Research on the flow around a circular cylinder near a wall for shear-thinning power-law fluids

In this study, direct numerical simulations (DNS) was used to investigate the flow behavior of power-law fluids flow around a circular cylinder near a wall at the Reynolds number of 200. The power-law index $n$ represents the typical situation of shear-thinning fluids ($n=0.2$ to 1.0), whereas the gap ratio $G/D$ ranges from 0.2 to 1.0 (where $G$ represents the gap between the cylinder and the plane wall and $D$ represents the diameter of the cylinder). This study aimed to analyze the influence of the power-law index and gap ratio on the time-averaged flow, vortex dynamics, and the force exerted on the cylinder. The results indicate that for $G/D\ge 0.5$ and $n\le 0.5$, two secondary vortex structures form behind the cylinder because of the induction of the primary vortices, and they are in reverse rotation. An analysis of the signed enstrophy revealed a positive correlation between the strengths of the primary and secondary vortices, both of which diminished as the gap ratio decreased and increased as the power-law index decreased. Notably, vortex shedding was observed at $G/D=0.3$ when $n\le 0.3$, which is absent in Newtonian fluids. Through the analysis of vorticity transport equation, the development of vorticity is attributed to changes in the convection term, viscosity diffusion term and viscosity gradient term. By examining the key points, the formation of secondary vortex structure and the reason of vortex shedding at $G/D=0.3$ in power-law fluids are explained. Furthermore, the time-averaged drag coefficient ${\overline{C}}_D$ initially decreases and then increases with decreasing $n$, and decreases with decreasing $G/D$. The time-averaged lift coefficient ${\overline{C}}_L$ exhibits a typical L-type curve with increasing gap ratios, where ${\overline{C}}_L$ initially decreases and then increases.