Flow characteristics around extremely low fineness-ratio circular cylinders

The accurate measurement of flows and aerodynamic characteristics around a bluff body has been a challenging task due to the existence of interference between the wake and mechanical model supports in wind-tunnel experiments. The present study focuses on a freestream-aligned circular cylinder with an extremely low fineness ratio (the ratio of the axial length to diameter) ranging from 0.30 to 0.50, which has never been investigated without interference from a mechanical model support. We employed a magnetic suspension and balance system to eliminate interference from the model support and measured the drag and velocity fields in the diameter-based Reynolds number between $2.0\times {10}^4$ and $7.7\times {10}^4$. As the fineness ratio decreases below 1.50, the size of the recirculation bubble increases and the velocity distribution on the central axis inside the bubble gradually converges to that of the circular disk. Furthermore, large-eddy simulations were performed in the Reynolds number of $4.0\times {10}^4$, whose drag coefficient agrees well with experiments. Based on those results, it was found that the drag coefficient monotonically converges to that of the circular disk without local maximum. This study revealed that in the low-fineness-ratio regime (0.10–0.50), a critical geometry, at which the drag coefficient shows a local maximum, does not exist in the circular cylinder. Subsequently, unsteady flow analyses were performed, where two characteristic frequencies, i.e., $\mathrm{St}=0.05$ and 0.155, were identified from power spectral densities of the drag coefficient and the pitching moment coefficient. The associated flow structures are then extracted by a phase-averaging procedure, where the phase-averaged flows with $\mathrm{St}=0.05$ represent the recirculation bubble pumping while the phase-averaged flows with $\mathrm{St}=0.155$ show nonaxisymmetric structures inside the recirculation bubble.

Figure 1

Schematic of the 0.3-m MSBS and definition of the coordinate system.

Figure 2

Circular cylinder model with $L/D=0.30$ (diameter 60 mm).

Figure 3

RMS values of PIV measurement uncertainty in the averaged flow fields for $L/D=0.30$ at ${\mathrm{Re}}_D=5.9\times {10}^4$ with the model diameter of $D=60$ mm.

Figure 4

Mean velocity field of the streamwise component, $u/U_{\infty }$: (a) $L/D=0.30$, (b) $L/D=0.40$; (c) $L/D=0.50$, (d) $L/D=1.00$; and (e) $L/D=1.25$, (f) $L/D=1.50$. [(a)–(c)] Present study ${\mathrm{Re}}_D=5.9\times {10}^4$ with the model diameter of $D=60$ mm; [(d)–(f)] reprocessed data from the previous study by Ref. [15] at ${\mathrm{Re}}_D=6.7\times {10}^4$).

Figure 5

Mean velocity profiles of circular cylinders (a) at the central axis, $z/D=0.0$; (b) $x/D=1.50$ (present study at ${\mathrm{Re}}_D=5.9\times {10}^4$ with model diameter $D=60$ mm and [15] at ${\mathrm{Re}}_D=6.7\times {10}^4$).

Figure 6

Characteristics of the recirculation bubble: Recirculation region length $L_{\mathrm{r}}/D$, width $W_{\mathrm{r}}/D$ at $x/D=1.5$, and center of recirculation flow $(x_{\mathrm{c}}/D,z_{\mathrm{c}}/D)$ (Ref. [27], ${\mathrm{Re}}_D=4.1\times {10}^5$; present study, ${\mathrm{Re}}_D=5.9\times {10}^4$ with model diameter $D=60$ mm; Ref. [15], ${\mathrm{Re}}_D=6.7\times {10}^4$).

Figure 7

Drag coefficients versus Reynolds number of circular cylinders with fineness ratios of 0.30–0.50, measured using the 0.3-m MSBS.

Figure 8

Effects of fineness ratio on drag and base-pressure coefficient of circular cylinder at ${\mathrm{Re}}_D={10}^4–{10}^5$ (present study; ${\mathrm{Re}}_D=5.9\times {10}^4$ and $7.7\times {10}^4$ for models with diameter $D=60$ and 80 mm, respectively).

Figure 9

PSDs of (a) the drag coefficient $C_{\mathrm{D}}$ and (b) the pitching moment coefficient $C_{\mathrm{M}}$ in the $L/D=0.30$ case at ${\mathrm{Re}}_D=7.7\times {10}^4$ with the model diameter of $D=80$ mm.

Figure 10

Phase-averaged flow fields based on $\mathrm{St}=0.05$ [in (a)–(d)] and $\mathrm{St}=0.155$ [in (e)–(h)]. Blue to red contour colors represent the phase fluctuation ${\tilde{u}}_{\phi }/U_{\infty }$, and black lines represent streamlines calculated from the phase-averaged velocity field $({\langle u\rangle }_{\phi },{\langle w\rangle }_{\phi })$.