ReCoVor

Abstract: Flow-induced vibrations (FIV) occur in a range of engineering applications, including mooring lines, pylons, and chimneys, where the suppression of these vibrations is paramount to structural fatigue mitigation. In contrast, renewable energy harvesting technologies seek to enhance these vibrations. Thus, a fundamental understanding of FIV is essential for the design of critical infrastructure and enabling emerging energy-harvesting technologies. 

Many studies have focused on the FIV of 2D bluff bodies such as circular cylinders. A singular elastically mounted cylinder is not subject to persistent vibrations beyond reduced velocities of U^*=U/f_{nw}D~12, where U is freestream velocity, f_{nw} is the natural frequency in water and D is body diameter. However, when placed in tandem behind a static cylinder, it can exhibit persistent monotonically increasing vibration response with increasing reduced velocities (Assi et al., JFM, 2010, 2013). An isolated sphere, on the other hand, has been reported to undergo persistent vibrations until U^*~300 (Jauvtis & Williamson, JFS, 2001). However, there is no published study yet investigating the FIV response of tandem spheres.

This talk will discuss the behavior of a spanwise elastically mounted sphere placed in tandem with an upstream static sphere of equal diameter. A series of systematic experiments are performed employing simultaneous displacement and wake measurements using a linear encoder and stereo article image velocimetry, respectively. The FIV response is characterized for a wide range of reduced velocities 2.5<U^* <22.5 and spacing ratios 1.5<L^* = L/D<10, where L is the separation distance between the two spheres . 

It is observed that at low reduced velocities (U^* < 10.5), an attenuated vibration response is observed for spacing ratios L^* <4, which presumably lies within the wake-deficit of the static sphere, thereby reducing the mean flow experienced by the sphere. Interestingly, at higher reduced velocities of U^* >10.5, vibrations monotonically increase with increasing reduced velocities for all spacing ratios. The vibrations were regularized and enhanced by up to 153% compared to an isolated sphere. These enhanced vibrations do not appear to be driven by streamwise vorticity known to drive vortex-induced vibrations of an isolated sphere. These vibrations are termed wake-enhanced vibrations and are characterized by significant energy transfer from fluid to the structure. This study advances our understanding of fluid-structure interaction mechanisms of tandem 3D bodies and motivates further work to understand the origins of fluid energy transfer to the system.

Abstract: A novel hierarchical decomposition for wake flows is introduced, enabling a nonlinear modeling framework for dissipation. The approach combines proper orthogonal decomposition with the maximal overlap discrete wavelet transform, yielding a method we denote as wPOD. The decomposition serves two purposes: (i) it provides a coherent reconstruction in space and time that isolates the shedding frequency and its harmonics, yielding modes whose temporal evolutions are narrowband and centered at the shedding frequency, its higher harmonics, and low-frequency components; and (ii) it extracts a representation of the dissipative small scales that remains nonlinearly correlated with the coherent motion. This nonlinear correlation reflects the well-known phenomenon of small scales riding on coherent structures and therefore sharing their convective velocity. Accordingly, both motions can be represented as convective waves of the form 

R(t)cos(2πft−k⋅x). For the large scales, the phase, cos(2πft−k⋅x), sustains the convective velocity Uc=f/kx, while the envelope R(t) varies slowly in time. For the small scales, the phase is irregular, whereas the envelope enforces the same convective velocity. By distinguishing these mechanisms, we characterize the dynamical coupling between coherent and dissipative scales and establish a physically grounded basis for nonlinear modeling of dissipation in wake vortex flows.