Green water is an extreme event that impacts ships and poses a risk to those on board. Conventional methods of screening assume a direct relation between exceedance and green water. This article demonstrates that the relation is not direct and identifies a difference between green water and exceedance that does not develop into a flow on deck. A proposed prediction method follows from the difference between green water and exceedance identified from analysing a big data set. The big data set is from experiments modelling 1945 full-scale hours and includes 409 green water events and 729 exceedance events which did not become green water. Pitch was identified as an important indicator for green water as green water events consistently occurred with large forward pitch motion, while exceedance also occurred with neutral pitch. A prediction method of probability is proposed that implements separate limits for the motions and wave elevation that occur simultaneously, thus including the phase difference between the motions and wave elevation. The result is a method for the prediction of the occurrence of green water on the deck of a ship with different forward velocities and in different sea states.

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The lack of suitable boundary conditions in practical surface wave simulations with maritime structures in current or at forward speed may cause energy in the computational domain to accumulate due to spurious wave reflection. The common way to prevent wave reflection is to use passive wave absorbers, such as damping zones or relaxation zones, which requires larger domains at the cost of computational effort. Our goal is to derive a local generating absorbing boundary condition (GABC) for long-crested irregular waves on top of a mean flow, using the flow to model the forward speed of a structure such as a ship. Earlier work has demonstrated that a local GABC for free surface waves has a performance similar to passive wave absorbers, but at a reduced computational effort. New in the present work is that we extend, verify and validate the GABC in the presence of a nonzero mean flow. The GABC is designed to be accurate for a range of wave components in irregular sea states, with the resulting reflection coefficients for each component lower than a chosen value, say 5%. Having used potential flow theory for its derivation means that the boundary should not be placed at the exact location where wave breaking is expected, such as very close to the structure in the domain, or in the surf zone in coastal modeling. For the application with ships in this article that does not pose a limitation. The performance is demonstrated for a range of dimensionless wave number between 0 and 6. Such a boundary condition is obtained through a rational approximation of the linear dispersion relation with a mean flow, in combination with vertical derivatives of the solution variables along the boundary. Local linearization means that the GABC incorrectly considers bound, nonlinear wave components to be freely propagating wave components. Bound components, however, tend to have smaller amplitudes and do not appear to affect performance for the considered cases. Results of simulations with regular and irregular waves, on top of flows with different magnitudes and directions, are found to agree with the theory. The main source of differences is the implementation of the second derivate in the GABC near the free surface. Simulations of a Wigley hull at forward speed in irregular waves are compared to an experiment that was conducted specifically for validating the ABC. The data of the experiment are available as open data through doi: 10.4121/21320604. The comparison between simulation and experiment demonstrates that the GABC with a mean flow can be applied not only for theoretical simulations with propagating waves, but also for more practical applications with a structure in the domain.

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As a result of more stable wind conditions and the depletion of near-shore locations, wind farms are moving farther offshore into deeper waters, challenging the current limits of offshore heavy-lift operations. This paper presents and verifies a novel frequency-domain framework to perform extensive site-specific analysis, of floating installations of wind-turbine towers, subjected to wind and wave loads. The versatility and potential of this framework is demonstrated with a case-study of a wind farm near the coast of Portugal. The results lead to the following conclusions: (1) Only considering beam-seas the yearly workability is 39 %; (2) Workability is mostly limited by wave loads; (3) Tower motions tend to decrease with tower size and are not significantly affected by hook-tower distance (sling length); and finally, (4) In this case-study the most contributing frequencies for tower motions are 0.3 and 0.4 rad/s, corresponding mainly to the first pendulation mode.

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Green water is a rare and complex wave impact event that can affect the safety of the ship and those aboard. During the design process, the risks that these events pose have to be mitigated, preferably by minimizing the probability of a high impact pressure. As green water events are rare and complex it is difficult to get a statistically representative dataset and thus previous work has mostly compared design variations through a limited number of events, instead of comparing the probabilities. The present study will use probabilities to compare design variations with different drafts and freeboards at the bow. A large set of green water events in irregular waves with forward velocity was experimentally obtained for six different bow designs. The dataset represents 57 hours of sailing per bow design and 3263 green water events. The data demonstrates that both freeboard and draft at the bow affect the probability of green water in a complex way. Increasing the draft at the bow increases the swell-up, reducing the effective freeboard and in turn, increasing the probability of green water. Increasing the freeboard results in a decrease in the probability of green water, as expected. However, the probability is not reduced equally for different green water impact pressures. The joint probability of green water occurrence and pressures shows that increasing the freeboard only decreases the probability of low-pressure events. Counter-intuitively, increasing the freeboard increases the probability of high-pressure events. These interesting results show the value of using statistically representative datasets when designing for green water.@en

Maritime structures in heavy seas can experience wave impact events with high loads. The loads can lead to structural failure and even loss of life. Wave breaking in said sea states causes air to be entrained in water as aeration cloads, remaining long enough to be transported and to play a role in the impulsive interaction with the structure. A small amount of air in water already forms a highly compressible mixture. Compressibility influences the magnitude of the impact loads. A new cartesian grid method for compressible multiphase flow is introduced to account for water, air and homogeneous mixtures of air and water. The method is designed to predict the hydrodynamic loads on moving bodies engaging with interfaces between fluids having large density ratios. An equation for conservation of energy is omitted by enforcing pressure-density relations. The interface between fluids is transported using a geometric Volume-of-Fluid method. The interface between fluids and structure is taken care of by a cut-cell method. An additional fraction field for the amount of air in water in combination with a new formulation for the multiphase speed of sound prevent overprediction of compressibility by artificial air entrainment. New experimental data of 2D wedge impacts with aerated water, made available as open data, are presented to demonstrate the validity of the numerical method. For low aeration levels, the simulation results in terms of the impact loads on the wedge and the frequencies of pressure waves generated upon impact are in good agreement with the experimental data. Increasing the level of aeration reduces the maximum impact load on the wedge. Reflected density waves lead to secondary loads on the wedge. The intensity of the secondary loads, relative to the primary load of impact, increases with the aeration level while the density wave frequency decreases.

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Energy from ocean surface waves is the most prominent form of marine energy. The waves are produced by gravitational water waves (2.2e5 Hz), in combination with the short wind and swell waves (0.03-1 Hz). The energy density and predictability of waves make them an extremely interesting form of sustainable energy. Wave energy is therefore an ideal addition to the energy mix. Research has confirmed that (part) synergy is possible with offshore wind farms because the energy production profile over time of wave energy (even on a relatively sheltered inland North Sea) is not synchronous with the energy profile of wind, mainly due to swell waves and therefore is, at least, partly complementary to that of offshore wind. Wave energy can be generated via so-called wave energy converters (WECs). This article describes the potential of an innovative WEC with existing regenerative robots to be used in energy harvesting in the North Sea.

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Europe has set an ambitious target to increase the offshore wind power capacity to approximately 30 GW by 2026. With nearshore locations already allocated, future wind farms must be installed in deeper waters, pushing the operational limits of currently used jack-up vessels. Utilizing existing floating heavy-lift vessels presents a viable alternative. This paper disseminates data gathered during the full-scale testing campaign of a floating installation of an offshore wind turbine tower. For this purpose, novel time-synchronized motion-tracking units were developed. Analysis of the obtained data reveals that approximately 96% of the motion response of the tower is due to wave action and 3% to vortex-induced vibrations caused by the presence of a passive tugger line, which shifted one of the system's natural frequencies towards the tower's vortex-shedding frequency. Next to wind and wave-induced motion, the data reveal that the hoisting itself induces tower vibrations, accounting for less than 1% of the tower motion response. The collected data offer a distinctive perspective on this type of installation, which is unlikely to be replicated at model scale due to the scaling limitations associated with the interdependence of waves and wind. The data can be used to validate motion control strategies to enhance the efficiency, safety, and workability of floating offshore wind turbine installations.

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The original goal of the present research is to investigate the influence of surge on green water and slamming. Long-running experiments with forward velocity and irregular waves were repeated with and without surge. Surge is found to increase the probability of green water events, but the impact pressures on deck and the probability of a green water event reaching the deck box decreases when the ship is free to surge. Green water and slamming events turned out to not occur independently as both event types cluster for large probabilities of occurrence. Clusters are caused by large pitch motions. Larger pressures on deck are found for clustered events.@en

Cavitation occurs when the local pressure, induced by high local velocities, drops below the vapor pressure, leading to the formation of vapor bubbles. The subsequent collapse of these bubbles can cause noise, erosion, and vibrations. Recent studies show that cavitation is sensitive to water quality, i.e., the nuclei populations, the chemical composition of water, and the presence of particles. Motivated by investigating the effects of water quality on cavitation, experiments are performed in a dedicated experimental facility. This consists in two co-axial disks that are initially at rest and mutually in contact, in a tank filled with water. The fast diverging movement of the top disk with respect to the bottom one produces a jet flow inside the gap between the disks, which leads to the formation of two counter-rotating vortices. The local pressure drop induced by high flow velocities leads to a phase change. To characterize the phenomenon, two optical techniques are applied, i.e., shadowgraphy and particle image velocimetry (PIV). In performing PIV reconstruction, the sum of correlation enhances the spatial resolution of the velocity vector fields. The pressure field in the region where the vortices occur is obtained from velocity data. The water quality effects on cavitation are investigated by adding salt and using water with an abundance of nuclei inside the tank.@en

A new bilinear interface reconstruction algorithm (BLIC) is presented to capture highly-curved interfaces more accurately on structured grids without a significant increase in computational costs compared to the standard piecewise linear interface calculation (PLIC) methods. The new reconstruction algorithm uses the initial PLIC segment and improves continuity of the interface using an averaging method. A curvature-weighted method improves the repositioning of the linear segments. A new unsplit donating quadrant advection (DQA) scheme is introduced that is conservative and can create consistency with the momentum flux for two-phase flow models with a staggered MAC arrangement of variables within a grid cell. The consistent discretization of the fluxes prevents spurious interface velocities, negative densities, and instabilities. Standard 2D test cases and benchmarks demonstrate the performance of the BLIC and the DQA scheme, showing high accuracy and low costs compared to other available methods.

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In head waves, water jet impacts due to run up can occur as a result of the structural configuration of some floating structures, reducing workability. Wave attenuation near the floater may reduce the risk of water jet impacts. This paper presents a numerical study of the performance and attenuation mechanisms of various plate type fixed free surface breakwaters and their ability to prevent water jet impacts on adjacent structures. Simulations are performed in two dimensions with a numerical method based on the Navier–Stokes equations in the presence of a free surface. The breakwater models are evaluated in two irregular sea states in terms of wave transmission, reflection and energy dissipation and by their ability to reduce water jets impacts on adjacent structures. A 60 degree inclined plate is found to induce a large wave energy reduction, little wave transmission and reflection and to experience little wave loading while effectively reducing water jet impacts.

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Surrogate modelling techniques such as Kriging are a popular means for cheaply emulating the response of expensive Computational Fluid Dynamics (CFD) simulations. These surrogate models are often used for exploring a parameterised design space and identifying optimal designs. Multi-fidelity Kriging extends the methodology to incorporate data of variable accuracy and costs to create a more effective surrogate. This work recognises that the grid convergence property of CFD solvers is currently an unused source of information and presents a novel method that, by leveraging the data structure implied by grid convergence, could further improve the performance of the surrogate model and the corresponding optimisation process. Grid convergence states that the simulation solution converges to the true simulation solution as the numerical grid is refined. The proposed method is tested with realistic multi-fidelity data acquired with CFD simulations. The performance of the surrogate model is comparable to an existing method, and likely more robust. More research is needed to explore the full potential of the proposed method. Code has been made available online at https://github.com/robertwenink/MFK-Extrapolation.

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The numerical prediction of two-phase flows with an interface is challenging, to a considerable extent because of the high density ratio at the interface. Numerical results become affected by momentum losses, diverging spurious interface velocities, free surface distortion, and even numerical instability. To prevent issues like these, consistent momentum and mass transport with an additional continuity equation were introduced. In this article, we describe how a consistent discretization was incorporated into our own method and extended for fluid-structure interaction (FSI) with moving rigid bodies. The new method was tested against benchmark simulations from literature confirming that consistent transport modeling gives a significant improvement compared to non-consistent modeling for the dynamics of two-phase flows. Newly devised proof of principle FSI simulations with momentum transfer from fluid to body in the presence of a high-density ratio between fluids are introduced that could serve as a benchmark for future studies. The simulations demonstrate that consistent modeling gives an order of magnitude improvement in terms of momentum conservation compared to non-consistent modeling. Simulations with the new method are also compared to FSI experiments from literature. Results obtained with the consistent method are closer to the measurements than results of the non-consistent method. The merit of consistent modeling with and without FSI becomes especially apparent for two-phase flows with a high-density ratio between fluids.

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This article proposes a method to quantify, first, the probability of occurrence of green water and, second, the expected maximum pressures during green water events using their statistical distribution for ships at forward speed. A large green water data set which represents 1945 hours of continuous sailing on full scale with different sea states, forward speeds and drafts was obtained with model test experiments in a wave–current tank. The data of the experiment are available as open data through https://doi.org/10.4121/21031981. With the large data set obtained, the distribution of the time between green water occurrences is identified as exponential, indicating that when green water occurs is independent of the time since the last occurrence. Two methods were compared to estimate the probability of green water occurrence. One method is based on the probability of water exceeding the deck and one on a ship’s freeboard and the significant wave height, the former being in better agreement with the data, the latter being more practical for designers. The maximum pressures caused by green water are distributed according to the Fréchet distribution, also called extreme value distribution II. With the newly identified distributions, finally, an equation to calculate the probability of a pressure limit being exceeded for a ship in operation is formulated.@en

The present research analyzes the nonlinear fluid–structure interaction (FSI) of free surface waves with large-scale polymer offshore floating photovoltaics (LPOFPV). The floating structure is modeled as a nonlinear Euler Bernoulli–von Kármán (EBVK) beam coupling with water beneath. The EBVK theory takes the in-plane force into consideration to account for the moderately large deflection slopes in LPOFPV. A multi-time-scale perturbation method leads to hierarchic partial differential equations by introducing the wave steepness squared as the perturbation. The analytical solution of the proposed nonlinear FSI model is obtained up to the second order. Pontoon structures and LPOFPV are studied and compared. The asymptotic solution provides the expressions of the propagating wave through the coupled system and its frequency–amplitude dispersion relation in a closed-form. A property of the solution is that the progressive plane wave through the coupled system remains linear for small dimensionless amplitudes, and features a second order correction for moderately large dimensionless amplitudes. Furthermore, it is also theoretically proven that no resonance occurs in the considered infinite problem. The proposed approach can be extended to the nonlinear coupling between a EBVK beam and Stokes waves.@en

The added resistance is a resistance component that is not yet satisfactorily predicted, although its accurate estimation is crucial-both from an environmental and economic point of view-from the design stage of a ship until its operation. One of the possible sources of overprediction is the occurrence of bow wave breaking. The first aim of this paper is to study the effect of bow wave breaking on added resistance by combining visual observations with resistance tests. On the other hand, as the bow region of a ship appears to be the most dominant contributor to added resistance, this paper introduces a dynamic waterline detection method involving stereo vision. This experimental method is applied to reach the second aim of this paper, which is to stress the importance of the relative wave elevation in the bow region of the ship. By placing stereo rigs inside the hull of a semi-transparent ship, the waterline at each momnent in time can be tracked using an edge detection algorithm. By performing resistance tests on the Delft Systematic Deadrise Series ship model no. 523, the added resistance is observed to be proportional to the relative wave height squared. The data of the experiment and the information necessary to reproduce the experiment are shared through https://doi.org/10.4121/19525852.

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This paper concerns the fully nonlinear fluid–structure interaction (FSI) of Large-scale floating photovoltaics (LFPV) in waves. The Euler Bernoulli–von Kármán beam models the structure while potential flow represents the fluid. A set of coupled dynamical equations is established. The fully analytic solution is sought with the unified Stokes perturbation method. The characteristic equation is derived up to third order, which has not been reported in literature before. The expressions obtained from the solution are applied to two typical cases of a pontoon LFPV and a membrane LFPV, with physical parameters from literature. The comparison with literature demonstrates our methodology for the membrane-type in waters of arbitrary depth and pontoon-type in relatively deep waters.

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PTO (Power Take-off) systems in WECs (Wave Energy Converters) are generally overrated with regard to the average extracted power, which is not economically favourable. However, there is no explicit and agreed approach on how to limit the absorbed power without damaging WECs. In this work, a generic point absorber and direct drive PTO are used as research objects. A frequency domain model and a cost model are established. Two possible approaches for downsizing PTO rating are investigated. The first approach is established by switching the control strategy of WECs between reactive control and passive control for making a compromise between extracted power and PTO rating. Alternatively, a novel design is proposed by integrating an adjustable draft system of buoy to release the excessive absorbed power. Based on the results, the performance of these two approaches are investigated and the techno-economic performance of these two approaches are compared.

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To study how an extreme wave load on a maritime structure causes structural deformation, an experiment is conducted to measure the response of a one degree-of-freedom pendulum in a focused, breaking wave. The tube that makes up the base of the pendulum covers almost the entire width of the tank so that three-dimensional effects can be considered small. The experiment varies the focus location with respect to the position of the pendulum as well as the vertical clearance between pendulum and mean free surface. Although the energy of the wave input was the same for all experiments, the response of the pendulum varied greatly with small variations of initial vertical clearance and wave focus location, with the wave breaking farthest away from the pendulum causing the largest response. A reduced-order model for the response of the pendulum shows the same behavior when initial clearance and focus location are varied. Even when initial clearance and focus location were kept the same between tests, large variability of the pendulum response was observed, meaning that the impulse exerted by the wave must have been different. This is different from the literature on breaking waves against rigid walls that found that local pressures show variability between experiments but that the impulse typically is the same. The experimental data and a description have been made available.

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Maritime structures operating out at sea experience large changes in wetted area because of free surface waves. Although these conditions are typical for maritime applications, a fundamental experiment that includes a structure in the air–water interface undergoing transitions from dry to wet and back does not appear to exist. This paper aims to fill that knowledge gap. We present an experiment in which a pendulum is suspended just above the still water level and then exposed to monochromatic free surface waves with different wave lengths. Additionally a reduced-order model is derived to compute the response of the pendulum and help interpret the experimental results. The motion response of the pendulum is demonstrated to depend highly on whether the wave period is much lower or higher than the dry natural period of the pendulum. Additionally, a sensitivity study with the wave amplitude in the model and a quantification of the variability in the experiment both indicate that the variability in the motion response of the pendulum is increased with respect to the variability of the incoming wave. We believe this experiment and the results make for an interesting benchmark of fluid–structure interaction in free surface waves. The properties of the pendulum and the experiment are available as open data at doi:10.4121/13187594 (Wellens and Bos, 2020).

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