Buoy Motion Research Articles

Transverse motion instability of a submerged moored buoy.

Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.

Estimation of the Motion-Induced Horizontal-Wind-Speed Standard Deviation in an Offshore Doppler Lidar

This work presents a new methodology to estimate the motion-induced standard deviation and related turbulence intensity on the retrieved horizontal wind speed by means of the velocity-azimuth-display algorithm applied to the conical scanning pattern of a floating Doppler lidar. The method considers a ZephIR™300 continuous-wave focusable Doppler lidar and does not require access to individual line-of-sight radial-wind information along the scanning pattern. The method combines a software-based velocity-azimuth-display and motion simulator and a statistical recursive procedure to estimate the horizontal wind speed standard deviation—as a well as the turbulence intensity—due to floating lidar buoy motion. The motion-induced error is estimated from the simulator’s side by using basic motional parameters, namely, roll/pitch angular amplitude and period of the floating lidar buoy, as well as reference wind speed and direction measurements at the study height. The impact of buoy motion on the retrieved wind speed and related standard deviation is compared against a reference sonic anemometer and a reference fixed lidar over a 60-day period at the IJmuiden test site (the Netherlands). Individual case examples and an analysis of the overall campaign are presented. After the correction, the mean deviation in the horizontal wind speed standard deviation between the reference and the floating lidar was improved by about 70%, from 0.14 m/s (uncorrected) to −0.04 m/s (corrected), which makes evident the goodness of the method. Equivalently, the error on the estimated turbulence intensity (3–20 m/s range) reduced from 38% (uncorrected) to 4% (corrected).

Hydrodynamic Analysis and Power Conversion for Point Absorber WEC with Two Degrees of Freedom Using CFD

Point absorber wave energy device with multiple degrees of freedom (DOF) is assumed to have a better absorption ability of mechanical energy from ocean waves. In this paper, a coaxial symmetric articulated point absorber wave energy converter with two degrees of freedom is presented. The mechanical equations of the oscillation buoy with power take-off mechanism (PTO) in regular waves are established. The three-dimensional numerical wave tank is built in consideration of the buoy motion based upon the CFD method. The appropriate simulation elements are selected for the buoy and wave parameters. The feasibility of the CFD method is verified through the contrast between the numerical simulation results of typical wave conditions and test results. In such case, the buoy with single DOF of heave, pitch and their coupling motion considering free (no PTO damping) and damped oscillations in regular waves are simulated by using the verified CFD method respectively. The hydrodynamic and wave energy conversion characteristics with typical wave conditions are analyzed. The numerical results show that the heave and pitch can affect each other in the buoy coupling motion, hydrodynamic loads, wave energy absorption and flow field. The total capture width ratio with two coupled DOF motion is higher than that with a single DOF motion. The wave energy conversion of a certain DOF motion may be higher than that of the single certain DOF motion even though the wave is at the resonance period. When the wave periods are high enough, the interaction between the coupled DOF motions can be neglected.

Numerical and experimental study on a hemispheric point-absorber-type wave energy converter with a hydraulic power take-off system

This study examined the performance of a hemispherical point-absorber wave energy converter (WEC) with a hydraulic power take-off (PTO) system. The hydraulic PTO system for power generation was modeled as an approximate coulomb damping force, which was recently proposed to reduce numerical error. To examine the hydrodynamic performance of the WEC, a three-dimensional frequency-domain numerical wave tank technique was adopted, in which the wave radiation problem and diffraction problem for a hemispherical buoy were solved in succession to obtain the hydrodynamic coefficients. The Cummins equation was also adopted to simulate the buoy displacement and extracted wave power in the time domain. For comparison, a three-dimensional wave tank experiment was conducted. Various viscous damping and energy loss from WEC system and hydraulic cylinder pressure of the PTO system were measured from the experimental results, and these values were added to the governing equation of buoy motion. Therefore, the final numerical model of the WEC system contained the viscous damping and hydraulic PTO forces as well as the potential-flow-based hydrodynamic coefficients. Using the developed numerical model, the hemispheric buoy displacement and extracted wave power were calculated for various hydraulic pressures and input wave conditions to determine the optimal conditions for the maximum wave power.

Numerical simulation of a novel ocean wave energy converter

Ocean waves are one of the energy resources, which have a potential to supply some parts of the world’s energy requirements. Recently, many researchers are interested in investigation of the ocean wave energy conversion (OWEC), because energy generation from this device is considered renewable and clean energy. A new wave energy converter named "Searaser" was invented with new technology in 2013. The primary aim of this research is to study the capability of Flow-3D commercial software in simulation of this energy converter. In order to validate the results, a comparison was made between numerical and experimental research, which showed a good agreement in motion of buoy. In this research, wave energy converter was simulated inside a wave tank including water. Furthermore, Reynolds Averaged Navier-Stokes equations were coupled with volume of fluid (VOF) model to generate three-dimensional numerical linear propagating waves as well as solving the fluid flow. Pressure and velocity contours were shown when wave passes the buoy. Although different methods are used for mesh generation of solid and fluid domains in this software, results indicate the capability of Flow-3D software for modelling the fluid structure interaction (FSI) problems including wave motions. However, more parametric studies need to be conducted for this new energy converter to illustrate more details about the power generation of this energy converter.

Wave interaction with a tethered buoy: SPH simulation and experimental validation

Understanding the interaction between surface waves and floating, moored structures is an important problem for the design of offshore structures. Experimental analysis has traditionally been used to study these problems, but using computational modelling could potentially reduce the number of experimental iterations required. In this paper we investigate the use of Smoothed Particle Hydrodynamics as a method for modelling these problems and thus reducing the number of experiments required. Validation data is obtained from generic experiments that contain the important features of wave-structure interaction. A moored spherical buoy oscillating both through and across a free surface, as well as interacting with an incident sinusoidal wave train are discussed and companion SPH simulations are run. We show here that SPH is capable of achieving accurate predictions of the buoy's motion when interacting with the free surface with appropriate particle resolutions. An initial transient motion was observed in the experiments as a long period oscillation of the buoy at its surge natural frequency. This transient motion was also predicted by SPH, but at reduced amplitude. Overall SPH was determined to be a good choice for modelling surface and structure interactions and we provide guidelines on appropriate particle resolution for such interactions.

Experimental and numerical investigation of a taut-moored wave energy converter: A validation of simulated buoy motions

This study presents an experimental and numerical investigation of a taut-moored wave energy converter (WEC) system with a point absorber type of WEC. The WEC system consists of a buoy, a unique three-leg two-segment mooring system with submerged floaters, and a power take-off system designed for the current experiment as a heave plate. The main objective of the study is to validate a numerical simulation model against experiments carried out in an ocean basin laboratory. Two physical models in model scales 1:20 and 1:36 were built and tested. The detailed experimental testing program encompasses tests of mooring system stiffness, decay tests, and different sea state conditions for ocean current, regular and irregular waves. A numerical model in the model scale 1:20 was developed to simulate coupled hydrodynamic and structural response analyses of the WEC system, primarily using potential flow theory, boundary element method, finite element method, and the Morison equation. Several numerical simulations are presented for each part of the experimental testing program. Results for the WEC buoy motions under operational conditions from the experiments and the numerical simulations were compared. This study shows that the simulation model can satisfactorily predict the dynamic motion responses of the WEC system at non-resonant conditions while at resonant conditions additional calibration is needed to capture the damping present during the experiment. A discussion on simulation model calibration with regard to linear and non-linear damping highlights the challenge to estimate these damping values if measurement data are not available.

Feasibility study of the three-tether axisymmetric wave energy converter

There are numerous designs and concepts that have been offered to extract energy from ocean waves. A heaving buoy is distinguished as the most popular device which predominantly harnesses energy from the vertical motion in waves. One such device is the bottom-referenced submerged heaving buoy represented by the Carnegie Clean Energy CETO system. The total power absorption of this converter can be increased by replacing the single-tether power take-off system by a three-tether mooring configuration thereby making motion controllable in heave and surge. The current paper provides a comparative performance analysis of the generic submerged heaving buoy connected to one tether and the three-tether converter in terms of the buoy motion, and design of the power take-off and mooring systems. This is accompanied by a techno-economic analysis of two converters.

Experimental investigations into the current-induced motion of a lifeboat at a single point mooring

This paper presents a series of model experiments on the current-induced motions of a 1:40 scale lifeboat at a single point mooring (SPM). The influence upon vessel and buoy motion of the mooring configuration factors of (a) three mooring line (hawser) lengths, (b) four buoy shapes and (c) two buoy sizes have been investigated. A motion tracking algorithm was successfully employed and validated against data from an inertial measuring unit allowing small scale testing without the influence of instrument cabling. The results show that the dominant translational motion, of the model lifeboat at a SPM, is sway and the rotational motion is yaw, with double pendulum-like fishtailing behaviour prevalent. Increasing the hawser length, when no buoy was present, resulted in an increase in the vessel's sway velocity. No significant effects on vessel motion were observed from changes in the shape of the 1:40 and 1:20 scale buoys. However, the presence and increasing size of the buoy was found to increase the sway velocity of the buoy and reduce the motions of the model lifeboat. These results suggest that changes in buoy size influence the motions of the model lifeboat which may enable mooring efficacy to be improved.

Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter

For a three-degree-of-freedom wave energy converter (heave, pitch, and surge), the equations of motion could be coupled depending on the buoy shape. This paper presents a multiresonant feedback control, in a general framework, for this type of a wave energy converter that is modeled by linear time invariant dynamic systems. The proposed control strategy finds the optimal control in the sense that it computes the control based on the complex conjugate criteria. This control strategy is relatively easy to implement since it is a feedback control in the time domain that requires only measurements of the buoy motion. Numerical tests are presented for two different buoy shapes: a sphere and a cylinder. Regular, Bretschnieder, and Ochi–Hubble waves are tested. Simulation results show that the proposed controller harvests energy in the pitch-surge-heave modes that is about three times the energy that can be harvested using a heave-only device. This multiresonant control can also be used to shift the energy harvesting between the coupled modes, which can be exploited to eliminate one of the actuators while maintaining about the same level of energy harvesting.

Survivability of wave energy converters using CFD

The survivability of Wave Energy Converters (WECs) in extreme waves is a critical issue faced by developers; typically assessed via small scale physical experiments with considerable uncertainties. Until recently, confidence in the ability of numerical tools to reproduce extreme wave events and their interaction with floating structures has been insufficient to warrant their use in routine design processes. In this work a fully nonlinear, coupled tool for simulating focused wave impacts on generic WEC hull forms is described and compared with physical measurements. Two separate design waves, based on the 100 year wave at Wave Hub and using the NewWave formulation, have been reproduced numerically as have experiments in which a fixed truncated circular cylinder and a floating hemispherical-bottomed buoy are subject to these focused wave events. The numerical model is shown to reproduce the wave events well with some inaccuracies observed in shallower water depths. The results for pressure and run-up on the cylinder surface, as well as the high-order free-surface behaviour, also compare well with experimental results. The floating buoy's motion and mooring load are reproduced exceptionally well showing that the tool presented here can be used to assess WEC survivability and complement existing physical modelling.

Dynamic analysis of propulsion mechanism directly driven by wave energy for marine mobile buoy

Marine mobile buoy(MMB) have many potential applications in the maritime industry and ocean science. Great progress has been made, however the technology in this area is far from maturity in theory and faced with many difficulties in application. A dynamic model of the propulsion mechanism is very necessary for optimizing the parameters of the MMB, especially with consideration of hydrodynamic force. The principle of wave-driven propulsion mechanism is briefly introduced. To set a theory foundation for study on the MMB, a dynamic model of the propulsion mechanism of the MMB is obtained. The responses of the motion of the platform and the hydrofoil are obtained by using a numerical integration method to solve the ordinary differential equations. A simplified form of the motion equations is reached by omitting terms with high order small values. The relationship among the heave motion of the buoy, stiffness of the elastic components, and the forward speed can be obtained by using these simplified equations. The dynamic analysis show the following: The angle of displacement of foil is fairly small with the biggest value around 0.3 rad; The speed of mobile buoy and the angle of hydrofoil increased gradually with the increase of heave motion of buoy; The relationship among heaven motion, stiffness and attack angle is that heave motion leads to the angle change of foil whereas the item of speed or push function is determined by vertical velocity and angle, therefore, the heave motion and stiffness can affect the motion of buoy significantly if the size of hydrofoil is kept constant. The proposed model is provided to optimize the parameters of the MMB and a foundation is laid for improving the performance of the MMB.

Dynamics of a mechanical frequency up-converted device for wave energy harvesting

This paper proposes a novel mechanical impact-driven frequency up-converted device for wave energy harvesting, which could bridge a gap between waves of frequency 0.03–1Hz and electrical generators of operation frequency hundreds hertz. The device mainly consists of a cylindrical buoy, beams and teeth. A mathematical model for the dynamics of such a device is presented, which incorporates the fluid–structure interaction between the wave and the buoy, and the structural interactions between the beams and the teeth. The momentum balance method and the coefficient of restitution are employed, which give rise to piecewise nonlinear equations governing the motions of the buoy and the beams. Experimental tests carried out in a wave flume validate the model and prove the effectiveness of frequency up-converted method in wave energy harvesting. The characteristics of frequency up-converted transformation from buoy motion to beams oscillation for wave energy harvesting are probed, and the effects of beam Young׳s modulus, beam number, wave period and wave height on strain power of the beams are explored.

Theoretical, experimental and numerical investigations into nonlinear motion of a tethered-buoy system

In this paper, we discuss nonlinear motion of a buoy connected vertically to the seabed via a tensioned tether (tethered-buoy). A series of scaled model tests has been conducted and a significant nonlinear behavior of the buoy motion, sub-harmonic motion in particular, is observed. Taking account of the influence of time-varying tether tension on the buoy motion, theoretical explanation is made for the sub-harmonic response. The stability of the tethered-buoy system is focused based on Mathieu instability theory. A strongly coupled numerical model between the buoy motion and the tether behavior is established to clarify the mechanism of the nonlinear motion of the tethered-buoy system. A comparison between the experiment data and simulation results is presented not only for the linear but also for the sub-harmonic components. Influential factors for the sub-harmonic motion are discussed in detail. It turned out that the sub-harmonic motion is dominated by the nonlinear coupling effect of time-varying tension in the tether with the buoy motion. Finally, the influential factors to the sub-harmonic motion are indicated throughout the comparison between two different buoy models.

Establishment of Motion Model for Wave Capture Buoy and Research on Hydrodynamic Performance of Floating-Type Wave Energy Converter

Abstract Floating-type wave energy converter has the advantages of high wave energy conversion efficiency, strong shock resistance ability in rough sea and stable output power. So it is regarded as a promising energy utilization facility. The research on hydrodynamic performance of wave capture buoys is the precondition and key to the wave energy device design and optimization. A simplified motion model of the buoys in the waves is established. Based on linear wave theory, the equations of motion of buoys are derived according to Newton’s second law. The factors of wave and buoys structural parameters on wave energy absorption efficiency are discussed in the China’s Bohai Sea with short wave period and small wave height. The results show that the main factor which affects the dynamic responses of wave capture buoys is the proximity of the natural frequency of buoys to the wave period. And the incoming wave power takes a backseat role to it at constant wave height. The buoys structural parameters such as length, radius and immersed depth, influence the wave energy absorption efficiency, which play significant factors in device design. The effectiveness of this model is validated by the sea tests with small-sized wave energy devices. The establishment methods of motion model and analysis results are expected to be helpful for designing and manufacturing of floating-type wave energy converter.

Theoretical study on the power take-off estimation of heaving buoy wave energy converter

Heaving buoy wave energy converter is applicable to small wave height and short wave period, which are the main characteristics of the China Sea. The device captures the wave power by buoy's heaving motion, transfers it by hydraulic system, and converts it into the electric power by generator. Power Take-Off (PTO) of the device is related to the resistance of the hydraulic system. However, effects of the hydraulic damping on the motion of buoy are often neglected and the study on the optimal hydraulic system is rare. In this paper, a new theoretical analysis has been developed, which is more applicable to the buoy considering hydraulic system. The paper establishes the governing equation considering buoyancy, wave dynamic force and hydraulic damping. The displacement and the velocity of the buoy are both obtained. The time-averaged power captured is calculated by integrating the square-velocity expression derived, and the existence of the maximum PTO is proved. Theoretical result is compared with the experimental result. The paper demonstrates the displacements and average output power of the buoy with different values of damping and inertia coefficients. The results of the study could be a guidance for the PTO design of the heaving buoy sets.

Marine Inertial Measurement Units: Communication, Capabilities, and Challenges

Abstract This paper describes the development of marine inertial measurement units (MIMUs) for the measurement of buoy motions. MIMUs are miniature, low-power, low-cost devices that utilize off-the-shelf microelectromechanical system (MEMS) components to monitor motion. Two MIMU devices have been deployed off the coast of Ireland—using SmartBay's test facilities and data infrastructure; these transmit buoy motion data to shore in real time. The recorded inertial data are used to develop algorithms that provide relevant information for marine applications, with the eventual aim of embedding these on the MIMU itself. Methods and results are presented of one such application—the measurement of significant wave height (Hs)—and are shown to be comparable to state-of-the-art solutions, at a fraction of the cost and power requirements. Additional applications and possible future developments of the work are also discussed.

A Methodology of Modelling a Wave Power System via an Equivalent RLC Circuit

The equivalent circuit method can be an effective modelling technique for system studies of point absorbing wave energy converters (WECs). For the continuously evolving design and study of WEC systems, an instruction on how to draw the corresponding equivalent RLC circuit model is needed. It is not only vital to make sure the model is correct, but to allow the model to be easily adapted for different cases and implemented by different researchers. This paper presents a force analysis-oriented methodology based on a typical WEC unit composed of a heaving buoy and a linear generator. Three cases are studied in order to demonstrate the procedures: the generator with a retracting spring, the connection line with a rubber damper, and buoy motion in both heave and surge directions. The presented methodology serves as a guide to produce nonlinear circuit models that give a reliable description of the dynamics of real wave energy systems.

A study of the optimum draft of multiple resonance power buoys for maximizing electric power production

To maximize electric power production using wave energy extractions from resonance power buoys, the maximum motion displacement spectra of the buoys can primarily be obtained under a given wave condition. In this study, wave spectra observed in shoaling water were formulated. Target resonance frequencies were established from the arithmetic means of modal frequency bands and the peak frequencies. The motion characteristics of the circular cylindrical power buoys with corresponding drafts were then calculated using numerical models without considering PTO damping force. Results showed that the heave motions of the power buoys in shoaling waters with insufficient drafts produced greater amplification effects than those in deep seas with sufficient drafts.

Robust and low computational cost controller for improving captured power in heaving wave energy converters

This study suggests a simple and robust control strategy for improving captured power in heaving wave energy converters (WEC). The controller aims at optimizing the captured power using a hierarchical control strategy (HCS), which consists of a higher and lower control levels. The top level control is responsible of producing the reference velocity that is used by the lower level controller to regulate the actual velocity of the WEC buoy. The reference is generated by solving an offline optimization problem for maximizing the absorbed energy subject to the buoy motion constraints. As an attempt to avoid computational complexity in real-time operation, a simple look-up table is produced for various sea-states conditions. In order to track this reference, sliding mode controller (SMC) is deployed. The design parameters of the SMC is tuned offline using a well-known model of WEC. Any perturbations, nonlinearities, and disturbances not covered by the used model will be handled by the robustness property of the SMC. Moreover, the used SMC does not add any further complexity to the overall control strategy. The proposed method is validated in both regular and irregular sea-states, as well as in both nominal and perturbed scenarios. Other control strategies were also used to further assess the performance of the proposed control strategy. Based on the simulation results, the proposed hierarchical controller outperformed the other controllers in both nominal and perturbed scenarios.