Flow of a power-law fluid across a rotating cylinder in a confinement

In the present work, the flow of a power-law fluid across a confined rotating cylinder has been investigated numerically over a wide ranges of conditions as follows: Reynolds number (10−3≤Re≤40), power-law index (0.3 ≤ n ≤ 1), blockage ratio (0.2 ≤ β ≤ 0.99) that quantifies the degree of confinement and asymmetry ratio (10−3≤γ≤1) that describes the position of the cylinder from the bottom wall of the channel. The angular velocity of the cylinder is set equal to the average velocity at the inlet of the bulk flow so that the two Reynolds numbers are equal. The flow field is visualized in terms of streamlines, and the resulting hydrodynamic forces and torque acting on the rotating cylinder are computed for a range of values of the aforementioned influencing parameters. The critical conditions for transition from the steady flow to a periodic time-dependent regime have been identified. In general, the moderate degree of cylinder confinement stabilizes the flow. At high Reynolds numbers, the stabilizing effect is outweighed by the shear-thinning behaviour of the fluid and the degree of symmetry and the flow field transits from the steady to time-dependent one at certain values of the Reynolds number. The transition is delayed as the cylinder approaches one of the channel wall. For the highly confined symmetric case such as β≥0.8,γ=1, lubrication analysis is shown to be applicable. Under these conditions, the analytical results obtained from the lubrication analysis in the narrow gap are very close to the numerical results.