Vortex formation in the wake of an oscillating cylinder

Williamson, C. H. K.; Roshko, A.

doi:10.1016/s0889-9746(88)90058-8

Cited by 1,300 publications

(933 citation statements)

References 11 publications

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“…8). The vortex wake asymmetry is most likely due to non-linear near-vortex-wake interactions, as found by Williamson and Roshko (1988) for vibrating cylinders. How the vortex interactions in the wake and the interactions with the foil induce the wake asymmetry is largely unclear.…”

Section: Visualization Setupmentioning

confidence: 64%

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Wake visualization of a heaving and pitching foil in a soap film

Muijres

Lentink

2010

Animal Locomotion

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Many fish depend primarily on their tail beat for propulsion. Such a tail is commonly modeled as a twodimensional flapping foil. Here we demonstrate a novel experimental setup of such a foil that heaves and pitches in a soap film. The vortical flow field generated by the foil correlates with thickness variations in the soap film, which appear as interference fringes when the film is illuminated with a monochromatic light source (we used a high-frequency SOX lamp). These interference fringes are subsequently captured with high-speed video (500 Hz) and this allows us to study the unsteady vortical field of a flapping foil. The main advantage of our approach is that the flow fields are time and space resolved and can be obtained time-efficiently. The foil is driven by a flapping mechanism that is optimized for studying both fish swimming and insect flight inside and outside the behavioral envelope. The mechanism generates sinusoidal heave and pitch kinematics, pre-described by the non-dimensional heave amplitude (0-6), the pitch amplitude (0°-90°), the phase difference between pitch and heave (0°-360°), and the dimensionless wavelength of the foil (3-18). We obtained this wide range of wavelengths for a foil 4 mm long by minimizing the soap film speed (0.25 m s -1 ) and maximizing the flapping frequency range (4-25 Hz). The Reynolds number of the foil is of order 1,000 throughout this range. The resulting setup enables an effective assessment of vortex wake topology as a function of flapping kinematics. The efficiency of the method is further improved by carefully eliminating background noise in the visualization (e.g., reflections of the mechanism). This is done by placing mirrors at an angle behind the translucent film such that the camera views the much more distant and out-of-focus reflections of the black laboratory wall. The resulting high-quality flow visualizations require minimal image processing for flow interpretation. Finally, we demonstrate the effectiveness of our setup by visualizing the vortex dynamics of the flapping foil as a function of pitch amplitude by assessing the symmetry of the vortical wake.

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Section: Visualization Setupmentioning

confidence: 64%

“…The kinematics of a two-dimensional foil can be described using different dimensionless variables; we chose an approach inspired by the work of Williamson and Roshko (1988). We have published this approach (Fig.…”

Section: Dimensionless Parameterization Of a Flapping Foilmentioning

confidence: 99%

Wake visualization of a heaving and pitching foil in a soap film

Muijres

Lentink

2010

Animal Locomotion

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“…The drag spectrum, on the other hand, shows low energy in a wide frequency range, indicating that no definite pattern is markedly present, as also noted by Gopalkrishnan (1993) for high imposed motion periods. .10, in which the x-velocity is presented, also shows that is difficult to define the vortex-shedding pattern, as identified by Williamson & Roshko (1988). In this case, St/f i = 2.0, which falls into the region where Williamson could not define a vortical pattern.…”

Section: Iterative Convergencementioning

confidence: 86%

“…This is consistent with strong f s energy and the observed higher harmonics. Williamson & Roshko (1988) are observed. Figure 8.8 shows the imposed motion traces and lift coefficients for the case with U R = 10.0, thus also out of the lock-in range.…”

Section: Iterative Convergencementioning

confidence: 90%

“…Furthermore, analyzing the study done by Williamson & Roshko (1988), in which the vortex patterns are determined in the plot of A/D over f s /f i (in fact, they derive f s assuming St = 0.2, resulting f s = 0.2), for the present case (A/D = 0.3 and St/f i = 0.61), the expected vortex pattern is the C-mode, meaning that "near the cylinder we have the 2S or P+S modes, but the smaller vortices coalesce (...) immediately behind the body". This is consistent with strong f s energy and the observed higher harmonics.…”

Section: Iterative Convergencementioning

confidence: 99%

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Desenvolvimento da modelagem de turbulência e interação fluido-estrutura para as vibrações induzidas por vórtices de cilindro rígido.

Rosetti¹

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Finite element study of vortex-induced cross-flow and in-line oscillations of a circular cylinder at low Reynolds numbers

Mittal

Kumar

1999

Int. J. Numer. Meth. Fluids

118

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Vortex-induced vibrations of a circular cylinder placed in a uniform flow at Reynolds number 325 are investigated using a stabilized space-time finite element formulation. The Navier-Stokes equations for incompressible fluid flow are solved for a two-dimensional case along with the equations of motion of the cylinder that is mounted on lightly damped spring supports. The cylinder is allowed to vibrate, both in the in-line and in the cross-flow directions. Results of the computations are presented for various values of the structural frequency of the oscillator, including those that are sub and superharmonics of the vortex-shedding frequency for a stationary cylinder. In most of the cases, the trajectory of the cylinder corresponds to a Lissajou figure of 8. Lock-in is observed for a range of values of the structural frequency. Over a certain range of structural frequency (FJ, the vortex-shedding frequency of the oscillating cylinder does not match F s exactly; there is a slight detuning. This phenom.enon is referred to as soft-lock-in. Computations show that this detuning disappears when the mass of the cylinder is significantly larger than the mass of the surrounding fluid it displaces. A self-limiting nature of the oscillator with respect to cross-flow vibration amplitude is observed. It is believed that the detuning of the vortex-shedding frequency from the structural frequency is a mechanism of the oscillator to self-limit its vibration amplitude. The dependence of the unsteady solution on the spatial resolution of the finite element mesh is also investigated.

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Vortex formation in the wake of an oscillating cylinder

Cited by 1,300 publications

References 11 publications

Wake visualization of a heaving and pitching foil in a soap film

Wake visualization of a heaving and pitching foil in a soap film

Desenvolvimento da modelagem de turbulência e interação fluido-estrutura para as vibrações induzidas por vórtices de cilindro rígido.

Finite element study of vortex-induced cross-flow and in-line oscillations of a circular cylinder at low Reynolds numbers

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