Flow Driven by a Torsionally-Oscillating Shrouded Endwall Disk

Abstract

A study is made of time-dependent flow of a viscous fluid driven by an oscillating shrouded disk in finite geometry. Numerical solutions to the Navier-Stokes equations are obtained for the flow in a cylindrical cavity with its upper endwall disk executing torsional oscillation at a velocity Ω cos λt. Details of the three-component velocity field are examined at high Reynolds number. The value of the nondimensional amplitude of disk oscillation, ε = Ω/λ, encompasses a range up to ε ≳ O(1). The numerical results for the azimuthal flow for ε ≪ 1 are consistent with the predictions of the earlier analytical model. The azimuthal flow is largely confined to the Stokes layer thickness. The analytical predictions of the meridional flow, based on a straightforward expansion technique, display discrepancies from the numerical results. The steady meridional streaming at finite values of ε is exhibited. The qualitative patterns of meridional steady streaming are verified by laboratory flow visualizations. The explicit effect of Re on the overall flow character is scrutinized. The numerical data are processed to describe the behavior of the torque coefficient at the oscillating disk.