Unconfined flow of a non-Newtonian power-law fluid past counter-rotating circular cylinders

TL;DR

The paper investigates unconfined, steady flow of power-law non-Newtonian fluids past two side-by-side counter-rotating circular cylinders using 2D FEM in COMSOL over ranges $1\le Re \le 40$, $0.2\le n \le 1.8$, $0.2\le G\le 1$, and $0\le α\le 2$. It analyzes how rheology, rotation, and geometry shape streamlines, centerline velocity, Cp distributions, and drag/lift coefficients, revealing wake suppression with rotation, topology changes in the wake for shear-thinning vs shear-thickening fluids, and complex, non-monotonic force responses. The study provides detailed domain- and grid-convergence validation, demonstrates symmetry/anti-symmetry in force components for counter-rotating cylinders, and clarifies the relative roles of pressure and viscous contributions in $C_D$ and $C_L$ under non-Newtonian effects. The results offer fundamental insights for engineering applications involving rotating bluff bodies in complex fluids, such as heat exchangers, mixing, and particulate transport, where rheology and confinement critically influence performance.

Abstract

This study numerically examines the steady unconfined laminar flow of incompressible non-Newtonian power-law fluids past a pair of side-by-side counter-rotating circular cylinders using the finite element method. The cylinders simultaneously rotate at equal angular speeds in opposite directions, with the upper cylinder (UC) rotating clockwise and the lower cylinder (LC) counterclockwise. The numerical simulations are performed over wide parameter ranges: power-law index ($0.2 \le n \le 1.8$), rotational rate ($0 \le α\le 2$), gap ratio ($0.2 \le G \le 1$), and Reynolds number ($1 \le Re \le 40$). The detailed influence of these flow parameters on key flow characteristics, including streamlines, surface pressure, centerline velocity, and individual as well as total drag and lift coefficients, is systematically analyzed. For stationary cylinders ($α= 0$), a twin-vortex structure forms in the wake, which progressively vanishes with increasing rotation ($α= 2$). The surface pressure coefficient attains its maximum values for shear-thickening fluids ($n > 1$) at higher rotational speeds, irrespective of the gap ratio. The total drag coefficient ($C_D$) decreases with increasing $α$ and $n$, whereas the lift coefficient ($C_L$) exhibits a more intricate dependence on the flow parameters. The results provide fundamental insights into the interplay between rotation, non-Newtonian rheology, and geometric confinement in determining the hydrodynamic behavior of rotating cylinder systems.

Figures (66)

• Figure 1: Schematic representation of an unconfined flow across a pair of side-by-side counter-rotating circular cylinders.
• Figure 2: Influence of gap ratio ($0.4\le G\le 1$), power-law index ($0.2\le n\le 1.8$) and rotational rate ($0\le \alpha\le 2$) on the streamline profiles for the extreme values of Reynolds number ($Re=1$, 40). The full-size images are included in \ref{['appendix:streamline']}.
• Figure 3: Influence of Reynolds number ($1\le Re\le 40$), power-law index ($0.2\le n\le 1.8$) and rotational rate ($0\le \alpha\le 2$) on the streamline profiles for the extreme values of gap ratio ($G=0.2$, 1). The full-size images are included in \ref{['appendix:streamline']}.
• Figure 4: Centerline velocity profiles ($U_x$ at line 6, Fig. \ref{['fig:1']}) for different power-law indices ($n$) at various rotational rates ($\alpha$ in rows) and Reynolds numbers ($Re$ in columns) for gap ratios $G = 0.2-1$. The full-size images are included in \ref{['appendix:velocity']}.
• Figure 5: Distribution of pressure coefficient on the surface of the upper and lower cylinders (UC & LC) for different $n$ with $\alpha$ (in rows) and $Re$ (in columns) at gap ratio $G=0.2-1$.