Hostname: page-component-7bb8b95d7b-qxsvm Total loading time: 0 Render date: 2024-09-16T07:11:33.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Upper bounds on the torque in cylindrical Couette flow

Published online by Cambridge University Press:  29 March 2006

E. C. Nickerson
E. C. Nickerson
Affiliation:
Engineering Research Center, Colorado State University
Get access Rights & Permissions [Opens in a new window]

Abstract

Upper bounds on the torque are derived for a fluid that is contained between two concentric rotating cylinders. Absolute upper bounds are obtained by requiring that the fluid satisfy the boundary conditions and the dissipation integral. Improved bounds are then found by requiring that the fluid satisfy continuity conditions. These bounds are in qualitative agreement with the data in that they reflect the asymptotic parameter dependence in the range of experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 4 , 6 October 1969 , pp. 807 - 815
Copyright
© 1969 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

Badri Narayanan, M. A. & Ramjee, V. 1968 On the criteria of reverse transition in a two-dimensional boundary layer flow. India Inst. of Sci. Rep. AE 68 FM 1.Google Scholar
Coles, D. 1962 Turbulent boundary layer in a compressible fluid. RAND. Rep. 403—PR.Google Scholar
Escudier, M. P. 1964 The distribution of mixing length in turbulent flows near walls. Imperial College, Mech. Eng. Dept. Rep. TWF/TN/1.Google Scholar
Hamel, G. 1917 Spiralformige Bewegungen zäher Flüssigkeiten Jber. dtsch. MatVer. 25, 34.Google Scholar
Herring, H. J. & Norbury, N. F. 1967 Some experiments on equilibrium turbulent boundary layers in favourable pressure gradient J. Fluid Mech. 27, 541.Google Scholar
Jeffrey, G. B. 1915 The two-dimensional steady motion of a viscous fluid. Phil. Mag. (6), 29, 455.Google Scholar
Jones, W. P. 1967 Strongly accelerated turbulent boundary layers. M.Sc. Thesis, Imperial College.
Launder, B. E. 1964a Laminarisation of the turbulent boundary layer in a severe acceleration J. App. Mech. 31, 707.Google Scholar
Launder, B. E. 1964b Laminarisation of the turbulent boundary layer by acceleration. M.I.T. Gas Turbines Lab. Rep. no. 77.Google Scholar
Launder, B. E. & Stinchcombe, H. S. 1967 Non-normal similar boundary layers. Imperial College, Mech. Eng. Dept. Rep. TWF/TN/21.Google Scholar
Mellor, G. I. & Gibson, D. M. 1963 Equilibrium turbulent boundary layers. Princeton University, Mech. Eng. Dept. Rep. FLD 14.Google Scholar
Millsaps, K. & Pohlhausen, K. 1953 Thermal distribution in Jeffrey–-Hamel flows between non-parallel plane walls J. Aero. Sci. 20, 187.Google Scholar
Moretti, P. M. & Kays, W. M. 1965 Heat transfer through an incompressible turbulent boundary layer with varying free-stream velocity and varying surface temperature. Stanford University, Thermo. Sci. Div. Rep. PG-1.
Patel, V. C. 1965 Calibration of the Preston tube and limitations on its use in pressure gradients J. Fluid Mech. 23, 185.Google Scholar
Patel, V. C. & Head, M. R. 1968 Reversion of turbulent to laminar flow. Aero. Res. Counc. 29 859–-F.M. 3929.Google Scholar
Patankar, S. V. 1967 Heat and mass transfer in turbulent boundary layers. Ph.D. Thesis, University of London.
Patankar, S. V. & Spalding, D. B. 1967 Heat and Mass Transfer in Boundary Layers. Morgan-Grampian.
Pohlhausen, K. 1921 Zur näherungsweisen Integration der Differentialgleichung der laminaren Grenzschicht Z. angew. Math. Mech. 1, 252.Google Scholar
Rosenhead, L. 1940 The steady two-dimensional radial flow of viscous fluid between two inclined plane walls. Proc. Roy. Soc. A 175, 436.Google Scholar
Schraub, F. A. & Kline, S. J. 1965 A study of the structure of the turbulent boundary layer with and without longitudinal pressure gradients. Stanford University, Thermo. Sci. Div. Rep. MD–-12.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Van Driest, E. R. 1956 On turbulent flow near a wall J. Aero. Sci. 23, 1007.Google Scholar