Wave Drift Forces Research Articles

A Wave Drift Force Model for Semi-Submersible Types of Floating Wind Turbines in Large Waves and Current

The correct prediction of slowly varying wave drift loads is important for the mooring analysis of floating wind turbines (FWTs). However, present design analysis tools fail to correctly predict these loads in conditions with current and moderate and large waves. This paper presents a semi-empirical method to correct zero-current potential-flow quadratic transfer functions (QTFs) of horizontal wave drift loads in conditions with current and moderate and large waves. The method is applicable to column-stabilized types of substructures or semi-submersibles. In the first step, the potential-flow QTF is corrected for potential-flow wave–current effects by applying a heuristic method. Second, the generalized Exwave formula corrects for viscous drift effects. Viscous drift effects become important for moderate and large waves. Conditions with current in the same direction as the waves increase the viscous drift contribution further. The method is validated by comparing QTF predictions with empirical QTFs identified from model test data for the INO Windmoor semi. While potential-flow QTFs agree well with the empirical data for small seastates without current, they underestimate the wave drift loads for moderate and large seastates. Conditions with current increase the underestimation. The semi-empirical correction method significantly improves predictions.

A rapid motion forecast strategy for ships in waves using seakeeping and maneuvering modules

This paper develops a new navigation assisted system for ships with time-varying wave disturbances. A new framework is presented using seakeeping and maneuvering modules to achieve the fast forecast of ship motions. S175 containership and KVLCC2 tanker are adopted to verify the seakeeping module. Based on the validated module, the heave, roll and pitch motions of a cruise ship in different conditions are calculated by using three-dimensional Rankine panel method. The horizontal surge, sway and yaw motions of ships can be rapidly evaluated by using MMG model considering the wave drift forces. Finally, the motion amplitudes of 6°-of-freedom can be forecasted rapidly by using seakeeping and maneuvering modules. The study provides the insight into the motions of ships in waves. It is of great engineering application value to evaluate the total ship motion amplitudes and to improve the safety of navigation of ships in waves.

Wave motion in a narrow gap coupling with the roll motion of a vessel next to an offshore terminal

Concerning the scenario of a vessel operating alongside an offshore terminal, the vessel being the floating body and the offshore terminal bottom-mounted. The closeness of the two bodies leads to the formation of a long narrow gap, within which the large amplification of the water-surface elevation could occur. The coupling effect between the roll motion of the vessel and the water-surface motion within the gap is primarily concerned. Under the assumption that the quay wall of the terminal is infinitely long and fully reflective, the imaging principle and a modified Green's function have been developed to investigate such an effect. Numerical models are developed based on the two proposed approaches, respectively, in conjunction with a higher-order boundary element method. For a small gap width, the p = 1 resonant mode of water-surface motion in the gap can apparently enhance the roll motion of the vessel. The radiation wave owing to the enhanced roll motion can in turn disturb the water-surface motion, increasing the frequency of the dominant peak while decreasing its amplitude. As the gap width increases, the water-surface elevation around the resonant frequency of roll motion gets more and more noticeable, gradually becoming the dominant peak. The effect of the mooring stiffness is also discussed, revealing the existence of a ꞌnon-resonance regionꞌ where no resonance occurs in this specific frequency region. It is also noted that the resonant water-surface motion of p = 1 mode can cause a remarkable amplification of the negative horizontal mean wave drift force, pushing the vessel away from the terminal.

Investigation of wave effects on motion of an unmanned surface vehicle at various scales

Motion characteristics of unmanned surface vehicle are mainly affected by sea wave during its operation. This paper shows the numerical results of the unmanned surface ship at various scales in irregular waves based on the boundary element method. The effects of different sea states on each scaled model in a head sea, bow quartering sea, and beam sea are analyzed to predict the safety region of the ship motion. The significant amplitudes of ship motion are obtained from the ship motion responses in regular waves. Steady wave drift forces in the cases of bow oblique sea are calculated to find the impact of second-order waves on the models. It is proved that the motion of model C is remarkable in the narrow frequency domain from 0.2 to 1.4 rad/s but the ship responses of model A are considerable in the range of frequency of 0.2 to 2.5 rad/s. The significant amplitude of surge and pitch motion reaches the peak values in head sea conditions while the peak values of yaw motion are in the oblique sea of 120 degrees. The left motion is maximum in head sea condition.

Numerical simulation of free-running turning test of ship in waves

In this study, the turning abilities of a KVLCC2 vessel in calm water and waves are studied using free-running simulations based on an open-source computational fluid dynamics (CFD) library. The flow fields are governed by the unsteady Reynolds-Averaged Navier-Stokes (RANS) equations with the stabilized k-ω SST turbulence modeling. To imitate free-running ships, the overset method is employed with body force propeller modeling. The numerical method is verified by conducting an uncertainty analysis suggested by the ITTC for the calm-water turning. In addition, it is validated for the various wave conditions selected in this study. Then the effects of wavelength and wave direction are studied. The results show difference within 15% with experimental data of turning parameters, trajectories, and time signals of the ship responses. During the turning phase, separate flows due to the ship drift angle caused a notable reduction in pressure near the propeller hub. The effect of the wavelength on the ship turning ability is the most remarkable for short wavelengths, mainly due to the increased sway wave drift force, causing a loss in the ship drift angle. The wave direction had a significant influence on the initial turning characteristics; however, as time passed, the turning characteristics remained unchanged.

Stereo Reconstruction Method for 3D Surface Wave Fields around a Floating Body Using a Marker Net in a Wave Tank

Spatial wave fields around floating bodies are important for the understanding of hydrodynamics, and particularly the wave drift forces, of floating bodies in waves; however, experimental measurement of these fields is challenging. This paper presents a stereo reconstruction method for three-dimensional (3D) surface wave fields around floating bodies in a wave tank. Styrofoam markers were attached to a flexible net in a regular grid, called a marker net, and were placed on the water surface to be used as targets for stereo cameras (SCs). A thin plate spline was applied to the markers detected by the SCs to reconstruct the 3D surface wave profile around a floating body model. The proposed method was validated by measuring the wave field around a cylindrical floating body with a footing at its bottom. These experiments were conducted under regular wave incidence conditions. A wave elevation time series measured using a servo-controlled wave gauge was used as the benchmark data. The 3D surface wave field reconstruction method was applied under three different conditions: without the model, with a fixed model, and with a freely oscillating model. The results showed reliable reconstructions of the scattering and radiation waves. The marker net’s effects on the floating body’s motion and the surrounding wave fields were shown to be negligible by comparing the results acquired with and without the marker net.

Numerical study of second-order wave forces using a Rankine panel method

Numerical analysis of the wave forces acting on ships can be complex primarily because of the interactions between incident waves and structures. In this paper, the three-dimensional frequency domain Rankine panel method is used to study the seakeeping and second-order wave drift forces of a ship in waves. The model considers second-order wave forces acting on the ship hull and therefore accounts for slow drift ship motions and the added resistance. The second-order wave forces are evaluated using the pressure integral method, also known as the near-field approach. The unsteady velocity potential is divided into three parts namely (a) incident, (b) diffraction and (c) radiation to satisfy the Laplace equation. To avoid wave reflection the Rayleigh’s artificial friction is used in way of the free surface boundary. This method is equivalent to introducing a numerical damping beach for energy dissipation. The numerical results are compared with those of experiments for Wigley-III hull in head waves and the SCb-84 hull in oblique waves. Good agreement is obtained.

Mean Drift Wave Forces on Arrays of Bodies Surrounded by Thin Porous Surfaces

A semi-analytical solution is presented for the evaluation of mean drift wave forces on arrays of structures composed of impermeable vertical cylindrical bodies and surrounded by thin, porous surfaces. The porous cell is assumed to have fine pores so that a linear pressure drop can be considered. The mean drift wave forces on the array are determined via two principally different approaches: the momentum conservation theory and the direct integration of all pressure contributions upon the bodies’ instantaneous wetted surfaces. A solution method that solves the corresponding diffraction problem following the multiple scattering approach is proposed to account for the hydrodynamic interaction phenomena between the waves and the bodies. Numerical results are presented which illustrate the consistency of each of the two approaches in accurately evaluating the mean wave drift forces on several examined array configurations. It is shown that the thin, porous surface significantly reduces the drift forces on the array of bodies, whereas at specific wave frequencies, local enhancements of the forces’ values are noted due to the amplified wave field between the members of the array.

Numerical study on mean wave drift forces and moment of ships using Rankine panel method in frequency domain

A three-dimensional frequency-domain seakeeping model based on the Rankine panel method is developed to compute the mean wave drift forces and moment acting on ships with forward speeds. Two different linearization models (the double-body and Neumann–Kelvin models) are applied to evaluate the mean wave drift forces and moment using a near-field method. In these models, the Rayleigh’s artificial friction is adopted in the free-surface boundary condition to suppress longer wave components in computational regions apart from the ship. A novel upwind difference scheme is introduced to calculate the first-order and second-order derivatives of the velocity potential on the free surface. Wigley I, Wigley III and S175 containership are adopted in numerical simulations to validate the effectiveness of the developed model. In the present study, the motion response amplitude operators in head, beam and oblique seas obtained using the two models are compared, and their contributions to the mean wave drift forces and moment are analyzed. Results show that in head seas, the pitch motions have significant effects on the surge-directional wave drift force Fx. In beam seas, the heave motions have the most effect on the mean wave drift forces and moment (Fx, Fy and Mz).

Investigation of second-order low-frequency wave forces approximations for moored floating structures

Floating structures are widely used in both shallow and deep waters in industries such as offshore oil, gas, and wind. However, the safety of floating structures subject to long-crested irregular waves is threatened by slowly varying wave drift forces. In this study, the mesh-convergence laws for a panel model, which is used to calculate second-order potentials using a near-field approach, are investigated using a semi-submersible platform as an example. The effect of the relative-wave-height component of low-frequency (LF) wave forces is sensitive to the mesh near the waterline; therefore, it should be fully refined. The key difference-frequency band of the quadratic transfer function (QTF) matrix is investigated using time-domain-coupled dynamic analysis with a truncated QTF matrix. The results show that a difference-frequency limit of 0.4 rad/s is sufficient to calculate the slow drift and mooring tension. Based on prior approximations of the second-order LF wave force, a new hybrid approximation method is proposed. The discrepancies between the approximations and the full-QTF method are investigated in the time domain. This shows that the approximations are greatly affected by the water depth and the spectral peak period. This is because shallow-water mooring systems are more rigid than deep-water mooring systems; thus, the structural response is strongly dependent on a wider difference frequency and the off-diagonal elements in the QTF matrix (with a bigger difference frequency), which contain more errors. In approximations, the mooring-tension error is more sensitive to the water depth than the slow drift owing to the effects of heave and pitch. If the maximum values of the drift offset and mooring tension are considered, the approximation without the free-surface integral and the proposed “WN + Newman” hybrid approximation are recommended for use in shallow water.

Turning circle tests with system-based simulations in irregular waves including wave drift and propeller side forces

Controlled motion in seas require mathematical modeling of ship motions under external disturbances. Waves are one of the most influential factors that undermine ship control. In this study, we investigate the maneuvering ability of the benchmark Japan Bulk Carrier (JBC) in calm water and in waves. Turning circle tests are conducted via system-based analysis and direct CFD method in calm water condition. Comparison of system-based analysis with experiments and direct CFD method have shown to be satisfactory. After validation of the mathematical model, empirical relations are used to include the ship drift in irregular wave conditions. Two different cases are considered. The first one is with constant significant wave height and changing wave angles. The second case is with constant wave angle but different significant wave height. The ship drift was observed to be in the direction of wave propagation, growing larger with increasing wave height. The maneuvering indices with changing wave directions were graphed and it revealed the maneuvering capability of JBC under the disturbance of waves.

Water wave cloaking using a floating composite plate

The trajectory of surface gravity waves in the potential flow regime is affected by the gravitational acceleration, water density and sea bed depth. Although the gravitational acceleration and water density are approximately constant, the effect of water depth on surface gravity waves exponentially decreases as the water depth increases. In shallow water, cloaking an object from surface waves by varying the sea bed topography is possible, however, as the water depth increases, cloaking becomes a challenge because there is no physical parameter to be engineered and subsequently affects the wave propagation. In order to create an omnidirectional cylindrical cloaking device for finite-depth/deep-water waves, we propose an elastic composite plate that floats on the surface around a to-be-cloaked cylinder. The composite plate is made of axisymmetric, homogeneous and isotropic annular thin rings which provide adjustable degrees of freedom to engineer and affect the wave propagation. We first develop a pseudo-spectral method to efficiently determine the wave solution for a floating composite plate. Next, we optimise the physical parameters of the plate (i.e. flexural rigidity and mass of every ring) using an evolutionary algorithm to minimise the energy of scattered waves from the object and therefore cloak the inner cylinder from incident waves. We show that the optimised cloak reduces the energy of scattered waves as high as 99 % for the target wave number. We quantify the effectiveness of our cloak with different parameters of the plate and show that varying the flexural rigidity is essential to control wave propagation and the cloaking structure needs to be at least made of four rings with a radius of at least three times of the cloaked region. We quantify the wave drift force exerted on the structures and show that the optimised plate reduces the exerted force by 99.9 %. The proposed cloak, due to its structural simplicity and effectiveness in reducing the wave drift force, may have potential applications in cloaking offshore structures from water waves.

Second-order hydroelastic analysis of a flexible floating structure under spatially inhomogeneous waves

In this study, a second-order hydroelastic analysis method for moored flexible floating structures under spatially inhomogeneous, long-crested waves is developed, based on the beam-connected-discrete-modules (BCDM) hydroelastic method. The continuous structure is first discretized into rigid modules connected by elastic beams to evaluate the first-order hydroelastic responses. The inhomogeneous wave field is spatially discretized by different isolated homogeneous waves. Based on the first-order motions, the mean drift force on each module is obtained in the frequency-domain. According to the discrete inhomogeneous wave field, the second-order slowly-varying wave drift forces by Newman’s approximation with the drift forces are calculated using the corresponding wave spectra. Finally, the second-order hydroelastic equation in inhomogeneous waves is established in the time-domain using Cummins’ equation. The mean drift force of flexible structures and the nonlinear time histories of motions under homogeneous waves using the proposed method are verified against the results obtained by general commercial software. Then, a limited case study using the proposed method is conducted by a flexible barge and an inhomogeneous wave condition, both of which are exaggerated. The results show that slowly-varying drift forces dominate the horizontal displacements and mooring forces, and the spatial inhomogeneity of waves has a significant effect on the second-order hydroelastic responses, especially in beam seas.

Numerical investigation on hopf bifurcation problem for nonlinear dynamics of a towed vessel in calm water and waves

In this study, the Hopf bifurcation problem with regard to the nonlinear dynamics of a towed vessel was numerically investigated. A time-domain simulation method based on three degrees-of-freedom maneuvering equations of motion was applied to study the nonlinear dynamic responses of a towed vessel in calm water, wind and waves. In the towing operation, it is assumed that a vessel is passively towed by a tug via a towline with a constant towing speed following a straight line. In the case of wind or wave conditions, the steady wind or wave drift forces are considered as additional external force components. The hydrodynamic forces acting on the towed vessel are modeled as a modular-type hull force model, and the towline force is simply modeled as a linear spring. First, for the validation, the motion trajectories of the towed vessel were compared between the experimental data and numerical simulation results under the calm water condition. Discussions are provided on the effect of skegs on the dynamics of the towed vessel and related Hopf bifurcation according to the skeg size. Next, the wind speed was changed, and the resulting limit cycles were studied. It can be observed that the Hopf bifurcation can be delayed according to the wind speed and direction. Finally, the dynamic characteristics of the towed vessel in regular waves were investigated via numerical simulations. The stability of the towed vessel with no skegs increases owing to the mean wave drift forces for both the model test and numerical simulation. The effects of the wave height and period on the Hopf bifurcation were studied based on numerical simulations. It was found that the occurrence of Hopf bifurcation for nonlinear dynamics of a towed vessel is sensitive to the conditions of wave height and period.

Comparative Study on Predicting Ship Maneuvering in Waves Using a Quasi-Steady Method and a Time Domain Approach

_ Numerical prediction of ship maneuvering in waves was considered in this article. The wave drift loads, computed using the potential flow theory, were added into the mathematical modeling group (MMG) equations to account for the effect of waves on the ship maneuvering. Two numerical methods were tested for dealing with the coupled maneuvering-seakeeping problem, namely a time domain approach and a quasi-steady method. For the former approach, a time domain seakeeping computation was conducted that parallels to the maneuvering simulation. For the later one, it is assumed that at each time of the maneuvering process, the wave-ship interaction is in a time harmonic status and, therefore, the wave drift loads could be evaluated using a frequency domain computation. Turning maneuvers of the S-175 container ship in regular waves were numerically tested. The results of the quasi-steady method and the time domain approach show good agreements, which proved the validity of the quasi-steady assumption. The wave drift loads during the turning process were also presented, demonstrating the significant effect of the added resistance on the maneuvering prediction, in contrast to the less remarkable effects of the lateral wave drift force and the wave drift yaw moment. Introduction Ship maneuverability is typically predicted under calm water condition. This provides valuable information at the ship design stage. However, an actual seagoing ship usually maneuvers in waves. To reliably assess a ship’s navigation safety and total performance in a seaway, it is deemed important to understand the maneuvering behavior of a ship in waves. Indeed, ship maneuverability in waves has been increasingly investigated in recent years. Although the physical experiment is still regarded as the most reliable way to investigate ship maneuverability in waves, there are more and more studies providing practical mathematical models of ship maneuvering prediction. Generally, a mathematical model that is suitable for investigating the maneuvering of a ship in waves has to encapsulate the traditional theories of calm water maneuvering and forward-speed seakeeping.

Study of the response characteristics of a spread moored FPSO in the bidirectional sea state

The difference frequency wave drift force may excite large resonant responses for a moored FPSO in horizontal motions, so the moored FPSO responds in both low frequency motion and wave frequency motion generally. In this study, the parameter sensitivity analysis is carried out to investigate the motion response characteristics of a spread moored FPSO in the bidirectional sea state comprised of wind sea and swell. The effects of water depth, loading condition, existence of mooring system, numerical method, sea state type, significant wave height and wave direction on the motion responses are studied in numerical simulation. The research shows that the wave frequency motion responses of FPSO are dominated by swell, and the low frequency motion responses are contributed from both wind sea and swell in the bidirectional sea state. The motion responses are proved to be affected indistinctively by the change of loading condition. The change of water depth affects the motion responses in some degrees. The responses of FPSO in roll can be enlarged by the spread mooring system, and the enlargement becomes more significant if the spread mooring system is arranged in deep water with large pretension force for the mooring lines.

Numerical Study of Wave Drift Load and Turning Characteristics of KVLCC2 Ship in Regular Waves Based on TEBEM

Maritime traffic has increased considerably in recent years, making energy efficiency and navigation safety of ships more crucial than ever. Hence, a two-time scale model based on the Taylor expansion boundary element method (TEBEM) is proposed to predict ship turning trajectories in regular waves. The maneuvering motion is calculated using a three degrees of freedom MMG model that considers the wave drift loads. TEBEM overcomes the shortcomings of the constant panel method in solving tangential induced velocity at a non-smooth boundary and that of the high-order boundary element method in dealing with a high-order derivative of the velocity potential at the corner. This significantly improves the calculation accuracy of the induced velocity and high-order derivative of velocity potential. Firstly, based on the TEBEM, the surge and sway wave drift forces and yaw moment of the KVLCC2 model with drift angle under full wave headings are calculated and compared with computational fluid dynamics results, using which the calculation accuracy of TEBEM is verified. Subsequently, the two-time scale model is used to calculate the turning trajectories of the KVLCC2 model in regular waves with different wave headings, wave frequencies, and wave steepness. The numerical results show that the drift angle has a certain effect on the wave drift loads of the ship, and the proposed model can effectively predict the ship’s turning motion in regular waves.

Research on a novel robot mooring system based on dual-parallel elastic under-actuated mechanisms

Parallel mechanisms have the advantages of a high carrying capacity, large stiffness and compact structure. To develop the theory and key technology of robot mooring systems, in this paper, focusing on a 266,000 m3 LNG ship model with a scale of 1:60, a novel robot mooring system based on dual-parallel elastic under-actuated mechanisms is proposed. The configuration, structure parameters and workspace of the system are determined by experiments and simulations of the ship model with conventional mooring arrangements. Based on the influence coefficient method, the global stiffness model of a parallel-robot mooring system (PRMS) is presented, yielding a stiffness matrix in tensor form. The boundary conditions for the PRMS-moored ship in an experimental basin are introduced and a dynamic equation is given considering the two work modes of the PRMS. Numerical simulations and experiments are carried out to obtain the motions of the PRMS-moored ship when encountering unidirectional irregular waves, and the results indicate that the system can reduce the frequency drift motions of ships in surge, sway and yaw induced by the second order wave drift force.

A unified ship manoeuvring model with a nonlinear model predictive controller for path following in regular waves

In this paper, a nonlinear model predictive controller for path following of a surface vessel in the presence of regular waves is studied. A model predictive controller is developed for a 3DoF unified manoeuvring model of the KVLCC2 crude oil tanker. The surge, sway and yaw motions of the ship are influenced by the second order wave drift forces and moments calculated based on a potential flow solver. Propeller thrust, rudder and hydrodynamic forces and moments are computed using empirical formulas available in the literature. For path following purposes, waypoints are assigned in head and beam wave conditions and a line of sight algorithm computes the reference heading angle. The rudder control is exerted by a nonlinear model predictive controller and the effectiveness of the controller is studied. The performance of the nonlinear model predictive controller is compared against that of a basic PID controller.

Hydrodynamics of a free-floating cylinder in front of an orthogonal vertical wall

ABSTRACT The paper deals with the analytical evaluation of the linearized exciting wave forces; hydrodynamic coefficients and wave drift forces acting on a free-floating vertical cylindrical body placed in front of a reflecting orthogonal vertical wall. Linear potential theory is assumed, and the associated diffraction and radiation problems are solved in the frequency domain. The hydrodynamic interactions among the body and the adjacent breakwater are taken into account by applying a theoretical model based on the method of images, considering the breakwater as a fully reflecting, bottom mounted and water surface piercing wall of infinite length. The theoretical approach is supplemented by a numerical model considering the orthogonal breakwater as a barrier of finite length. The results of both formulations are compared with the ones corresponding to an isolated cylindrical body demonstrating the amplified scattered and reflected waves at specific frequency ranges originating from the presence of the orthogonal breakwater.