On the flow between two rotating disks enclosed by a cylinder

Abstract

The flow field inside a cylindrical container caused by the impulsively started constant co-rotation or counter rotation of the top-bottom endwalls with fixed sidewall is described. After a transient phase from an initial state at rest a steady flow situation is reached. The unsteady axisymmetric Navier-Stokes equations describing the transient flow are expressed in vorticity-stream function form. For large values of Reynolds number (based on angular velocity on the lower endwall) an upwind differencing in the spatial derivatives for the convective terms is used. A fourth-order accurate compact difference scheme is applied to solve the Poisson equation. The results show that the slight co-rotation of the topbottom endwalls induces a breakdown 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 flow due to rotation either of the top or bottom end wall. On the other hand, a weak counter-rotation of top-bottom endwalls suppresses the vortex breakdown. The question of whether the similarity solutions are locally useful in describing the flow between finite disks is also addressed.