The flow field induced inside a cylindrical container by the rotation of the two end walls is described. It is shown that stagnation points leading to separation bubbles occur on the axis of rotation and/or the bottom end wall for certain ranges of the characteristic parameters; the Reynolds number, the aspect ratio of the container, and the ratio of the rotation rates of the end walls. Flow fields in a container of aspect ratio 2.0 are examined for Reynolds numbers from 100 to 3000 and ratios of the rotation rates of the top and bottom end walls from −0.10 to 1.0. For a range of ratios of the rotation rates of the top and bottom end walls and Reynolds numbers it is shown that ring vortices surrounding a columnar vortex core exist.
Issue Section:
Research Papers
1.
Brown
G. L.
Lopez
J. M.
1990
, “Axisymmetric Vortex Breakdown. Part 2. Physical Mechanisms
,” Journal of Fluid Mechanics
, Vol. 221
, p. 553
553
.2.
Daube
O.
Sorensen
J. N.
1989
, “Simulation nume´rique de l’e´coulement pe´riodique axisyme´trique dans une cavite´ cylindrique
,” Comptes Rendus de l’Academie des Sciences des Paris
, Vol. 308
, p. 463
463
.3.
Doedel, E. J., and Kernevez, J. P., 1985, “Software for Continuation Problems in Ordinary Differential Equations with Applications,” Preprint, California Inst. of Tech., Pasadena, CA.
4.
Escudier
M. P.
1984
, “Observations of the Flow Produced in a Cylindrical Container by a Rotating End Wall
,” Experiments in Fluids
, Vol. 2
, p. 189
189
.5.
Gelfgat
A. Y.
Bar-Yoseph
P. Z.
Solan
A.
1996
a, “Stability of Confined Swirling Flow with and Without Vortex Breakdown
,” Journal of Fluid Mechanics
, Vol. 311
, p. 1
1
.6.
Gelfgat
A. Y.
Bar-Yoseph
P. Z.
Solan
A.
1996
b, “Steady States and Oscillatory Instability of Swirling Flow in a Cylinder with Rotating Top and Bottom
,” Physics of Fluids
, Vol. 8
, p. 2614
2614
.7.
Jahnke
C. C.
Valentine
D. T.
1996
, “Boundary Layer Separation in a Rotating Container
,” Physics of Fluids
, Vol. 8
, p. 1408
1408
.8.
Leibovich
S.
1968
, “Axially-Symmetric Eddies Embedded in a Rotational Stream
,” Journal of Fluid Mechanics
, Vol. 32
, p. 529
529
.9.
Leibovich
S.
1984
, “Vortex Stability and Breakdown: Survey and Extension
,” AIAA Journal
, Vol. 22
, p. 1192
1192
.10.
Lopez
J. M.
1990
, “Axisymmetric Vortex Breakdown. Part I. Confined Swirling Flow
,” Journal of Fluid Mechanics
, Vol. 221
, p. 533
533
.11.
Lopez
J. M.
Perry
A. D.
1992
, “Axisymmetric Vortex Breakdown. Part 3. Onset of Periodic Flow and Chaotic Advection
,” Journal of Fluid Mechanics
, Vol. 234
, p. 449
449
.12.
Lugt
H. J.
Abboud
M.
1987
, “Axisymmetric Vortex Breakdown with and Without Temperature Effects in a Container with a Rotating Lid
,” Journal of Fluid Mechanics
, Vol. 179
, p. 179
179
.13.
Lugt
H. J.
Haussling
H. J.
1982
, “Axisymmetric Vortex Breakdown in Rotating Fluid within a Container
,” ASME Journal of Applied Mechanics
, Vol. 49
, p. 921
921
.14.
Roesner, K. G., 1990, “Recirculating Zones in a Cylinder with Rotating Lid,” Topological Fluid Mechanics, Proc. IUTAM Symp. Cambridge, 1989 (Moffat, K.; Tsinober, A.), London, Cambridge University Press.
15.
Ronnenberg, B., 1977, “Ein selbstjustierendes 3-Komponenten-Laserdoppler-anemometer nach dem Vergleichsstrahlverfahren, angewandt fu¨r Untersuchungen in einer stationa¨ren zylinder-symmetrischen Drehstro¨mung mit einem Ru¨ckstromgebiet,” Max-Planck-Institut fu¨r Stro¨mungsforschung, Go¨ttingen, Bericht, 20.
16.
Spohn, A., 1991, “Ecoulement et e´clatement tourbillonaires engendre´ par une disque tournant dans une enceinte cylindrique,” The`se de Doctorat d’Universite`, Universite´ Joseph Fourier Grenoble I.
17.
Spohn
A.
Mory
M.
Hopfinger
E. J.
1993
, “Observations of Vortex Breakdown in an Open Cylindrical Container with a Rotating Bottom
,” Experiments in Fluids
, Vol. 14
, pp. 70
–77
.18.
Tsitverblit
N.
1993
, “Vortex Breakdown in a Cylindrical Container in the Light of Continuation of a Steady Solution
,” Fluid Dynamics Research
, Vol. 11
, p. 19
19
.19.
Valentine
D. T.
Jahnke
C. C.
1994
, “Flows Induced in a Cylinder with Both End Walls Rotating
,” Physics of Fluids
, Vol. 6
(8
), pp. 2702
–10
.20.
Vogel, H. U., 1968, “Experimentelle Ergebnisse u¨ber die laminare Stro¨mung in einem zylindrischen Geha¨use mit darin rotierender Scheibe,” Max-Planck-Institut fu¨r Stro¨mungsforschung, Go¨ttingen, Bericht 6.
21.
Vogel, H. U., 1975, “Ru¨ckstro¨mungsblasen in Drallstro¨mungen. Festschrift 50 Jahre,” Max-Planck-Institut fu¨r Stro¨mungsforschung, Go¨ttingen, Bericht, 1925.
22.
Watson
J. P.
Neitzel
G. P.
1996
, “Numerical Evaluation of a Vortex-Breakdown Criterion
,” Physics of Fluids
, Vol. 8
, p. 3063
3063
.
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