Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T01:50:29.205Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barcilon, A. & Brindley J. 1984 Organized structures in turbulent Taylor–Couette flow. J. Fluid Mech 143, 429.Google Scholar
Barcilon A., Brindley J., Lessen, M. & Mobbs F. R. 1979 Marginal instability in Taylor–Couette flows at a very high Taylor number. J. Fluid Mech. 94, 453.Google Scholar
Benjamin, T. B. & Mullin T. 1982 Notes on the multiplicity of flows in the Taylor experiment. J. Fluid Mech. 121, 219.Google Scholar
Cliffe, K. A. & Mullin T. 1985 A numerical and experimental study of anomalous modes in the Taylor experiment. J. Fluid Mech. 153, 243.Google Scholar
Coughlin, K. & Marcus P. 1992a Modulated waves in Taylor–Couette flow. Part 1. Analysis. J. Fluid Mech. 234, 1.Google Scholar
Coughlin, K. & Marcus P. 1992b Modulated waves in Taylor–Couette flow. Part 2. Numerical simulation. J. Fluid Mech. 234, 19.Google Scholar
Fasel, H. & Booz O. 1984 Numerical investigation of supercritical Taylor-vortex flow for a wide gap. J. Fluid Mech. 138, 21.Google Scholar
Fenstermacher P. R., Swinney, H. L. & Gollub J. P. 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94, 103.Google Scholar
Floryan, J. M. & Saric W. S. 1984 Wavelength selection and growth of Görtler vortices. AIAA J. 22, 1529.Google Scholar
Görtler H. 1954 On the three-dimensional instability of laminar boundary layers on concave walls. NACA TM 1375.Google Scholar
Hall P. 1982 Taylor–Görtler vortices in fully developed or boundary-layer flows: linear theory. J. Fluid Mech. 124, 475.Google Scholar
Hall P. 1983 The linear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 130, 41.Google Scholar
Ioos G. 1986 Secondary bifurcations of Taylor vortices into wavy inflow or outflow boundaries. J. Fluid Mech. 173, 273.Google Scholar
Jones C. A. 1981 Nonlinear Taylor vortices and their stability. J. Fluid Mech. 102, 249.Google Scholar
Lee S. H.-K. 1990 The effect of drag reducing polymer additives on Taylor–Couette flows. M.S. thesis, dept. of M & AE, Rutgers University.
Smith, G. P. & Townsend A. A. 1982 Turbulent Couette flow between concentric cylinders at large Taylor number. J. Fluid Mech. 123, 187.Google Scholar
Sparrow E. M., Munro, W. D. & Jonsson V. K. 1964 Instability of the flow between rotating cylinders: the wide gap problem. J. Fluid Mech. 20, 35.Google Scholar
Swearingen, J. D. & Blackwelder R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255.Google Scholar
Taylor G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders Phil. Trans. R. Soc. Lond. A 223, 289.Google Scholar
Townsend A. A. 1984 Axisymmetric Couette flow at large Taylor numbers. J. Fluid Mech. 144, 329.Google Scholar
Vastano, J. & Moser R. 1991 Short-time Lyapunov exponent analysis and the transition to chaos in Taylor–Couette flow. J. Fluid Mech. 233, 83.Google Scholar
Walowit J., Tsao, S. & DiPrima R. C. 1964 Stability of flow between arbitrarily spaced concentric cylindrical surfaces including the effect of a radial temperature gradient. Trans. ASME E: J. Appl. Mech. 31, 585.Google Scholar