Spinup from rest in a differentially rotating cylinder
Abstract
Spinup from rest in a cylinder with top and bottom endwall disks rotating at different rates, denoted by Omega(T) and Omega(B), respectively, is investigated by integrating numerically the unsteady NavierStokes equations. The approximate analytical model developed by Wedemeyer (1964) and Venezian (1970) is outlined. Numerical solutions are presented for three sets of Omega(T)/Omega(B) for a cylinder of a given aspect ratio and a minute Ekman number. The results are detailed flowfield data displaying the transient azimuthal velocity profiles, axial vorticity distributions, and the meridional flow patterns. It is pointed out that an azimuthal velocity shear front that separates the rotating from the nonrotating fluid propagates radially inward. As Omega(T)/Omega(B) approaches unity, the propagation speed of the front increases and the spinup in the interior is more effective. The axial vorticity is zero ahead of the front and is more than twice as large as the finalstate angular speed of the fluid behind the front. As Omega(T)/Omega(B) deviates from unity, the meridional circulation is no longer antisymmetric about the cylinder middepth. The finalstate meridional circulation in the interior comprises purely vertical flows pulled toward the faster rotating endwall disk.
 Publication:

AIAA Journal
 Pub Date:
 September 1983
 DOI:
 10.2514/3.8240
 Bibcode:
 1983AIAAJ..21.1278H
 Keywords:

 Flow Distribution;
 NavierStokes Equation;
 Rotating Cylinders;
 Spin Dynamics;
 Angular Velocity;
 Aspect Ratio;
 Computational Fluid Dynamics;
 Ekman Layer;
 Vorticity;
 Fluid Mechanics and Heat Transfer