Dynamics of two-dimensional flow around a circular cylinder with flexible filaments attached

A direction adaptive approach for the reduction of drag and the suppression of lift fluctuation in flow passing a circular cylinder is developed. Flexible filaments are attached to the surface of the cylinder, and different configurations, including the number, lengths, and angles of attachment of the filaments, as well as their tension and bending features, are investigated. In this comprehensive numerical study, the configuration with two filaments ${180}^{\text{o}}$ apart is found to be optimal for drag reduction and lift fluctuation suppression and is adaptive to the direction of the incoming flow. A drag reduction of $10.8\%$ and a lift fluctuation suppression of $34.6\%$ can be achieved as one filament is attached to the rear stagnation point and the other to the front stagnation point. The hairy coating resembled by 12 evenly attached filaments is also considered. Though marked drag reduction has not been found for this configuration, we leave it an open question for future studies to explore various properties of the filaments in turbulent flow, whose interaction with the filaments would be significant.

Figure 1

Definition of the attaching angle $\theta$ of a filament.

Figure 2

Schematics of the (a) computational domain, in which the rectangular and circle zones are mesh refined, and (b) mesh distributions around the circular cylinder.

Figure 3

Phase diagram of the drag and lift coefficients for flow around a circular cylinder for different mesh sizes, in the range $H=0.05D–0.00625D$.

Figure 4

(a) Time histories of lift and drag coefficients and (b) vortical contours (solid lines for positive values and dashed lines for negative values) for the flow around a circular cylinder at $\text{Re}=100$.

Figure 5

Time histories of the filament lengths for the flow around a cylinder with a single filament attached to its downstream stagnation point, with different values of $k_s$ considered. The inset shows their corresponding phase diagrams of the drag and lift coefficients.

Figure 6

Phase diagram of the drag and lift coefficients for flow around a circular cylinder attached with a single filament at various attaching points marked by different colors. The filament lengths are (a) $L=0.5D$ and (b) $L=1.0D$.

Figure 7

Ranges of motion for a filament attached to the cylinder (a) $\theta =0^{\text{o}}$ and (b) $\theta ={180}^{\text{o}}$ for $L=0.5D$ and ${\omega }_r=1.15$; (c) $\theta =0^{\text{o}}$ and (d) $\theta ={180}^{\text{o}}$ for $L=1.0D$ and ${\omega }_r=4.60$.

Figure 8

Phase diagram of the drag and lift coefficients for flow around a circular cylinder with two filaments attached ${180}^{\text{o}}$ apart.

Figure 9

Ranges of motion for two filaments ${180}^{\text{o}}$ apart with angles (a) $0^{\text{o}}$ and (b) ${90}^{\text{o}}$, for $L=0.5D$ and ${\omega }_r=1.15$.

Figure 10

256 evenly spaced contours of spanwise vorticity between -100 (blue) and $+100$ (red) (left column), and their corresponding pressure coefficients between -1.94 and 1.3 (right column). The attachment angles are $0^{\text{o}}$, ${30}^{\text{o}}$, and ${90}^{\text{o}}$, respectively, from top to bottom. Note that the vorticity is scaled by $\nu /D^2$, and the pressure coefficient is calculated by $c_p=p/(1/2\rho U_{\infty }^2)$.

Figure 11

Phase diagram of the drag and lift coefficients for flow around a circular cylinder with 12 filaments and ${\rho }_s/{\rho }_f=0.1$ and $k_b=0.005$. Note that the filaments are evenly distributed with one of them attached to the downstream stagnation point, and three lengths are considered.

Figure 12

Ranges of motion for 12 filaments attached to the cylinder, with three different lengths considered, and ${\rho }_s/{\rho }_f=0.1$, $k_b=0.005$, corresponding to Fig. 11. Instantaneous streamlines have also been included.

Figure 13

Phase diagram of the drag and lift coefficients for the flow around a circular cylinder with 12 filaments, with different bendings ($k_b$), and the length and the density ratio are fixed at $L=0.25D$ and ${\rho }_s/{\rho }_f=0.1$, respectively