Wave-to-Wire models play an important role in the development of wave energy converters. They could provide insight into the complete operating process of wave energy converters, from the power absorption stage to the power conversion stage. In order to cover a set of relevant nonlinear effects, wave-to-wire models are predominately established in the time domain. However, the low computational efficiency of time-domain modeling is hindering the extensive application of wave-to-wire models, especially in early-stage design and optimization where a large number of iterations are required. To address this issue, a spectral-domain wave-to-wire model is proposed, and the nonlinear effects are incorporated by stochastic linearization. This model can significantly reduce the computational load and maintain good accuracy. The reference concept studied in this paper is defined as a heaving point absorber coupled with a linear permanent-magnet generator. Four representative nonlinear effects involved in both the hydrodynamic stage and the electrical stage of the concept are considered. The proposed model is verified against a corresponding nonlinear time-domain wave-to-wire model, and a good agreement is observed. The relative error of the proposed spectral-domain wave-to-wire model is around 2 % in typical operational regions and is still within 7 % for wave states with large significant wave heights, regarding the estimate of the power conversion efficiency. Meanwhile, the computational load of the spectral-domain wave-to-wire model is reduced by 2 to 3 orders of magnitudes compared with the conventional time-domain approach. Finally, a case study of tuning the PTO damping to maximize power production is conducted to demonstrate the performance of the proposed spectral-domain wave-to-wire model.

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An adjustable draft point absorber was recently proposed as a novel approach to improve power absorption with constrained power take-off (PTO) capacities. The key feature of the novel wave energy converter (WEC) concept is to adjust the buoy draft by regulating the ballast water inside the buoy, which aims to enable variation of the natural frequency of the WEC. Although previous research has shown benefits for the energy absorption stage, the impact of the draft adjustment on the power conversion efficiency and overall performance has not been examined yet. Therefore, a wave-to-wire model is established to provide an in-depth insight into the systematic performance of the adjustable draft point absorber integrated with a linear permanent magnet generator. Both a nonlinear hydrodynamic model and an analytical generator model are derived, thus the complete process from the wave power input through the whole WEC system to the usable electricity is covered. Based on the established model, wave-to-wire responses of the novel concept are obtained and analyzed. The negative effects of the draft adjustment on the stroke and overlap between the stator and translator are demonstrated. Moreover, a comparison is made between this novel WEC and conventional fixed draft WEC, and both regular and irregular wave states are considered. The results show that the adjustable draft system could increase not only the absorbed power but also the generator conversion efficiency. In specific conditions, the delivered electrical power of the adjustable draft WEC was over 20 % and 10 % higher than a traditional fixed draft system for regular and irregular waves respectively.

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A spectral domain model is established to analyze the performance of a recently proposed wave energy concept, namely the adjustable draft point absorber. The non-linear hydrostatic force is incorporated in the spectral domain model. To improve the accuracy of the proposed model, the incident wave elevation is considered in the statistic linearization of the non-linear term. The proposed model is verified by the results obtained by the non-linear time domain simulations. The results suggest that the proposed spectral domain model could include the non-linear hydrostatic force while maintaining a higher computational efficiency than the non-linear time domain model. Based on the proposed model, the power performance of the adjustable draft WEC is identified. Furthermore, a techno-economic analysis is performed to reveal the benefits of the adjustable draft WEC for a given European sea site. The results show that the adjustable draft WEC is associated with higher power absorption in powerful sea states compared with the conventional fixed draft WEC. In addition, the adjustable draft system could contribute to the improvement of the annual energy production as well as the reduction of the levelized cost of energy of WECs.

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A crucial part of wave energy converters (WECs) is the power take-off (PTO) mechanism, and PTO sizing has been shown to have a considerable impact on the levelized cost of energy (LCOE). However, as a dominating type of PTO system in WECs, previous research pertinent to PTO sizing did not take modeling and optimization of the linear permanent magnet (PM) generator into consideration. To fill this gap, this paper provides an insight into how PTO sizing affects the performance of linear permanent magnet (PM) generators, and further the techno-economic performance of WECs. To thoroughly reveal the power production of the WEC, both hydrodynamic modeling and generator modeling are incorporated. In addition, three different methods for sizing the linear generator are applied and compared. The effect of the selection of the sizing method on the techno-economic performance of the WEC is identified. Furthermore, to realistically reflect the relevance of PTO sizing, wave resources from three European sea sites are considered in the techno-economic analysis. The dependence of PTO sizing on wave resources is demonstrated. @en

The power take-off (PTO) system is a main component in wave energy converters (WECs), and it accounts for a notable proportion in the total cost. Sizing the PTO capacity has been proven to be significant to the cost-effectiveness of WECs. In the numerical modeling, the PTO size is normally represented by a force constraint. Therefore, to accurately evaluate the power performance of WECs with various PTO sizes, it is necessary to take the PTO force limitation, a nonlinear effect, into consideration. In this paper, a computationally-efficient spectral domain model of the PTO force saturation is developed for a heaving point absorber, and the nonlinear term is included by statistical linearization. For comparison, a frequency domain and nonlinear time domain model are implemented, and the developed spectral model is verified with the results of the nonlinear time domain model. Compared with the frequency domain model, the spectral domain model remarkably reduces the relative errors in predicting the power performance of WECs with force constraints, while the computational demand is much lower than the nonlinear time domain model. Furthermore, a case study is conducted to size the PTO capacity for reducing the levelized cost of energy (LCOE) in a chosen wave site. Three different numerical models are applied respectively. The frequency domain model could lead to a misestimate of the optimal PTO capacity, with a maximum relative error on the prediction of the annual energy production (AEP) of 24%. In contrast, the spectral domain model indicates the same optimal PTO size with the time domain modeling, and its relative errors on the prediction of the AEP are within 4.3%.

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The Power Take-Off (PTO) rating of Wave Energy Converters (WECs) is generally much higher than the average extracted power. Scientific literature has indicated that downsizing the PTO capacity to a suitable level is beneficial for improving the techno-economic competitiveness. In this paper, a novel design, namely the adjustable draft system, is proposed for point absorbers to implement PTO downsizing. A frequency domain model is established to calculate the performance of the proposed device. From frequency domain analysis, two potential advantages are identified by installing the adjustable draft system. Firstly, the excitation force can be controlled by adjusting the buoy draft, which could be utilized to reduce the required PTO force. This is helpful for downsizing the PTO capacity. Secondly, the relevant natural frequency of the point absorber can be adapted to the operating wave states by varying the buoy draft, which improves the power absorption. A nonlinear approach is adopted specifically for the spherical buoy to include the nonlinear Froude–Krylov force and viscous drag force. The results show that the nonlinear forces have a significant influence on the power absorption when operating close to resonance regions. However, the advantages resulting from the proposed system still can be observed while considering the nonlinear forces. The power absorption can be improved by 27% and 12% in particular cases of regular and irregular wave states respectively.

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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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Downsizing the Power Take-off (PTO) rating has been proven to be beneficial for decreasing the Levelized Cost of Energy (LCOE) of wave energy converters (WECs). However, the linear permanent magnet (PM) generator has not yet been modelled and optimized in detail in previous feasibility studies. This paper extends the study of the PTO downsizing to further investigate the influence of the linear PM generator sizing on a WEC's techno-economic performance. The generator is sized for providing different maximum forces, and the effect of sizing on the generator performance is presented. The efficiency map of the selected linear generator design is applied to evaluate the annual energy production (AEP) and finally identify its influence on the techno-economic performance of a WEC.

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Currently, the techno-economic performance of Wave Energy Converters (WECs) is not competitive with other renewable technologies. Size optimization could make a difference. However, the impact of sizing on the techno-economic performance of WECs still remains unclear, especially when sizing of the buoy and Power Take-Off (PTO) are considered collectively. In this paper, an optimization method for the buoy and PTO sizing is proposed for a generic heaving point absorber to reduce the Levelized Cost Of Energy (LCOE). Frequency domain modeling is used to calculate the power absorption of WECs with different buoy and PTO sizes. Force constraints are used to represent the effects of PTO sizing on the absorbed power, in which the passive and reactive control strategy are considered, respectively. A preliminary economic model is established to calculate the cost of WECs. The proposed method is implemented for three realistic sea sites, and the dependence of the optimal size of WECs on wave resources and control strategies is analyzed. The results show that PTO sizing has a limited effect on the buoy size determination, while it can reduce the LCOE by 24% to 31%. Besides, the higher mean wave power density of wave resources does not necessarily correspond to the larger optimal buoy or PTO sizes, but it contributes to the lower LCOE. In addition, the optimal PTO force limit converges at around 0.4 to 0.5 times the maximum required PTO force for the corresponding sea sites. Compared with other methods, this proposed method shows a better potential in sizing and reducing LCOE. @en

A jet pump is used to transport a variety of working media and is especially suitable for dredged soil transporting. In this study, a three-dimensional numerical study of a jet pump that is used for slurry delivery was carried out. The characteristics of the internal flow field of the mixing chamber with different working parameters were comprehensively analyzed. The results indicate that the pressure of the axial line decreases with increasing flow ratio (ratio of suction flux and inlet flux) while the pressure of the injected slurry shows a downward trend. With the increase in the flow ratio, the pressure ratio (difference between inlet pressure and suction pressure divided by the difference between exit pressure and suction pressure) falls off while the efficiency presents a parabolic distribution. The pressure ratio can be promoted by properly increasing the length of the mixing chamber so that the available efficiency is broadened. When the mixing chamber length is L = 2.5D_n~4.0D_n (D_n is nozzle outlet diameter), the highly efficient area is wide; in particular, when L = 3.5D_n, the jet slurry pump with the highest efficiency of 27.6% has the best performance.

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In this paper, a fair evaluation method of WECs (Wave Energy Converters) is established based on frequency domain simulation. In this fair evaluation, size optimization and downsizing of PTO (Power Take-Off) capacity are included to minimize the Cost of Energy for the concerned wave location. Based on this fair evaluation, a techno-economic evaluation of a generic point absorber is conducted for a specific wave location, and two different control strategies of PTO are considered. The results show that this fair evaluation method can contribute to the improvement of techno-economic performance of WECs. Furthermore, a comparison among three different size optimization methods of WECs is performed.@en

In dredging, production estimating is carried out mainly with analytical physical models of the different dredging processes. Slurry transport of settling slurries and cutting processes in sand, clay and rock are already covered in two other books by the author. Other processes like hopper sedimentation and erosion, water jet fluidization, cutter head spillage, pump/pipeline dynamics and clamshell dredging are covered in this Special Topics Edition. New topics may be added in the near future.@en

Production Engineers are asked to provide estimated productions and operational guidance for dredging plant that works in a rapidly changing and dynamic environment. These engineers use models to apply scientific principles and engineering practices. The models must have three properties; they must be tractable, discernable and informative. Tractability means the ability to quickly setup and run the model, as the engineer has to quickly evaluate multiple scenarios. Discernable models use parameters and inputs likely to be known to the engineers and eschew parameters that are unknowable or unimportant. By informative, we mean that the output of the model must provide a direct answer to the specific engineering question, provide other outputs that can be used as operational guidance, and to check and calibrate the model. To satisfy these requirements the models are generally analytical, based on fundamental or empirical equations that reflect the underlying physics. The paper contrasts such engineering models to those used in design engineering and to scientific models used for research purposes.

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One of the main types of equipment is the cutter suction dredge (CSD). The theoretical soil production Qc equals the cross section of the cutter head in the bank cutting, perpendicular to the swing velocity vs times the swing velocity vs. If the theoretical soil production is 100%, usually less than 100% will enter the suction pipe. The real production. The difference between the theoretical production and the real production is the spillage. So, this is the percentage of the theoretical production not entering the suction pipe. Now in practice it is more difficult to define the spillage, because often a number of swings at different levels is necessary to excavate a bank. The spillage of a previous swing may be cut a second time during the current swing and thus enter the suction pipe in the current swing. So, the spillage of one swing does not have to be spillage overall. In this report however just one swing is considered, assuming a fresh bank, where all the soil that does not enter the suction pipe is considered spillage. The model is derived based on the Euler equation for centrifugal pumps, including inner and outer radii and blade angles. The model is first calibrated based on the limited experimental data mentioned in den Burger (2003). This paper covers the theory and the validation, with many experimental data of Miltenburg (1983), a cold case never published before. This paper shows the state of the art of the spillage modeling.@en

In dredging, trenching, (deep sea) mining, drilling, tunnel boring and many other applications, sand, clay or rock has to be excavated.The book covers horizontal transport of settling slurries (Newtonian slurries). Non-settling (non-Newtonian) slurries are not covered.@en

In dredging soil is excavated with dredging equipment. One of the main types of equipment is the cutter suction dredge (CSD). The CSD consists of a floating pontoon, with in the back a spud pole penetrating the soil. In the front there is a ladder, which can rotate around a horizontal bearing. By means of this rotation the cutter head, mounted at the end of the ladder, can be positioned in the bank. Also, at the end of the ladder two swing wires are connected (port and starboard wires) enabling the CSD to rotate around the spud pole and thus letting the cutter head make a circular movement through the bank. During this rotation, with a circumferential swing velocity vs at the centre of the cutter head, the cutter head (also rotating around its axis with a certain rpm) is excavating the soil. The theoretical soil production Qc equals the cross section of the cutter head in the bank cutting, perpendicular to the swing velocity vs times the swing velocity vs. The cutter head consists of the cutter axis connected to the hub, 5 or 6 arms on one side connected to the hub and on the other side connected to the ring and a suction pipe to catch the soil cut and transport the soil to its destination.
The difference between the theoretical production and the real production is the spillage. So, this is
the percentage of the theoretical production not entering the suction pipe.@en

Slurry transport is a very important means of transporting solids through a pipeline. To improve the efficiency of slurry transport, especially in coarse particle transport, which is subject to problems such as strong resistance and easy blockage, more of the internal structure of the flow must be known. Empirical and analytical models are inadequate for this purpose. Therefore, in this study, a coupling mechanism is established between the computational fluid dynamics (CFD) and discrete element method (DEM). The CFD-DEM coupling was applied and research was conducted on the internal flow structure characteristics of microscopic motion and flow transition for coarse particles in a pipeline. The flow-regime transition processes of coarse 10-mm particles were analyzed qualitatively at velocities of 2 m·s ⁻¹ , 5 m·s ⁻¹ , 8 m·s ⁻¹ and 10 m·s ⁻¹ in a 0.1524-m diameter pipe, and quantitative analyses were performed on both the concentration distribution and the pressure gradient of particles in regimes of fixed bed flow, sliding bed flow and heterogeneous flow. Moreover, from the perspective of force analysis of particles, the law of sedimentation movement of particles is discussed, and the reason for the change in concentration distribution is explained. The research presented here provides insight into the internal structure of the flow and gives quantitative indications of pressure gradient and concentration distributions.

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Spillage is a problem for many dredging projects that make use of a Cutter Suction Dredge (CSD). In addition to higher energy consumption for delivering the targeted depth, spillage can lead to a variety of environmental issues. Equally important is the operator's uncertainty as to how much spillage can be expected when drafting a tender. For this reason, this paper presents a tool to predict spillage rates when cutting sand or rock named the Sand-Rock Cutting Spillage Model. The tool focusses on centrifugal advection and rapid redeposition of sediment, the most significant spillage mechanisms. Centrifugal advection is defined as spillage due to the centrifugal forces acting on disintegrated soil inside the cutter as described in the Sand Cutting Spillage Model of Werkhoven et al. (2018). Rapid redeposition is induced by low mixture velocities that cause suspended particles to settle back onto the bank before reaching the suction mouth. This paper derives an improved mathematical foundation for the Sand Cutting Spillage Model and describes five model mechanisms that more accurately capture a number of observed dynamics. First, to more accurately predict cutter head flows, the internal and external cutter head densities are included. Second, the addition of axial flow in the cutter is investigated. Third, a formulation for the effects of rapid redeposition is incorporated. Fourth, an enhanced representation of the geometry of the cutter allows for a more accurate spillage prediction for the cutting of sand. The tool results compare well with measurements of Miltenburg (1983). For the cutting of rock, Den Burger (2003) observed that the downscaled rock material in his experiment easily settled at the cutter bottom. To this end, the fifth contribution of the Sand-Rock Cutting Spillage Model is the introduction of a concentration difference for rapid redeposition flow in comparison to other flow terms. The five mechanisms underlying the Sand-Rock Cutting Spillage Model bring the model in good agreement with experimental data for rock spillage rates by Den Burger (2003).

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Currently, a fundamental relation between cohesion and adhesion in cohesive soils has not been established. Yet, it is of great importance to get a better understanding of the relationship between cohesive and adhesive forces, because the large surfaces on dredging tools can generate a lot of resistance, meanwhile limiting the production for materials with increasing adhesion. Because the relationship is not exactly known, the adhesive strength of a clay is usually expressed as a fixed fraction of the cohesive strength, varying between 60% for hard clays and 100% for soft clays. Material tests of cohesive soil have been undertaken to detect the actual relation between the adhesion and cohesion of cohesive soil. The experimental results can directly help the implementation of the Delft sand, clay and rock cutting model, as a result the optimal cutting angle in dredging practice can be calculated. In this way, the designs of dredging tools are improved, which can help to increase the overall production rate in dredging operations. This paper gives detailed description of the experiment setup and results.

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The behavior of fully-suspended slurry flow in horizontal pipeline can be simulated through two very distinct models, the Computational Fluid Dynamics (CFD) model and the Delft Head Loss & Limit Deposit Velocity (DHLLDV) model. The predicted results from simulations are compared with a series of experiment data from the literature, involving the effects of different particles volume concentration (9–42%), particle size (90–440 μm), mixture velocity (1–9 m/s), and pipe diameter (51.5–263 mm) on hydraulic gradient and particles concentration distribution, and revealing excellent agreements between two model predictions and the experimental data. Both CFD and DHLLDV, however, still have some deviations in the near-wall concentration distribution as for larger particles. Though it is observed that the accuracy for CFD will decline when particle size increases and further research is needed for improving the accuracy of the models for the near-wall flow of larger particles, it can be concluded that both CFD model and DHLLDV model apply to calculations for fully-suspended flow.

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