Numerical Solution of the Navier-Stokes Equations for Flows in the Disk-Cylinder System

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Abstract
A numerical computation of a viscous incompressible fluid confined in a circular cylindrical chamber has been carried out, where the top disk is rotating with a constant angular velocity, and the bottom disk and side wall are held fixed. Using the full Navier‐Stokes equations, steady secondary flows were calculated for various Reynolds numbers ( Re = Ωb 2 /ν) up to a maximum value of 400. It is found that, for the Reynolds numbers below 10, the governing equations are essentially linear and the numerical solution agrees very well with the analytic solution. For higher Reynolds numbers, the flow near the boundary is intensified. The detailed flow patterns are compared with previous work of a single disk and two infinite disks. The volume flow rate of the secondary flow due to the centrifugal action and the frictional moment of the disk were also calculated.

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