Numerical studies of viscous incompressible flow between two rotating concentric spheres
The problem of determining the induced steady axially symmetric motion of an incompressible viscous fluid confined between two concentric spheres, with the outer sphere rotating with constant angular velocity and the inner sphere fixed, is numerically investigated for large Reynolds number. The gove...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X04402095 |
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| Summary: | The problem of determining the induced steady axially symmetric
motion of an incompressible viscous fluid confined between two
concentric spheres, with the outer sphere rotating with constant
angular velocity and the inner sphere fixed, is numerically
investigated for large Reynolds number. The governing
Navier-Stokes equations expressed in terms of a stream
function-vorticity formulation are reduced to a set of nonlinear
ordinary differential equations in the radial variable, one of
second order and the other of fourth order, by expanding the flow
variables as an infinite series of orthogonal Gegenbauer
functions. The numerical investigation is based on a finite-difference
technique which does not involve iterations and which
is valid for arbitrary large Reynolds number. Present
calculations are performed for Reynolds numbers as large as 5000.
The resulting flow patterns are displayed in the form of level
curves. The results show a stable configuration consistent with
experimental results with no evidence of any disjoint closed
curves. |
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| ISSN: | 1110-757X 1687-0042 |