Numerical Simulation of Fluid Resonance in a Moonpool by Twin Rectangular Hulls with Various Configurations and Heaving Amplitudes

Fluid resonance in a moonpool formed by two identical rectangular hulls during in-phase heaving motion is investigated by employing a two-dimensional numerical wave flume based on OpenFOAM package with Re-Normalization Group(RNG) turbulent model. The focus of the study is to examine the influence of heaving frequency and amplitude with various moonpool configurations on fluid resonant behavior. It is found that the resonant frequency of wave response in moonpool tends to decrease with the increase of moonpool breadth and hulls draft. The decrease of resonant amplitude can be observed for large moonpool breadth. The influence of hulls draft on resonant amplitude is not remarkable, especially for large heaving amplitude. The increase in heaving amplitude results in the decrease of relative resonant amplitude in an approximate power function, implying a complicated dependence of the resonant amplitude on heaving amplitude. Flow patterns in the vicinity of the moonpool are also analyzed, mainly regarding the dependence on the heaving frequency. The negligible influence of vortices on the wave response in moonpool is expected for low-frequency excitation because it is hard to observe the vortex structures. Intensive vortical flow and vortex structure can be identified under resonant condition, which gives rise to significant dissipation and accounts for the smaller relative resonant amplitude in moonpool. As for high-frequency excitation, the vortex motion is rather weak and dissipates rapidly, leading to insignificant effect on wave response amplitude.

Fluid Resonance Between Twin Floating Barges with Roll Motion Under Wave Action

The wave-induced fluid resonance between twin side-by-side rectangular barges coupled with the roll motion of the twin barges is investigated by both numerical simulation and physical model test.A 2D numerical wave flume,based on an open source computational fluid dynamics(CFD)package OpenFOAM,is applied for the numerical simulation.After numerical validations and convergent verifications,the characteristics of the fluid resonance in the gap between the twin rolling side-by-side barges are examined.The resonant frequency of the oscillating fluid in the gap between the twin rolling barges decreases compared with that between the twin fixed barges.Generally,the twin barges roll in the opposite directions,and their equilibrium positions lean oppositely with respect to the initial vertical direction.A physical model test is carried out for a further investigation,in which the twin barges are set oppositely leaning and fixed.From the present experimental results,a linear decrease of the resonant frequency with the increasing leaning angle is found.Combined with the numerical results,the deflection of the equilibrium positions of the twin barges is a relevant factor for the resonant frequency.Besides,the effects of the gap width and incident wave height on the fluid resonance coupled with roll motion are examined.

Excitation of Zonal Flows by ion-temperature-gradient Modes Excited by the Fluid Resonance

We apply the reductive perturbation method to the simple electrostatic ion-temperature-gradient mode in an advanced fluid description. The fluid resonance turns out to play a major role for the excitation of zonal flows. This is the mechanism recently found to lead to the low-to-high （L-H） mode transition and to the nonlinear Dimits upshift in transport code simulations. It is important that we have taken the nonlinear temperature dynamics from the Reynolds stress as the convected diamagnetic flow. This has turned out to be the most relevant effect as found in transport simulations of the L-H transition, internal transport barriers and Dimits shift. This is the first time that an analytical method is applied to a system which numerically has been found to give the right experimental dynamics.

Modelling of multi-bodies in close proximity under water waves——Fluid resonance in narrow gaps

Viscous fluid model and potential flow model with and without artificial damping force(f=-μV,μ the damping coefficient and V the local averaging flow velocity) are employed in this work to investigate the phenomenon of fluid resonance in narrow gaps between multi-bodies in close proximity under water waves.The numerical results are compared with experimental data available in the literature.The comparison demonstrates that both the viscous fluid model and the potential flow model are able to predict the resonant frequency reasonably well.However the conventional potential flow model(without artificial damping term) significantly over-predicts the wave height in narrow gaps around the resonant frequency.In order to calibrate the appropriate damping coefficient used for the potential model and make it work as well as the viscous fluid model in predicting the resonant wave height in narrow gaps but with little computational efforts,the dependence of damping coefficient μ on the body geometric dimensions is examined considering the parameters of gap width Bg,body draft D,body breadth ratio Br and body number n(n = 2,3),where Br = BB/BA for the case of two bodies(Body A and Body B) with different breadths of BA and BB,respectively.It was confirmed that the damping coefficient used for the potential flow model is not sensitive to the geometric dimensions and spatial arrangement.It was found that μ∈ [0.4,0.5] may guarantee the variation of Hg/H0 with kh to be generally in good agreement with the experimental data and the results of viscous fluid model,where Hg is the excited wave height in narrow gaps under various dimensionless incident wave frequencies kh,H0 is the incident wave height,k = 2π/L is the wave number and h is the water depth.

Study of fluid resonance between two side-by-side floating barges

The hydrodynamic interaction between two vessels in a side-by-side configuration attracted research attentions in recent years. However, because the conventional potential flow theory does not consider the fluid viscosity, in the hydrodynamic results, the wave elevations were overestimated in the narrow gap under resonance conditions. To overcome this limitation and investigate the complex fluid flow around multiple bodies in detail, this study examines the fluid resonance between two identical floating barges using a viscous flow analysis program FLOW-3D. The volume of fluid method is implemented for tracking the free surface, and a porous media model is used near the outflow boundary to enhance the wave absorption. A three-dimensional numerical wave basin is established and validated by comparison with the waves generated using theoretical values. On this basis, a computational fluid dynamics （CFD） simulation of the two barges in a resonance wave period is performed, and the wave elevations, the fluid flow around the barges, and the motions of the barges are discussed. The numerical simulation is verified by comparison with results of corresponding experimental data.

Hydrodynamic Behavior of Gap Resonance in Multiple-Box Systems with Sharp and Round Inlet Configurations

Fluid resonance within narrow gaps in multiple-box systems with sharp and round inlet configurations are investigated by using the potential flow and viscous fluid flow models in the OpenFOAM^(■)package.Evident discrepancy between two numerical models can be observed for sharp inlet configurations.In addition to the dramatical decrease of resonant amplitude in narrow gaps,some peak values at the higher resonant frequencies predicted by the potential flow model even disappear in the viscous fluid flow results.The decreased normalized resonant amplitudes with the increase of incident wave amplitude can be observed for sharp inlet configurations.However,the hydrodynamic behaviors of multiple-box system with round inlet configurations between potential flow and viscous fluid flow models are quite similar with each other.The normalized resonant amplitudes are nearly independent of incident wave amplitudes for multiple-box systems with round inlet configurations.This implies that the energy dissipation associated with fluid viscosity and flow rotation plays an important role in the gap resonance for sharp inlet configurations;while it is insignificant for round inlet configurations.

Effects of Free Heave Motion on Wave Forces on Two Side-by-Side Boxes in Close Proximity Under Wave Actions

Wave forces on two side-by-side boxes in close proximity under wave actions were analyzed using the OpenFOAM package.The upstream box heaved freely under wave actions,whereas the downstream box remained fixed.For comparison,a configuration in which both boxes were fixed was also considered.The effects of the heave motion of the upstream box on the wave loads,including the horizontal wave forces,vertical wave forces,and moments on the boxes,were the focus of this study.Numerical analyses showed that all frequencies at which the maximum horizontal wave forces,maximum vertical wave forces,and maximum moment appeared are dependent on the heave motion of the upstream box and that the effects of the heave motion on these frequencies are different.Furthermore,these frequencies were observed to deviate from the corresponding fluid resonant frequency.Moreover,the heave motion of the upstream box reduced the wave forces acting on both boxes and altered the variation trends of the wave forces with the incident wave frequency.

Theoretical and numerical investigations of wave resonance between two floating bodies in close proximity

A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The relationship among the resonant response amplitude and frequency, the reflection and transmission coefficients, the gap width, and the damping coefficient is obtained. A quantitative link between the damping coefficient of the theoretical dynamic model（ε） and that devised for the modified potential flow model（μ_p） is established, namely, μ_p=3πεω_n/8 （where ω_n is the natural frequency）. This link clarifies the physical meaning of the damping term introduced into the modified potential flow model. A new explicit approach to determine the damping coefficient for the modified potential model is proposed, without resorting to numerically tuning the damping coefficient by trial and error tests. The effects of the body breadth ratio on the characteristics of the gap resonance are numerically investigated by using both the modified potential flow model and the viscous RNG turbulent model. It is found that the body breadth ratio has a significant nonlinear influence on the resonant wave amplitude and the resonant frequency. With the modified potential flow model with the explicit damping coefficient, reasonable predictions are made in good agreement with the numerical solutions of the viscous fluid model.