Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-19T13:44:29.829Z Has data issue: false hasContentIssue false
  • English
  • Français

Self-similar spin-up and spin-down in a cylinder of small ratio of height to diameter

Published online by Cambridge University Press:  26 April 2006

F. V. Dolzhanskii ,
V. A. Krymov  and
D. Yu. Manin
F. V. Dolzhanskii
Affiliation:
Institute of Atmospheric Physics, 3, Pyzhevsky, Moscow, 109017, USSR
V. A. Krymov
Affiliation:
Institute of Atmospheric Physics, 3, Pyzhevsky, Moscow, 109017, USSR
D. Yu. Manin
Affiliation:
Institute of Atmospheric Physics, 3, Pyzhevsky, Moscow, 109017, USSR
Get access Rights & Permissions [Opens in a new window]

Abstract

A new approach to the well-known spin-up from rest problem is proposed based on a search for self-similarity. The Wedemeyer (1963) model is first tested for spin-down to rest and then used for spin-up. The general-form solution is found and is shown to tend to a self-similar limiting stage. Experimental results in a cylinder of small height-to-diameter ratio are analysed to demonstrate this self-similarity in a certain range of external parameters.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 234 , January 1992 , pp. 473 - 486
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

Benton, E. R. 1973 Non-linear hydrodynamic and hydromagnetic spin-up driven by Ekman-Hartmann boundary layers. J. Fluid Mech. 57, 337–360.Google Scholar
Benton, E. R. 1979 Vorticity dynamics in spin-up from rest. Phys. Fluids 22, 1250–1251.Google Scholar
Dolzhanskii, F. V. 1985 Motion of a fluid between rotating cones. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza No. 2, 58.Google Scholar
Dolzhanskii, F. V. & Krymov, V. A. 1985 Spin-down of a fluid in a low cylinder. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza No. 1, 19.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Greenspan, H. P. & Howard, L. N. 1963 On a time-dependent motion of a rotating fluid. J. Fluid Mech. 17, 385–404.Google Scholar
Greenspan, H. P. & Weinbaum, S. 1963 On non-linear spin-up of a rotating fluid. J. Math. Phys. 44, 66–85.Google Scholar
Hyun, J. M., Leslie, F., Fowlis, W. W. & Warn-Varnas, A. 1983 Numerical solutions for spin-up from rest in a cylinder. J. Fluid Mech. 127, 263–281.Google Scholar
Kitchen, C. W. 1980 Navier—Stokes solutions for spin-up in a filled cylinder. AIAA J. 18, 929.Google Scholar
Krymov, V. A. & Manin, D. Yu. 1986a Spin-down of a fluid in a low cylinder at large Reynolds numbers. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza No. 3, 39–46 (referred to herein as K & Ma).Google Scholar
Krymov, V. A. & Manin, D. Yu. 1986b Spin-down of a fluid between infinite cones. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza No. 4, 37–4 (referred to herein as K & Mb).Google Scholar
Mathis, D. M. & Neitzel, G. P. 1985 Experiments on impulsive spin-down to rest. Phys. Fluids 28, 449–455.Google Scholar
Proudman, I. 1956 The almost-rigid rotation of viscous fluid between concentric spheres. J. Fluid Mech. 1, 505–516.Google Scholar
Rogers, M. H. & Lance, G. N. 1960 The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating fluid. J. Fluid Mech. 7, 617.Google Scholar
Sava¸, Ö. 1985 On flow visualization using reflective flakes. J. Fluid Mech. 152, 235–248.Google Scholar
Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3, 17–26.Google Scholar
Venezian, G. 1969 Spin-up of a contained fluid. Topics in Ocean Engng 1, 212.Google Scholar
Venezian, G. 1970 Nonlinear spin-up. Topics in Ocean Engng 2, 87.Google Scholar
Watkins, W. B. & Hussey, R. G. 1973 Spin-up from rest: limitations of the Wedemeyer model. Phys. Fluids 16, 1530.Google Scholar
Watkins, W. B. & Hussey, R. G. 1977 Spin-up from rest in a cylinder. Phys. Fluids 20, 1596–1604.Google Scholar
Wedemeyer, E. H. 1964 The unsteady flow within a spinning cylinder. J. Fluid Mech. 20, 383–399.Google Scholar
Weidman, P. D. 1976a On the spin-up and spin-down of a rotating fluid. Part 1. Extending the Wedemeyer model. J. Fluid Mech. 77, 685–708.Google Scholar
Weidman, P. D. 1976b On the spin-up and spin-down of a rotating fluid. Part 2. Measurements and stability. J. Fluid Mech. 77, 709–735.Google Scholar