Bendable ring vibration in a uniform flow

Abstract

An improved version of the immersed boundary (IB) method is developed for simulat-ing bendable ring clamped at one point with tension and bending stiffness in a uniform flow. The boundary of the ring consists of a flexible filament with tension and bending stiffness, which can be modeled as a linear spring with spring constant k and unstretched initial length. The internal area of the ring is conserved through the penalty method. For the Reynolds number of 100, resonance is observed at specific tension stiffness with fixed bending stiffness and also at specific bending stiffness with fixed tension stiffness in the same manner. The vibration phenomena and drag forces abruptly change through the resonance. The optimal tension and bending coefficient that minimize the drag force of the bendable ring is found. In our simulation we observe bistable states, one stationary and another oscillatory, that coexist over a range of flow velocities.