Transverse vortex-induced vibration of two elliptic cylinders in tandem: Effects of spacing

Renewable energy converters, such as bio-inspired fluttering foils, are gaining popularity due to their eco-friendly properties. However, the system with multiple objects has received scant attention. Here, we analyze how spacing influences the transverse (one-degree-of-freedom) vortex-induced vibration of two tandem identical elliptic cylinders at a constant Reynolds number by employing a wide range of reduced velocities (U-r is an element of[2,14]) and space ratios (L-& lowast;is an element of[2,6]). The incompressible Navier-Stokes equations are solved using the overset mesh method in the OpenFOAM (R) library. The findings indicate that the wake structure goes through eight distinct wake modes, as well as two gap flow patterns (reattachment and co-shedding). Vibrational responses, force parameters, and flow patterns determine three spacing configurations. At a small spacing (L-& lowast;=2), the upstream cylinder (UC) has the traditional lock-in (the frequency ratio f(y)/f(n)similar or equal to 0.95-1.05) at the reduced velocity (U-r similar or equal to 7), and the downstream cylinder (DC) has a narrow lock-in region around U-r similar or equal to 9. However, the UC has a wide soft-lock-in (the synchronization region of f(y)/f(n)similar or equal to 1.15) at high reduced velocities (U-r similar or equal to 8-10). Here, the transverse vibrations of both cylinders, but especially the DC, reach relatively high amplitudes. At a moderate spacing (L-& lowast;=3), the UC bears a lock-in zone analogous to a single cylinder with the same mass ratio, while the DC shows a vast soft-lock-in zone (U-r similar or equal to 8-14). At a large spacing (L-& lowast;=4, 5, and 6), the amplitude of the DC is often larger than that of a single cylinder when it is in the lock-in region. The DC exhibits a peak in amplitude at U-r = 7 and a wake-galloping region for U-r > 12.