The piston mode fluid resonance in the narrow gap between a moored floating body and a bottom-mounted vertical wall is numerically investigated based on a two-dimensional potential flow model and viscous numerical simulations. This study focuses on understanding the effect of mooring stiffness on the coupling dynamics of the gap resonance and the sway or heave motion of the floating body in regular waves. Numerical studies show that the resonant wave amplitude in the gap is reduced by the sway and heave motions. The reduction is highly dependent on the mooring stiffness. Two resonant frequencies are confirmed, and both increase with the mooring stiffness. Different modes of motions are identified in terms of the phase difference between the oscillatory motions of the gap flow and the floating body. Higher harmonic components of responses are found for the specific mooring stiffness. The performance of potential flow models in predicting resonant responses is revisited based on the understanding that the overall damping effect consists of two parts: (1) radiation damping and (2) viscous dissipation. It is confirmed that a potential model is also able to produce reasonable predictions as radiation damping plays a dominant role, for example, at the second resonant frequencies of coupling the gap resonance with the sway motion. Otherwise, as viscous dissipation dominates radiation damping, noticeable over-predictions by a potential model occur as recognized before, for example, the present results at the second peak response of gap resonance with the heave motion. The relative viscous dissipation is quantified with the reflection coefficient of viscous numerical results, while the radiation damping is quantified based on a specially designed radiation potential model with inputs of viscous numerical solutions.
This article presents numerical results of flow-induced rotary oscillation of a circular cylinder with rigid splitter plate in steady flow. Different from the previous examinations with freely rotatable assembly which mainly considered linear restoring force, the rotary oscillation of the structure in this work is modelled by a Duffing oscillator with both linear and nonlinear restoring force, denoted by dimensional k and ε, respectively. Numerical simulations were carried out for various reduced velocities Ur ∈ [9 to 15] and ε ∈ [0 to 20] at a relatively low Reynolds number. Our previous investigations of a purely linear oscillator (i.e., ε = 0) show that the equilibrium position of the rotary oscillation is not parallel to the free stream as the reduced velocity exceeds a critical value, that is, bifurcation occurs. The present numerical studies suggest that, for a specific reduced velocity Ur, the increase in the nonlinear stiffness ε can eliminate the undesirable bifurcation. The numerical results also suggest that both odd and even-number lift frequency components appear for bifurcate cases, while only odd-number lift frequencies are observed for non-bifurcate cases. The dynamic mode decompositions for the wake flow corresponding to each lift frequency are presented.
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