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

Abstract

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 (Ur∈[2,14]) and space ratios (L∗∈[2,6]). The incompressible Navier–Stokes equations are solved using the overset mesh method in the OpenFOAM® 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∗=2), the upstream cylinder (UC) has the traditional lock-in (the frequency ratio fy/fn≃0.95–1.05) at the reduced velocity (Ur≃7), and the downstream cylinder (DC) has a narrow lock-in region around Ur≃9. However, the UC has a wide soft-lock-in (the synchronization region of fy/fn≃1.15) at high reduced velocities (Ur≃8–10). Here, the transverse vibrations of both cylinders, but especially the DC, reach relatively high amplitudes. At a moderate spacing (L∗=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 (Ur≃8–14). At a large spacing (L∗=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 Ur = 7 and a wake-galloping region for Ur > 12.