Wave Power Absorption Research Articles

Hydrodynamic analysis of an oscillating water column wave energy converter in the stepped bottom condition using CFD

The primary efficiency of the Oscillating Water Column (OWC) Wave Energy Converter (WEC) device in the stepped sea bottom condition is investigated using both experimental and numerical approaches. Wave flume tests were undertaken to investigate the hydrodynamic behaviour of the device in regular waves. A 2D numerical model was developed in the open source computational fluid dynamics (CFD) software package OpenFOAM implementing the fully non-linear Reynolds Averaged Navier-Stokes (RANS) equations to simulate the wave power absorption and wave structure interactions. The numerical results have been validated against the experimental data. The influence of the wave characteristic as well as damping of the power take-off unit on the performance of the device, wave reflection coefficient and the energy dissipation rate is evaluated using the results obtained from the numerical simulations. Furthermore, as was proved in previous studies that the application of the stepped sea bottom condition might increase the efficiency of the OWC devices, the CFD simulation results have been implemented to present and discuss about the power absorption mechanism as well as the flow pattern characteristics in the vicinity area of the step.

Performance evaluation of a dual resonance wave-energy convertor in irregular waves

A new waterproof point absorber, named Dual Resonance wave-energy convertor (DR-WEC), is put forward in this paper. A geometry with low viscous effect is adopted for the waterproof outer floater of DR-WEC and two resonance frequencies can be found due to the existence of two sets of mass-spring subsystems. The motions and absorbed power of the DR-WEC in regular and irregular waves are investigated using the linear wave theory and the spectral analysis method with viscous effect being considered. The influence of three mechanical parameters, i.e., the internal mass, stiffness of spring and damping of power-take off (PTO) system, on the capture width ratio is studied. The mechanical parameters can affect the shapes of power response curves, which bring the possibility to enhance the wave power absorption by manipulating these parameters according to the characteristics of encountered waves. The Generalized Pattern Search (GPS) algorithm is employed to find these optimal mechanical parameters in both short-term and long-term sea states. The numerical results have confirmed that not all of the three mechanical parameters are needed to vary during operation. Some of the three parameters can be fixed for the balance of cost efficiency and wave power absorption. When the number of variable mechanical parameters is two, one, and zero, declinations of the annual average power relative to that with three are 4.1%, 13.0%, and 36.4%, respectively. At last, solutions for realizing an internal parameter-variable mechanism are discussed.

The dynamics and power absorption of cone-cylinder wave energy converters with three degree of freedom in irregular waves

Considering the coupling between pitch and surge, the hydrodynamics and power absorption of cone-cylinder wave energy converters (WECs) in surge, heave and pitch, are investigated in irregular waves. The fitting of the infinity frequency added masses and the parametric model identification for convolution items in motion equations are performed. The influences of the power take-off (PTO) damping on the power absorptions in surge, heave and pitch, are analyzed. The optimal PTO dampings are predicted for different cases. The influences of the buoy diameter (D), the draft (T) and the centre-of-gravity position (zg) on the motion responses and power absorptions in three directions are investigated. The average powers absorbed in heave and pitch increase with increasing D. The mean power absorbed in surge increases with increasing T. The mean power absorption in pitch increases with decreasing zg. An optimized cone-cylinder WEC is selected with D = 8 m, T = 4 m and zg = −1 m. The wave power absorption and the absorption efficiency of the optimized WEC at six stations off the coast of Southern East China is predicted. The optimized cone-cylinder WEC can absorb between 37.98% and 47.95% of the incident wave power at six stations.

Performance assessment of the CECO wave energy converter: Water depth influence

Abstract CECO is a recently proposed Wave Energy Converter (WEC), which harnesses both the kinetic and potential energy of waves. Currently, CECO is at the third level of technology readiness (TRL3). In this context, maximising the wave energy absorption under a wide range of wave conditions is crucial for the future development of the device. Therefore, this work aims to explore in detail the main parameters (operating water depth and wave conditions) that influence CECO's performance in terms of Captured Energy ( C E ) and Captured Energy Efficiency ( C E E f f ). For this purpose, a panel-based model, which was calibrated from previous physical model tests was used to construct the CECO matrices of absorbed wave power at different operating water depths. The wave conditions of the Atlantic coast of the Iberian Peninsula (2005–2014), which were modelled using SWAN, were used as case study. Overall, CECO offers promising results for C E and C E E f f , reaching values up to 600 M W h and 45%, respectively. In addition, it was found that CECO's power absorption reaches its maximum for values of peak wave periods ( T p ) ranging from 10 to 13 s and the fact that the operating water depth does not impact significantly the performance of the device.

Hydrodynamic responses and efficiency analyses of a heaving-buoy wave energy converter with PTO damping in regular and irregular waves

Abstract Experimental investigation on the power performance of a heaving-buoy wave energy converter (WEC) with power take-off (PTO) damping was conducted under regular and irregular waves. The effects of the main influential parameters, including the incident wave height, wave frequency and PTO damping, on the maximum heave displacement, phase difference between the buoy velocity and wave elevation, and capture width ratio were quantitatively studied. For regular waves, with decreasing incident wave height or increasing PTO damping, the nonlinearity between the heave motion and surrounding wave elevation became pronounced and three modes of the buoy, i.e., linear motion, non-linear motion and non-motion, can be found. Based on analyses of the capture width ratio in both regular and irregular waves, the present WEC can obtain an optimal power efficiency at frequency ratio of ω / ω n ≈ 0.8 and PTO damping ratio of ζ p ≈ 0.5. It has been examined that H 1/10 can generally provide better approximation of the incident wave energy than H 1/3 and H AVG for irregular waves based on the linear wave theory. The statistical power performance of the WEC in irregular waves generally has the same trend as that in regular waves. The capture width ratio in irregular waves is found to be (approximately 5–40%) higher than that in regular waves for the same wave parameters, though the absolute incident and absorbed wave power in irregular waves are only half of those in regular waves. Finally, the flow structures around the heaving buoy are analyzed. The formation of vortices around the bottom corner provides flow interpretation on the viscous loss of wave energy for a heaving-buoy WEC with a flat bottom.

Influence of the wave climate seasonality on the performance of a wave energy converter: A case study

CECO is a novel Wave Energy Converter (WEC) concept, which has shown promising results in previous studies. The present work focuses on assessing the performance of CECO for a 11-year horizon in relation to the characteristics of the wave climate (intra and inter-annual seasonal variations) by means of two performance indicators defined ad hoc: Captured Energy (CE) and Captured Energy Efficiency (CEEff). For this purpose, the CECO matrix of absorbed wave power was constructed for an operating water depth of 30 m using the panel-based model ANSYS®-AQWA™. The Atlantic coast of the Iberian Peninsula, which presents a highly seasonal and energetic wave climate, was used as case study. Overall, it was found that CECO is able to capture large amounts of wave energy, especially for milder wave conditions, with values of CEEff exceeding 40%. However, for harsher wave conditions the results of CEEff decrease considerably ranging from 10% to 20%, which may result from the current design of CECO. In this context, the results obtained offer some valuable insight into the future evolution of CECO with the purpose of addressing the limitations of the current design and to optimise its performance according to the wave conditions for specific locations.

Analytical study of the wave polarisation in the ‘three-ion’ radio frequency heating scheme

The ‘three-ion’ scheme (Kazakov et al 2015 Nucl. Fusion 55 032001) is a new, high-potential ion cyclotron resonance heating scheme that has recently been proposed and experimentally tested. In this paper a simple cold plasma analytical model is introduced, which shows the beneficial effect of the changes of wave polarisation brought about by a tiny third minority when added to 2 majority ion species. This causes a second ion–ion hybrid layer to appear and allows to maximise the absorption of wave power on the minority ions. We also show by analytical modelling the effect of the wave interference on double-pass wave absorption in plasmas with two ion–ion hybrid layers.

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 KT<0.5 and the total capture width ratio ηtotal>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 protection effect of periodic row of bottom-hinged flap-type wave energy converters

A flap-type wave energy converter (WEC) is combined with a nearshore breakwater to expand the application of WECs both economically and environmentally. Based on the linear potential theory, an eigenfunction expansion solution is developed for a periodic row of bottom-hinged flap-type WECs exposed to normal waves. Additionally, the viscous effect is considered using the ship rolling solution method with a viscous damping term included in the equation of motion, and the viscous damping expression is also described. The proposed solution is verified by comparison with published literatures. The results including the wave energy conversion efficiency, the reflected and transmitted proportion of the incident wave energy are presented for a range of wave periods and geometric ratios. It is demonstrated that better wave protection effects can be attained with smaller gaps between the WECs, where the transmitted proportion of the incident wave energy is lower. An optimal geometric ratio thus exists for a given wave power absorption and a specific wave period.

Wave power absorption by a submerged balloon fixed to the sea bed

The possibility of absorbing wave energy using a submerged balloon fixed to the sea bed is investigated. The balloon is in the form of a fabric encased within an array of meridional tendons which terminate at a point at the top of the balloon and at some radius at the bottom. The expansion and contraction of the balloon in waves pump air via a turbine into and out of a chamber of constant volume. A more refined model than that used by Kurniawan and Greaves [Proc. Second Offshore Energy and Storage Symp., 2015] predicts a similarly broad-banded response, but the maximum absorption is less than previously predicted. Both approaches are compared and discussed.

Numerical calculations of non-inductive current driven by microwaves in JET

Recent studies at JET focus on analysis of the lower hybrid (LH) wave power absorption and current drive (CD) calculations by means of a new ray tracing (RT)/Fokker–Planck (FP) package. The RT code works in real 2D geometry accounting for the plasma boundary and the launcher shape. LH waves with different parallel refractive index, , spectra in poloidal direction can be launched thus simulating authentic antenna spectrum with rows fed by different combinations of klystrons. Various FP solvers were tested most advanced of which is a relativistic bounce averaged FP code. LH wave power deposition profiles from the new RT/FP code were compared to the experimental results from electron cyclotron emission (ECE) analysis of pulses at 3.4 T low and high density. This kind of direct comparison between power deposition profiles from experimental ECE data and numerical model were carried out for the first time for waves in the LH range of frequencies. The results were in a reasonable agreement with experimental data at lower density, line averaged values of . At higher density, , the code predicted larger on-axis LH power deposition, which is inconsistent with the experimental observations. Both calculations were unable to produce LH wave absorption at the plasma periphery, which contradicts to the analysis of the ECE data and possible sources of these discrepancies have been briefly discussed in the paper. The code was also used to calculate the LH power deposition and CD profiles for the low-density preheat phase of JET’s advanced tokamak (AT) scenario. It was found that as the density evolves from hollow to flat and then to a more peaked profile the LH power and driven current move inward i.e. towards the plasma axis. A total driven current of about 70 kA for 1 MW of launched LH power was predicted in these conditions.

Effects of bottom profile of an oscillating water column device on its hydrodynamic characteristics

The oscillating water column, OWC device is one of the more promising devices for the extraction of energy from ocean waves. The present study mainly focuses on the influence of bottom profile configuration in the OWC on its hydrodynamic performance. Four different bottom profiles flat, circular curve of radius 300 mm, slope of 1:1 and 1:5 were tested in a wave flume. The said models were simultaneously subjected to both regular and random waves. The hydrodynamic performance was studied in terms of wave amplification factor, wave power absorption coefficient, hydrodynamic efficiency, lip wall pressure ratio (pressure at in front of lip wall/pressure due to incident wave) and air pressure ratio (air pressure/pressure due to incident wave). It is found that the natural period of the system was around 1.9 s. The OWC with circular curve bottom profile exhibited a better performance in terms of its effective wave energy conversion and wave amplification factor inside the chamber. The peak magnitude of hydrodynamic efficiency for circular curve bottom profile was 0.71. The performance of the OWC model is found to be better when closer to the natural period of the device.

Analytical and Numerical Study of Nearshore Multiple Oscillating Water Columns

In the present study, the performance of two chamber nearshore oscillating water columns (OWCs) in finite water depth is analyzed based on the linearized water wave theory in the two-dimensional Cartesian coordinate systems. The barriers are assumed to be fixed and the turbine characteristics are assumed linear with respect to the fluctuations of volume flux and pressure inside the chamber. The free surface inside the chambers is modeled as a nonplane wave surface. Two different mathematical models are employed to solve the hydrodynamic problem: the semi-analytic method of matched eigenfunction expansion and the numerical scheme of boundary integral equation method (BIEM). The numerical results are compared with the semi-analytic results and show good agreement. The effects of the distance between the barriers and the length of the barriers on the efficiency of the OWC device are investigated. The results of two chambers OWC are also compared with the results for an equivalent single OWC chamber. Further, the effect of the water depth on the capacity of the wave power absorption is discussed.

Influence of Sea State and Tidal Height on Wave Power Absorption

The wave energy converter developed at Uppsala University (Uppsala, Sweden) consists of a linear generator placed on the seabed and driven by the motion of a buoy on the water surface. The buoy is connected to the moving part of the linear generator, the translator, which is made of ferrite magnets. The translator moves vertically inducing voltage in the windings of a fixed component, the so-called stator. The energy conversion of the linear generator is affected by the sea state and by variations of mean sea level. The sea state influences the speed and the stroke length of the translator, while the variation of tidal level shifts the average position of the translator with respect to the center of the stator. The aim of this study is to evaluate the energy absorption of the wave energy converter at different locations around the world. This goal is achieved by developing a hydromechanic model which analyses the optimum generator damping factor for different wave climates and the power absorbed by the generator, given a fixed geometry of the buoy and a fixed stroke length of the translator. Economic considerations regarding the optimization of the damping factor are included within the paper. The results suggest a nominal damping factor and show the power absorption losses at various locations, each of them characterized by a different wave climate and tidal range. The power losses reach up to 67% and in many locations a tidal compensation system, included in the design of the wave energy converter, is strongly motivated.

Fundamental formulae for wave-energy conversion.

The time-average wave power that is absorbed from an incident wave by means of a wave-energy conversion (WEC) unit, or by an array of WEC units—i.e. oscillating immersed bodies and/or oscillating water columns (OWCs)—may be mathematically expressed in terms of the WEC units' complex oscillation amplitudes, or in terms of the generated outgoing (diffracted plus radiated) waves, or alternatively, in terms of the radiated waves alone. Following recent controversy, the corresponding three optional expressions are derived, compared and discussed in this paper. They all provide the correct time-average absorbed power. However, only the first-mentioned expression is applicable to quantify the instantaneous absorbed wave power and the associated reactive power. In this connection, new formulae are derived that relate the ‘added-mass’ matrix, as well as a couple of additional reactive radiation-parameter matrices, to the difference between kinetic energy and potential energy in the water surrounding the immersed oscillating WEC array. Further, a complex collective oscillation amplitude is introduced, which makes it possible to derive, by a very simple algebraic method, various simple expressions for the maximum time-average wave power that may be absorbed by the WEC array. The real-valued time-average absorbed power is illustrated as an axisymmetric paraboloid defined on the complex collective-amplitude plane. This is a simple illustration of the so-called ‘fundamental theorem for wave power’. Finally, the paper also presents a new derivation that extends a recently published result on the direction-average maximum absorbed wave power to cases where the WEC array's radiation damping matrix may be singular and where the WEC array may contain OWCs in addition to oscillating bodies.

Recent Upgrading of ECRH System and Studies to Improve ECRH Performance in the LHD

This paper reports the recent status of the ECRH system in the LHD and introduces the experimental results that suggest the reasonable effects of the wave-plasma interaction in the plasma boundary including outside the LCFS. With increasing the available ECRH power, ECRH/ECCD have been performed in higher density target plasmas where the mode coupling between the O-mode and the X-mode caused by the magnetic shear occurs for long distance in the low density region of the plasma boundary including the ergodic layer outside the LCFS. In such a case, the incident polarization should be set by taking into account the mode coupling effect. Moreover, the refraction in the boundary region should be considered for accurate numerical prediction of the wave trajectory and power absorption with use of the ray-tracing calculation.

Time-dependent simulation of lower hybrid current drive in JET discharges

In this paper we report on simulations of lower hybrid current drive (LHCD) in JET closely comparing the simulation results to the available experimental data. The simulations are performed all over the relevant discharge duration by ASTRA. The LHCD module, FRTC, is based on a standard ray-tracing Fokker–Planck model. The purpose of the paper is to understand the present LHCD experiments issues within the limit of the LH linear propagation model. These issues are: (i) analysis of non-resonant collisional absorption (NRCA) of LH wave power in the main JET plasma during the current ramp-up phase and in steady-state (SS) scenarios, (ii) the lack of penetration of LHCD in high-density plasmas, (iii) current diffusion during the LHCD-assisted current ramp-up and (iv) assessment of the current profile alignment in JET SS discharges in the presence of LHCD.In recent experiments from FTU, JET and C_MOD, LHCD effects at high plasma density are either completely absent or less than expected. It has been shown, both in FTU and ALCATOR-C_MOD, that NRCA of LH wave power can be responsible for that. Indeed NRCA is estimated to be small in JET plasmas, at least in the main heating phase and therefore it is not expected to be responsible for the lack of penetration of LHW in high-density JET plasmas, however here we show for the first time that it can be effective during the early phase of the current ramp-up, when the plasma is still collisional. On the contrary it is suggested that the reduction of LHCD effects at high density may be attributed at least partially to the loss of accessibility of the n‖ spectrum effectively launched into the plasma. Furthermore it is shown that the linear propagation model provide very broad and stable LH current density profiles, with no need to include any non-linear spectral broadening.The current diffusion during the LHCD-assisted current ramp-up is investigated and a careful comparison between the simulated q-profiles and the measured ones is performed over time. The implications of the observed difference are discussed.Finally the important question of the alignment of all the current profile components is analysed in JET SS discharges at high βN.

The method of imbedded Lagrangian element to estimate wave power absorption by some submerged devices

A simple approach is described to estimate the wave power absorption potential of submerged devices known to cause wave focusing and flow enhancement. In particular, the presence of a flow-through power take-off (PTO) system, such as low-head turbines, can be accounted for. The wave radiation characteristics of an appropriately selected Lagrangian element (LE) in the fluid domain are first determined. In the limit of a vanishing mass, the LE reduces to a patch of distributed normal dipoles. The hydrodynamic coefficients of this virtual object are then input in a standard equation of motion where the effect of the PTO can be represented, for example, as a dashpot damping term. The process is illustrated for a class of devices recently proposed by Carter and Ertekin (2011), although in a simplified form. Favorable wave power absorption is shown for large ratios of the LE wave radiation coefficient over the LE added mass coefficient. Under optimal conditions, the relative flow reduction from the PTO theoretically lies between 0.50 and \(1/\sqrt 2 \approx 0.71\), with lower values corresponding to better configurations. Wave power capture widths, the sensitivity of results to PTO damping and sample spectral calculations at a typical site in Hawaiian waters are proposed to further illustrate the versatility of the method.

Spatio-spectral analyses of electromagnetic wave energy absorption and heating effect

This study presents a theoretical analysis method to calculate electromagnetic (EM) wave power absorption spectrum of materials by using attenuation coefficients. The heating effect of EM waves is modeled to analyze spectral distribution of temperature rises inside material body as a result of EM wave power absorption. These analyses are very useful for the investigation of electromagnetic wave-material interaction on the bases of electro-physical material parameters (permittivity, permeability and conductivity). An illustrative analysis of spatio-spectral distribution of EM wave energy absorption and resulting heating effect were conducted for muscle tissues and the results are discussed.

Maximum wave power absorption by slender bodies of arbitrary cross sections in oblique seas

Published results for the maximum wave power absorption by slender bodies subjected to vertical deformations are extended. To this end, a more general form of the Kochin function is derived for floating or submerged slender bodies of arbitrary (asymmetric) cross sections undergoing vertical or horizontal deformations. The Kochin function allows a determination of the theoretical maximum wave power absorption in oblique seas. It is shown that in beam seas, two-dimensional limits can be recovered when the slender body length tends to infinity. This establishes a formal continuity in behavior from attenuators (head seas) to terminators (beam seas). The wavelike vertical and horizontal deformations of a flexible body, as well as the hinge motions of an articulated raft are also considered in oblique seas. In the former case, results suggest an equivalence between the maximum absorption width of bodies with symmetric cross sections and two degrees of freedom, and that of bodies with optimal cross sections and one degree of freedom. Overall, the potential for significant wave power absorption from horizontal motions is also demonstrated.