small counter-rotating circumferential vortices in Taylor–Couette flow was examined using the laser induced fluorescence and alumina particle flow visualization techniques. The objective of the study was to critically evaluate the hypothesis of Barcilon et al. (1979) and Barcilon & Brindley (1984) that Görtler vortices form close to the cylinder walls at moderately high Taylor numbers. Three radius ratios spanning an order of magnitude, 0.084 [les ] Rn/Rt [les ] 0.877, were examined over a Taylor number range of 3 × 104 [les ] Ta [les ] 3 × 108. Still-photograph sequences taken from video records of the LIF experiments are presented showing vortex pairs close to the inner cylinder wall at Taylor numbers an order of magnitude smaller than those reported by Barcilon and co-workers. Measurements of the core-to-core separation between counter-rotating vortices were made in order to estimate the wavenumber of the instability. These measurements agree remarkably well with the theoretical analysis of Barcilon and co-workers particularly for the small- and medium-gap experiments. The present measurements indicate that there is a $-\frac{1}{3}$ power law relationship between the Görtler wavelength and Taylor number. This is consistent with the work of Barcilon & Brindley (1984). However, the present study indicates that the Görtler vortices first form at the inner cylinder wall, and that a full theoretical treatment must include inner-wall effects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 47 - 68
Copyright
© 1992 Cambridge University Press

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