Coupling between vortex flow and whisker sensor in cylinder wakes with time-varying streamwise gaps

The flow-induced vibration of a whisker in the wake of a movable circular cylinder with time-varying streamwise gaps was experimentally investigated to understand how whiskers detect the variation of upstream target's swimming status. A time-resolved particle image velocimetry was used to characterize the vortex flow dynamics and vibrations of whisker across various initial gaps and gap growth rates. Results showed that despite the time-varying gaps, the evolution of vortex flow and whisker dynamics remained overall synchronized. Due to the nonlinear decaying rate of vortex strength along streamwise direction, the vibrations of whisker sensor were more sensitive to gap growth rates with smaller initial gaps. However, the sensitivity of whisker (i.e., the decaying rate of whisker vibration intensity over unit time) to gap growth rates gradually decreased when such growth rate became sufficiently high, regardless of initial gaps. Using a physical model based on the balance between whisker inertial force, system damping, restoring force, and flow loading with time-varying magnitudes, we well described the response of whisker sensor in the cylinder wake flow; the model revealed that the reduction of whisker's sensitivity under high gap growth rate was attributed to the sufficiently strong vortices initiated by the fast movement of upstream cylinder, which compensated the influence of vortex strength decay due to the growth of gap. In addition to cases with whisker vibrating in the wake centerline, our complementary measurements with the whisker in the cylinder edge highlighted the time-varying equilibrium vibration positions of whisker sensor due to the “wake-stiffness” effect.

Figure 1

The analogy between seal whisker sensing and our experimental design.

Figure 2

(a) Layout and top view of the circular cylinder and whisker sensor under flow; (b) the “fixed-gap” WIV intensity of the whisker ${\sigma }_{\mathrm{ss}}$ under various gap distance $S_x$ and reduced velocity $U_r$. ${\sigma }_{\mathrm{ss}}$ is the root-mean-square (RMS) value of the spanwise displacements; (c) schematic of the experimental setup and the geometry of whisker sensor; (d) velocity of the upstream cylinder during the acceleration progress.

Figure 3

Time series (black solid lines) of whisker displacements for selected cases. Green vertical lines represent the time when upstream cylinder started to move at $t=0$. Red vertical lines denote the instant $T_{tr}$ when the induced wake signal reached the whisker sensor. The blue lines denote the time series of whisker displacements in open water flow (i.e., without upstream cylinder) under $U_f$, and gray dotted lines represent the corresponding $\pm {\sigma }_{\mathrm{ss}}$.

Figure 4

Time-varying WIV intensity ${\sigma }_w$ of the whisker sensor for (a) $S_x=50d_w$, (b) $S_x=90d_w$, and (c) $S_x=130d_w$.

Figure 5

Decaying rate of WIV intensity over unit time ${\gamma }_{\text{amp}}$ across various $U_c$ and $S_x$.

Figure 6

Selected snapshots of (a) vorticity magnitude and (b) spanwise velocity distributions during one cycle of whisker vibration within “fixed-gap” WIV stage at $S_x=90d_w$. The instantaneous positions of whisker sensor are superimposed as green ellipses.

Figure 7

Same as Fig. 6 but in the moment after cylinder movement with $S_x=90d_w, U_c=0.2U_f$, and instantaneous gap $x_g/d_w\approx 280$.

Figure 8

Same as Fig. 7 but in the moment with $S_x=50d_w, U_c=0.45U_f$, and $x_g/d_w\approx 90$.

Figure 9

Distribution of wake circulation strength $\mathrm{\Gamma }$ across instantaneous gaps for selected cases with (a) $S_x=50d_w$ and (b) $S_x=130d_w$. Panel (c) summarizes the results from panels (a) and (b) with $\mathrm{\Gamma }$ normalized by $(U_c+U_f)d_c$.

Figure 10

Spectra of whisker displacements within $t>T_{\text{tr}}$ for selected cases with (a) $S_x=50d_w$ and (b) $S_x=90d_w$. The gray dashed line denotes the frequency following Strouhal number of $\text{St}=0.19$.

Figure 11

Distribution of wake circulation strength $\mathrm{\Gamma }$ and the associated hydrodynamic force coefficient $C_y$ as a function of streamwise gap $x_{\mathrm{ss}}$ measured from “fixed-gap” WIV. Subplot reveals the relations between $\mathrm{\Gamma }$ and $C_y$ which follows $C_y\propto {\mathrm{\Gamma }}^2$.

Figure 12

Measured (black dashed lines) and modeled (red solid lines) time series of whisker displacements for selected cases.

Figure 13

The distribution of modeled hydrodynamic load decaying rate ${\gamma }_{\text{load}}$ superimposed with measured ${\gamma }_{\text{amp}}$ across various $S_x$ and $U_c$.

Figure 14

Time series of whisker displacements for selected cases with $S_y=5d_w$. The gray dot line denotes the equilibrium position of whisker sensor in static water.

Figure 15

Time series of equilibrium whisker vibration positions ${\mu }_w$ for selected cases with (a) $S_x=50d_w$; (b) $S_x=90d_w$; (c) $S_x=130d_w$. The horizontal gray dashed line denotes the equilibrium position in static water.

Figure 16

Decaying rate of whisker vibration intensity ${\gamma }_{\text{amp}}$ at both $S_y=0$ and $S_x=5d_w$.

Figure 17

Normalized vorticity magnitude distribution in the cylinder wake; the subplot shows extracted vorticity magnitude profile along streamwise distance at $y=0$ (black) and $y=0.5$ (red).