Active pitching of short splitters past a cylinder: Drag increase and wake

The flow and drag induced by active pitching of plates in the wake of a cylinder of diameter $d$ were experimentally studied for various plate lengths $L$ as well as pitching frequencies $f_p$ and amplitudes $A_0$ at Reynolds number $\text{Re}=1.6\times {10}^4$. Planar particle image velocimetry and a load cell were used to characterize the flow statistics and mean drag of a variety of cylinder-splitter assemblies. Results show the distinctive effect of active pitching on these quantities. In particular, flow recovery was significantly modulated by $L$, $f_p$, or $A_0$. Specific pitching settings resulted in a wake with dominant meandering patterns and faster flow recovery. We defined a modified version of the amplitude-based Strouhal number of the system ${\mathrm{St}}_A$ to account for the effect of the cylinder in active pitching. It characterizes the drag coefficient $C_d$ across all the cases studied, and reveals two regions intersecting at a critical value of ${\mathrm{St}}_A\approx 0.035$. Below this value, the $C_d$ remained nearly constant; however, it exhibited a linear increase with increasing ${\mathrm{St}}_A$ past this critical point. Inspection of the integral momentum equation showed the dominant role of velocity fluctuations in modulating $C_d$ past the critical ${\mathrm{St}}_A$.

Figure 1

(a) Schematic of the experimental setup illustrating a representative cylinder-splitter assembly and the field of view (FOV) of the PIV flow measurements. (b) Plain view of the assembly showing basic parameters.

Figure 2

Time-averaged streamwise velocity distributions, $U/U_0$, past the cylinder-splitter assemblies sharing the oscillation patterns with $f_p/f_v=1$ and $A_0={12}^{\circ }$ but plate lengths of $L/d=$ (a) 1/4, (b) 1/2, and (c) 1. The white areas in the velocity contours contain the splitter motions in the PIV measurements. (d) Comparison of the spanwise velocity profiles at selected locations.

Figure 3

Time-averaged streamwise velocity distributions, $U/U_0$, past the cylinder-splitter assemblies sharing the $L/d=1$ and $A_0={12}^{\circ }$ but frequencies of $f_p/f_v=$ (a) 1/4, (b) 1/2, and (c) 3/4. (d) Comparison of the spanwise velocity profiles at selected locations.

Figure 4

Time-averaged streamwise velocity distributions, $U/U_0$, past the cylinder-splitter assemblies sharing the $f_p/f_v=0.75$ and $L/d=0.5$ but $A_0=$ (a) $6^{\circ }$, (b) ${12}^{\circ }$, and (c) ${18}^{\circ }$. (d) Comparison of the spanwise velocity profiles at selected locations.

Figure 5

Time-averaged streamwise velocity distributions, $U/U_0$, along the system centerline $y=0$. (a) $f_p/f_v=1$ and $A_0={12}^{\circ }$, (b) $L/d=1$ and $A_0={12}^{\circ }$, and (c) $f_p/f_v=0.75$ and $L/d=0.5$.

Figure 6

Turbulence kinetic energy, TKE, distribution past the cylinder-splitter assemblies sharing the $L/d=0.5$ and $f_p/f_v=1$ but $A_0=$ a) $6^{\circ }$, (b) ${12}^{\circ }$, and (c) $A_0={18}^{\circ }$. (d),(e) Turbulence intensity of the streamwise (${\sigma }_u/U_0$) and transverse (${\sigma }_v/U_0$) velocity fluctuations of case (c).

Figure 7

Snapshots of velocity fields with superimposed swirling strength with $L/d=0.5$ and plate motions characterized by (a) static plate; (b) $A_0={12}^{\circ },f_p/f_v=0.75$; (c) $A_0={18}^{\circ },f_p/f_v=0.75$; (d) $A_0={12}^{\circ },f_p/f_v=1$. The subplot in (b) shows streamwise velocity $U/U_0$ profiles at $x/d=1$ for the cases with the splitter static (dashed curve) and under pitching given by $A_0={12}^{\circ }$ and $f_p/f_v=0.75$ (solid curve).

Figure 8

(a) Distribution of the mean drag coefficient $C_d$ as a function of the system amplitude-based Strouhal number ${\mathrm{St}}_A$ at $\text{Re}=1.6\times {10}^4$. The circle, square, and triangle symbols represent cases with $A_0=6^{\circ }$, ${12}^{\circ }$, and ${18}^{\circ }$ with a variety of $L/d$ and $f_p/f_v$; whereas the red, black, and blue symbols refer to $L/d=0.25$, 0.5, and 1. The dot-dashed, continuous, and dotted horizontal lines correspond to the $C_d$ values of the static splitters with $L/d=0.25$, 0.5, and 1. The inclined, dashed line in $R2$ illustrates the basic trend. (b) Comparison of the measured (filled symbols) and Eq. (4)-calculated (empty symbols) $C_d$ within $R2$. The subplot illustrates examples of the $C_d$ calculated using the momentum integral equation at various locations for the cases sharing $L/d=1$ and $A_0={12}^{\circ }$ but $f_p/f_v=0.625$ (symbols in continuous line) and $f_p/f_v=1$ (symbols in dashed line). (c) Estimation of $C_d$ neglecting the flow fluctuation contribution.

Figure 9

(a) Selected streamwise profiles of the streamwise velocity, $U/U_0$, along the centerline ($y=0$). (b), (c) Transverse profiles of $U/U_0$ and $({\sigma }_v^2-{\sigma }_u^2)/U_0^2$ at streamwise locations sharing $U(x,0)/U_0=0.5$. (d), (e) Same as (b), (c) but with $U(x,0)/U_0=0$. The solid, dashed, and dot-dashed lines correspond to cases with ($L/d=1,f_p/f_v=0.5,A_0={12}^{\circ }$), ($L/d=0.25,f_p/f_v=1,A_0={18}^{\circ }$), and ($L/d=0.5,f_p/f_v=1,A_0={18}^{\circ }$).