Abstract The second order force of a floating structure can be expressed in terms of a time independent quadratic transfer functions along with the incident wave elevation, through which it is possible to evaluate the second order wave exciting forces in the frequency domain. Newman’s approximation has been widely applied in approximating the elements of the quadratic transfer function matrix while numerically evaluating the second order wave induced force. Through Newman’s approximation, the off-diagonal elements can be numerically approximated with the diagonal elements and thus the numerical calculation efficiency can be enhanced. Newman’s approximation assumes that the off-diagonal elements do not change significantly with the wave frequency and that hydrodynamic phenomenon regarding the low difference frequency are usually of interest. However, it is obviously less satisfying when an element that is close to the diagonal line in the quadratic transfer function matrix shows an extremum if the corresponding wave frequency is close to the natural frequency of the certain motion. In this paper, the full derivation and expression of the second order wave forces and moments applied to a floating structure have been presented, through which the numerical results of the quadratic transfer function matrix including the diagonal and the off-diagonal elements will be illustrated. This work will present the basis of numerically evaluating the second order forces in the frequency domain. The comparisons among various approximations regarding the second order forces in deep water will also be presented as a meaningful reference.

Abstract Estimating added resistance and motions of a ship in waves are essential to predict fuel consumption and speed loss. The added resistance and motions of the 3600 TEU KRISO container ship (KCS) in regular head waves under different wavelengths are investigated using Reynolds-Averaged Navier-Stokes (RANS) method. Volume of Fluid (VOF) method is applied to capture the free surface. The in-house computational fluid dynamics solver, naoe-FOAM-SJTU, is used to compute the added resistance and motions of KCS in regular head waves. Firstly, the first-order Stokes waves in deep water are adopted and generated in naoe-FOAM-SJTU as a numerical wave tank. Secondly, it is presented that the KCS with a Froude number of 0.261 advances in these waves. Regular wave conditions with a wide range of wavelength (0.65 < λ/L < 1.95) are considered. The variations of resistance, pitch and heave show good agreement with experimental results. To investigate nonlinear behaviors of predicted results, Fast Fourier Transform (FFT) is applied to analyze the results of resistance, heave and pitch with in head wave ( μ = 180°). KCS with and without motions is also compared to investigate the relationship between components of resistance and wavelengths. The results of added resistances show that the added resistance of KCS is mainly induced by ship diffraction in short waves. The wave diffraction is not affected by wave frequency. In addition, CFD can accurately calculate the problem on added resistance and ship motions.

Abstract Direct numerical simulation (DNS), based on solution of the Navier Stokes equations, is used to study the characteristics of the transformation of monochromatic waves over a simplified fringing reef, including wave shoaling, and wave breaking that occurs under certain circumstances. The reef geometry involves a sloped plane beach extended with a simple submerged horizontal reef flat. The characteristics are studied for several case studies involving a selection of submergence depths on the reef flat and for a range of incident wave conditions, corresponding to nonbreaking, a spilling breaker and a plunging breaker, are considered. The results are compared with those of laboratory experiments (Kouvaras and Dhanak, 2018). Consistent with other studies, generation of harmonics of the fundamental wave frequency is found to accompany the wave transformation over the reef and the process of transfer of energy through wave breaking. The energy flux decreases dramatically in the onshore direction when the waves break. The more severe the wave breaking process, the greater the decrease in energy flux, particularly in the wave shoaling process. Most of the wave energy is carried by the first harmonic throughout its passage over the fringing reef. In nonbreaking waves, the energy gradually transfers from the first harmonic to the second harmonic due to bottom effects in terms of flat wave troughs and secondary waves. The further the distance away from the fore edge of the reef, the larger the percentage of the transmission, resulting in a single dominant harmonic frequency at the end of the wave surfing zone. For breaking waves, the energy carried by the first harmonic gradually decreases in the onshore direction. Energy transmission between harmonics is not as efficient as nonbreaking waves, while wave dissipation is significant in the wave breaking process.

Abstract Nowadays, in maritime industries, container ships increase in size and they have large flares, which may induce nonlinear wave loads in large-amplitude waves. It is also well known that hydrodynamic forces acting on a ship and resulting ship motions show nonlinearities at some range of wave frequencies. Therefore, we should investigate not only correct estimation of wave loads and ship motions, but also nonlinear ship-motion characteristics in large-amplitude waves. However, it is not that clear which nonlinear hydrodynamic force terms are dominating for the nonlinearity in the ship motions. Although the linear equations of motion have been used, they should be modified to incorporate at least the most important nonlinear hydrodynamic forces and to establish a practical calculation method taking account of only the indispensable nonlinear terms. In this research, we did extensive experimental measurement of hydrodynamic forces and wave-induced ship motions, with which we aim to understand what are practically important nonlinear terms, and to derive practical nonlinear ship motion equations through numerical computation and comparison with experimental data.

Abstract This work considers the numerical modelling of wave interaction with thin porous structures, based on tests conducted in simplified conditions. Wave flume tests were conducted to measure the wave loads on thin porous sheets extending over the full water column. The porous sheets tested had a range of porosities, hole separation distances and thicknesses. Numerical and analytic models for the wave forces on the porous sheet are formulated under the assumptions of either a linear or quadratic pressure loss across the porous sheet. An iterative boundary element method (BEM) model is formulated to solve the quadratic pressure loss across the porous sheet. It is shown that the assumption of a linear pressure loss at the porous boundary is inadequate to capture the variation in the wave load with both wave frequency and amplitude, but that the quadratic model is in good agreement with the measured forces. The porosity of the sheet is shown to have the dominant effect on the wave loads. The hole separation distance affects the phase of the force on the porous wall, but has only a small effect on the amplitude of the force. The sheet thickness is shown to have a small effect on the amplitude of the force but a significant effect on the phase of the force. The results are of interest for numerical modelling of structures with thin porous boundaries in a wide range of contexts such as breakwaters, aquaculture and offshore structures with porous elements designed to reduce loads.

Abstract Water wave propagation over shallowly submerged structures is of much interest in the context of submerged wave energy devices, breakwaters or barrier reefs. This work examines waves passing over a two-dimensional shallowly submerged fixed step extending to the seabed. The problem has been modelled in CFD using the open source toolbox OpenFoam utilising the Reynolds Averaged Navier-Stokes Equations. These simulations are compared to experimental work from a previous study as means of validation and extended to larger amplitude waves for a single incident wave frequency. The flow over the step is characterised and examined in the context of developing an efficient hybrid numerical model for the problem.

Abstract The wave-induced responses in the bridge girder of long floating bridges supported by pontoons are often dominated by the vertical modes, coupled horizontal modes and rotational modes about the longitudinal axis of the bridge girder. Pontoons with and without bottom flanges have been seen in recent floating bridge designs. Viscous flow separation around the sharp edges of the pontoon or the bottom flange may have strong influences on the hydrodynamic performance of the pontoon in terms of wave excitation, added mass and damping effects. Morison-type wave and current loads are normally included empirically in the early design phases to account for the viscous effects that cannot be covered by a potential-flow solution alone. Empirical drag coefficients and perhaps a correction to the potential-flow added mass are the inputs to such numerical models, which represents a part of the modelling uncertainties. Previous sensitivity studies using different drag coefficients in the ongoing Bjørnafjord floating bridge project in Norway indicate an influence up to 15% on the maximum vertical bending moment around the weak axis of the bridge girder. This paper contributes to the understanding of viscous effects on the hydrodynamic characteristics, e.g. the added mass, damping and wave excitation loads, of a floating bridge pontoon with and without keel plate. This is achieved by exploring existing model tests for floating bridge pontoons, performing 2D Computational Fluid Dynamic (CFD) analysis for pontoon cross sections and numerical calibration in a simplified frequency-domain model with linearized drag loads. Scale effects are also investigated through CFD analyses in model and full scales.

Abstract The DP capability plot is a useful tool to show the limitations of a dynamic positioning system for ships or offshore structures under loading from wind, waves and ocean currents. At the preliminary design stage, it is desirable to use fast methods for calculating the forces and moments caused by the environment, preferably without the need for CFD simulations or model experiments. Empirical methods are available for predicting aerodynamic forces and moments, and hydrodynamic forces and moments from currents, but little is published for second order wave drift forces. Wave drift forces and moment calculations have been carried out using WAMIT, for a series of ship hulls from OSVs to VLCCs and the effects of wave direction and frequency on the Surge, Sway, and Yaw forces and moment have been studied. The presentation of the results allows the user to interpolate the resulting drift forces and moments as a function of wave direction for a given ship size. In terms of wave drift loads calculation, it is found that the very large vessels are dominant in the low frequency waves, while smaller size ships are in high frequencies. The wave frequency and direction in which maximum drift load occurs depends on the ship size.

Abstract Nowadays, more and more 20,000 twenty-foot equivalent unit (TEU) class ultra large container ships (ULCS) have been built in service across the worldwide. It is paramount that hydroelastic specialists become paying close attention to structural responses and loads predictions due to up to a 400m length of the ships. First of all, mesh convergence by finite element analysis is necessary to determine in the numerical calculation. In this paper, based on the three-dimension linear frequency domain hydroelasticity theory, the hydrodynamic meshes convergence is discussed when modelling the hull surface of the ULCS. Ascribe to the Sunway TaihuLight, rank 3 in the current TOP500 supercomputer list, the Message Passing Interface and the multi-level parallel programming model are used aimed to the wetted panels, the wave frequencies and so on. Several sets of different global grid density and grid distribution along the ship’s length for the containership are calculated to compare the hydrodynamic coefficients such as added mass, damping, wave exciting force, ship motions and exterior loads with several typical service speeds in the head regular wave. It has been concluded that sensitivity of numerical modelling converges to a stable state with increasing the panel numbers per ship. Therefore, one set of grid division optimised, and superposed elastic modes numbers are recommended in the hydroelastic analysis of numerical hydroelastic prediction of springing and whipping.

Abstract In this paper, an in-house CFD code HUST-Ship is used for the numerical simulation of parametric rolling phenomena of ONR Tumblehome in regular head wave. Preliminary resistance and roll decay simulations at Fr = 0.2 were carried out and compared with existed INSEAN experimental data. Following, three DOFs’ ship motions in regular head wave with an initial roll angle of 30 degrees was calculated to examine the possibility of occurrence of parametric rolling. Finally, a simulation without initial roll disturbance was performed to investigate its influence to the steady roll amplitude. By conducting fast Fourier transform of the time history of motions, forces and moments, the characteristics are analyzed and co-related with wave frequency. Results can be concluded that the in-house code has the ability to perform the parametric rolling simulation, and that the final steady roll amplitude is not affected by the initial disturbance. In addition, heave and pitch motions are dominantly affected by wave characteristic, roll frequency is about half that of wave, and that forces and moments in x direction exhibit high-order non-linearity.

Abstract The new age of oil and gas industry is being driven by cost effective solutions, aiming to provide cheaper, faster and better products/services. The industry 4.0 brings an opportunity to transform systems and processes to be more efficient, making use of digitalization and new technologies, including the use of artificial intelligence algorithms applied to engineering problems. In Brazilian offshore fields, the operating conditions for flexible riser applications (deep-water, mean wave frequencies, floating units and corrosive fluids) make the metallic layer’s fatigue failure mode one of the drivers in its design. In a daily basis, nonlinear dynamic finite element analysis uses regular wave scatter diagrams as an equivalent way to model the wave elevation, avoiding the time consuming irregular wave representation. The analysis performed with regular waves are faster but carries conservatisms with it. In a deep-water scenario, the wave height and period ranges of the wave scatter diagram can be refined to improve the fatigue results obtained, leading to a considerable increase in the total amount of wave classes that need to be evaluated. Great part of the wave classes has a very low participation in the total fatigue damage, spending an unnecessary time to analyze them. Helped by a robust design of simulation experiment (DoSE) and machine learning regressors, a lean representation of the regular wave scatter can be done, where some of them are simulated and the rest of the results can be accurately predicted. This paper presents the application of supervised learners that are used to predict riser fatigue damage at different riser locations, given partial simulations of a regular wave scatter diagram. The techniques support the strategy to reduce the total amount of fatigue analysis required within a project design phase. The focus stays on the evaluation of the fatigue of metallic layers at two main critical regions, bend stiffener and touch down zone. Hidden patterns inside each scatter diagram are discovered, minimizing the total number of finite element analysis (FEA) required. The amount of the wave class reduction starts from 50% going up to 75%, maintaining a good level of accuracy on the predicted damage values.

Abstract The ocean is full of untapped energy, however it is a wild place where harsh conditions can occur that can damage wave energy converters (WEC’s). During high load conditions, many WEC’s must go into survival mode to prevent damage or are overdesigned to continue operating in high sea states, which can increase capital costs. The authors propose a different approach, where geometry control is used to change to an absorber shape that experiences minimal hydrodynamic loads during high sea states. This could allow for a decrease in capital costs while increasing the operating range of WEC’s. This paper seeks an optimal geometry of a submerged planar pressure differential WEC that minimizes heave excitation force or motion magnitudes without using the power take-off system. Simple elliptical and circular absorbers as well as optimized absorbers are compared to quantify heave load reductions. Optimized absorbers are generated using a summation of Fourier terms with controllable weights and phases that are optimized with a genetic algorithm for two regular wave conditions. Heave load reductions are found to depend on wave frequency, orientation angle, and elongation. It is shown that peak loads can be reduced by up to 60% when comparing to a circular absorber.

Mechanism of torque induced by chain twist and its effects on the predicting fatigue lives of mooring chains of a semi-submersible operated in OWA (Offshore Western Africa) are investigated in this paper. The fatigue lives of mooring chains are estimated based on a fracture mechanics analysis. Stress ranges on the mooring chains induced by tension ranges acting on the twisted chains are achieved by a finite element analysis. The low frequency (LF) and wave frequency (WF) tension processes induced by the motions of LF and WF are regarded as two random loading processes and the combined tension process of LF and WF is predicted by a dual narrow-band method. The mooring chains are treated as round bars and initial surface cracks are assumed to propagate at the surface of mooring chains. The influence of the chain twist on the fatigue lives of mooring chains is investigated and the results show that when the twist angle is less than 20 degree, fatigue lives of mooring chains are increased with the increase of the twist angle. However, when the twist angle approaches lock-up angle of 30 degree, fatigue lives of mooring chains are significantly decreased due to the torque effects induced by the chain twist.

The paper presents calibration of a time domain numerical model for the motions of the Exwave Semi in high seastates with current. The time domain equations of motion combine linear radiation, linear diffraction and second order wave drift forces, based on MULDIF diffraction code, with nonlinear forces from quadratic damping and from the mooring system. Calibration is performed by comparing simulations with model test data and adjusting hydrodynamic coefficients known to be affected by uncertainty. These include wave drift force coefficients, damping and added mass coefficients. Correction of the drift coefficients is based on empirical quadratic transfer functions (QTFs) identified from the test data by a nonlinear data analysis technique known as “cross-bi-spectral analysis”. Initial “uncalibrated” numerical models are based on input from the mooring, vessel mass, MULDIF hydrodynamic analysis, decay tests and current coefficients. They need adjustments for surge and sway. Empirical drift coefficients, natural periods and damping coefficients are then adjusted by matching low frequency surge and sway spectra. Wave-frequency coefficients need no adjustment. Low frequency wave drift forces, damping and added mass need increase in high sea states, in particular with current. Final motion simulations show 30%–40% underestimation in initial simulations, while final calibrated simulations are close to the measured records.

In global aero-hydro-servo-elastic analyses of floating wind turbines (FWTs), the hydrodynamic loads are usually found from potential flow theory and applied in a single point of a rigid hull. When the hull is relatively stiff, this approach ensures correct behaviour for the six rigid body degrees-of-freedom (DOFs), but provides no information about the internal loads in the hull. The current work considers a simplified method to include distributed, large volume hydrodynamics in the global analysis, where frequency-dependent loads from potential theory are applied on a finite element (FE) model of the hull in a strip-wise manner. The method is compared to conventional load models for a braceless 5MW semi-submersible FWT, and validated against experimental results from model tests with focus on internal loads and rigid body motions in the main wave-frequency range. The global motions are accurately predicted by the distributed model for all investigated load cases. Good agreement with experimental results is also seen for the column base bending moment in wave-only conditions, although extreme values are not captured correctly due to limitations in linear theory. In combined wave-wind conditions, the measured bending moments are significantly increased because of the wind-induced mean angle of the platform. This effect is not considered in the numerical model, which therefore underestimates the moment response. However, an approach which calculates the loads in the actual mean configuration of the hull is found to give reasonably accurate results, at least in moderate wave conditions.

A numerical model based on blade element momentum theory was developed to investigate the effects of floater motion on the dynamic responses of a floating tidal turbine in this paper. SJTU-FTT, a floating tidal turbine system, was introduced. A simplified numerical approach was proposed, in which the 6-DOF motion of the floater was calculated in frequency domain in advance and then was transferred to the unsteady BEM model as inputs. The hydrodynamic coefficients including (added mass, damping, and RAOs) of the floater were presented. The response spectra of the thrust, torque and blade bending moments on the tidal turbine were discussed. Two peaks in the response spectra can be clearly identified, caused by surge and pitch motion of the floater. It was seen that the dynamic loads considering 6-DOF floater motion were much larger than the results from wave only cases.

In this paper the three-dimensional numerical simulation is conducted for Oscillating Wave Surge Converters (OWSCs) using computational fluid dynamics (CFD) software FLOW-3D, based on the wave climate of the offshore sea in northeast Taiwan, that is, 1.5 meters of wave height and 7 seconds of the wave period. The results are compared with that using the wave energy converter simulation toolbox, WEC-Sim. The effects of the parameters, including the flap thickness, flap width, the position of the mass center, and flap density, are investigated, especially their influence of the energy capturing efficiency or the capture factor (C F ). The simulation results show that, bigger flap thickness (d), smaller flap width (B), smaller flap density, and lower flap’s center of mass will result in a higher efficiency for power capture performance. Among the four parameters, the flap thickness is the most dominant parameter. From hydrodynamic respect, a larger drag force may occur at the sidewalls of the thick flap, and the shear force accelerate the pitch motion of the flap, in turn increasing the absorption efficiency. From a practical design aspect, the variation of the C F around the peak value is smoother for wider flap, which suggests a broad bandwidth in receiving various wave frequency in irregular waves.

Dynamical characteristics of the H-type floating VAWT (vertical axis wind turbine) were studied. The wind turbine blades and the tower were treated as flexible bodies, and the floating foundation was treated as the rigid body. Considering the nonlinear deformations of the flexible bodies, the Lagrangian equation was used to establish the dynamic equations of wind turbine system. The loads included the wave forces, the wind loads, the mooring forces and the damping forces of the wind turbine system. A numerical calculation code was developed and verified. The innovation of the code is the coupling of rigid-flexible-aerodynamic-hydrodynamic of the floating wind turbine system. Taking the 5MW wind turbine as an example, the directions of the wind and the wave were considered as the same. Then the dynamic responses of the floating foundation, the tower and the blades were calculated. The results show that the wave frequency is the main frequency component of the responses of pitch, heave and surge of the floating foundation. 2P frequency (P is the rotational frequency of the wind turbine) accounts for a higher proportion for the sway, roll and yaw of the floating foundation. 2P and 4P are the main frequency components of the tower motions. 1P is the main frequency component of the blades’ motions. The 2nd mode of the blades and tower are considered. In the following research, the higher modes should be considered to improve the calculation accuracy. Besides, the model test is needed to verify the model further in the subsequent work.

It is known that the fatigue strength decreases in corrosive environment and many experiments were carried out to comprehend the decrease in fatigue strength in corrosive environment. In order to comprehend the actual state, a cycle speed of fatigue test loads should correspond to a wave frequency. Therefore, an experiment in the long life region is practically difficult, then the corrosion fatigue data available for the life assessment of the structure is quite limited. In this study, the fatigue strength of the welded joints in long life service was evaluated according to the calculations of corrosion fatigue crack propagation subjected to the random loadings which followed an exponential distribution. In the crack propagation calculations, the progress of corrosion wastage from the plate surface and the resultant stress increase were considered simultaneously. In the high stress and the short life region, the decrease in fatigue strength due to the accelerated crack propagation in corrosive environment was dominant because the progress of corrosion wastage was little. On the other hand, in the low stress and the long life region, the decrease in fatigue strength became dull as longer the fatigue life because the corrosion fatigue crack propagation was suppressed by the corrosion wastage, but after that the fatigue strength showed the precipitous decrease due to the increase in stress resulted by the progress of corrosion wastage.

When approaching or leaving a port a ship often needs to perform manoeuvres in the presence of waves. At the same time the water depth is still limited for deep drafted vessels. For manoeuvring simulation purposes this requires a manoeuvring model which includes phenomena such as short crested waves and squat effects. The present paper addresses the manoeuvring problem in shallow water waves numerically and experimentally. The numerical study is conducted by means of potential theory, incorporating first and second order exciting wave forces, and their superposition to the calm water manoeuvring models. The applicability of such an approach is also investigated. The experimental work has been conducted at Flanders Hydraulics Research (in cooperation with Ghent University) with a scale model of an ultra large container vessel. Captive model tests comprise harmonic yaw tests and steady straight line tests with and without waves, at different forward speeds, wave frequencies and amplitudes, in head and following waves. Waves are chosen to represent conditions commonly met by ships in the Belgian coastal zone of the North Sea.