Flow driven by a shrouded spinning disk with axial suction and radial inflow

Abstract

The viscous flow confined in a finite cylinder when one endwall disk and the sidewall are spinning about the central axis is studied. We examine the internal flow when a uniform axial suction through the spinning disk and a concomitant uniform radial inflow through the spinning sidewall are imposed. The rotational Reynolds number is large and the cylinder aspect ratio is 0(1). Finite-difference techniques are employed to integrate numerically the full Navier-Stokes equations. The core rotation rate, which is uniform in the axial direction, increases as the suction increases. Under a sufficiently strong suction, the core rotation rate exceeds that of the spinning disk. The flows in the core away from the sidewall are depicted well by the predictions of the infinite disk model. A physical description based on an angular momentum argument is given. Due to the presence of the sidewall, the angular velocities in finite configuration vary in the radial direction, and this variation is pronounced under a strong suction. The meridional flow patterns are displayed. When the suction is weak, the bulk of the meridional fluid transport from the sidewall to the spinning disk takes route via the boundary layer near the stationary disk. Under a strong suction, the meridional fluid transport through the main body of flow field increases. At small and moderate radii, the radial velocities nearly vanish in the core; the axial velocities increases in magnitude as the suction increases. When the suction is strong, the dynamic effects are concentrated in the Ekman layer near the spinning disk.