The problem of non-linear radiated waves generated by a submerged circular cylinder undergoing a forced heaving oscillation is studied. The Linear Potential Flow (LPF) theory approximation is used as a reference to the solution. A Computational Fluid Dynamics (CFD) commercial software FLOW-3D® is used to simulate Euler approximation of Navier-Stokes equations and generate radiated water wave data. Results show that non-linear radiated waves are not proportional to the heave amplitude and that the geometric decay follows a similar trend as linear waves. Moreover, for large heave amplitudes, in the vicinity of the cylinder, the radiated waves are horizontally asymmetric, and converge to their symmetric structure when propagating away.
The investigation is motivated by the large amplitude, resonant motions of wave energy converters (WECs). Recent literature on modelling of WEC hydrodynamics shows that non-linear models are required for accurate predictions of WEC motions during the resonant phase, and, thus, their energy absorption and performance (Schubert et al., 2020). However, the properties of the wave field during the resonant phase is a knowledge gap that will affect the performance of WEC arrays. According to linear potential flow (LPF) theory, which will be used as a reference in this study, the wave field surrounding a WEC consists of diffracted waves and radiated waves (Linton and McIver, 2001). In this paper, we will study the radiated waves created by a submerged cylinder undergoing large amplitude forced motions, where, for simplicity, the cylinder is restricted to heave oscillation.
The classical problem of a heaving surface piercing cylinder was treated by Yeung (1981), using the analytical solution of LPF theory. The formulation of the linear problem states that the radiated velocity potential, hence the radiated water waves, are proportional to the heave amplitude, and that away from the body the generated wave amplitude decays proportionally to the square root of the distance from the cylinder (also known as the geometric decay). Yeung (1981), studied the behaviour of the hydrodynamic coefficients (added mass and hydrodynamic damping) as the geometry and heave frequency of the cylinder changes. He found, for example, that at high frequencies the damping coefficient tends to zero and the added mass tends to a non-zero asymptotic value. Jiang et al. (2014) used LPF theory to model the hydrodynamic behaviour of a submerged heaving cylinder and found broadly similar behaviours to Yeung (1981). Sabuncu and Calisal (1981) showed that, for a surface piercing circular cylinder undergoing a forced oscillatory motion (i.e. heave, pitch and sway), there exist a difference between the hydrodynamics coefficients predicted by LPF theory and those derived from experimental data. They suggested that the discrepancy is related to viscosity, which is neglected by LPF theory.
