Flow between a stationary and a rotating disk with suction

Abstract

The equations for the viscous flow between two coaxial infinite disks, one stationary and the other rotating, are solved numerically. The effects of applying a uniform suction through the rotating disk are determined. Initially, the fluid and disks are at rest. The angular velocity of one disk and the amount of suction through it are gradually increased to specific values and then held constant. At large Reynolds numbersR, the equilibrium flow approaches an asymptotic state in which thin boundary layers exist near both disks and an interior core rotates with nearly constant angular velocity. We present graphs of the equilibrium flow functions forR= 104and various values of the suction parametera(0 ≤a≤ 2). Whena= 0, the core rotation rate ωcis 0·3131 times that of the disk. Fluid near the rotating disk is thrown centrifugally outwards. Asaincreases, ωcincreases and the centrifugal outflow decreases. Whena> 1·3494, the core rotation rate exceeds that of the disk and the radial flow near the rotating disk is directed inwards. We also present accurate tabular results for two flows of special interest: (i) the flow between a stationary and a rotating disk with no suction (a= 0) and (ii) Bödewadt flow. The latter can be obtained by suitable scaling of the boundary-layer solution near the stationary disk for anya≥ 0. Since several solutions to the steady-state equations of motion have been reported, the question arises as to whether other solutions to the time-dependent equations of motion with zero initial conditions can be found. We exhibit a rotational start-up scheme which leads to an equilibrium solution in which the interior fluid rotates in a direction opposite to that of the disk.