On the flow between two rotating disks enclosed by a cylinder

The flow field inside a cylindrical container caused by the impulsively sta rted constant co-rotation or counter rotation of the top-bottom endwalls wi th fixed sidewall is described. After a transient phase from an initial sta te at rest a steady flow situation is reached. The unsteady axisymmetric Na vier-Stokes equations describing the transient flow are expressed in vortic ity-stream function form. For large values of Reynolds number (based on ang ular velocity on the lower endwall) an upwind differencing in the spatial d erivatives for the convective terms is used. A fourth-order accurate compac t difference scheme is applied to solve the Poisson equation. The results s how that the slight co-rotation of the top-bottom endwalls induces a breakd own bubble at a critical value of the Reynolds number which is much smaller than the value of the Reynolds number for the onset of Vortex breakdown in a now due to rotation either of the top or bottom end wall. On the other h and, a weak counter-rotation of top-bottom endwalls suppresses the vortex b reakdown. The question of whether the similarity solutions are locally usef ul in describing the flow between finite disks is also addressed.