Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T09:51:41.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical experiments on time-dependent rotational Couette flow

Published online by Cambridge University Press:  29 March 2006

D. C. S. Liu  and
C. F. Chen
D. C. S. Liu
Affiliation:
TRW Systems Group, Redondo Beach, California
C. F. Chen
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, N.J.
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow induced by impulsively starting the inner cylinder in a Couette flow apparatus is investigated by using a nonlinear analysis. Explicit finite-difference approximations are used to solve the Navier–Stokes equations for axisymmetric flows. Random small perturbations are distributed initially and periodic boundary conditions are applied in the axial direction over a length which, in general, is chosen to be the critical wavelength observed experimentally. Simultaneous occurrence of Taylor vortices is obtained at supercritical Reynolds numbers. The development of streamlines, perturbation velocity components and the kinetic energy of the perturbations is examined in detail. Many salient features of the physical flow are observed in the numerical experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 1 , 5 June 1973 , pp. 77 - 95
Copyright
© 1973 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

Chen, C. F. & Kirchner, R. P. 1971 Stability of time-dependent rotational Couette flow. Part 2. Stability analysis J. Fluid Mech. 48, 365–384.Google Scholar
Donnelly, R. J. & Simon, N. J. 1960 An empirical torque relation for supercritical flow between rotating cylinders J. Fluid Mech. 7, 401–418.Google Scholar
Kirchner, R. P. & Chen, C. F. 1970 Stability of time-dependent rotational Couette flow. Part 1. Experimental investigation J. Fluid Mech. 40, 39–47.Google Scholar
Liu, D. C. S. 1971 Physical and numerical experiments of time-dependent rotational Couette flow. Ph.D. thesis. Dept. of Mechanics and Materials Science, Rutgers University.
Meyer, K. A. 1967 Time-dependent numerical study of Taylor vortex flow Phys. Fluids, 10, 1874–1879.Google Scholar
Meyer, K. A. 1969 Three-dimensional study of flow between concentric rotating cylinders Phys. Fluids, 12, II-165–II-170.Google Scholar
Richtmyer, R. D. & Morton, K. W. 1967 Difference Methods for Initial Value Problems, 2nd edn. Interscience.
Strawbridge, D. R. & Hooper, G. T. J. 1968 Numerical solutions of the Navier—Stokes equations for axisymmetric flows J. Mech. Engng Sci. 10, 389–401.Google Scholar
Todd, J. 1962 Survey of Numerical Analysis. McGraw-Hill.
Torrance, K. E. 1968 Comparison of finite difference computations of natural convection. J. Res. Nat. Bur. Stand. B 72, 281–301.Google Scholar