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Wake dynamics behind a seal-vibrissa-shaped cylinder: a comparative study by time-resolved particle velocimetry measurements

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Abstract

The wake dynamics behind a seal-vibrissa-shaped cylinder, which are closely related to the seal’s extraordinary ability to faithfully track the hydrodynamic trails of its upstream prey, were extensively studied by using time-resolved particle image velocity. Four cylindrical configurations that shared the same hydrodynamic diameter (i.e., a circular cylinder, an elliptical cylinder, a wavy cylinder, and a vibrissa-shaped cylinder) were chosen for the comparative study at the Reynolds number 1.8 × 103. The instantaneous flow fields behind the cylinders were measured along their vertical and horizontal planes. The distinct global differences between the wakes were determined from the streamline patterns, the reverse-flow intermittences, and both the streamwise and longitudinal velocity fluctuation intensities. Compared to the other three systems tested, the vibrissa-shaped cylinder system was characterized by a considerably reduced recirculation zone in the nodal plane, the existence of a very stably reversed flow, and substantial reductions in the streamwise and longitudinal velocity fluctuation intensities. Further cross-correlation of the fluctuating longitudinal velocities showed that the unsteady events behind the vibrissa-shaped cylinder were poorly organized by sequence and considerably constrained in their spatial extent. Finally, a dynamic mode decomposition (DMD) was performed on the instantaneously varying wake flows. In the wavy cylinder system, a single dominant DMD mode at St = 0.2 (corresponding to Karman vortex street) was detected in both the saddle and nodal planes. Although the dominant DMD modes at St = 0.23 and 0.3 were determined in the saddle and nodal planes of the vibrissa-shaped cylinder system, respectively, the spatial pattern of these two DMD modes showed resolved vortical structures that were highly distorted and constrained to an extremely limited space. These DMD modes had much less energy than those in the other three systems. The phase-dependent variations of the wake flows disclosed that the complex unsteady behavior at distinctly different frequencies in the saddle and nodal planes disrupted the regular vortex shedding process, suppressing the vortex-induced vibration of the vibrissa-shaped cylinder.

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Abbreviations

CCD:

Charge-coupled device

CMOS:

Complementary metal oxide semiconductor

DMD:

Dynamic mode decomposition

PIV:

Particle image velocimetry

POD:

Proper orthogonal decomposition

RAID:

Redundant arrays of independent disks

SSD:

Solid-state disk

TR-PIV:

Time-resolved particle image velocimetry

VIV:

Vortex-induced vibration

B :

System matrix

C :

Companion matrix

D h :

Hydraulic diameter [m]

Re D :

Reynolds number (based on the hydraulic diameter)

f :

Frequency [Hz]

U :

Discrete velocity matrix

U 0 :

Free-stream velocity [ms−1]

\(Uc\) :

Convection speed of the vortices [ms−1]

\({\bar{u}}\) :

Time-averaged streamwise velocity [ms−1]

u′:

Fluctuating part of the streamwise velocity [ms−1]

\({u}_{\text{rms}}^{{\prime }}\) :

Root mean square of the streamwise velocity fluctuations [ms−1]

v′:

Fluctuating part of the longitudinal velocity [ms−1]

x :

Streamwise coordinate [m]

y :

Longitudinal coordinate [m]

z :

Spanwise coordinate [m]

x 0 :

Streamwise coordinate of the reference point [m]

St :

Strouhal number

\(\rho_{vv}\) :

Two-point spatial v–v correlation

\(\rho_{uu}\) :

Two-point spatial u–u correlation

\(\tau\) :

Time delay [s]

\(\gamma_{t}\) :

Reverse-flow intermittency coefficient

\(\varPhi\) :

Dynamic modes

\(\parallel {\phi} \parallel\) :

DMD eigenfunction

\(\lambda_{ci}\) :

Swirling strength

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Acknowledgments

The authors gratefully acknowledge financial support for this study from the National Natural Science Foundation of China (Grant No. 11372189).

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Authors and Affiliations

  1. Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

    Shaofei Wang & Yingzheng Liu

  2. Gas Turbine Research Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

    Shaofei Wang & Yingzheng Liu

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  1. Shaofei Wang
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  2. Yingzheng Liu
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Correspondence to Yingzheng Liu.

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Wang, S., Liu, Y. Wake dynamics behind a seal-vibrissa-shaped cylinder: a comparative study by time-resolved particle velocimetry measurements. Exp Fluids 57, 32 (2016). https://doi.org/10.1007/s00348-016-2117-9

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  • DOI: https://doi.org/10.1007/s00348-016-2117-9

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