Irregular Sea Research Articles

Simulation based calculation of ship motions in extreme seas with a body-exact strip theory approach

For all design phases of naval vessels, the fidelity of seakeeping calculations in extreme seas is open to discussion due to the inadequacy of the linear theory of ship motions. Currently the computer-generated time series of ship responses and wave height (the real time computer experiments) are utilized to calculate the distribution of the vertical distortion, shear force and bending moment by means of “ship hydroelasticity theory”. Inspired by these studies a simulation based calculation of symmetric ship motions is performed in long crested irregular head seas, in addition with a body-exact strip theory approach. The scope of this study is limited to the ship motions only. Verification is achieved utilizing the spectral analysis procedure which contains the discrete Fourier transform (DFT) and the smoothing algorithms. The results are compared with the experimental data, and the ANSYS AQWA software results. The simulation results provide adequate data for the extreme responses. This state-of-the-art method in addition with a “body-exact strip theory approach” ensures the consistent assessment of the seakeeping performance in extreme sea condition. As a result, it is evaluated that this calculation method can be used in the design stages of naval platforms.

Mixture distribution model for extreme mooring tension and mooring fatigue analysis due to snap loads

Three hybrid moorings are proposed for the station keeping of wave energy converters. The hybrid mooring leg consists of top synthetic fibre rope (nylon or polyester), intermediate buoy and bottom chain (with or without clumped weights attached). The dynamic responses of the point absorber wave energy converter-mooring system are experimentally studied in three irregular sea states. A mixture Rayleigh-Gamma-Weibull distribution is proposed for extreme mooring tension and mooring fatigue damage analysis, and the parameters of this mixture model are estimated by the Expectation Maximization algorithm. The performance of this mixture model is studied by comparing its results with that of the other commonly used distributions. A large number of snap loads are found in survival wave conditions, and a de-clustering procedure is used for the extreme tension analysis. The influence of de-clustering procedure settings on predicted extreme tension is investigated. The rainflow counting approach is applied to calculate mooring fatigue damage and the results are acted as reference values. The Rayleigh, Weibull, Gamma and mixture model are applied to fit the probability density function of rainflow counting tension amplitude for mooring fatigue damage analysis. The accuracy of these models is evaluated by comparing corresponding estimated mooring fatigue damage with the reference values.

Non-linearity Analysis of Ship Roll Gyro-stabilizer Control System

A gyro-stabilizer is the interesting system that it can apply to marine vessels for diminishes roll motion. Today it has potentially light weight with no hydrodynamics drag and effective at zero forward speed. The twin-gyroscope was chosen. Almost, the modelling for designing the system use linear model that it might not comprehensive mission requirement such as high sea condition. The non-linearity analysis was proved by comparison the results between linear and non-linear model of gyro-stabilizer throughout frequency domain also same wave input, constrains and limitations. Moreover, they were cross checked by simulating in time domain. The comparison of interested of linear and non-linear close loop model in frequency domain has demonstrated the similar characteristics but gave different values at same frequency obviously. The results were confirmed again by simulation in irregular beam sea on time domain and they demonstrate the difference of behavior of both systems while the gyro-stabilizers are switching on and off. From the resulting analysis, the non-linear gyro-stabilizer model gives more real results that correspond to more accuracy in a designing gyro-stabilizer control system for various amplitudes and frequencies operating condition especially high sea condition.

Theoretical determination of roll angular jerk of ships in irregular beam seas using PDF line integral method

The time derivative of acceleration is called a jerk, which is an important property to evaluate ride comfort in elevators, cars, and so on. Likewise, evaluation of motion sickness or ride comfort on a vessel could be achieved by this jerk property in the future. In this paper, we utilize the PDF Line Integral Method (PLIM), which was newly contrived in our previous research, for calculating not only roll angular acceleration but also roll angular jerk. The derivation of this theory, as well as numerical comparison with Monte Carlo simulation (MCS) results, are presented. Although the utilized restoring curve (GZ curve) exhibits strong asymmetricity, the proposed method successfully calculates roll angular jerk for such a condition. Since roll angular jerk is a high-order differential property, the biggest advantage of PLIM is that it only requires the information of roll and roll rate joint probability density function (PDF) to provide the PDF of jerk.

Theoretical determination of asymmetric rolling amplitude in irregular beam seas

A methodology for predicting the probability density function of roll motion for irregular beam seas is developed in the author’s previous research. In this paper, two methods for the prediction of the probability density function (PDF) of the rolling amplitude are examined. One of these methods is an approach based on a non-Gaussian PDF with the use of the equivalent linearization and the moment method, which has been used by Maki in the field of naval architecture. In the framework of this method, the instantaneous joint PDF of the roll and roll rate can be calculated. Thereby, the transformation from the joint PDF to the PDF of the total energy H is necessary. In this paper, the transformation from the joint PDF of instantaneous roll and rate to the PDF of H was conducted. The other method is the energy-based stochastic averaging method, whereby the PDF of the total energy H is determined from which the roll amplitude is calculated. It is noteworthy that the proposed theory aims to predict the PDF of the amplitude of the vessel due to wind or flooding. For such conditions, the restoring curve (GZ curve) has asymmetricity. To take into account this asymmetricity, a new theory for the transform of the PDF of the total energy H to the PDFof amplitude is proposed. The obtained theoretical results show almost complete agreement, and both of the two theoretical methods i.e., the energy-based stochastic averaging method and the non-Gaussian PDF method with the use of the equivalent linearization and moment method, show equivalent prediction performance even in the asymmetric condition.

Performance analysis of a raft-type wave energy converter with a torsion bi-stable mechanism

In this study, a torsion bi-stable mechanism is proposed to enhance the absorption efficiency of the raft-type wave energy converter (WEC). The torsion bi-stable mechanism and a power take-off (PTO) system are settled at the joint between hinged rafts. The dynamic model in the time domain of the raft-type WEC has been established in conjunction with a simplified model of the bi-stable mechanism. In order to analyze the performance of the whole system more rapidly, the convolution integral term of the dynamic model has been replaced by the state space model. The performances of the WECs are analyzed in both regular and irregular sea conditions. Compared with the corresponding linear model, the numerical results indicate that the bi-stable mechanism can enhance the capture efficiency of the raft-type WEC significantly and extend the range of the high efficiency to the lower frequencies.

Prediction of Ship Motions in Irregular Waves Based on Response Amplitude Operators Evaluated Experimentally in Noise Waves

Abstract The most common methods for predicting ship roll motions in a specified sea state are direct measurements of motions in a representative irregular wave realisation (time domain) or calculations of motions from response amplitude operators (RAOs) in the frequency domain. The result of the first method is valid only for the tested sea state, whilst the second method is more flexible but less accurate. RAO-based predictions are calculated assuming a linear model of ship motions in waves. RAO functions are usually evaluated by means of tests in regular waves for a limited number of frequencies and a constant wave amplitude. This approach is time-consuming and the discrete form of the RAO functions obtained for a limited number of frequencies may lead to discrepancies in the prediction of seakeeping and often does not allow the actual amplitude of the response in resonant frequency to be determined. Another challenge is the appropriate selection of wave amplitude for tests due to the considerable influence of viscous damping on roll response in irregular sea waves. There are alternative methods for the experimental determination of RAO functions and one of them is presented in this study. The presented approach allows RAO functions to be evaluated in one run by the generation of irregular waves characterised by a white or coloured noise spectrum. This method reduces the experiment duration, with almost continuous RAO characteristics obtained. The flat (white noise) and linear (coloured noise) wave spectral energy characteristics are considered in the experiment and the obtained predictions are compared with the results of accurate measurements in irregular waves.

Geometry assessment of a sloped type wave energy converter

Oscillatory wave energy converters of the sloped type may allow absorbing power from ocean waves efficiently if a valid optimal design is used. In earlier studies, the optimized geometry for the CECO device was defined by implementing a simplified frequency-domain model. In this paper, that geometry is evaluated against the former one by taking into consideration a more realistic modelling approach and assessment scenario. The two geometries were benchmarked through a time-domain model, which allows taking into account realistic sea states and the use of end-stops to limit the amplitude of CECO motions. It was concluded that the optimized geometry allows extra energy production for most of the irregular sea states evaluated (45% more annual energy production). Performance indices were also used to compare the two geometries and it was concluded that the optimized geometry was particularly advantageous for the more energetic sea states. Overall, this study clearly shows that the choice of the generator rated power and end-stops span length are key aspects in determining realistically the annual energy production of sloped-motion wave energy converters.

Mooring Analysis of a Floating OWC Wave Energy Converter

This investigation focuses on the modelling of a floating oscillating water column (FOWC) wave energy converter with a numerical code (ANSYS AQWA) based on potential flow theory. Free-floating motions predicted by the numerical model were validated against experimental data extrapolated from a 1:36 scale model device in regular and irregular sea states. Upon validation, an assessment of the device’s motions when dynamically coupled with a four-line catenary mooring arrangement was conducted at different incident wave angles and sea states ranging from operational to survivable conditions, including the simulation of the failure of a single mooring line. The lack of viscosity in the numerical modelling led to overpredicted motions in the vicinity of the resonant frequencies; however, the addition of an external linear damping coefficient was shown to be an acceptable method of mitigating these discrepancies. The incident wave angle was found to have a limited influence on the magnitudes of heave, pitch, and surge motions. Furthermore, the obtained results indicated that the mooring restoring force is controlled by the forward mooring lines under the tested conditions.

Mooring tension prediction based on BP neural network for semi-submersible platform

The design and optimisation of a mooring system for a floating platform typically necessitates engineering experience and time-consuming numerical simulations. A novel hybrid BPNN–FEM approach, based on the modified BP neural network and FEM is proposed to more conveniently predict the statistic pretension and dynamic tension series of mooring systems with several design variables under irregular sea states. The accuracy of this approach has been validated using several statistical error metrics. This procedure can be used to optimize the mooring system design of the floating platform in a more economical manner than time-intensive numerical simulations. An optional mooring selection is proposed based on the maximum safe operation window and the requirements for the platform drift and mooring line safety performance. A deep-water semi-submersible platform is presented as an example to demonstrate the hybrid approach. This platform comprises twelve mooring lines, and the design variables include the mooring radius, values for the azimuthal spacing of the mooring lines, and the length of the various segments of the mooring lines. The impact of environmental load incidences is also considered in this process. The prediction results are in reasonable agreement with those obtained using the FEM.

Meta‐heuristic optimisation approach for wave energy converter design by means of a stochastic hydrodynamic model

A methodology to automate the sizing of a wave energy converter (WEC) is presented. The preliminary design of WEC geometry is addressed as a mathematical program by means of a meta-heuristic optimisation, which includes as key aspects the use of a multi-objective differential evolutionary (DE) algorithm and the implementation of a stochastic hydrodynamic model of the WEC. In this methodology, the WEC concept, the control strategy, the power take-off characteristics and the location have been taken into consideration due to their strong influence on the WEC design. As a case example, a real project has been selected, and the methodology has been applied to two test locations. Stochastic models are used to handle irregular sea states and to obtain statistical information while reducing the calculation effort when compared to time-domain models. The output derived from the proposed methodology is a set of feasible solutions so-called Pareto frontier. These solutions can be used as inputs for a detailed design process. Data from real projects could be used to further develop the sizing methodology by improving the algorithm convergence, refining the requirements, or including new restrictions.

Investigation on abnormal wave dynamics in regular and irregular sea states

Peregrine breather solution of the nonlinear Schrödinger (NLS) equation can be treated as one of the excellent backbone models for abnormal wave in the ocean. Fully nonlinear numerical simulations performed with the higher-order spectral method reveal that its maximum amplification factor can be larger than the theoretical prediction in the regular background wave and that such breather dynamics has a high probability to persist even in a chaotic environment. Evidently, in both cases the maximum wave height attainable and the corresponding spatial evolutionary distance required are significantly affected by the initial background waves. In fact, whether the abnormal wave induced by breather dynamics can be generated, is mainly a localized behaviour, strongly dependent on the initial wave group energy as well as the detailed structure of this group.

Wave power absorption by an oscillating water column (OWC) device of annular cross-section in a combined wind-wave energy system

This paper deals with a new combined concept consisting of an oscillating water column (OWC) device and an offshore wind turbine for the multi-purpose utilization of offshore renewable energy resources. The wind turbine is supported by a monopile foundation, and the attached OWC is coaxial with the foundation. Within the chamber, the exterior shell of the OWC and the monopile foundation are connected by four vertical stiffening plates. Correspondingly, the whole chamber is divided into four equivalent fan-shaped sub-chambers. A higher-order boundary element method is then adopted to model the wave interaction with the combined system. Numerical models based on two different approaches, namely ‘Direct’ and ‘Indirect’, are both developed in this study. In addition, a self-adaptive Gauss integration method is developed to treat the nearly singular integration that occurs when the field and source points are very close to each other. A detailed numerical analysis is then conducted for the case of an OWC integrated into a NREL 5 MW wind turbine in both regular and irregular sea states. Numerical results illustrate that a significant energy extraction efficiency is attained when remarkable piston-like fluid motion is induced within each sub-chamber, and the wave power absorption by the OWC is not restricted by wave direction. The air compressibility makes a negative effect on the wave power absorption especially when the wave frequency is less than the resonance frequency of the piston-mode motion of the fluid in the chamber. In addition, the wave forces on the OWC and the monopile can balance each other at specific wave conditions, leading to a nearly zero net wave force on the whole system. The results also illustrate that by using an optimal turbine parameter, the wave power production by the OWC can be an important supplement to the combined system in operational sea states.

Response of a self-powered offshore floating support structure with an OWC for powering a LIDAR device

To give an effective response to the increasing demand to characterise wind availability and intensity for the installation of future offshore wind farms, SPAR buoy OWCs with LIDAR present a clear benefit, due to their stability, mechanical and operational simplicity and lower cost, when compared to wind measuring towers, serving as an alternative to the latter, mainly for deep water.This paper proposes a compromise between a stable SPAR buoy for wind measurements (average speed, gusts, etc.) and a sufficiently capable energy generating OWC device for long-term self-sustainability. Key parameters such as mass distribution and geometry were accounted for, in order to achieve both outcomes.The performance of an oceanic SPAR buoy OWC was analysed numerically and experimentally tested at 1:16 scale, under regular and irregular sea states, in order to quantify its hydrodynamic behaviour and capability to generate electrical energy, using two different PTO configurations. Depending on the sea-states, different PTO configurations result in better performance. For higher significant wave heights, the 39% porosity membrane used as a PTO performed better from a power perspective, whereas for lower significant wave height, the 70% porosity membrane presented better results. Low energy consumption wind measuring equipment may benefit from this application.

Confined-crest impact: Forces dimensional analysis and extension of the Goda's formulae to recurved parapets

In this paper, an extended numerical analysis of the “confined-crest impact” (hereinafter referred as “C–CI”), induced by non-breaking waves on recurved parapet walls, is presented to better understand the physics and characteristics of this impulsive wave phenomenon, which significantly depends on the geometry of the parapet (here made by a sector of circumference) as well as on non-breaking wave steepness. A dimensional analysis of the forces has been carried out and used to analyse the results obtained by numerical CFD computations. The numerical simulations, performed for different radii of curvature, opening angles and incoming wave characteristics (changing both the wave height H and wave period T), have shown that the maximum impulsive pressure: (i) takes place on the top of the recurved parapet and decreases moving towards the SWL, where it tends to vanish; (ii) tends to decrease as the radii of curvature and the incoming wave characteristics (wave height H and period T) increase. However, this reduction in the maximum pressure, is always accompanied by an increase of the forces acting on the recurved parapet and a decrease of the wave overtopping volumes. Moreover, the maximum wave induced pressures have been examined by means of regular and irregular wave conditions in order to analyse the possibility of schematising the effects (i.e. forces) of an irregular sea state with those of a regular one, providing an equivalent force and therefore saving computational time. Based on the new results, a schematization of the pressure diagram induced by the C–CI impact has been proposed, used to extend the Goda-Takahashi pressure diagrams, valid for vertical walls in non-breaking wave conditions, including recurved walls.

An adaptive and energy-maximizing control optimization of wave energy converters using an extremum-seeking approach

In this paper, we systematically investigate the feasibility of different extremum-seeking (ES) control and optimization schemes to improve the conversion efficiency of wave energy converters (WECs). Continuous-time and model-free ES schemes based on the sliding mode, relay, least-squares gradient, self-driving, and perturbation-based methods are used to improve the mean extracted power of a heaving point absorber subject to regular and irregular waves. This objective is achieved by optimizing the resistive and reactive coefficients of the power take-off (PTO) mechanism using the ES approach. The optimization results are verified against analytical solutions and the extremum of reference-to-output maps. The numerical results demonstrate that except for the self-driving ES algorithm, the other four ES schemes reliably converge for the two-parameter optimization problem, whereas the former is more suitable for optimizing a single parameter. The results also show that for an irregular sea state, the sliding mode and perturbation-based ES schemes have better convergence to the optimum in comparison to other ES schemes considered here. The convergence of PTO coefficients toward the performance-optimal values is tested for widely different initial values in order to avoid bias toward the extremum. We also demonstrate the adaptive capability of ES control by considering a case in which the ES controller adapts to the new extremum automatically amid changes in the simulated wave conditions. Moreover, no explicit knowledge of (future) wave excitation forces is required in the algorithm, which implies that the model-free ES can be used as a causal controller for WECs. Our results demonstrate that the continuous-time and model-free ES method achieves the optimum within a single simulation, which is in contrast to evolution-based optimization strategies that typically require a large number of (possibly expensive) function evaluations. This makes ES control optimization schemes suitable for nonlinear computational fluid dynamics simulations, where typically evolutionary strategies are used for performing black-box optimization.

The interplay of carbonate systems and volcanics: Cues from the 3D model of the Middle Triassic Sciliar/Schlern platform (Dolomites, Southern Alps)

In the Dolomites (Southern Alps), the original stratigraphic relationships and depositional geometries of Middle Triassic carbonate systems are exceptionally preserved and exposed, and well-constrained in a high-resolution sequence stratigraphic and bio-chronostratigraphic framework. During the late Ladinian, the region experienced a strong tectono-magmatic event, leading to local uplifts and sinks, partial collapses of carbonate edifices and large submarine landslides, as well as the emplacement of thick volcanic and volcanoclastic deposits. The relationships between carbonate and magmatic bodies can be observed in detail in the area between the Sciliar/Schlern mountain group and the Alpe di Siusi/Seiser Alm.In order to better constrain the distribution, geometries and relationships between carbonate, volcanic and volcanoclastic facies, a 3D geological model of the Anisian-Ladinian platform-to-basin system of the Sciliar and Catinaccio carbonate platforms has been developed.The input data set is composed by a net of geological sections built on an updated geological map, field data and formation boundaries digitized on a high-resolution DTM.The resulting pre-volcanic, platform-to-basin system shows a slightly arcuate shape of the margin part facing a starved basin. The volcanic stage is accompanied by strong tectonic subsidence in local sectors of the investigated area, with infilling by mass flow deposits, volcanic rocks, and volcanoclastic material. Major fault-scarps related to the collapse of pre-volcanic carbonate platforms have been modeled. The distribution and thickness of magmatic bodies in the area is however quite variable. The modeled post-volcanic platform-to-basin system shows the impact of the Late Ladinian irregular sea bottom on the distribution and thickness of the younger (mixed carbonate and volcanoclastic) basinal sediments. The model also show that the post-volcanic edifices extended beyond the collapsed portions and occupied an area slightly larger than their pre-volcanic predecessors. The last interval documents the development of lowstand fringing reefs around the older carbonate platform and possibly around demised volcanic areas.

Numerical Investigation on the Added Resistance and Seakeeping Performance of KVLCC2 with the SWENSE Method

In this study, the added resistance and seakeeping performance of the KVLCC2 ship is investigated by using the spectral wave explicit Navier–Stokes equations (SWENSE) method. The SWENSE method is based on the decomposition of the total field into an incident part explicitly obtained by the wave potential flow theory and a complementary part solved with a modified Reynolds-averaged Navier–Stokes solver. Therefore, the computational efficiency can be achieved by using a relatively coarse mesh in the far field, retaining the accuracy of the incident waves. A parametric study is performed under regular wave conditions with 3Degree of Freedom (DOF) motions of the hull. The results are compared with the large literature available. An additional case is simulated to demonstrate the capability of the present method in simulating seakeeping problems in irregular sea states. Good agreement between the computed results with the reference data can be observed for the hull model, which indicates that the added resistance and seakeeping performances can be well predicted by the present method. Introduction In recent years, the Energy Efficiency Design Index (EEDI) has been introduced by the International Maritime Organization to restrict greenhouse gas emissions from ships. In the EEDI formula, the evaluation of the added resistance is required and defined as the increased resistance in the actual sea state due to waves, winds, etc. compared with the resistance in the calm sea condition. The resistance in actual sea states could be up to 30% greater than that in the calm water resistance (Lee et al. 2017). Therefore, prediction of the added resistance induced by waves is an important subject for ship design and is the focus of the present study.

Optimization-based calibration of hydrodynamic drag coefficients for a semisubmersible platform using experimental data of an irregular sea state

For the simulation of the coupled dynamic response of floating offshore wind turbines, it is crucial to calibrate the hydrodynamic damping with experimental data. The aim of this work is to find a set of hydrodynamic drag coefficients for the semisubmersible platform of the Offshore Code Comparison Collaboration, Continuation, with Correlation and unCertainity (OC6) project which provides suitable results for an irregular sea state. Due to the complex interaction of several degrees of freedom (DOF), it is common to calibrate drag coefficients with the time series of decay tests. However, applying these drag coefficients for the simulation of an irregular sea state results in misprediction of the motions. By using numerical optimization, it is possible to calibrate multiple drag coefficients simultaneously and effectively, while also considering several DOF. This work considers time series of structural displacements from wave tank tests of the OC6 project and from simulations of the same load cases in OpenFAST. Results are transferred into the frequency domain and the deviation between power spectral densities of surge, pitch and heave from experiment and numerical simulation is used as an objective function to obtain the best fitting drag coefficients. This novel numerical optimization approach enables finding one set of drag coefficients for different load cases, which is a major improvement compared to decay-test-tuned drag coefficients.

Joint optimization of the number, type and layout of wind turbines for a new offshore wind farm

Prominent problems, including the high investment cost and limited generation revenue of offshore wind farms, are of concern. To tackle these problems, a bi-level model is proposed, whose upper level represents the offshore wind farm optimization for the target of maximizing the profit, and the lower level represents the day-ahead market clearing with the participation of an offshore wind farm. In the upper level, the number, type, and coordinates of wind turbines are simultaneously optimized on the premise of the determined sea area. The layout of an offshore wind farm in irregular sea areas can be obtained by constructing specific penalty functions. In the lower level, under different wind conditions and load, the day-ahead market with the goal of maximizing social welfare is cleared, and the cleared wind power and local marginal prices of an offshore wind farm are provided for the upper level model. Finally, the optimal number, type, and coordinates of wind turbines are obtained by solving the two-layer model. In a rectangular planned sea area, the bi-level optimization model is successfully applied. The test results show that when 27 wind turbines with a rated capacity of 6.45 MW are placed in the planned sea area, the annual investment profit reaches the maximum value of 22.6 × 106 euros. When the optimized layout of an offshore wind farm is used, the power deviation of 67% wind turbines caused by the wake effect can be controlled within 7%, which verifies that the optimized layout plays a role in reducing the wake effect.