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.

Numerical Study on Aerodynamic Performance of Floating Dual-Rotor Wind Turbines in Heave and Surge Motions

Compared with the traditional wind turbine of a single rotor,dual-rotor wind turbines(DRWTs)have higher wind energy capture efficiency and a more complex structure.Therefore,the aerodynamic performance of the DRWT installed on the floating platform will be greatly affected by the motion caused by wind and wave loads.In this paper,5 MW and 750 kW single rotor wind turbines(SRWTs)are combined into a 5 MW-5 MW DRWT and a 5 MW-750 kW DRWT,and their power output and wake field characteristics in different motions are studied.The flow field is obtained by solving the Reynolds-averaged Navier–Stokes equation(RANS).The overset grid technique is employed to achieve the large-amplitude multiple-degree-of-freedom motion of the DRWT.The overall performance of the 5 MW single rotor wind turbine is determined by a numerical method.For the DRWTs,numerical results show that the surge motion and heave motion both have a negative effect on the power output of the DRWT.The surge motion is a critical factor that causes the power output of the DRWT to periodically change with motion.The average power output of the DRWT influenced by motion is lower than that of a DRWT with a fixed bottom.The surge motion significantly disturbs the wake of the DRWT due to the mutual interference between the upstream and downstream rotors.Under the influence of heave motion,low-velocity regions downstream of the blade tip are enhanced.This study indicates that attenuating the surge and heave motion of offshore DRWT is very significant for improving its efficiency and should be taken into consideration during the design procedure.

A novel tuned heave plate system for heave motion suppression and energy harvesting on semi-submersible platforms

Deepwater offshore structures such as semi-submersible platforms suffer powerful ocean waves due to their location and site condition. The long distance away from the shore also brings many difficulties to energy supply for the platform operation. How to reduce the response of the platform and convert the wave energy into electrical power is a meaningful topic. In this paper, a tuned heave plate system(THP) is presented and designed to be employed on a semi-submersible platform for heave motion suppression and energy harvesting. This THP system is composed of spring supports, a power take-off system(PTO), and a heave plate. The PTO system is a permanent magnet linear generator(PMLG), which could directly convert the kinetic energy of the heave plate into electronic power. The stiffness of the spring supports is designed based on the principle of the tuned mass damper(TMD). The numerical model of the platform and the THP system is established according to the hydrodynamic analysis results of the platform. The model is tested and modified by scale model tests on the platform in the wave tank. A parameter study, including the size, tuned period, and damping ratio of the THP system, is conducted systematically based on the numerical model. The optimal parameters of the THP are selected due to the maximum heave motion reduction under severe wave conditions in South China Sea. The performance of the semi-submersible with and without the THP system under different wave conditions is analyzed. It is demonstrated that this novel tuned heave plate system could reduce the heave motion of the semi-submersible platform significantly and generate considerable power, which makes the THP system have a broad prospect for development.

Study on Transient Gap Resonance with Consideration of the Motion of Floating Body

In this paper, the transient fluid resonance phenomenon inside a narrow gap between two adjacent boxes excited by the incident focused waves with various spectral peak periods and focused wave amplitudes is simulated by utilizing the open-sourced computational fluid dynamics software, Open FOAM. The weather-side box is allowed to heave freely under the action of waves, and the lee-side box keeps fixed. This paper mainly focuses on how both the spectral peak period and the focused wave amplitude affect the free-surface amplification inside the gap, the motion of the weather-side box, and the wave loads(including the vertical and the horizontal wave forces) acting on both boxes.For comparison, another two-box system with both boxes fixed is also considered as a control group. It is found that the motion of the weather-side box significantly changes the characteristics of the transient gap resonance, and it would cause that the fluid resonant period becomes 1.4-1.6 times that of the two-box system with both boxes fixed.All the concerned physical quantities(i.e., the free-surface amplification in the gap, the motion of the weather-side box, the wave loads) are found to closely depend on both the spectral peak period and the focused wave amplitude.

Investigation of Pitch Motion Portion in Vertical Response at Sides of a Tension-Leg Platform

Tendons vertically moor Tension-Leg Platforms （TLPs）, thus, a deep understanding of physical tendon stresses requires the determination of the total axial deformation of the tendons, which is a combination of the heave, pitch, and surging responses. The vertical motion of the lateral sides of the TLP is coupled with surge and constitutes a portion of the pitch motion. Tendons are connected to the sides of the TLP; hence, the total displacement of the lateral sides is related to the total deformation of the tendons and the total axial stress. Therefore, investigating the total vertical response at the sides of the TLP is essential. The coupling between various degrees of freedom is not considered in the Response Amplitude Operator （RAO）. Therefore, in frequency domain analysis, the estimated vertical RAO is incomplete. Also, in the time domain, only the heave motion at the center of TLP is typically studied; this problem needs to be addressed. In this paper, we investigate the portion of the pitch motion in the vertical response at the sides of the TLP in both the frequency and time domains. Numerical results demonstrate a significant effect of the pitch motion in the vertical motion of the edges of the TLP in some period ranges.

Numerical Simulation of the Motion of A Floating Body with Partially Filled Tanks by A Pressure-Convection Particle Method

The moving particle semi-implicit（MPS）method has demonstrated its usefulness in practical engineering applications.Although it has wide applicability,it is still hard to predict the pressure precisely using the MPS method.A pressure-convection particle method based on the MPS method is proposed to overcome this problem.The improved performance of this new method is validated with computational and measured results.The approach is also applied to compute the problem of sloshing associated with floating body motion in waves.The pressure-convection MPS method demonstrated its capability to improve the prediction of pressure.

Experimental Study of A Pile-Restrained Floating Breakwater Constructed of Pontoon and Plates

A pile-restrained pontoon-plate floating breakwater is proposed in this paper. The laboratory physical-model tests are conducted to investigate the wave-dissipation property and heave-motion response of a model. The influence of the model＇s geometric parameters including relative pontoon width, plate width, number of plates and pontoon draft on wavedissipation performance and heave-motion response are discussed, as well as the correlation between these two factors. The result indicates that wave-dissipation performance of the proposed structure is better than the pontoon structure： its transmission coefficient and heave-motion height are reduced by 0.2 and 0.3, respectively, in comparison with those of the pile-restrained pontoon model at a relative pontoon width of 0.2.

Investigation on Effects of Vertical Degree of Freedom on Gap Resonance Between Two Side-by-Side Boxes Under Wave Actions

The possible wave resonance in the narrow gap formed by the parallel arrangement of ships will lead to the sharp increase of wave loads and the rapid growth of motion response.The fluid resonance inside a narrow gap between two side-by-side boxes is investigated numerically based on an open-source CFD package,OpenFOAM.The upstream box remains fixed,while the downstream box is allowed to heave freely under wave actions.This work aims to examine the influence of the motion of the downstream box on the fluid resonant behaviors inside the gap.The hydrodynamic behaviors considered include the wave height inside the gap,the heave displacement,and the reflection,transmission,and energy loss coefficients.Gao et al.(2021)reported the influence of the motion of the upstream box on gap resonant behaviors.For comparative study,some results of Gao et al.(2021)are also presented in this work.It is found that the heave motion of any box in the two-box system leads to a smaller resonant wave height amplification and a larger fluid resonance frequency.The frequency at which the maximum heave displacement of the downstream box occurs is less than the fluid resonant frequency.The heave motion of any box in the two-box system results in a larger reflection coefficient and a smaller energy loss coefficient.

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.

A Practical Hull Form Design of Ferry Using Hybrid Scheme Method and Performing Experiment

Prediction of ship performance in preliminary ship design is an important consideration. It could guarantee ship in safe and comfort. However, many design works did not involve simultaneously ship performances predictions in preliminary design. Moreover, ship designers sometimes modified a ship form to obtain proper design without ship performance consideration. Therefore, this study concerns on predictions of total resistance and added wave resistance of a ferry using a hybrid particle-grid method and then its motions response after modifying bow and stern parts by conducting experiment. Research results show total resistance and added wave resistance have a significant different, therefore, it would be an important consideration in determining ship powering in preliminary ship design. The non-dimensional added wave resistance increases in increasing wave length from λ/Lpp = 0.5 to 1.0 and it decreases after L/λ = 1.0. In addition, it tends to decrease caused by increasing ship speed. The comparison of averaged heave and pitch amplitudes between basic forms after modifying bow and stem parts is quiet similar. However, the rolling amplitude of the modified form is significantly higher comparing with the basic form. We conclude that a ship could be design in preliminary design take into account performances predictions by using numerical method and experimental work.

The Investigation of the Effect of Heaving and Pitching on Wave-Induced Vertical Hull Vibration of a Container Ship in Regular Waves

The aim of this paper is to investigate the effect of heaving and pitching of ship motion due to springing bending moment. The investigation was conducted both experimentally and validated theoretically. Series of experiment were carried out using a container model-ship of which length was 3 meter, and the possibility of the so-called nth resonant springing vibration is tested by taking n from n = 2 to n = 4. The bending moment due- to vibration is also measured. The following conclusions were obtained： （l） Occurance of the higher order resonant vibration between 2nd-4th is recognized experimentally; （2） The results indicated that heaving and pitching of ship motion influenced the springing bending moment accurately.

Aerodynamic Performance of a Flapping Foil with Asymmetric Heaving Motion near a Wall

The effect of asymmetric heaving motion on the aerodynamic performance of a two-dimensional flapping foil near a wall is studied numerically. The foil executes the heaving and pitching motion simultaneously. When the heaving motion is symmetric, the mean thrust coefficient monotonically increases with the decrease in mean distance between foil and wall. Meanwhile, the mean lift coefficient first increases and then decreases sharply. In addition, the negative mean lift coefficient appears when the foil is very close to the wall. After the introduction of asymmetric heaving motion, the influence of wall effect on the force behavior becomes complicated. The mean thrust coefficient is enhanced when the duration of upstroke is reduced. Moreover, more and more enhancement can be achieved when the foil approaches the wall gradually. On the other hand, the positive mean lift coefficient can be observed when the duration of downstroke is shortened. By checking the flow patterns around the foil, it is shown that the interaction between the vortex shed from the foil and the wall can greatly modify the pressure distribution along the foil surface. The results obtained here might be utilized to optimize the kinematics of the Micro Aerial Vehicles （MAVs） flying near a solid wall.

Numerical study of fluid resonance of a two-dimensional heaving-free moonpool in a wide range of incident waves

The fluid resonance of a moonpool freely heaving in a beam sea is studied by an in-house constrained interpolation profile(CIP)code.Generally,the moonpool behaves as in the piston mode with a narrow opening.The numerical studies are carried out for a wide range of the incident waves,and a new secondary resonant region is identified in the low frequency region of the incident waves,besides the ordinary main resonant region.Numerical results demonstrate that the horizontal wave forces are significant in the secondary resonant region,although the resonant wave elevations are less remarkable than those of the main resonant region.It is concluded that the fluid resonance of the low frequency is excited mainly by the heave motion of the moonpool.Parameter studies of the moonpool draft and the gap width of the moonpool based on the fluid resonance are also performed.

Numerical simulations of 2-D floating body driven by regular waves

An improved meshing method based on Fluent is used to update the computational meshes in solving the Navier-Stokes （N-S） equations for viscous and incompressible free surface flows with the volume of fluid （VOF） method. To maintain the mesh quality when updating meshes for a moving structure, the computational domain is separated into several parts and each part corre- sponds to a specific type of body motion. The numerical results of the interaction between the floating body and the regular waves agree well with the experimental data. A total of eight typical motion types are simulated separately to understand the correlation between the motion types and the wave transmission as well as the forces acting on the floating body. Numerical experiments show that the wave transmission increases in the case of sway and heave motions and decreases in the case of pitch motion as compared with the stationary case. It is also found that the sway motion reduces the horizontal wave force acting on the floating body, while the heave motion enhances the vertical wave force.

STATE-SPACE MODELLING OF DYNAMIC SYSTEMS IN OCEAN ENGINEERING

Pertaining to dynamic systems in general, a review is given of relations between mathematical descriptions in the frequency domain or time domain and state-space descriptions. For the analysis of hydrodynamic problems in ocean engineering wave forces may be represented by convolution integrals. The paper presents a method to construct a finite-order state-space model which represents a good approximation to such a convolution integral. The method utilizes a particular algorithm to compute the partial derivative of the exponential function of a (state-space) matrix with respect to the matrix elements. The method is applied to an example of fitting a state space model of order five to the free oscillations corresponding to wave radiation in a transient experiment with an oscillating water column.