The wake characteristics and hydrodynamic forces of a near-wall circular cylinder with the splitter plate

Flow around a near-wall circular cylinder with the splitter plate is numerically performed at Reynolds number of 500, with the objective of investigating the wake characteristics and hydrodynamic forces. Five gap ratios $G∕D=0.1,0.3,0.5,0.7$ and $0.9$ (G is the gap between the lower surface of the cylinder and the wall, D is the diameter of the cylinder) are selected, and the splitter plate length $L∕D$ ranges from 0 to $4.5$. The flow characteristics of an isolated cylinder with the splitter plate are investigated first for comparison, and four wake flow modes are observed, which include 2S mode ($L∕D\le 0.15$), P+S mode ($0.3\le L∕D\le 1.0$), 2S+S mode ($1.25\le L∕D\le 2.0$) and 2P mode ($L∕D\ge 3.0$). As $L∕D$ increases from 0 to $0.75$, the mean drag coefficient ($\overline{C_D}$) is decreased, and there is a slight increase of $\overline{C_D}$ for $0.75<L∕D\le 1.25$. In addition, the cases of $L∕D=0.75$ and $L∕D=1.0$ produce a very significant reduction of drag, and the $\overline{C_D}$ is reduced by as much as $39\%$ and $38\%$, respectively. The wake characteristics and hydrodynamic forces of a near-wall cylinder with the splitter plate are investigated in detail, and five wake regimes are observed, which include the wake vortex merging regime I, merged vortex attaching regime II, steady flow regime III, wall shear layer elongation regime IV and upper shear layer attaching regime V. For $G∕D=0.1$, the wake vortex shedding is suppressed. For $G∕D\ge 0.3$, the Strouhal number (St) is decreased as $L∕D$ increases from 0 to 1.0, and there is an increase of St at $L∕D=1.25$. At $L∕D\ge 1.25$, the St of the near-wall cylinder is larger than that of the isolated cylinder, and the increase in St is affected by the deflected gap flow. What is more, the hydrodynamic characteristics are affected by the wall. For $G∕D>0.1$, the variations of $\overline{C_D}$ with $L∕D$ are similar to that of the isolated cylinder. It is found that the cases of $L∕D=0.75$ and $L∕D=1.0$ still produce a significant reduction of drag for $G∕D>0.3$, and the $\overline{C_D}$ is increased for all cases of $L∕D$ as $G∕D$ increases.