Irregular Sea Research Articles

Design and costs benefits of shared anchors and shared mooring lines of floating wind turbines at farm level

This paper focuses on innovative mooring layouts using shared anchors and shared mooring lines. Three studies with the ActiveFloat semi-submersible floater supporting a 15MW wind turbine are presented. Those include two studies of shared anchors layouts, with a semi-taut mooring system at a deep-water site subjected to extreme conditions (Morro Bay) and a catenary mooring at a moderate water depth with gentle environment (Gran Canaria). The third study focuses on shared mooring layout at Morro Bay. The mooring system at this site is semi-taut, made of polyester, with chain close to the sea surface and the anchors. At Gran Canaria, ActiveFloat is featured with a catenary mooring system made of chain lines. Both sites are subjected to irregular sea states and turbulent wind. Time domain simulations in ULS are performed using OrcaFlex models that combine potential flow theory and Morison drag coefficients. Aerodynamic load time series are applied at the tower top. Results show that shared anchor layouts are technically feasible but do not improve the mooring system procurement costs due to the spacing constraint between each turbine. Sharing mooring lines at farm level seems more promising and could help reduce costs, due to the decrease in amount of material use.

Effect of tertiary interactions on free-surface motion of a fixed box in realistic irregular sea states

Tertiary interactions between irregular incident waves and their reflections from a rectangular box are investigated experimentally. New experiments feature uni-directional seas with normal and oblique incidence to the side of the box and spread seas, where data is notably lacking in the literature. NewWave conditioning analysis is applied to show that the delays in maximum response associated with tertiary interactions are present in front of the box for both uni-directional and spread sea states. However, only in the uni-directional sea states with normal incidence is there significant amplification of free-surface elevation in front of the box beyond the linear diffraction levels. The nature of the large nonlinear run-up in this case is studied in detail. As an important finding, this work shows that localised tertiary interactions, whilst an interesting physical phenomenon, are unlikely to be important for wave–structure interactions in general, in realistic open ocean wave conditions.

A new probability density function for the surface elevation in irregular seas

To date, the predominant means for computing the probability density function (p.d.f.) for the free surface elevation of a nonlinear, irregular water wave field, free of assumptions involving narrow-bandedness and small directionality, is the approximate Gram–Charlier series solution of Longuet-Higgins (J. Fluid Mech., vol. 17, 1963, pp. 459–480, hereafter LH63). In this paper we re-visit the derivation of this p.d.f. to second order in the wave steepness, utilizing both moment and cumulant generating functions. We show that LH63's approximate solution based on the cumulant generating function, in fact, matches that derived from the moment generating function. Moreover, through a change of variables coupled with complex analysis, it is shown that the approximation employed by LH63 is unnecessary, and the second-order p.d.f. stemming from the cumulant generating function can be represented exactly in terms of the Airy function. The new second-order p.d.f. predicts increased probability of extreme positive surface elevations typical of e.g. rogue waves, relative to both second- and third-order solutions of LH63. This heavy positive tail is inherent, and is explained through comparison of the asymptotic limits of the p.d.f.s for large surface elevations. A semi-theoretical method is also proposed for remedying non-physical spurious oscillations that arise in the negative tail, based on the envelope of the Airy function with negative arguments. This modified negative tail is valid for irregular wave fields having skewness less than or equal to 0.2. The new p.d.f.s are compared against those based on data sets generated from second-order irregular wave theory as well as a fully nonlinear, spectrally accurate numerical wave model. Good accuracy is collectively demonstrated for directionally spread irregular seas in both finite and infinite water depths for a range of directional spreading.

Hydrodynamic forces acting on mechanical systems in linear and nonlinear ocean waves

AbstractThe hydrodynamic forces acting on prescribed free‐floating mechanical systems are studied. Regular and irregular sea states are considered using Stokes wave theory of first and second order. It is analyzed how much the magnitude and temporal behavior of the forces can differ using nonlinear theories of different orders instead of the linear wave theory. The corresponding effects on the mechanical dynamics of the system are investigated. Therefore, the fluid–structure interaction and hydrodynamic forces are computed, solving the corresponding partial differential equations of the linear and nonlinear wave theory. In this way, the nonlinear interactions of the different wave components in irregular seas and the disturbances of the sea due to the presence of the mechanical system are captured.

Basin testing of the 1-2-1 M4 WEC

The M4 family of Wave Energy Converters consist of 3 rows of floats, with the front two rows rigidly connected and a hinged connection(s) to the back row. The various possible configurations are commonly identified by the number of floats in each row – hence 1-2-1 has 1 float in front, 2 in the middle, and 1 at the rear. A study by Stansby et al 2017 [1] showed that the 1-2-1 and 1-3-2 variants had the lowest cost of energy of all configurations studied. The 1-3-2 variant has subsequently been extensively studied as it provides greater power per machine. However, the 1-2-1 machine has received less attention. In this paper we report, for the first time, wave basin testing of a 1-2-1 variant. The design is a 1:15 scaled version of a 1-2-1 M4 suitable for deployment in the prevailing short period wind waves in King George Sound, Albany, on the south coast of Western Australia. 
 
 The tests were carried out in the Model Test Basin at the Australian Maritime College, Tasmania. This basin is 35 m x 12 m and tests were run with a water depth of 0.8 m. For modelling operational conditions, the power take-off was represented by a pneumatic ram; in extreme seas the power take-off was removed.
 
 Decay tests, irregular operational seas and irregular extreme seas were tested. All waves were long crested. Sea states tested were taken from the scatter diagram for the deployment site in King George Sound. Body displacements, mooring loads, run-up on the middle floats and forces in the PTO (where installed) were measured. Measured motions and power were compared to a linear model. The level of agreement is compared with previous tests on other variants of M4 in the published literature, including the 1-3-2 variant tested in Carpintero-Moreno et al [2] and the 1-1-1 variant tested in Stansby et al [3]. Compared to some other configurations (such as 1-3-2) the 1-2-1 M4 is more prone to roll. Implications of the test results for deployment in King George Sound are discussed.
 
 [1] Stansby, P., Moreno, E.C. and Stallard, T., 2017. Large capacity multi-float configurations for the wave energy converter M4 using a time-domain linear diffraction model. Applied Ocean Research, 68, pp.53-64.
 
 [2] Carpintero-Moreno, E. and Stansby, P., 2019. The 6-float wave energy converter M4: Ocean basin tests giving capture width, response and energy yield for several sites. Renewable and Sustainable Energy Reviews, 104, pp.307-318.
 
 [3] Stansby, P., Moreno, E.C. and Stallard, T., 2015. Capture width of the three-float multi-mode multi-resonance broadband wave energy line absorber M4 from laboratory studies with irregular waves of different spectral shape and directional spread. Journal of Ocean Engineering and Marine Energy, 1, pp.287-298.

Hydrodynamic performance of a self-protected hybrid offshore wind-wave energy system

The load-bearing capacity is a pivotal consideration in the design of offshore renewable energy structures. This paper aims to address the technical challenges associated with the additional wave loads caused by the integrated devices in a hybrid system for the multi-purpose utilization of coastal renewable energy. A self-protected hybrid wind-wave energy system is proposed, in which an oscillating water column (OWC) device is attached at a monopile foundation of an offshore wind turbine. In the meantime, the OWC is connected by a submerged horizontal perforated plate at its exterior shell, which is expected to minimize the wave loads on the system. The hydrodynamic performance of the system is investigated. A novel approach is developed to model the wave interaction with the hybrid system. This efficient approach removes the necessity of decomposing the wave-scattering field into diffraction and pressure-dependent radiation components. Detailed numerical computation is then conducted for both regular and irregular sea states. Various hydrodynamic properties related to the system, such as wave energy harvesting, wave force/moment, and free-surface elevation, have been evaluated. Numerical results manifest the feasibility of imposing a negligible effect on the high wave energy harvesting while reducing the high wave loads by manipulating the submerged horizontal perforated plate. The impact of the perforated plate on the dominant wave energy harvesting in the long-period region is found to be trivial. In contrast, it can affect the high bending moment in the short-period region, which causes a reduction of greater than 15%.

Design of an electrical energy storage system for hybrid diesel electric ship propulsion aimed at load levelling in irregular wave conditions

This paper focuses on the design stage of an electrical energy storage system which is intended to be used to level the power required by ships for propulsion when sailing in irregular seas. Particularly, a preliminary analysis has been carried out aimed at choosing, between two storage technologies namely battery and ultracapacitor, the more adequate storage system for the levelling action with respect to the period of the sea waves. A sizing procedure based upon a Hilbert transform decomposition of load demand is used. More specifically, a specified threshold frequency has been identified such that, power fluctuations related to irregular seas which are characterized by frequencies higher than the specified threshold, indicate the ultracapacitor as the more appropriate device for load levelling. For sizing the storage device, the load demand has been decomposed into two signals without overlapping frequencies. An optimal control strategy is proposed, by exploiting the decomposition of the load power, which allows simulating ultracapacitor real-time operation within the previously determined size constraints. Numerical results have been carried out referring to a Ro-Pax ferry powered by an electrical motor.

Optimization of a coupled launching process considering hydrodynamic interaction effects

Crane-assisted launching and recovering of small boats from a large vessel is common in a wide range of operational scenarios and may be required during research missions or in emergency situations for rescue boats. As the mothership moves in natural irregular seas, the resulting accelerations and motions of the small boat can lead to dangerous situations, such as a collision between the mothership and the small boat or a slamming of the small boat onto the free water surface can occur, posing a great danger to the people involved. In the paper, the development of a coupled simulation method for the motions of the mothership and the small boat during the launching in the time-domain is described. The developed simulation method is based on the impulse response function. The implementation of the suspension on a crane is realised by a holonomic constraint and a Lagrange’s equation. The parameter influencing the launching operation include the current sea state, the stationary wave field induced by the motherships forward speed, at which the small boat is launched and the initial position of the small boat relative to the water surface. By varying the above mentioned parameters, the process can be optimised for different sea states in terms of forces and accelerations. In considering the forward speed of the mother boat during the launching process, it can be observed that in many cases the small boat is operated at high Froude numbers of greater than 0.4. This leads to an exceedance of the operational limits of the programmes used in this paper.

Sensitivity of Mass Distribution with Respect to Pitch Motions of High-Speed Craft

Beside of environmental conditions, ship characteristics also greatly affect in ship behavior when operating at sea, called seakeeping ability. The shape of the hull, appendages, damping, and the weight distribution of ship are some of the factors that determine how the ship motion response occurred. This paper examines how much the pitch motion is influenced in high-speed craft due to the changing of the gyration radius. By using the strip theory method, and by taking the irregular head sea condition and a wave height of 4 meters, then the ship speed and the wave period are varied to determine the pitch motion amplitude at 3 values ​​of gyration radius: 0.2, 0.25 and 0.3 of the ship's length. The results of the study show that at higher ship speeds, the gyration radii greatly influence the pitch amplitude. As for changes in the wave period, the influence is significant at value of 5 second. From these two results, it is clear that the ship's gyration radii must be determined precisely to be able to predict an accurate pitch motion response on a high-speed craft.

A second-order slender-body approach for computing wave induced forces with application to a simplified semi-submersible FOWT model

This paper presents a slender-body approximation to evaluate the first- and second-order wave loads acting on a floating structure comprised of slender cylinders. It combines Rainey’s equation, which can be seen as an extension of the inertial part of Morison’s equation to include nonlinear terms, with Pinkster’s formulation for the low-frequency second-order loads on floating bodies. The objective is to obtain expressions that allow the evaluation of second-order wave loads considering the mean body position, so that an Inverse Fast Fourier Transform algorithm can be used to efficiently compute the second-order wave loads in a real sea condition directly in time domain. Similarly to Morison’s equation, this approach is incapable of modeling wave scattering and radiation effects, but this is acceptable as long as the diameters of the cylinders that compose the structure are small in face of the length of the incoming waves. To verify the method, it is applied to the computation of the slow motions of a simplified semi-submersible FOWT model, first under the action of bichromatic waves and then of an irregular sea, and the results are compared with the ones obtained with WAMIT, OpenFAST and experiments.

A comparison of two wave energy converters’ power performance and mooring fatigue characteristics – One WEC vs many WECs in a wave park with interaction effects

The production of renewable energy is key to satisfying the increasing demand for energy without further increasing pollution. Harnessing ocean energy from waves has attracted attention due to its high energy density. This study compares two generations of floating heaving point absorber WEC, WaveEL 3.0 and WaveEL 4.0, regarding their power performance and mooring line fatigue characteristics, which are essential in, e.g., LCoE calculations. The main differences between the two WECs are the principal dimensions and minor differences in their geometries. The DNV software SESAM was used for simulations and analyses of these WECs in terms of buoy heave motion resonances for maximising energy harvesting, motion characteristics, mooring line forces, fatigue of mooring lines, and hydrodynamic power production. The first part of the study presents results from simulations of unit WEC in the frequency domain and in the time domain for regular wave and irregular sea state conditions. A verification of the two WECs’ motion responses and axial mooring line forces is made against measurement data from a full-scale installation. In the second part of the study, the influence of interaction effects is investigated when the WECs are installed in wave parks. The wave park simulations used a fully-coupled non-linear method in SESAM that calculates the motions of the WECs and the mooring line forces simultaneously in the time domain. The amount of fatigue damage accumulated in the mooring lines was calculated using a relative tension-based fatigue analysis method and the rainflow counting method. Several factors that influence the power performance of the wave park and the accumulated fatigue damage of the mooring lines, for example, the WEC distance of the wave park, the sea state conditions, and the direction of incoming waves, are simulated and discussed. The study's main conclusion is that WaveEL 4.0, which has a longer tube than WaveEL 3.0, absorbs more hydrodynamic energy due to larger heave motions and more efficient power production. At the same time, the accumulated fatigue damage in the moorings is lower compared to WaveEL 3.0 if the distance between the WECs in the wave park is not too short. Its motions in the horizontal plane are larger, which may require a larger distance between the WEC units in a wave park to avoid losing efficiency due to hydrodynamic interaction effects.

Machine learning simulation of one-dimensional deterministic water wave propagation

Deterministic phase-resolved prediction of the evolution of surface gravity waves in water is challenging due to their complex spatio-temporal dynamics. Physics-based methods of varying complexity are available, but the conflicting objectives of numerical efficiency and accuracy impede real-time wave prediction. Data-driven methods may be able to overcome this challenge by using training data generated by complex numerical methods. This work explores the potential of a machine learning (ML) approach based on a fully convolutional encoder–decoder architecture for the efficient and accurate prediction of water waves. The high-order spectral (HOS) method forms the foundation for the generation of the training data. The HOS method is applied for different, consecutive orders of nonlinearity starting from first order up to fourth order. The JONSWAP wave energy spectrum serves as the basis for modeling the one-dimensional irregular sea states. The overall objective of this work is to evaluate whether the complex non-linear physical processes can be identified and learned by the ML approach. The trained ML flow mapper is used to perform time integration of an initial sea state. The results indicate that the proposed ML approach is able to reproduce the distinctive physical processes of the different orders of nonlinearities. It is shown that the ML approach enables fast and accurate predictions of one-dimensional waves over a time horizon that spans multiple peak periods.

Physical and numerical modelling of extreme wave conditions

This paper presents the results of an experimental and numerical investigation into the generation of realistic model scale extreme waves for survivability testing of offshore structures. The objective of this investigation was to develop a numerical method to accurately model the maximum wave height (Hmax) and wave spectrum of a realistic focused wave group that was embedded into an irregular sea state. The sea state selected for this investigation was based on extreme conditions recorded during a Tropical Cyclone. The sea state was experimentally modelled using NewWave theory and was subsequently replicated in a computational fluid dynamics (CFD) numerical wave tank. The wave component amplitudes and phase angles were derived from the experimental data, which were then used to generate a polychromatic wave in CFD. The NewWave formula was then modified by applying an exponential function which intended to explicitly amplify the largest waves in the wavefield while applying minimal amplification to the remainder of the waves. This technique reduced the difference between the experimental and numerical Hmax while maintaining a level of spectral similarity. The methodologies presented in this paper are appropriate for modelling realistic extreme sea states for model scale survivability testing of offshore structures.

Nonlinear servocompensator for fault-tolerant control of a wave energy converter

This paper addresses the problem of controlling a wave energy converter (WEC) susceptible to faults in its braking subsystems, characterized through nonlinear damping. By considering the necessity of robust trajectory tracking related to the sea waves for maximizing the converted energy, one aims to preserve such a trajectory in the presence of faults to avoid physical damage in the structure of the WEC. To achieve this objective, this paper proposes a fault-tolerant control (FTC) that combines two systems: (i) a novel nonlinear servocompensator (NSC) and (ii) a fault diagnosis subsystem (FD). The NSC is based on a variable structure control that generalizes the internal model principle for robust tracking. The reference signal is computed from real-time measurements of the irregular sea waves. The FD subsystem estimates the faults related to the wear of the brakes via an unknown input observer. Due to its independent performance from the FD, the global scheme can be considered as a passive FTC. By considering the faulty model of a WEC based on the Archimedes wave swing prototype, theoretical formulation and the convergence proof are given for the NSC and the FD. The performance of the proposed design is verified with numerical simulations of the WEC with the incidence of irregular sea waves under different fault scenarios in the upper and lower brakes.

Performance of a Closed Cycle Power Takeoff for a Shore-Based Wave Energy Device

A promising class of devices for ocean wave energy conversion is called the oscillating water column in which the wave power is transferred to an airflow that rotates a turbine. A closed cycle power takeoff (CCPTO), in which air is forced through two valves and a turbine, has two main benefits for such a system: it allows a unidirectional turbine, and it smooths the large variations in pressure due to irregular (i.e., polychromatic) seas. This paper presents the design of a CCPTO for a shore-based installation, with particular attention paid to the turbine. The entire system is simulated with a reduced order model for a range of sea states to estimate the operating conditions of the turbine. It is found that the pressure drop range is modest but strongly dependent on the tide and sea chamber geometry. The geometry of the turbine is initially developed with a 1D preliminary design of the blades and then the turbine performance is analysed and the design is refined using Reynolds Averaged Navier–Stokes simulations. The design process is conducted based on the geometry and the sea climate of a real-life wave energy installation located in Mutriku (Spain). A turbine that displays efficient performance over a wide range of sea states is obtained. The overall performance of this turbine as part of the entire CCPTO system is assessed and leads to an energy output of ∼1500 kWh for one month in sea conditions at Mutriku wave power plant in Spain. It is concluded that the CCPTO deserves further development in any fixed oscillating wave column system.

Experimental investigation on the coupling response of a multi-floating side-by-side system between a single-point mooring carrier and an articulated floating platform

As an important equipment, side-by-side mooring system and its safety are crucial during offloading operation. Experimental investigation on coupling response of an articulated floating platform and cargo carrier side-by-side single point mooring system is presented. In the case of regular wave and irregular sea, the properties of relative motions in a multi-floating side-by-side single point mooring system is analysised. Comparisons of performance levels between connection systems in different sea conditions reveal effects of wave load are drawn based on the analysis results, which can be used to guide further studies of the multi-floating side-by-side single point mooring system offloading operations.

Seakeeping analysis of a tanker with hard sail-based wind propulsion system in various seaways

A hard sail is a type of wind-assisted ship propulsion (WASP) technology that incorporates wind energy to propel the ship with the help of sails and can significantly reduce the ship's energy consumption. This study focuses on the seakeeping analysis of a hard sail-assisted KVLCC2 ship in different wave conditions. A numerical simulation of the aerodynamic performance of a sail system consisting of two sails was done on ANSYS Fluent and compared with corresponding experimental data. The motion response and added resistance of a KVLCC2 hull in regular waves were numerically predicted in STAR CCM + software and compared with corresponding seakeeping experimental test data. The numerical results obtained for the tanker in regular waves show reasonable accuracy in predicting the hydrodynamic responses of the ship as compared to experimental data. A static analysis was conducted in MAXSURF software to verify the stability of the full-scale ship after the installation of the hard sails. Finally, computational analysis was carried out for the sail-installed KVLCC2 hull to evaluate its hydrodynamic performance for different wave conditions like the regular and irregular head sea as well as beam sea conditions along with expected operational and severe wind speeds corresponding to the model scale hull. The results show that the added resistance and motion amplitudes for the sail-assisted KVLCC2 ship do not change significantly in both operational and severe head sea conditions. However, in the case of a beam sea, there is a significant increase in both added resistance and motion amplitudes.

Safety evaluation of lashed trailer motions in ferry operations under rough sea conditions

Safety evaluation of a lashed trailer on the cargo deck of ships is essential for ferry operations. Although ferry accidents have occurred worldwide, few studies have focused on the dynamic analysis of trailer motion in irregular sea states. To date, effective counterapproaches have not been established. Thus, first, ferry masters were interviewed to summarize the difficulty in cargo management during rough sea voyages. Second, a modified simulation model of lashed trailer motions was constructed to evaluate the safety of cargo management, considering wave, seakeeping, and trailer motion simulations. Few studies apply the model to the irregular sea state in actual seas, using a combination of three different kinds of models. A simulation was conducted to analyze the collapse of a trailer loaded on a ferry in high waves owing to rapidly developing atmospheric pressures. Essentially, the model can reproduce the collapse of trailers, especially when a shift in the center of gravity is considered when accelerations occur in loaded cargo inside trailers. The model enables the estimation of trailer motions and lashing wire tensions in ferry operations, considering suitable lashing arrangements.

Sloshing-induced motions of a spar inside a cylindrical dock with baffles in waves

The motions of a free floating offshore wind turbine’s (OWT) spar-type platform inside a bottom-less moored cylindrical dock are investigated for incident wave frequencies near the first lateral sloshing resonance, focusing on surge on pitch motions. The radiation and diffraction problems of the two-body system are first solved through a domain decomposition (DD) approach under linear potential flow assumptions. This semi-analytical model is extended to include the effects of solid and perforated baffles in the annular domain between the dock and the spar, adapting the method developed in our previous paper for the dock alone. Results are compared with those obtained with model tests, performed at scale 1:100 for both regular waves with low steepnesses and irregular sea states. The resonant peak amplitudes of the spar’s surge and pitch motions are reduced by almost half when a solid baffle is installed, with a strong dependency on the incident wave height due to viscous dissipation caused by the flow separation at the sharp edge of the baffle.

Experimental Assessment of Generalised Super-Twisting Control for Optimal Reference Tracking in Wave Energy Systems

Maximising wave energy extraction is essential for the successful operation of wave energy converters, and appropriate control strategies play a vital role in achieving this objective. This paper presents a control scheme for an experimental wave energy converter setup. The strategy combines an optimal moment-based reference generation technique with a higher-order sliding mode tracking controller, which provides robust tracking of the associated reference, regardless of the uncertainty present in the experimental operation. The device is tested with two different irregular sea states, and results show that the control structure effectively deals with the system's underlying uncertainty, achieving excellent tracking performance while guiding the system to the corresponding surface following the theoretical phase plot convergence. Furthermore, the comparison with a PID tracking control structure indicates that a proper modification of the tracking element of the loop can improve energy extraction. Finally, consistent tracking error and phase plot evolution behaviour are observed for both sea states.