Ekman matching condition in a partially filled, rapidly rotating cylinder
The use of an analytical matching condition in lieu of grid refinement and direct application of the no-slip boundary condition in a finite-difference calculation is considered for the case of a partially filled, rapidly rotating cylinder. The right circular cylinder is rotating fast enough that the liquid-air interface is nearly vertical. A non-wheel-flow velocity is induced by the differential rotation of the top lid. For the flow conditions of interest, the Ekman boundary layers on the horizontal surfaces are quite thin and their resolution using a very fine mesh makes the overall calulation very time-consuming and costly. We discuss the appropriate form of the Ekman matching condition, which has been widely used in rotating flow theory, to the case of a cylinder which is only partially full, and the fully implicit implementation of that condition into a MAC-derived, time-marching finite-difference calculation. The resulting algorithm is stable and efficient and the results compare quite well with calculations made using grid refinement and direct application of th no-slip condition and with recently published LDV measurements.
- Research Organization:
- Department of Mechanical and Aerospace Engineering, Research Laboratoires for the Engineering Sciences, School of Engineering and Applied Science, University of Virginia, Charlottesville, Virginia 22901
- DOE Contract Number:
- AC05-82OR20900
- OSTI ID:
- 6587402
- Journal Information:
- J. Comput. Phys.; (United States), Journal Name: J. Comput. Phys.; (United States) Vol. 53:2; ISSN JCTPA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ALGORITHMS
BOUNDARY CONDITIONS
BOUNDARY LAYERS
CYLINDERS
FINITE DIFFERENCE METHOD
FLUID FLOW
INCOMPRESSIBLE FLOW
ITERATIVE METHODS
LAYERS
MATHEMATICAL LOGIC
MOTION
NUMERICAL SOLUTION
ROTATION