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In this study, two-dimensional time-resolved particle image velocimetry (2D-TR-PIV) was used to investigate the effect of the external domain on oscillating jets from double-feedback fluidic oscillators. Two different cases with different Re numbers (2680–10,730), as free external domain and fully confined were studied. Time-averaged results showed although a self-oscillating jet was attained for the free external domain, it could not be achieved for a fully confined geometry. For a fully confined geometry at Re = 2680, two symmetric vortices did not allow the jet to oscillate and at Re = 6440, the flow pattern in the external region became non-symmetric due to the Coanda vortex, subsequently, the self-oscillating jet was not observed. At Re = 10,730, the strength of the jet was inclined to cope with such vortices and tended to oscillate. However, strong vortices were created near the exit region of the fluidic oscillator, which led to an almost non-symmetric pattern. In addition, the proper orthogonal decomposition (POD) method and phase-averaged analysis were applied to obtain the unsteady behavior of flow and the most energetic dynamic structure. Interestingly, at Re = 6440, the third mode was still energetic for fully confined, but for other cases, the first two modes were the most energetic modes, which showed vigorous coherent structures.

Vortex-induced vibration (VIV) of a two degree-of-freedom (DOF) circular cylinder, placed in the test section of a recirculating water tunnel and free to oscillate in its first two vibrational modes in the crossflow direction, is studied experimentally. The dynamic response of the cylinder is studied for a reduced velocity range of $U^*=4\unicode{x2013}30$ for eigenfrequency ratios in the range of 1.3–3.0. For the two DOF system, while the onset of the VIV response followed a similar lock-in region as those observed for a classical VIV response of a single DOF system, by increasing the reduced velocity a secondary lock-in region was observed over which the oscillations of the cylinder were locked into the system's second mode. In addition, there existed an intermediate range of reduced velocity over which the VIV response consisted of oscillations at a combination of the first two natural modes of the system. As the eigenfrequency ratio between the first two modes increased, the secondary lock-in range was extended to higher reduced velocities and the reduced velocity range over which multi-modal oscillations were observed was decreased. A full map of vortex dynamics in the wake of the cylinder was developed qualitatively and quantitatively using hydrogen bubble flow visualization and time-resolved volumetric particle tracking velocimetry techniques, respectively. A Q-criterion analysis revealed the existence of highly three-dimensional vortex structures in the wake of the cylinder. The spatiotemporal mode analysis using the proper orthogonal decomposition technique revealed strong coupling between the vortex shedding modes in the wake of the cylinder and the structural vibration modes.

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