Wave excitation tests on a fixed sphere with the center at the still water level were carried out with three different physical wave basin setups. The tests were completed as a continued effort of the working group OES Wave Energy Converters Modeling Verification and Validation to increase confidence in numerical models of wave energy converters by generation of accurate benchmarks datasets for numerical model validation. An idealized test case with wave excitation of a fixed sphere to be used with the benchmarks was formulated. The three investigated physical wave basin setups included: 1) a six degree-of-freedom load cell mounted to the top of the sphere, 2) a bending beam force transducer mounted to the top of the sphere, and 3) a system of six pretensioned wires mounted to the top and bottom of the sphere with force transducers attached to each wire. The aim of the present paper is to identify the best representation of the idealized test case. To this end, the three experimental setups are inter-compared in terms of dynamic properties, sensitivity, and disturbances of the water phase from the presence of measurement equipment. Low inter-experiment variability was disclosed, ie, 5-8% depending on wave-nonlinearity, indicating accurate representations of the idealized test case across all setups. Setup 3 was found to be the more accurate representation and further work with this setup to release a public benchmark dataset was planned.
Accurate prediction of wave transformation is key in the design of coastal and nearshore structures which typically depends on numerical models. Turbulent and rotational effects call for the use of Computational Fluid Dynamics (CFD) solvers of which a large range of formulations including free surface treatments exists. Physical wave flume tests of wave propagation over a submerged bar with various levels of nonlinearity, regularity, and wave-breaking, dedicated to numerical model benchmarking or validation, were carried out in the Ocean and Coastal Engineering Laboratory of Aalborg University. Three fundamentally different CFD models each widespread within their category are benchmarked against the experimental data. The CFD models are based on (i) the Volume of Fluid (VoF) based interFoam solver of OpenFOAM, (ii) the sigma-transformation solver of MIKE 3 Waves Model FM, and (iii) the weakly compressible delta-SPH solver of DualSPHysics. Accuracy of the numerical models is assessed from surface elevation time series, evaluation metrics (averaged errors on surface elevations, amplitudes, phases, and wave set-up), and spectral analyses to calculate the amplitude and phase contents of primary and higher-order components along the wave flume. Applicability is assessed from computational costs and ease-of-use factors such as the effort to configure the numerical models and achieve convergence. In general, the numerical models have high correlation to the physical tests and are as such suitable to model complex wave transformation with an accuracy sufficient for most coastal engineering applications. The VoF model performs more accurately under the turbulent conditions of breaking waves, increasing its relative accuracy in the prediction of downwave surface elevation. The sigma transformation model has simulation times one to two orders of magnitude lower than those of the VoF and SPH models.
Accurate prediction of wave transformation is key in the design of coastal and nearshore structures which typically depends on numerical models. Turbulent and rotational effects call for the use of Computational Fluid Dynamics (CFD) solvers of which a large range of formulations including free surface treatments exists. Physical wave flume tests of wave propagation over a submerged bar with various levels of nonlinearity, regularity, and wave-breaking, dedicated to numerical model benchmarking or validation, were carried out in the Ocean and Coastal Engineering Laboratory of Aalborg University. Three fundamentally different CFD models each widespread within their category are benchmarked against the experimental data. The CFD models are based on (i) the Volume of Fluid (VoF) based interFoam solver of OpenFOAM, (ii) the sigma-transformation solver of MIKE 3 Waves Model FM, and (iii) the weakly compressible delta-SPH solver of DualSPHysics. Accuracy of the numerical models is assessed from surface elevation time series, evaluation metrics (averaged errors on surface elevations, amplitudes, phases, and wave set-up), and spectral analyzes to calculate the amplitude and phase contents of primary and higher-order components along the wave flume. Applicability is assessed from computational costs and ease-of-use factors such as the effort to configure the numerical models and achieve convergence. In general, the numerical models have high correlation to the physical tests and are as such suitable to model complex wave transformation with an accuracy sufficient for most coastal engineering applications. The VoF model performs more accurately under the turbulent conditions of breaking waves, increasing its relative accuracy in the prediction of downwave surface elevation. The sigma transformation model has simulation times one to two orders of magnitude lower than those of the VoF and SPH models.
The design of large diameter monopiles (8–10 m) at intermediate to deep waters is largely driven by the fatigue limit state and mainly due to wave loads. The scope of the present paper is to assess the mitigation of wave loads on a monopile by perforation of the shell. The perforation design consists of elliptical holes in the vicinity of the splash zone. Wave loads are estimated for both regular and irregular waves through physical model tests in a wave flume. The test matrix includes waves with Keulegan–Carpenter (KC) numbers in the range 0.25 to 10 and covers both fatigue and ultimate limit states. Load reductions in the order of 6%–20% are found for KC numbers above 1.5. Significantly higher load reductions are found for KC numbers less than 1.5 and thus the potential to reduce fatigue wave loads has been demonstrated.
We present the results of a numerical model which has been developed for estimating the contribution to the methane slip from different sources in a four-stroke dual-fuel marine engine running on natural gas. The model is a thermodynamic three-zone zero-dimensional full engine cycle model and considers methane slip contributions from short-circuiting, crevices and wall quenching. The model is applied to analyze the methane slip from a four-stroke dual-fuel medium speed marine engine using natural gas as primary fuel. At low loads, wall quenching is found to be the dominant contribution to the methane slip. At full load, the wall quenching contribution is comparable to the level of the short-circuiting and crevice contributions which only vary relatively little with load. At 75% load, the contribution from short-circuiting is highest. In addition, we found that in-cylinder post-oxidation of unburned fuel remaining after the main combustion is negligible.
The stability formula for rock slopes under wave attack was revised in Van der Meer (2021), replacing the mean period Tm with the spectral period Tm-1.0. This rewritten formula closely resembles the Modified Van der Meer formula as in the Rock Manual (2007), with differences primarily in coefficients and the use of H2% in the Rock Manual and H1/3 in Van der Meer (2021).
The wave characteristics change significantly in shallow water due to nonlinearities and wave breaking. The result is a significant change in the wave height and period, especially when severe breaking occurs and infragravity waves become significant or even dominate the spectrum. This may lead to very large breaker parameters. At a certain point, existing stability formulas may thus become inaccurate, both the original and the Modified formula for shallow water. The primary objective of this paper is to identify when and where shallow water stability results deviate from established formulas and how these deviations can be described.
The analysis involves an in-depth examination of datasets from Van Gent et al. (2003), Eldrup (2019), and other relevant data to increase the understanding of waves in shallow water and how they affect rock slope stability.
The use of H2% in the Modified Van der Meer formula gives some difficulties as no reliable prediction method is available for that parameter when the relative depth is small, h/Hm0 depth < 1.5. The Van der Meer (2021) formula applies the significant wave height, and it may be chosen as either Hm0 or H1/3. These two parameters are almost identical in deep water for which the formula was derived, but significant differences may occur in shallow water. The application of the Van der Meer formula in shallow water indicates a preference for the use of Hm0 as it describes nonlinear waves better. The main conclusion is that the Van der Meer (2021) formula seems valid much further into the shallow water region than what the Rock Manual (2007) recommends and at least to relative water depths of h/Hm0 deep > 1.5. For shallow water with h/Hm0 depth < 1.5 no systematic trend with the energy period is observed anymore and constant combined stability numbers are given for guidance in preliminary design.
The levelized costs of energy (LCoE) of wave power is still not fully competitive with other sources of renewable energy. However, wave energy is partly in a different phase than other renewable energy types and could thus contribute to a better predictability and smoothed power output. This work focuses on co-location of wave and wind power by investigating the intermittency of wind and waves power based on measured historical data from several hundreds of locations worldwide. Employing wind power curves and wave power matrices, the sites are evaluated based on several different metrics. The results indicate that there are several spots where wave power has a much lower intermittency than wind power providing reliable energy supply. Best sites for co-location in terms of energy yield were found in North-Western Europe. However, both wind and wave production have the same seasonal variability in these sites. Only a handful of sites found in California showed the possibility of seasonal power smoothing using the combination of wind and wave.
Mooring systems for floating wave energy converters often rely on floaters to allow for minimum restraints of the body motion in heavy. However, the inclusion of floaters also introduce possible slack-taut scenarios induced by the dynamic response of the floater in relation to the fair-lead point of the mooring. This can increase the occurrence of snap loads. The present study outlines the work to include floaters and sinks into a high-order discontinuous Galerkin model for mooring cable dynamics. Numerical simulations of a mooring leg adapted from the Waves4Power full-scale device are performed, and the results from varying the floater geometry are analyzed.
For this case the floater influence on the occurrence of snap loads was clearly evident. There is a strong correlation between floater pitch response and cable slack in the upper mooring cable. For a floater with constant buoyancy, increasing the floater height and thereby increasing the pitch inertia of the floater is shown to decrease the range of frequencies where cable slack occurs. It is illustrated that for some cases, changing floater geometry can avoid slack altogether. A careful design of the floater geometry can thus make a large difference for the dynamic load factor of the mooring system.
This work presents the verification and validation of the freely available simulation tool MoodyMarine, developed to help meet some of the demands for early stage development of MRE devices. MoodyMarine extends the previously released mooring module MoodyCore (Discontinuous Galerkin Finite Elements) with linear radiation-diffraction bodies, integrated pre-processing workflows and a graphical user interface. It is a C++ implementation of finite element mooring dynamics and Cummins equations for floating bodies with weak nonlinear corrections. A newly developed nonlinear Froude-Krylov implementation is verified in the paper, and MoodyMarine is compared to CFD simulations for two complex structures: a slack-moored floating offshore wind turbine and a self-reacting point-absorber with hybrid mooring.
Marine cables are primarily designed to support axial loads. The effect of bending stiffness on the cable response is therefore often neglected in numerical analysis. However, in low-tension applications such as umbilical modeling of ROVs or during slack events, the bending forces may affect the slack regime dynamics of the cable. In this paper, we present the implementation of bending stiffness as a rotation-free, nested local Discontinuous Galerkin (DG) method into an existing Lax–Friedrichs-type solver for cable dynamics based on an hp-adaptive DG method. Numerical verification shows exponential convergence of order P and P + 1 for odd and even polynomial orders, respectively. Validation of a swinging cable shows good comparison with experimental data, and the importance of bending stiffness is demonstrated. Snap load events in a deep water tether are compared with field-test data. The bending forces affect the low-tension response for shorter lengths of tether (200–500 m), which results in an increasing snap load magnitude for increasing bending stiffness. It is shown that the nested LDG method works well for computing bending effects in marine cables.