Power Take-off Damping Research Articles

An Experimental Study of a Bottom-Hinged Wave Energy Converter with a Reflection Wall in Regular Waves—Focusing on Behavioral Characteristics

The hybrid system of wave energy converters (WECs) using coastal structures is an attractive issue in terms of a decrease in construction costs and an improvement of the ability to capture wave energy. Most studies on the utilization of reflected waves from structures, which is one of the hybrid systems, are limited to mathematical analysis based on linear theories. Therefore, this paper presents fundamental experimental results in the presence of a reflection wall simplified as a coastal structure behind a bottom-hinged flap-type WEC under unidirectional regular waves. The behavioral characteristics and the power generation efficiency ke of the flap were investigated, focusing on wave steepness, initial water depth, and distance from the reflection wall. The results show that the condition of the initial water depth being smaller than the flap height is more effective in terms of avoiding unstable rotating of the flap. The maximum ke appeared slightly far from the node position of the standing waves because the flap shape and the power take-off (PTO) damping induce the phase difference between the reciprocating behavior of the flap and the period of the standing wave. The results imply that the optimum position of a WEC is dependent on WEC shape, PTO damping, and installation water depth.

Power capture performance of a heaving wave energy converter for varying brad/bpto ratio

In this study, power capture performance of a heaving wave energy converter has been optimized by investigating the effect of variation of power take-off damping. The wave energy converter model used in this study utilizes the sliding discrete Fourier transform technique to estimate the local wave frequency. The power take-off parameters are adjusted according to the estimated wave frequency. As a part of the study, two different cases are evaluated. In the first case, the conventional approach based on using power take-off damping equal to radiation damping which is a function of the estimated wave frequency is considered. In the second part of the study, as a proposed approach, the power take-off damping is calculated with a gain factor. This gain factor varies the hydrodynamic analysis-based frequency-dependent radiation damping by multiplying with it. The results show that the captured power results can be increased from 1.64 to 10.38%, while, in average, the power capture increase covering all datasets is 5.95%.

Proof-of-concept study on a wave energy converter based on the roll oscillations of multipurpose offshore floating platforms

Inspired by observing the motions of vessels at sea, the E-Motions has been proposed as an innovative concept capable of converting wave (and wind) induced roll oscillations on multipurpose offshore floating platforms into electricity. The device can be integrated, theoretically, into any type of offshore floating structure, given its simple 3-component design: floating platform, encasing and sliding Power Take-Off. This latter component can be sheltered from the marine environment by being placed within a casing, at deck level, or the hull of the offshore structure. With so much potential for application at sea, it was important to subject the E-Motions to an initial proof-of-concept, as done for other wave energy converters. This paper presents and discusses the main results and conclusions of an experimental study, carried out with a 1:40 reduced scale physical model, aimed at demonstrating the technical and technological viability of the E-Motions. It was found that, for the considered study variables, the device can operate without major incident and convert electricity from wave induced roll oscillations. Four ballast configurations were considered, of which two yielded higher power outputs. The average measured power reached as high as 11 kW and 13 kW, respectively, with the values reducing for wave period further away from the resonance range and lower wave heights. Power Take-Off damping was found to be an important variable that can considerably influence the energy generation process, yet it will be imperative to further assess this variable in combination with other pertinent variables, such as an external attached mass and different generators. This is key to better understand and describe the complex and non-linear relationship between the motions of the Power Take-Off and the floating platform components.

Comparison of wave–structure interaction dynamics of a submerged cylindrical point absorber with three degrees of freedom using potential flow and computational fluid dynamics models

In this paper, we compare the heave, surge, and pitch dynamics of a submerged cylindrical point absorber, simulated using potential flow and fully resolved computational fluid dynamics (CFD) models. The potential flow model is based on the time-domain Cummins equation, whereas the CFD model uses the fictitious domain Brinkman penalization technique. The submerged cylinder is tethered to the seabed using a power take-off (PTO) unit, which restrains the heave, surge, and pitch motions of the converter and absorbs energy from all three modes. It is demonstrated that the potential theory overpredicts the amplitudes of heave and surge motions, whereas it results in an insignificant pitch for a fully submerged axisymmetric converter. It also underestimates the slow drift of the buoy, which the CFD model is able to capture reliably. Furthermore, we use fully resolved CFD simulations to study the performance of a three degrees of freedom cylindrical buoy under varying PTO coefficients, mass density of the buoy, and incoming wave heights. It is demonstrated that the PTO coefficients predicted by the linear potential theory are sub-optimal for waves of moderate and high steepness. The wave absorption efficiency improves significantly when a value higher than the predicted value of the PTO damping is selected. Simulations with different mass densities of the buoy show that converters with low mass densities have an increased tension in their PTO and mooring lines. Moreover, the mass density also influences the range of resonance periods of the device. Finally, simulations with different wave heights show that at higher heights, the wave absorption efficiency of the converter decreases and a large portion of available wave power remains unabsorbed.

Development and analysis of a numerical model for a two-oscillating-body wave energy converter in shallow water

The Energy Double System (EDS) is a two-degree-of-freedom (2DOF), nearshore, point absorber wave energy converter (WEC). It is composed of a heaving float and a surging paddle, which are interconnected and each one has its own Power Take-Off (PTO). In this work, a numerical model of the EDS was developed on the basis of the existent laboratory model, which had already been the object of several studies at the Politecnico di Milano. Firstly, a general mechanical scheme of the EDS was developed, which is simplified with respect to the laboratory model. This is a mass-spring-damper 2DOF system, described by a couple of equations linearized around the equilibrium position. Once that the mechanical equivalence with the laboratory model was established, the simplified EDS geometry was set in a Computational Fluid Dynamics (CFD) model, together with the experimental boundary conditions: the EDS is placed in shallow water depth along a sloping beach, undergoing regular waves. Numerical results fairly agree with the experimental ones, although slightly overestimate the energy absorption of the float (+20%) and the paddle (+10%). Finally, new cases were simulated: different values of PTO damping and random waves were tested.

Determination of hydrodynamic parameters of a fixed OWC by performing experimental and numerical free decay tests

Physical experimental and 3D numerical free decay tests are performed for a stationary oscillating water column (OWC) device with various underwater opening heights and power take-off (PTO) mechanisms. Numerical model results are verified with experimental data. Equivalent linear damping of the system is found by using logarithmic decrement method. Natural and resonant frequencies and added mass are calculated. For the OWC with the orifice, it is found that damping ratio decreases quadratically with increasing orifice ratio and linearly with increasing relative opening. Resonant frequency is found to be a linear function of both opening size and PTO damping. Calculated natural frequency values are compared with extensively used formulas, which are found to overestimate the OWC natural frequency. For the first time, an empirical formula for the natural frequency of a fixed OWC is proposed. Added mass is found to be independent of orifice size and underwater opening height. For the OWC with the porous layer, no noteworthy change is observed for the natural frequency and added mass compared to those of OWC with orifice. However, damping of the system is quite altered, while its change due to the variations in the permeability and under water opening height has similar characteristics.

Experimental investigation of multiple Oscillating Water Column Wave Energy Converters integrated in a floating breakwater: Energy extraction performance

Currently, ocean wave energy technology is in its infancy relative to the mature renewable energy technologies such as wind and solar. Due to its early stage of development, ocean wave energy has high associated Levelised Cost of Electricity (LCOE), a measure of lifetime costs relative to lifetime energy production. Several solutions have been derived in an attempt to reduce this high LCOE, of which breakwater integration of wave energy converters presents a viable option. Current full-scale commercial and demonstration devices indicate that OWC device integrated breakwaters are typically limited to nearshore and onshore operational regions. However, industries such as aquaculture and offshore wind are exploring the viability of placing these structures in deeper waters, where these traditional concepts would not be applicable, providing opportunity for the development of floating offshore multi-purpose structures. This article describes a proof-of-concept for a floating breakwater integrated with Oscillating Water Column (OWC) Wave Energy Converters (WEC). For an integrated device of this type there are multiple key aspects that are inter-related and each must be understood: energy extraction performance, wave attenuation and quantifying platform motions. In order to adequately report on each aspect in a logical manner the study is presented in two parts. This paper covers the energy extraction aspects, while the second part deals with wave attenuation and motion characteristics [1]. The wave energy extraction characteristics of the installed devices are explored across parameters including device configurations, breakwater width, power take-off damping, wave height and motion constraints, all of which was achieved through model scale hydrodynamic experimentation. The major findings indicate that OWC device spacing is a key parameter in the design of multi-device structures, as device-device interaction can have constructive or destructive interferences on the energy extraction. Additionally, the results of the OWC device performance, under the influence of the aforementioned parameters, provides new insights to the development of floating offshore multi-purpose structures and their feasibility.

Concept and performance of a novel wave energy converter: Variable Aperture Point-Absorber (VAPA)

Ocean waves are a huge and largely untapped resource of green energy. In order to extract energy from waves, a novel wave energy converter (WEC) consisting of a floating, hollow cylinder capped by a roof with a variable aperture is presented in this paper. The power take-off (PTO) system is composed of a linear generator attached to the seabed, driven by the heave motion of the floating cylinder through a tether line. The air pressure within the cylinder can be modified by adjusting the roof aperture. The hydrodynamic characteristics of this WEC are investigated through an analytical model based on potential flow theory, in which the wave diffraction/radiation problems are coupled with the air pressure fluctuation and PTO system. Analytical expressions are derived for the maximum power absorbed by the WEC under different optimization principles, revolving around the PTO damping, roof aperture damping and non-negative mooring stiffness. We find that the best power absorption is obtained when the aperture is either completely open or entirely closed, depending on the wave conditions. Intermediate values of the aperture are useful to minimize the heave motion and thus ensure survivability under extreme sea states.

Experimental Study on Interaction Between Degrees of Freedom in a Wave Buoy

Increasing degrees of freedom (DOFs) is a useful way to raise the power capture efficiency of oscillating wave energy converters. Thus, this study proposes a buoy with three DOFs, which are surge, heave, and pitch. The hydrodynamic performance and power capture efficiency of the buoy is physically modeled. Amplitudes of unidirectional and coupled motions are compared to analyze the interaction effect between freedoms under conditions with and without power take-off damping. The capture width ratio and corresponding growth rates are also calculated. Results show that the buoy makes a periodic sinusoidal (or approximate) movement in every DOF. Coupling effect can cause an increase in the amplitude in one DOF and a decrease in the amplitudes of the others. This phenomenon shows that the kinematic energy of the buoy redistributes to all DOFs compared with the unidirectional conditions. Adding DOFs can improve the power absorption of the buoy in most cases, but the number of DOFs is not the more the better.

Experimental investigations on the performance of a fixed-oscillating water column type wave energy converter

Oscillating water column (OWC) type wave energy converters are the most promising candidates to harvest untapped ocean wave energy. OWC front wall opening and power take-off (PTO) damping optimization are very significant for feasible energy extraction. A comprehensive experimental investigation was performed for a bottom-fixed oscillating water column to determine the influence of the underwater opening height of the chamber, power take-off damping and wave steepness on the energy converter efficiency. A broad range of opening heights and power take-off dampings was utilized in physical experiments under various wave steepness values. Water column displacements, velocities and motion behaviors were also examined. Optimal orifice ratios were determined to obtain maximum efficiency under different wave steepness values. Based on the results, the key finding of this study is, for a certain range of wave steepness, optimal damping that should be applied on the system does not only depend on the wave characteristics, but also opening height of the chamber. The motion of water column surface behavior also affects the performance of the converter considerably.

A numerical tool for modelling oscillating wave surge converter with nonlinear mechanical constraints

Mechanical constraints have a non-negligible influence in the motion of oscillating wave surge converter (OWSC) devices. The key novelty of this paper is a numerical simulation tool for OWSCs that does not neglect or significantly compromise mechanical constraints such as hydraulic power take-off (PTO) system, revolute joints and frictional contacts among components. The paper is aimed at presenting the key components of the numerical simulation tool and at validating it with laboratory data featuring an OWSC with mechanical constraints under regular and irregular waves. It is based on the implementation of the multibody solver of Project Chrono under the Smoothed Particle Hydrodynamics (SPH) model of DualSPHysics, where the SPH solver resolves the interaction between wave and flap and the multibody solver resolves the interaction between flap and mechanical constraints. Comparison between numerical results and experimental data show that the numerical simulation tool properly predicts the dynamics of the OWSC. Furthermore, in what concerns hydrodynamics of the near-flap flow, the computed and measured free-surface elevations and phase-averaged flow field show reasonable agreement. Once properly validated, the numerical simulation tool is then applied to study the influence of several mechanical constraints, PTO damping characteristics and flap inertia on the hydrodynamic of the OWSC. The viability of OWSC design solutions based on the developed numerical simulation tool is emphasised, in view of its performance in the test cases to which it was subjected.

Power enhancement of pontoon-type wave energy convertor via hydroelastic response and variable power take-off system

Wave energy has gained its popularity in recent decades due to the vast amount of untapped wave energy resources. There are numerous types of wave energy convertor (WEC) being proposed and to be economically viable, various means to enhance the power generation from WECs have been studied and investigated. In this paper, a novel pontoon-type WEC, which is formed by multiple plate-like modules connected by hinges, are considered. The power enhancement of this pontoon-type WEC is achieved by allowing certain level of structural deformation and by utilizing a series of optimal variable power take-off (PTO) system. The wave energy is converted into useful electricity by attaching the PTO systems on the hinge connectors such that the mechanical movements of the hinges could produce electricity. In this paper, various structural rigidity of the interconnected modules are considered by changing the material Young's modulus in order to investigate its impact on the power enhancement. In addition, the genetic algorithm optimization scheme is utilized to seek for the optimal PTO damping in the variable PTO system. It is observed that under certain condition, the flexible pontoon-type WEC with lesser connection joints is more effective in generating energy as compared to its rigid counterpart with higher connection joints. It is also found that the variable PTO system is able to generate greater energy as compared to the PTO system with constant/uniform PTO damping.

Load shedding characteristics of an oscillating surge wave energy converter with variable geometry

This study investigates performance and load shedding capabilities of an oscillating surge wave energy converter (OSWEC) that utilizes adjustable geometry to control hydrodynamic coefficients. The body consists of a bottom-hinged rectangular paddle in which the frame holds five horizontal flaps spanning the interior of the frame. Each flap can rotate independently about its center of rotation to alter hydrodynamic coefficients. A 1:14 scale model was built for wave tank tests where the OSWEC's natural response to regular waves was measured. Tests with the paddle fixed vertically were conducted to measure the moment induced by incident waves. Results were compared to numerical simulations which determined that flap orientation significantly affected wave energy transmission past the device. Numerical simulations with the addition of a linear rotational damper power take-off (PTO) suggested that with flaps open, the resistive moment was reduced by up to 47%, the surge force on the foundation up to 55%, and the capture width up to 72% over a range of wave periods and PTO damping values. The experimental nondimensional excitation moments and reflection coefficients were reduced by up to 54%. Overall, the flaps provide mechanical means to reduce loads, thus improving the design life of a WEC system.

Numerical investigation of the dynamic response and power capture performance of a VLFS with a wave energy conversion unit

This paper numerically investigates the dynamic response and power capture performance of a Very Large Floating Structure (VLFS) with a Wave Energy Conversion (WEC) unit. The VLFS is composed of two hinged modules of which the relative pitch motion induced by waves is converted into electricity by the WEC unit. The discrete-module-beam-bending based hydroelasticity method is used to establish the equations of motion for the VLFS. A theoretical model is derived for optimizing the power take-off damping of the WEC unit. Based on the numerical results, it is found that (i) placing hinge near the foreside of VLFS is a good option for both the reduction of hydroelastic response and the enhancement of power absorption; (ii) for medium and long waves a larger wave incidence angle corresponds to a larger vertical displacement, a smaller bending moment and a decreased power capture width ratio of the VLFS; and (iii) the decrease of structural bending stiffness brings an increase of vertical displacement and a reduction of bending moment while its effect on power absorption is insignificant except for a very large bending stiffness.

Experimental Study of a Moored Floating Oscillating Water Column Wave-Energy Converter and of a Moored Cubic Box

This paper describes experimental research on a floating moored Oscillating Water Column (OWC)-type Wave-Energy Converter (WEC) carried out in the wave flume of the Coastal Engineering Research Group of Ghent University. This research has been introduced to cover the existing data scarcity and knowledge gaps regarding response of moored floating OWC WECs. The obtained data will be available in the future for the validation of nonlinear numerical models. The experiment focuses on the assessment of the nonlinear motion and mooring-line response of a 1:25 floating moored OWC WEC model to regular waves. The OWC WEC model motion has 6 degrees of freedom and is limited by a symmetrical 4-point mooring system. The model is composed of a chamber with an orifice on top of it to simulate the power-take-off (PTO) system and the associated damping of the motion of the OWC WEC model. In the first place, the motion response in waves of the moored floating OWC WEC model is investigated and the water surface elevation in the OWC WEC chamber is measured. Secondly, two different mooring-line materials (iron chains and nylon ropes) are tested and the corresponding OWC WEC model motions and mooring-line tensions are measured. The performance of these two materials is similar in small-amplitude waves but different in large wave-amplitude conditions. Thirdly, the influence of different PTO conditions is investigated by varying the diameter of the top orifice of the OWC WEC model. The results show that the PTO damping does not affect the OWC WEC motion but has an impact on the water surface elevation inside the OWC chamber. In addition, an unbalanced mooring configuration is discussed. Finally, the obtained data for a moored cubic model in waves are presented, which is a benchmarking case for future validation purposes.

CFD modelling of a small–scale fixed multi–chamber OWC device

Wave Energy Converters (WECs) have excellent potential as a source of renewable energy that is yet to be commercially realised. Recent attention has focused on the installation of Oscillating Water Column (OWC) devices as a part of harbor walls to provide advantages of cost–sharing structures and proximity of power generation facilities to existing infrastructure. In this paper, an incompressible three–dimensional CFD model is constructed to simulate a fixed Multi–Chamber OWC (MC–OWC) device. The CFD model is validated; the simulation results are found to be in good agreement with experimental results obtained from a scale physical model tested in a wave tank. The validated CFD model is then used for a benchmark study of 96 numerical tests. These investigate the effects of the PTO damping caused by the power take–off (PTO) system on device performance. The performance is assessed for a range of regular wave heights and periods. The results demonstrate that a PTO system with an intermediate damping can be used for all chambers in the MC–OWC device for most wave period ranges, except for the long wave periods. These require a higher PTO damping. An increased incident wave height reduces the device capture width ratio, but there is a noticeable improvement for long wave periods.

Experimental Assessment of the Performance of CECO Wave Energy Converter in Irregular Waves

The performance assessment of a wave energy converter (WEC) is a key task. Depending on the layout of the WEC system and type of power take-off (PTO) mechanism, the determination of the absorbed power at model scale involves several challenges, particularly when the measurement of PTO forces is not available. In irregular waves, the task is even more difficult due to the random character of forces and motions. Recent studies carried out with kinetic energy harvesters (KEH) have proposed expressions for the estimation of the power based only on the measured motions. Assuming that the WEC behaves as a KEH at model scale, the expressions for power estimation of KEHs have been heuristically adapted to WECs. CECO, a floating-point absorber, has been used as case study. Experimental data from model tests in irregular waves are presented and analyzed. Spectral analyses have been applied to investigate the WEC responses in the frequency domain and to derive expressions to estimate the absorbed power in irregular waves. The experimental transfer functions of the WEC motions demonstrated that the PTO damping is significantly affected by the incident waves. Based on KEH approach's results, absorbed power and PTO damping coefficients have been estimated. A linear numerical potential model to compute transfer functions has been also implemented and calibrated based on the experimental results. The numerical results allowed the estimation of combined viscous and losses effects and showed that although the KEH approach underestimated the absorbed power, qualitatively reproduced the WEC performance in waves.

Hydrodynamic performance of a pile-supported OWC breakwater: An analytical study

A pile-supported OWC breakwater is a novel marine structure in which an oscillating water column (OWC) is integrated into a pile-supported breakwater, with a dual function: generating carbon-free energy and providing shelter for port activities by limiting wave transmission. In this work we investigate the hydrodynamics of this novel structure by means of an analytical model based on linear wave theory and matched eigenfunction expansion method. A local increase in the back-wall draft is adopted as an effective strategy to enhance wave power extraction and reduce wave transmission. The effects of chamber breadth, wall draft and air chamber volume on the hydrodynamic performance are examined in detail. We find that optimizing power take-off (PTO) damping for maximum power leads to both satisfactory power extraction and wave transmission, whereas optimizing for minimum wave transmission penalizes power extraction excessively; the former is, therefore, preferable. An appropriate large enough air chamber volume can enhance the bandwidth of high extraction efficiency through the air compressibility effect, with minimum repercussions for wave transmission. Meanwhile, the air chamber volume is found to be not large enough for the air compressibility effect to be relevant at engineering scales. Finally, a two-level practical optimization strategy on PTO damping is adopted. We prove that this strategy yields similar wave power extraction and wave transmission as the ideal optimization approach.

Assessment of damping coefficients of power take-off systems of wave energy converters: A hybrid approach

The damping coefficient of the power take-off (PTO) system is a key parameter in the performance assessment of a wave energy converter (WEC). However, since in most WEC studies the focus is mainly on the absorbed power, damping estimation is generally overlooked on the assumption that a single constant coefficient can properly characterize the WEC's damping of a given configuration for all wave conditions. Recently, while analyzing the experimental tests of CECO, a floating-point absorber WEC, significant discrepancies were found among their experimental responses under different incident waves. Instead of attributing those differences to nonlinear hydrostatic or Froude-Krylov effects, it was hypothesized that variations in the PTO damping associated to incident waves was the main cause. This study presents the experimental evidences of that behavior for regular and irregular waves. Furthermore, a hybrid approach for the assessment of damping coefficients is proposed and applied to CECO's experimental responses. The results demonstrated that: a) damping coefficients were significantly affected by wave conditions; b) higher PTO damping coefficients were obtained for milder irregular waves than for rougher regular waves; c) the hybrid approach reliably and efficiently estimated the WEC power in regular and irregular waves.

Frequency-domain hydrodynamic modelling of dense and sparse arrays of wave energy converters

In this work, we develop a frequency-domain model to study the hydrodynamic behaviour of a floater blanket (FB), i.e., an array of floater elements individually connected to power take-off (PTO) systems, which constitutes the core technology of the novel Ocean Grazer (OG) wave energy converter (WEC). The boundary element method open-source code NEMOH is used to solve the scattering and radiation problem. The aforementioned floater elements that comprise the FB are mechanically interconnected via (cylindrical, revolutional or spring) joints, which add extra constraint equations to the multibody problem. Various scenarios are investigated to understand the hydrodynamic response of the FB. The variation of the capture factor, PTO damping coefficients, q-factor and response amplitude operator (RAO) of each scenario are analysed, in order to quantify the device performance. A new concept based on a negative-stiffness spring joint is proposed to increase the energy output of the FB. Attention is also paid to the anti-resonance that is found in the numerical simulations. This study provides further insight into the hydrodynamic behaviour of dense or sparse interconnected arrays of WECs, which is fundamental for the design and optimisation of the OG-WEC.