Flow past a rotating hydrophobic/nonhydrophobic circular cylinder in a flowing soap film

Flow past a rotating cylinder of various surface characteristics is investigated experimentally in a flowing soap film of a soap film tunnel. Experiments are carried out at Reynolds numbers $\sim 200$ and 250 with cylinders of different levels of hydrophobicity and normalized rotation rates (ratio of surface speed of cylinder to free-stream velocity) varying from 0 to 4.36. The diagnostic is done with flow visualization using interference technique, and quantitative measurements are obtained with particle image velocimetry. Global wake structure of a rotating hydrophobic/nonhydrophobic cylinder at various rotation rates is presented in this work. Reynolds number and hydrophobicity are found to have a substantial effect on the onset of the transition regime. Interestingly, the transition of von Kármán vortex shedding to single-signed vortex shedding occurred at a transition zone with no evidence of region of suppression in soap film tunnel experiments. The shed single-signed vortices at a rotation rate above the transition regime are of an opposite sense to the cylinder rotation direction. The experimental evidence of this new vortex shedding mode in a soap film tunnel is presented using flow visualization and particle image velocimetry. In addition, inequality in the shedding frequency of counterclockwise and clockwise vortices is observed whose value reaches maximum before the transition zone and then decreases. A higher rotation rate of 4.36 made the counterclockwise vorticity completely wrap around the cylinder at Reynolds number $\sim 250$. Consequently, the stagnation point got lifted off from the surface at $\sim {135}^{\circ }$. The relative circulation of shed clockwise vortices to counterclockwise vortices is observed to be increasing with rotation rate and reaches maximum at the transition zone. The variation of the Strouhal number with rotation rate for shed clockwise vortices is observed to be increasing until the transition regime, and subsequently it decreases. The Strouhal number for hydrophobic cylinders was found to be less compared to nonhydrophobic cylinder and was also observed to decrease with increase in hydrophobicity. The study of the far-wake structure shows the evidence of distortion in the wake structure due to the elongation of vortex pairs for both hydrophobic and nonhydrophobic cylinders.

Figure 1

Problem schematic showing rotating hydrophobic/nonhydrophobic cylinder of diameter, $D=10$ mm, rotating in a counterclockwise sense while viewing from the top.

Figure 2

Test section schematic.

Figure 3

(a) Nonhydrophobic cylinder, (b) hydrophobic cylinder of level I, (c) hydrophobic cylinder of level II, (d) hydrophobic cylinder of level III. (i) Dimensions of grooves over the various hydrophobic cylinders, (ii) contact angle made by various hydrophobic cylinders with water $(\mathrm{a})88.3^{\circ }$, (b) $99.2^{\circ }$, (c) $109.9^{\circ }$, (d) $123.9^{\circ }$.

Figure 4

Schematic of the experimental setup for flow visualization and PIV experiments. (i) Schematic for flow visualization; (ii) schematic for PIV.

Figure 5

Mean velocity obtained by flow visualization and PIV technique at 32 ml/min for a $X\sim 12.5D$ long test section.

Figure 6

Normalized velocity profiles at 32 ml/min flow rate at various locations downstream of the flow.

Figure 7

Initiation of von Kármán vortex shedding at $\text{Re}\sim 42$.

Figure 8

Wake structures of the nonhydrophobic rotating cylinder at various counterclockwise rotation rates at $\text{Re}\sim 250$.

Figure 9

Variation in the ratio of shedding frequency of counterclockwise to clockwise vortices with rotation rate, $\alpha$.

Figure 10

Instantaneous vorticity field $(\omega$ D/$U_o)$ variation of nonhydrophobic rotating cylinder at various rotation rates at $\text{Re}\sim 250$. The cylinder is rotating counterclockwise.

Figure 11

Formation length variation with rotation rate using PIV experimentation.

Figure 12

Variation of the normalized circulation of vortices shed from the cylinder with rotation rate, $\alpha$.

Figure 13

Variation of ratio of circulation $\left({\mathrm{\Gamma }}_{cw}/{\mathrm{\Gamma }}_{ccw}\right)$ of vortices shed from the cylinder with rotation rate, $\alpha$.

Figure 14

Mean vorticity field $(\omega$ D/$U_o)$ variation over a nonhydrophobic rotating cylinder with rotation rate, $\alpha$ at $\text{Re}\sim 250$.

Figure 15

Variation of the mean normalized circulation around the cylinder with rotation rate, $\alpha$.

Figure 16

Variation of ratio of mean circulation, ${\mathrm{\Gamma }}_{cw}/{\mathrm{\Gamma }}_{ccw}$ of around the surface of the cylinder with rotation rate, $\alpha$.

Figure 17

Mean streamline flow over nonhydrophobic rotating cylinder with rotation rate, $\alpha$, at $\text{Re}\sim 250$. Front stagnation point, saddle point, node, and vortex center are represented by black, yellow, red, and green dots, respectively. The lifted-off stagnation point for $\alpha =3.85$ and 4.36 is shown with a black dot.

Figure 18

Motion of front stagnation point (averaged data) in degrees with rotation rate, $\alpha$.

Figure 19

Wake structures of hydrophobic cylinder of level I at various counterclockwise rotation rates for $\text{Re}\sim 250$.

Figure 20

Wake structures of hydrophobic cylinder of level II at various counterclockwise rotation rates at $\text{Re}\sim 250$.

Figure 21

Wake structures of hydrophobic cylinder of level III at various counterclockwise rotation rates at $\text{Re}\sim 250$.

Figure 22

Variation in ratio of shedding frequency of counterclockwise vortices to clockwise vortices for nonhydrophobic/hydrophobic cylinder of levels I, II, and III with rotation rate, $\alpha$ at (a) $\text{Re}\sim 200$ and (b) $\text{Re}\sim 250$, respectively.

Figure 23

Effect of Reynolds number and hydrophobicity over the onset of transition zone. (a) Nonhydrophobic cylinder, (b) hydrophobic cylinder of level I, (c) hydrophobic cylinder of level II, and (d) hydrophobic cylinder of level III.

Figure 24

Strouhal number variation for (a) non-hydrophobic cylinder, (b) hydrophobic cylinder of level I, (c) hydrophobic cylinder of level II, (d) hydrophobic cylinder of level III, with rotation rate at $\text{Re}\sim 200$ and 250, and transition region is shown for $\text{Re}\sim 200$ and 250 as dotted and solid vertical lines, respectively.

Figure 25

Strouhal number variation with the level of hydrophobicity of stationary cylinders at $\text{Re}\sim 200$ and 250.

Figure 26

Illustration of wavelength, $\lambda$, measurement.

Figure 27

Normalized wavelength variation with rotation rate at $\text{Re}\sim 250$ for (a) nonhydrophobic cylinder, (b) hydrophobic cylinder of level I, (c) hydrophobic cylinder of level II, and (d) hydrophobic cylinder of level III, with transition zone marked with solid vertical lines.

Figure 28

Downstream wake structures of nonhydrophobic cylinder at various counterclockwise rotation rates at $\text{Re}\sim 250$.

Figure 29

Downstream wake structure of hydrophobic cylinders at various counterclockwise rotation rates at $\text{Re}\sim 250$, shown at location $X\sim 56D–84D$.