Near-optimal control of a wave energy device in irregular waves with deterministic-model driven incident wave prediction

This paper investigates wave-by-wave control of a wave energy converter using incident wave prediction based on up-wave surface elevation measurement. The goal of control is to approach the hydrodynamically optimum velocity leading to optimum power absorption. This work aims to study the gains in energy conversion from a deterministic wave propagation model that accounts for a range of group velocities in deriving the prediction. The up-wave measurement distance is assumed to be small enough to allow a deterministic propagation model, and further, both wave propagation and device response are assumed to be linear. For deep water conditions and long-crested waves, the propagation process is also described using an impulse response function (e.g. [1]). Approximate low and high frequency limits for realistic band-limited spectra are used to compute the corresponding group velocity limits. The prediction time into the future is based on the device impulse response function needed for the evaluation of the control force. The up-wave distance and the duration of measurement are then determined using the group velocity limits above.A 2-body axisymmetric heaving device is considered, for which power capture is through the relative heave oscillation between the two co-axial bodies. The power take-off is assumed to be linear and ideal as well as capable of applying the necessary resistive and reactive load components on the relative heave oscillation. The predicted wave profile is used along with device impulse response functions to compute the actuator force components at each instant. Calculations are carried out in irregular waves generated using a number of uni-modal wave spectra over a range of energy periods and significant wave heights. Results are compared with previous studies based on the use of instantaneous up-wave wave-profile measurements, both without and with oscillation constraints imposed. Considerable improvements in power capture are observed with the present approach over the range of wave conditions studied.     

Analytical investigation of hydrodynamic performance of a dual pontoon WEC-type breakwater

Based on the linear potential flow theory and matching eigen-function expansion technique, an analytical model is developed to investigate the hydrodynamics of two-dimensional dual-pontoon floating breakwaters that also work as oscillating buoy wave energy converters (referred to as the integrated system hereafter). The pontoons are constrained to heave motion independently and the linear power take-off damping is used to calculate the absorbed power. The proposed model is verified by using the energy conservation principle. The effects of the geometrical parameters on the hydrodynamic properties of the integrated system, including the reflection and transmission coefficients and CWR (capture width ratio, which is defined as the ratio of absorbed wave power to the incident wave power in the device width). It is found that the natural frequency of the heave motion and the spacing of the two pontoons are the critical factors affecting the performance of the integrated system. The comparison between the results of the dual-pontoon breakwater and those of the single-pontoon breakwater shows that the effective frequency range (for condition of transmission coefficient K_T < 0.5 and the total capture width ratio η_total > 20%) of the dual-pontoon system is broader than that of the single-pontoon system with the same total volume. For the two-pontoon system, the effective frequency range can be broadened by decreasing the draft of the front pontoon within certain range.     

Wave climate scatter performance of a cycloidal wave energy converter

A lift based cycloidal wave energy converter (WEC) was investigated using potential flow numerical simulations in combination with viscous loss estimates based on published hydrofoil data. This type of wave energy converter consists of a shaft with one or more hydrofoils attached eccentrically at a radius. The main shaft is aligned parallel to the wave crests and submerged at a fixed depth. The operation of the WEC as a wave-to-shaft energy converter interacting with straight crested waves was estimated for an actual ocean wave climate. The climate chosen was the climate recorded by a buoy off the north-east shore of Oahu/Hawaii, which was a typical moderate wave climate featuring an average annual wave power P_W = 17 kWh/m of wave crest. The impact of the design variables radius, chord, span and maximum generator power on the average annual shaft energy yield, capacity factor and power production time fraction were explored. In the selected wave climate, a radius R = 5 m, chord C = 5 m and span of S = 60 m along with a maximum generator power of P_G = 1.25 MW were found to be optimal in terms of annual shaft energy yield. At the design point, the CycWEC achieved a wave-to-shaft power efficiency of 70%. In the annual average, 40% of the incoming wave energy was converted to shaft energy, and a capacity factor of 42% was achieved. These numbers exceeded the typical performance of competing renewables like wind power, and demonstrated that the WEC was able to convert wave energy to shaft energy efficiently for a range of wave periods and wave heights as encountered in a typical wave climate.     

海洋中波浪下迎浪驳船运动对两矩形驳船间窄缝内水体共振的影响

A three-dimensional time-domain potential flow model is developed and applied to simulate the wave resonance in a gap between two side-by-side rectangular barges. A fourth-order predict-correct method is implemented to update free surface boundary conditions. The response of an up-wave barge is predicted by solving the motion equation with the Newmark-β method. Following the validation of the developed numerical model for wave radiation and diffraction around two side-by-side barges, the influence of up-wave barge motion on the gap surfaceresonance is investigated in two different locations of the up-wave barge relative to the back-wave barge at various frequencies. The results reveal that the freely floating up-wave barge significantly influences the resonance frequency and the resonance wave amplitude. Simultaneously, the up-wave barge located in the middle of the back-wave barge leads to a reduction in the resonance wave amplitude and motion response when compared with other configurations.     

Constrained near-optimal control of a wave energy converter in three oscillation modes

This paper investigates the performance of a small axisymmetric buoy under wave-by-wave near optimal control in surge, heave, and pitch modes in long-crested irregular waves. Wave prediction is obtained using a deterministic propagation model. The paper describes the overall formulation leading up to the derivation of the feedforward control forces in surge and heave, and the control moment in pitch. The radiation coupling between surge and pitch modes is accounted for in the model. Actuation is relative to deeply submerged reaction masses. Heave oscillations are constrained by the swept-volume limit. Oscillation constraints are also applied on the surge and pitch oscillations. The paper discusses time-domain simulations for an irregular wave input with and without the present control. Also discussed are results obtained over a range of irregular wave conditions derived for energy periods from 7 s to 17 s, and a significant wave height of 1 m. It is found that, while the gains in power capture enabled by the present control are significant, the actuation forces are also very large, given the small size of the buoy. Further, due to the small size, heave is found to be the dominant contributor to power capture, with relatively modest contributions from surge and pitch.     

Impact of long separating distances on the energy production of two interacting wave energy converters

In this paper, wave farms composed of two either surging or heaving wave energy converters are considered. Using a numerical model which takes into account wave interactions, the impact on the absorbed wave power of the separating distance between the two systems and the wave direction is studied. In regular waves, a modified q_mod factor is introduced and it is found to be more relevant than the usual q factor for identifying this impact. Then, it is shown that, asymptotically, the alteration of the energy absorption due to wave interaction effects decreases with the square root of the distance. This is a slow decay, which leads to a still significant modification of the wave energy absorption at long distance (up to 15% at a distance of 2000 m). In irregular waves, it is shown that constructive and destructive effects compensate each other, particularly when considering the mean annual power. It leads to a smaller impact of the wave interactions on the absorbed energy and shorter distances (smaller than 10% for distances greater than 400 m). Finally, conclusions on if wave interactions should be taken into account or not when designing a wave farm are drawn in function of the distance.     

Impulse control method for hydraulic propulsion system used in 3500 m work-class ROV

In terms of the nonlinear characteristics of hydraulic propulsion system used in 3500 m rated work-class ROV (remotely operated underwater vehicle), the paper improved the responsiveness of the hydraulic propulsion system by adding an impulse signal to the input end of the system. Because the maximum static damping moment provided from water is much larger than the dynamic damping moment, it results in large dead zone of thrust during the startup process of the hydraulic propulsion system. The dead zone of thrust caused by static damping moment can be effectively reduced by adding a specific impulse signal to the input end of the propulsion system. The results of numerical simulations and underwater experiments show that using this method, the nonlinear characteristics of the hydraulic propulsion system have been significantly improved.     

Solitary wave generation dynamics at Luzon Strait

A high resolution modeling study is undertaken, with a 2.5-dimensional nonhydrostatic model, of the generation of internal waves induced by tidal motion over the ridges in Luzon Strait. The model is forced by the barotropic tidal components K1, M2, and O1. These tidal components, along with the initial density field, were extracted from data and models. As the barotropic tide moves over the Luzon Strait sills, there is a conversion of barotropic tidal energy into baroclinic tidal energy. Depressions are generated that propagate towards the Asian Seas International Acoustics Experiment (ASIAEX) test site on the Chinese continental shelf. Nonlinear effects steepen the depressions, frequency and amplitude dispersion set in, and disintegration into large amplitude solitary waves occurs. The effects of varying the initial density field, tidal component magnitudes, as well as adding a steady background current to represent the occasional excursions of the Kuroshio Current into the strait, are considered.Depressions are generated at each of the two sills in Luzon Strait which radiate away, steepening and evolving into internal solitary wave trains. Baroclinic fluxes of available potential energy, kinetic energy and linear are calculated for various parameter combinations. The solitary wave trains produced in the simulations generally consist of large amplitude wave trains alternating with small amplitude wave trains. During strong tidal flow, Kelvin–Helmholtz type instabilities can develop over the taller double-humped sill. The solitary waves propagating towards the ASIAEX test site have been observed to reach amplitudes of 120–250 m, depending on the tidal strength. ASIAEX observations indicate amplitudes up to 150 m and the Windy Island Experiment (WISE) measurements contain magnitudes over 200 m. The model results yield solitary wave amplitudes of 70–300 m and half widths of 0.60–3.25 km, depending on parameter values. These are in the range of observations. Measurements by Klymak et al. (2006), in the South China Sea, exhibit amplitudes of 170 m, half widths of 3 km and phase speeds of 2.9 m s^?1. Model predictions indicate that the solitary waves making up the wave packet each experience different background currents with strong near surface shear.The energy in the leading soliton of the large amplitude wave trains ranges between 1.8 and 9.0 GJ m^?1. The smaller value, produced using barotropic tidal currents based on the Oregon State University data base, is the same as the energy estimated to be in a solitary wave observed by Klymak et al. (2006). Estimates of the conversion of barotropic tidal energy into radiating internal wave energy yield conversion rates ranging between 3.6% and 8.3%.     

Spectral distribution of wave energy dissipation by salt marsh vegetation

Spectral energy dissipation of random waves due to salt marsh vegetation (Spartina alterniflora) was analyzed using field data collected during a tropical storm. Wave data (significant wave heights up to 0.4 m in 0.8 m depth) were measured over a two-day period along a 28 m transect using 3 pressure transducers. The storm produced largely bimodal spectra on the wetland, consisting of low-frequency swell (7–10 s) and high-frequency (2–4.5 s) wind-sea. The energy dissipation varied across the frequency scales with the largest magnitude observed near the spectral peaks, above which the dissipation gradually decreased. The wind-sea energy dissipated largely in the leading section of the instrument array in the wetland, but the low-frequency swell propagated to the subsequent section with limited energy loss. Across a spectrum, dissipation did not linearly follow incident energy, and the degree of non-linearity varied with the dominant wave frequency. A rigid-type vegetation model was used to estimate the frequency-dependent bulk drag coefficient. For a given spectrum, this drag coefficient increased gradually up to the peak frequency and remained generally at a stable value at the higher frequencies. This spectral variation was parameterized by employing a frequency-dependent velocity attenuation parameter inside the canopy. This parameter had much less variability among incident wave conditions, compared to the variability of the bulk drag coefficient, allowing its standardization into a single, frequency-dependent curve for velocity attenuation inside a canopy. It is demonstrated that the spectral drag coefficient predicts the frequency-dependent energy dissipation with more accuracy than the integral coefficient.     

Coastal defence through wave farms

The possibility of using wave farms for coastal defence warrants investigation because wave energy is poised to become a major renewable in many countries over the next decades. The fundamental question in this regard is whether a wave farm can be used to reduce beach erosion under storm conditions. If the answer to this question is positive, then a wave farm can have coastal defence as a subsidiary function, in addition to its primary role of producing carbon-free energy. The objective of this work is to address this question by comparing the response of a beach in the face of a storm in two scenarios: with and without the wave farm. For this comparison a set of ad hoc impact indicators is developed: the bed level impact (BLI), beach face eroded area (FEA), non-dimensional erosion reduction (NER), and mean cumulative eroded area (CEA); and their values are determined by means of two coupled models: a high-resolution wave propagation model (SWAN) and a coastal processes model (XBeach). The study is conducted through a case study: Perranporth Beach (UK). Backed by a well-developed dune system, Perranporth has a bar between − 5 m and − 10 m. The results show that the wave farm reduces the eroded volume by as much as 50% and thus contributes effectively to coastal protection. This synergy between marine renewable energy and coastal defence may well contribute to improving the viability of wave farms through savings in conventional coastal protection.     

Numerical study of turbulence and wave damping induced by vegetation canopies

Vegetation canopies control mean and turbulent flow structure as well as surface wave processes in coastal regions. A non-hydrostatic RANS model based on NHWAVE (Ma et al., 2012) is developed to study turbulent mixing, surface wave attenuation and nearshore circulation induced by vegetation. A nonlinear k − ϵ model accounting for vegetation-induced turbulence production is implemented to study turbulent flow within the vegetation field. The model is calibrated and validated using experimental data from vegetated open channel flow, as well as nonbreaking and breaking random wave propagation in vegetation fields. It is found that the drag-related coefficients in the k − ϵ model C_fk and C_fϵ can greatly affect turbulent flow structure, but seldom change the wave attenuation rate. The bulk drag coefficient C_D is the major parameter controlling surface wave damping by vegetation canopies. Using the empirical formula of Mendez and Losada (2004), the present model provides accurate predictions of vegetation-induced wave energy dissipation. Wave propagation through a finite patch of vegetation in the surf zone is investigated as well. It is found that the presence of a finite patch of vegetation may generate strong pressure-driven nearshore currents, with an onshore mean flow in the unvegetated zone and an offshore return flow in the vegetated zone.     

Observations of surfzone alongshore pressure gradients onshore of an ebb-tidal delta

The relative importance of radiation stress gradients and alongshore pressure gradients to surfzone dynamics is investigated using observations of water levels, waves, and flows measured onshore of a large ebb-tidal delta. Incident wave heights measured along the ~ 11-m depth contour varied about 10% over a 1.2-km alongshore transect, resulting in alongshore wave setup differences on the order of 10 cm over the 600-m extent of the surfzone instrument array in 1.5-m depth. Despite the moderate alongshore variability in wave heights, the southerly alongshore pressure gradient, associated with the alongshore variability of wave-driven set-up, was typically twice as large as the northerly radiation stress gradient forcing, consistent with the observed southerly currents during the week-long experiment. The magnitude of the alongshore forcing and resulting alongshore velocity is reproduced by the two-dimensional depth-averaged numerical model of Shi et al. (JGR-Oceans, 2011). These observations, together with the numerical results, indicate that moderate alongshore wave height gradients (O(10^− 4)) outside the surfzone owing to alongshore variations in the offshore bathymetry can result in alongshore pressure gradients that are larger than radiation stress gradients.     

Wave propagation through dense vertical cylinder arrays: Interference process and specific surface effects on damping

The purpose of this research work is to study the effect of specific surface s, the fluid–solid contact surface per volume unit, on the wave energy dissipation by porous structures consisting in dense arrays of emergent vertical cylinders. Experiments have been carried out in a 10 m long wave flume. Three cylinder diameters D are considered in order to study the effects of the specific surface while keeping the porosity constant. In a first series, the length of the porous zone is kept constant for the three cylinder diameters tested. The measurements, which include various wave steepness conditions, demonstrate the role of specific surface s on both wave attenuation and interference processes. The larger the specific surface is, the stronger the wave damping is. Damping is found to be almost proportional to 1/D when laminar, turbulent and inertial effects are of same order. Results are compared to numerical calculations based on either a constant rate of wave damping within the porous medium per unit wavelength or a quadratic damping developed using a force expression based on the work of [26]. This latter model, calibrated with drag and inertia coefficients, shows a good agreement with measurements. In a second series, both porous length and water depth are kept proportional to the cylinder diameter for the three diameters. Scale effects are then discussed and underline the importance of the flow regime within the porous medium.     

Ocean wave energy harvesting with a piezoelectric coupled buoy structure

An expedient piezoelectric coupled buoy energy harvester from ocean waves is developed. The harvester is made of several piezoelectric coupled cantilevers attached to a floating buoy structure, which can be easily suspended in the intermediate and deep ocean for energy harvesting. In the buoy structure, a slender cylindrical floater is attached on a large sinker. The energy harvesting process is realized by converting the transverse ocean wave energy to the electrical energy via the piezoelectric patches mounted on the cantilevers fixed on the buoy. A smart design of the buoy structure is developed to increase the energy harvesting efficiency by investigation of the effects of the sizes of the floater and the sinker. A numerical model is presented to calculate the generated electric power from buoy energy harvester. The research findings show that up to 24 W electric power can be generated by the proposed expedient buoy harvester with the length of the piezoelectric cantilevers of 1 m and the length of the buoy of 20 m. The technique proposed in this research can provide an expedient, feasible and stable energy supply from the floating buoy structure.     

Short-term statistics of waves measured off Ratnagiri,eastern Arabian Sea

The short-term wave characteristics are required for design and operation of industrial facilities within the coastal areas. Water surface displacement measured using waverider buoy moored at 13 m water depth in the eastern Arabian Sea off the west coast of India have been analyzed to study the short-term statistics of waves covering full one year period. The study indicates that the values of the observed maximum wave height as a function of duration are not consistent with the theoretical expected value. There is significant variation (1.29–2.19) in the ratio between highest 1% wave and significant wave height compared to the theoretical value of 1.67. The data recorded at 13 m water depth indicates that the significant wave height is ∼8% lower than that predicted by the conventional Rayleigh distribution. The theoretical bivariate log-normal distribution represents the joint distributions of wave heights and periods for the study area.     

Modeling wave-mud interaction on the central chenier-plain coast,western Louisiana Shelf,USA

The strong coupling between hydrodynamics and seafloors on shallow muddy shelves, and resulting bed reworking, have been extensively documented. On these shelves, spectral wave transformation is driven by a complex combination of forcing mechanisms that include nonlinear wave interactions and wave energy dissipation induced by fluid-mud at a range of frequencies. Wave-mud interaction is investigated herein by using a previously validated nonlinear spectral wave model and observations of waves and near-bed conditions on a mildly-sloping seafloor off the muddy central chenier-plain coast, western Louisiana Shelf, United States. Measurements were made along a cross-shelf transect spanning 1 km between 4 and 3 m water depths. The high-resolution observations of waves and near-bed conditions suggest presence of a fluid mud layer with thickness sometimes exceeding 10 cm under strong long wave action (1 meter wave height with 7 s peak period at 4 meter depth). Spectral wave transformation is modeled using the stochastic formulation of the nonlinear Mild Slope Equation, modified to account for wave-breaking and mud-induced dissipation. The model is used in an inverse manner in order to estimate the viscosity of the fluid mud layer, which is a key parameter controlling mud-induced wave dissipation but complicated to measure in the field during major wave events. Estimated kinematic viscosities vary between 10⁻⁴-10⁻³ m²/s. Combining these results of the wave model simulations with in-depth analysis of near-bed conditions and boundary layer modeling allows for a detailed investigation of the interaction of nonlinear wave propagation and mud characteristics. The results indicate that mud-induced dissipation is most efficient when the wave-induced resuspensions of concentrations  > 10 g/L settle due to relatively small bottom stresses to form a fluid mud layer that is not as thin and viscous as a consolidated seafloor in absence of wave action but also not as thick and soft as a near-bed high concentration layer that forms during strong wave action.     

Offshore wind farm impacts on surface waves and circulation in Eastern Lake Ontario

A coupled wave and hydrodynamic model was applied to the Kingston Basin of eastern Lake Ontario, a region with bathymetric variability due to channels and shoals, to assess the potential impacts on surface waves and wind-driven circulation of an offshore wind farm. The model was used to simulate a series of storm events with time-varying wind forcing and validated against wave, current and water level observations. The wind farm was simulated by adding semi-permeable structures in the surface wave model to represent the turbine monopiles, and by adding an energy loss term to the fluid momentum equations in the hydrodynamic model to represent the added drag of the monopiles on the flow. The results suggest that the wind farm would have a small influence on waves and circulation throughout the wind farm area, with spatial variability due to focussing of wave energy and re-direction of the flow. Overall, the results indicate that the wave height in coastal areas will be minimally affected with changes in significant wave height predicted to be < 3%. Larger changes to the strength of circulation occur inside the wind farm region with localized changes in current magnitude of up to 8 cm s^− 1. The results of this study may help to understand the impacts of future offshore wind farms and other offshore structures in the Great Lakes.     

Time domain simulation of side-by-side floating bodies using a 3D numerical wave tank approach

The coupled system of two side-by-side fixed and/or floating bodies interacting with a large amplitude nonlinear wave is studied using a direct time domain solution method. The numerical model is based on a three-dimensional mixed Eulerian–Lagrangian (MEL) method under certain simplifying approximations permitting Rankine panel scheme to be implemented over a time-invariant boundary surface to solve the boundary value problem for the unknown velocity potentials. A 4th order Adams–Bashforth–Moulton scheme is used for time marching of rigid-body motion histories of the individual bodies and evolution of the free-surface including the gap region in which large resonant fluid motions occur. A systematic study has been carried out to evaluate the performance of the developed time domain method in simulating the forces and motions as well as the fluid motion in the gap region for the two body system under various arrangements and in different wave-headings. At first, the computed numerical results have been validated and verified with computational and experimental results available in literature for standard geometries such as vertical truncated cylinders and rectangular boxes. Secondly, effectiveness of the damping lid model which is introduced to suppress wave resonance in the gap region is investigated including its influence on maximum sway forces on fixed and floating rectangular barges in side-by-side configurations. Thirdly, comparative studies on absolute and relative motion response for two cases (two rectangular barges, and a FLNG-FPSO + shuttle tanker) in side-by-side arrangement are detailed to bring out the importance of nonlinearities arising due to steep nonlinear incident waves. Finally, coupled motions of the two-body system of an FPSO and a shuttle tanker floating in side-by-side configuration in a steep nonlinear wave field are studied in which the two bodies are connected through hawsers, and also the FPSO is moored to the ground. Additionally there is a fender between the two bodies.