Flow-induced rotation of circular cylinder in Poiseuille flow of power-law fluids

The Poiseuille flow of power-law fluid over a free rotating cylinder eccentrically situated in a two-dimensional channel is numerically investigated via a BGK lattice Boltzmann method. Effects of power-law index, eccentricity ratio and Reynolds number on flow patterns and rotational behavior of the pinned cylinder are systematically explored within wide ranges of Reynolds numbers (1 ≤ Re ≤ 100), eccentricity ratios (0 ≤ λ ≤ 11/12) and power-law indexes (0.6 ≤ n ≤ 1.4). Results show that the 'anomalous' rotation (clockwise rotation) of the pinned cylinder is mainly induced by flow inertia. The mean rotating velocity generally decreases with an increase in Reynolds number except in low Reynolds number region and it also increases with power-law index because viscosity progressively becomes essential. Such effect of power-law index on the mean rotating velocity is greater at moderate local Reynolds number and intermediate eccentricity ratio. A physical argument is created to characterize the combined effect of Reynolds number and power-law index. In the vicinity of channel wall or near the centerline, the pinned cylinder tends to rotate in a normal way. The 'anomalous' rotation is inclined to appear at intermediate eccentricity ratio. Moreover, the critical Reynolds numbers beyond which the pinned cylinder changes the rotating direction are evaluated at various combinations of eccentricity ratio and power-law index. In addition, the instantaneous rotating velocity of the pinned cylinder is more stable at a lower Reynolds number, higher power-law index, considerably higher eccentricity ratio or quite near the channel centerline.