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The Deepwater Horizon Mobile Offshore Drilling Unit (MODU) was one of several classes of floatable drilling systems. The explosion on April 20, 2010 led to fatalities and the worst oil spill in the U.S. We present an independent estimate of the oil-flow rate into The Gulf caused by the drill-pipe rupture. We employed the NASA Moderate-Resolution Imaging-Spectroradiometer (MODIS) satellite photographs, starting from the days immediately following the disaster, to determine the magnitude of spill. From these images, we obtained the surface area of the spill and calculated the oil flow rate by two different methods based on contrasting luminance within that area. The first assumes a constant thickness for the total area with upper and lower bounds for the thickness. The second separates the area into different patches based on the luminance levels of each. The probability density function (PDF) of such luminance plots showed natural groupings, allowing patches be identifiable. Each patch maps to a specific thickness. This second approach provides a more accurate average thickness. With the assumption that evaporation and other loss amounted to ~40% of the spill, we obtained, from the first method, a flow rate ranging from 9,300 barrels per day (BPD) to 93,000 BPD. A value of 51,200 BPD was obtained using patch-separation method. This latter estimate was a plausible value, obtained from the current analysis, but with no details presented in an Extended Abstract in OMAE2012, is remarkably consistent with the "official U.S.-Govt. estimates". [ABSTRACT FROM AUTHOR]

Highlights • A hybrid integral-equation method for axisymmetric point-absorber WECs is presented. • The hydrodynamic properties of various types of bodies in waves are computed. • Two different designs of a dual-cylinder WEC are evaluated using the current method. • Good agreement between computations and experiments is observed in the WEC analysis. • Heave motion of WEC is accurately predicted with constant viscous damping correction. Abstract To assist in the prototyping and controller design of point-absorber wave energy converters (WECs), an easy-to-implement hybrid integral-equation method is presented for computing the frequency-domain hydrodynamic properties of bodies with a vertical axis of symmetry in waves. The current hybrid method decomposes the flow domain into two parts: an inner domain containing the body and an outer domain extending to infinity. The solution in the inner domain is computed using the boundary-element method, and the outer-domain solution is expressed using eigenfunctions. Proper matching at the domain boundary is achieved by enforcing continuity of velocity potential and its normal derivative. Body symmetry allows efficient computation using ring sources in the inner domain. The current method is successfully applied to three different body geometries including a vertical truncated floating cylinder, the McIver toroid, and the coaxial-cylinder WEC being developed in the authors' laboratory. In particular, the current results indicate that, by replacing the flat bottom of the coaxial-cylinder WEC with the Berkeley-Wedge (BW) shape, viscous effect can be significantly reduced with only minor negative impact on wave-exciting force, thus increasing WEC efficiency. Finally, by comparing to experimental measurements, the current method is demonstrated to accurately predict the heave added mass and wave-exciting force on the coaxial-cylinder WEC with BW geometry. If a viscous damping correction factor is used, the heave motion amplitude can also be accurately computed. [ABSTRACT FROM AUTHOR]

Highlights • An efficient semi-analytical method is used to model hydrodynamics of cylinder arrays. • The Haskind relation is generalized for wave-exciting forces on an array or a member. • Cylinders need not be identical and can oscillate independently with 6 DOFs. • Effects of cylinder spacing and layout symmetry on power extraction are examined. • Optimal power of a large farm with multiple arrays is studied by a combined method. Abstract A semi-analytical method is developed to investigate surface-wave interactions among an array of wave-energy converters, each modeled as a truncated cylinder, and the interaction effects on power absorption from the array is studied. Each cylinder can have independent movements with six degrees of freedom. The method of matched eigen-function expansions is applied to solve the wave radiation problem. To achieve fast computation, effects of evanescent modes of local scattering waves from one cylinder is neglected in the near fields of neighboring cylinders, but the far-field radiated waves are retained. Wave-exciting forces and moments on an individual cylinder or a group of cylinders, situated among an array, are evaluated by a new, generalized form of the "Haskind relation" applicable to an array of arbitrary configuration, which only requires the solution to the radiation problem. Hydrodynamic properties and wave-exciting loads are presented for arrays of different configurations. This efficient computation facilitates investigating wave-interaction effects on the optimal power output of a cylinder array. Effects of the cylinder numbers, their spacing, and the layout geometry on power extraction are discussed. The interaction factor for a large wave farm consisting of multiple small arrays was evaluated by the current method combined with the point-absorber approximation. [ABSTRACT FROM AUTHOR]

Highlights • Potential flow over arbitrarily shaped thin plates in free space is considered. • The flow is modeled as the solution of a hypersingular integral equation. • A Galerkin approach to solution is found to maintain simplicity and efficiency. • Results are presented for circular, square and triangular plates not heretofore known. • Effects of presence of holes in plates on added mass and added inertia are shown. Abstract We present results for the added mass and moment of inertia of infinitely thin plates of arbitrary shapes in an infinite potential field. The problem is modeled using a hypersingular boundary-integral equation and is treated directly using a Galerkin approach without regularization. The results are used to fill some gaps in the literature of the values of added mass for these plates, particularly those plates with openings or holes and we compare the exact numerical results with those obtained by simply subtracting the added mass or inertia from those of the full plate (an algebraic approximation). The algebraic approximation gives incorrect values compared with actual three-dimensional results. [ABSTRACT FROM AUTHOR]

Model-predictive control (MPC) has shown its strong potential in maximizing energy extraction for wave-energy converters (WECs) while handling hard constraints. However, the computational demand is known to be a primary concern for applying MPC in real time. In this work, we develop a cost function in which a penalty term on the slew rate of the machinery force is introduced and used to ensure the convexity of the cost function. Constraints on states and the input are incorporated. Such a constrained optimization problem is cast into a Quadratic Programming (QP) form and efficiently solved by a standard QP solver. The current MPC is found to have good energy-capture capability in both regular and irregular wave conditions, and is able to broaden favorably the bandwidth for capturing wave energy compared to other controllers in the literature. Reactive power required by the power-take-off (PTO) system is presented. The effects of the additional penalty term are discussed. [ABSTRACT FROM AUTHOR]

To provide guidance for improving the survivability of asymmetrical wave-energy converters (AWECs), the forces experienced by them in breaking-waves condition were analyzed and reported. “The Berkeley Wedge” (TBW), a highly efficient wave-energy converter and floating breakwater, was used as a canonical study. The forces were obtained by computation using the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method and by model-scale experiments. Breaking waves were first generated upstream for both physical and computational modeling by developing appropriate time histories of a wavemaker. Plunging breakers and wave forces from the computational model were verified by experiments for different drafts. To increase the survivability, while retaining the same operational draft of TBW, pressure-relief channel (PRC), a novel scheme that allowed water to flow through TBW was modeled and its effectiveness in extreme-waves was demonstrated computationally. A design was proposed to operate the PRCs so as to increase the survivability of such AWECs. [ABSTRACT FROM AUTHOR]

To accommodate ocean-wave energy extraction in a wide operating range of sea-states, a nonlinear model predictive control (NMPC) methodology was applied to a lab-scale dual coaxial-cylinder wave-energy converter (WEC), coupled with a permanent-magnet linear generator (PMLG) as the power take-off (PTO). The paper focuses on the experimental implementation of the optimal damping control of the PMLG as guided by the NMPC process, which yielded intermediate values of damping subjected to prescribed damping capacity. This damping behavior was implemented electronically in the coupled PTO-WEC system by employing a solid-state relay (SSR) with pulse-width modulation (PWM) technique so as to mimic analog current flow. The effectiveness of the combination of SSR and PWM was demonstrated. Successful real-time lab-scale testing in regular and irregular waves was experimentally confirmed. Peak values of energy capture and a broadened bandwidth were favorably improved compared to those obtained using just constant, non-time-varying damping control. [ABSTRACT FROM AUTHOR]

The prediction of roll motion of a ship with bilge keels is particularly difficult because of the nonlinear characteristics of the viscous roll damping. Flow separation and vortex shedding caused by bilge keels significantly affect the roll damping and hence the magnitude of the roll response. To predict the ship motion, the Slender-Ship Free-Surface Random-Vortex Method (SSFSRVM) was employed. It is a fast discrete-vortex free-surface viscous-flow solver developed to run on a standard desktop computer. It features a quasi-three-dimensional formulation that allows the decomposition of the three-dimensional ship-hull problem into a series of two-dimensional computational planes, in which the two-dimensional free-surface Navier-Stokes solver Free-Surface Random-Vortex Method (FSRVM) can be applied. In this paper, the effectiveness of SSFSRVM modeling is examined by comparing the time histories of free roll-decay motion resulting from simulations and from experimental measurements. Furthermore, the detailed two-dimensional vorticity distribution near a bilge keel obtained from the numerical model will also be compared with the existing experimental Digital Particle Image Velocimetry (DPIV) images. Next, we will report, based on the time-domain simulation of the coupled hull and fluid motion, how the roll-decay coefficients and the flow field are altered by the span of the bilge keels. Plots of vorticity contour and vorticity isosurface along the three-dimensional hull will be presented to reveal the motion of fluid particles and vortex filaments near the keels. [ABSTRACT FROM AUTHOR]

Active control based on nonlinear model predictive control (NMPC) methodology is applied to a candidate but realistic dual coaxial-cylinder wave-energy extractor system with the objective of maximizing energy capture over a range of incident ocean-wave conditions. The extractor consists of an outer cylinder (floater) moving relative to a tension-tethered inner cylinder, driving a permanent-magnet linear generator (PMLG) to acquire power take-off (PTO). The floater dynamics is solved in the time domain with the NMPC to constrain maximum floater motion and simultaneously incorporating the PMLG damping capability. The numerical model of the coupled floater and PTO dynamics is formulated in the state-space representation. The mechanical to electrical conversion efficiency of the PMLG, which was experimentally determined as a function of its power-extraction damping, is considered in the numerical simulation. The NMPC process yields a time-varying profile for the generator damping as the control strategy. Simulation results indicate strongly time-dependent and discontinuous generator-damping requirements for both regular and irregular incident-wave scenarios. However, the NMPC-controlled system significantly outperforms a passive-control, constant-damping system by exhibiting higher peak values of energy-extraction and a broader capturing bandwidth, thus confirming the feasibility and success of the control strategy. [ABSTRACT FROM AUTHOR]

The flow past a Bach-type vertical-axis wind or current turbine is simulated using a viscous Discrete-Vortex Method at a Reynolds number of 1500. The main purpose of the study is to evaluate the suitability of Bach-type turbines for use as micro-scale energy harvesters that can be applied to power, for example, sensor nodes of a wireless sensor network. The maximum power coefficient of the turbine operating at a prescribed constant tip-speed ratio is found to be 0.18, which is comparable to the performance of the same turbine at much higher Reynolds numbers, thus indicating only minimal performance penalty for miniaturization. The speed of the turbine has a strong influence on the evolution of vortical flow structures. A new wake-capturing mechanism that boosts the performance of the turbine is discovered from the simulations for a certain range of tip-speed ratios where the vortex shed by the advancing blade helps drive the returning blade. In addition to prescribed rotation, free rotation of a steel Bach-type turbine in water is also investigated. Significant fluctuation in angular velocity over one period of rotation is observed. This speed fluctuation is found to be detrimental to energy extraction, reducing the maximum power coefficient to approximately 0.16. The estimated power generating capacity of a micro-scale turbine indicates that it can significantly extend the life expectancy of a wireless sensor node or even maintain the node in a low-power state indefinitely. [ABSTRACT FROM AUTHOR]

The full and partial ground effects on the lift generation of a flapping airfoil in normal hovering mode are investigated numerically using the discrete vortex method in two dimensions. To achieve full ground effect, the airfoil of chord c is made to hover above the center of a finite-sized platform of length 10c. We have observed the force-enhancement, force-reduction, and force-recovery regimes at low, medium, and high ground clearances in line with the existing literature. This paper puts special focus on partial ground effect when the airfoil is hovering near the edge of the platform. Lift-modifying mechanisms not previously observed under full ground effect have been discovered. When stroke reversal occurs near the edge of the platform, a relatively stationary strong vortex may form above the platform edge. This strong vortex can either increase or decrease the instantaneous lift force on the airfoil depending on the position of the airfoil relative to the platform edge. Also, the platform edge may lead to the formation of an additional vortex pair which increases the instantaneous lift force as the airfoil sweeps past the edge under suitable conditions. Lastly, the platform edge can lead to the formation of a reverse von Kármán vortex street that extends well below the stroke plane under suitable geometric arrangements. [ABSTRACT FROM AUTHOR]

This paper evaluates the theoretical application of nonlinear model predictive control (NMPC) to a model-scale point absorber for wave energy conversion. The NMPC strategy will be evaluated against a passive system, which utilizes no controller, using a performance metric based on the absorbed energy. The NMPC strategy was setup as a nonlinear optimization problem utilizing the interior point optimizer (IPOPT) package to obtain a time-varying optimal generator damping from the power-take-off (PTO) unit. This formulation is different from previous investigations in model predictive control, as the current methodology only allows the PTO unit to behave as a generator, thereby unable to return energy to the waves. Each strategy was simulated in the time domain for regular and irregular waves, the latter taken from a modified Pierson-Moskowitz spectrum. In regular waves, the performance advantages over a passive system appear at frequencies near resonance while at the lower and higher frequencies they become nearly equivalent. For irregular waves, the NMPC strategy leads to greater energy absorption than the passive system, though strongly dependent on the prediction horizon. It was found that the ideal NMPC strategy required a generator that could be turned on and off instantaneously, leading to sequences where the generator can be inactive for up to 50% of the wave period. [ABSTRACT FROM AUTHOR]

Fluid viscosity is known to influence hydrodynamic forces on a floating body in motion, particularly when the motion amplitude is large and the body is of bluff shape. While traditionally these hydrodynamic force or force coefficients have been predicted by inviscidfluid theory, much recent advances had taken place in the inclusion of viscous effects. Sophisticated Reynolds-Averaged Navier-Stokes (RANS) software are increasingly popular. However, they are often too elaborate for a systematic study of various parameters, geometry or frequency, where many runs with extensive data grid generation are needed. The Free-Surface Random-Vortex Method (FSRVM) developed at UC Berkeley in the early 2000 offers a middle-ground alternative, by which the viscous-fluid motion can be modeled by allowing vorticity generation be either turned on or turned off. The heavily validated FSRVM methodology is applied in this paper to examine how the draft-to-beam ratio and the shaping details of two-dimensional cylinders can alter the added inertia and viscous damping properties. A collection of four shapes is studied, varying from rectangles with sharp bilge corners to a reversed-curvature wedge shape. For these shapes, basic hydrodynamic properties are examined, with the effects of viscosity considered. With the use of these hydrodynamic coefficients, the motion response of the cylinders in waves is also investigated. The sources of viscous damping are clarified. [ABSTRACT FROM AUTHOR]

This paper evaluates two aspects of enhancements made to a generic ocean-wave energy extraction device, developed recently at University of California (UC)-Berkeley with features reported in Yeung et al. (2010, "Design, Analysis, and Evaluation of the UC-Berkeley Wave-Energy Extractor," ASME J. Offshore Mech. Arct. Eng., 134(2), p. 021902). First, the differences in hydrodynamic performance between flat- and hemi-spherical bottom floaters were investigated theoretically using the LJC Berkeley 2D viscous-flow solver: FSRVM (Seah and Yeung, 2008, "Vortical-Flow Modeling for Ship Hulls in Forward and Lateral Motion," Proceedings of the 27th Symposium on Naval Hydrodynamics, Seoul, Korea). The predicted enhancement was compared with experimental results, demonstrating that an increase in motion of over 50% was realizable. Second, important modifications to the design, fabrication, and material of the rotor and stator of the permanent magnet linear generator (PMLG) were made with the aim to increase both power output and mechanical-to-electrical conversion efficiency, ηel. Increased power extraction and efficiency were achieved, doubling what had been previously reported. The nonlinear relationship between the generator damping and the magnet-coil gap width was also investigated to verify that the conditions for optimal power extraction presented in Yeung et al. (2010, "Design, Analysis, and Evaluation of the UC-Berkeley Wave-Energy Extractor," ASME J. Offshore Mech. Arct. Eng., 134(2), p. 021902) were achievable with the PMLG. Experimental results, obtained from testing the coupled floater and PMLG systems in a wave tank, revealed that realized capture widths were more than double those from the previous design. These results further confirmed that matching of the generator and floater damping significantly increased the global efficiency of the extraction process. [ABSTRACT FROM AUTHOR]

An array of ocean-wave energy converters, compared to a stand-alone device, provides lower energy-production costs but affects the aggregate power performance. Previous studies suggested that wave-interaction effects within the array could increase energy production by over 15% per device. However, no physical constraints on the WECs were considered in these studies; as a result, the devices can experience unrealistically large motions. A control strategy is thus desirable to coordinate individual WECs and maximize the energy extraction. We apply model-predictive control (MPC) to an array of point-absorber-type WECs by developing a formulation that accommodates hard constraints on the motion of each device and on the Power-takeoff (PTO) forces with excellent computational efficiency. Full multi-body wave-interaction effects are computed by a semi-analytical method within linear-wave theory. This framework enables us to demonstrate results of realistic maximal power production for arrays of two, three, and four devices operating under constraints in sea waves of various incident angles. It is observed that wave–body interactions have actually destructive effects on the array power production for the majority cases in irregular sea waves. Also discussed are effects of the reactive power produced by the PTO unit and the possibility of removing it within the MPC framework. • A control method is proposed for WEC arrays to maximize power and satisfy constraints. • The constrained optimization problem is cast into a convex QP and solved efficiently. • Discussions are made on Q factors of a WEC array under hard constraints. • The method is applicable to PTOs with or without ability of handling two-way power flow. • Demonstrative results are shown for multi-device arrays in real-sea conditions. [ABSTRACT FROM AUTHOR]

This work, presented at the OMAE-2002 Special Symposium in honor of John V. Wehausen, is dedicated to him, an admirable teacher, colleague, and scholar. A general open boundary condition for time-dependent wave-body interaction problems is developed. The technique is based on domain decomposition and a use of the unsteady free-surface Green function in an outer region. The boundary condition results in a shell condition which may be applied to a variety of interior solution methods. When the interior solution method is a boundary-integral method, an implicit matching can be done. When a volumediscretization method is used in the interior region, a newly developed explicit matching procedure is performed. Demonstrations of the transparent properties of this shell are made for several types of unsteady problems. [ABSTRACT FROM AUTHOR]

The resonant behavior in a moonpool of a floating circular solar pond, with an entrapped two-layer fluid, is studied. The problem is solved by applying a domain-decomposition method using eigenfunction matching. The surface- and internal-wave elevations and the hydrodynamic coefficients of a typical floating solar pond under forced heave or surge motion are computed. The effects of density stratification on surface-wave elevation, added mass, and damping coefficients are analyzed. A collection of resonance frequencies of surface and internal waves is examined, together with the corresponding variations of modal shapes. For heave resonance, the surface and internal waves are characterized by axisymmetric sloshing modes, as opposed to antisymmetric sloshing modes under surge resonances. A frozen-mode approximation method that treats the moonpool fluid as a density-stratified solid is developed to estimate piston-mode frequencies. Non-dimensional resonance frequencies corresponding to antisymmetric and axisymmetric sloshing modes are estimated based on the standing-wave approximation and reciprocity relations between surface and internal wavenumbers. Satisfactory agreement between the estimated resonance frequencies and those computed by eigenfunction matching method is achieved. It is found that the first resonance of the internal wave, rather than higher-order resonances, is more likely to affect the surface-wave behavior, whereas resonances of the surface-wave modes have significant effects on the internal waves. Parametric analyses are performed to study the effects of geometry configurations of the pond. It is found that the resonance frequencies of internal waves under forced heave or surge motion decrease with an increasing density ratio. [ABSTRACT FROM AUTHOR]

Ships often have to pass each other in proximity in harbor areas and waterways in dense shipping-traffic environment. Hydrodynamic interaction occurs when a ship is overtaking (or being overtaken) or encountering other ships. Such an interactive effect could bemagnified in confined waterways, e.g., shallowand narrow rivers. Since Yeung published his initial work on ship interaction in shallow water, progress on unsteady interaction among multiple ships has been slow, though steady, over the following decades. With some exceptions, nearly all the published studies on ship-to-ship problem neglected free-surface effects, and a rigid-wall condition has often been applied on the water surface as the boundary condition.When the speed of the ships is low, this assumption is reasonably accurate as the hydrodynamic interaction is mainly induced by near-field disturbances. However, in many maneuvering operations, the encountering or overtaking speeds are actually moderately high (Froude number Fn > 0.2,where Fn ≡ U √gL p,Uis ship speed, g is the gravitational acceleration, and L is the ship length), especiallywhen the lateral separation between ships is the order of ship length. Here, the far-field effects arising from ship waves can be important. The hydrodynamic interaction model must take into account the surface-wave effects. Classical potential-flowformulation is only able to dealwith the boundary value problem when there is only one speed involved in the free-surface boundary condition. For multiple ships traveling with different speeds, it is not possible to express the freesurface boundary condition by a single velocity potential. Instead, a superposition method can be applied to account for the velocity field induced by each vessel with its own and unique speed. The main objective of the present article is to propose a rational superposition method to handle the unsteady free-surface boundary condition containing two or more speed terms, and validate its feasibility in predicting the hydrodynamic behavior in ship encountering. Themethodology used in the present article is a three-dimensional boundary-elementmethod based on a Rankine-type (infinite-space) source function, initially introduced by Bai and Yeung. The numerical simulations are conducted by using an in-house--developed multibody hydrodynamic interaction program "MHydro." Waves generated and forces (or moments) are calculated when ships are encountering or passing each other. Published model-test results are used to validate our calculations, and very good agreement has been observed. The numerical results show that free-surface effects need to be taken into account for Fn > 0.2. [ABSTRACT FROM AUTHOR]

Real-time hybrid testing of floating wind turbines is conducted at model scale. The semisubmersible, triangular platform, similar to the WindFloat platform, is built instead to support two, counter-rotating vertical-axis wind turbines (VAWTs). On account of incongruous scaling issues between the aerodynamic and the hydrodynamic loading, the wind turbines are not constructed at the same scale as the floater support. Instead, remote-controlled plane motors and propellers are used as actuators to mimic only the tangential forces on the wind-turbine blades, which are attached to the physical (floater-support) model. The application of tangential forces on the VAWTs is used to mimic the power production stage of the turbine. A control algorithm is implemented using the wind-turbine generators to optimize the platform heading and hence, the theoretical power absorbed by the wind turbines. This experimental approach only seeks to recreate the aerodynamic force, which contributes to the power production. In doing so, the generator control algorithm can thus be validated. The advantages and drawbacks of this hybrid simulation technique are discussed, including the need for low inertia actuators, which can quickly respond to control signals. [ABSTRACT FROM AUTHOR]

The study on close-quarter manoeuvring of vessels is of great importance for the safety and efficiency of maritime operations. In this paper, the hydrodynamic interactions between two vessels in moderate-speed overtaking manoeuvres are studied. Computational investigation by free-surface panel method is performed, and the results are assessed against experimental measurements from towing-tank model tests. The influences of overtaking speed and the speed difference between vessels on the hydrodynamic loads are studied. It is found that the free-surface deformation, on account of the blockage effects of the bodies, wave-making properties of the vessels, and the interference of unsteady wave patterns between the vessels, considerably affects the hydrodynamic interactions. In addition, it is also discovered that the influence fromthe unsteady heave and pitch motions of the hulls on the hydrodynamic loads can be non-negligible. Furthermore, it is found that the slower vessel to be overtaken generally experiences larger loads with more variation than the overtaking vessel. The loads on both vessels become more similar to those of a steady-state di-hull system when the speed difference between vessels is small. [ABSTRACT FROM AUTHOR]

Abstract To adapt to an ocean environment of changing wave period, a novel point-absorber concept is proposed: a fully-enclosed Dual Mass-Spring-Damper (DMSD) floater system that has an internal mass and spring so that its resonance frequency can be varied by changing the movable internal mass and spring. In a waterproof floater, this one-degree-of-freedom heaving energy converter can float or be submerged to evade excessive storm load. Optimization of the internal mass, spring and damping system in the frequency domain is first developed to demonstrate that favorable capture width is achievable for a range of incident-wave frequency. Next, power and motion response of this system in an ISSC wave spectrum are studied in time domain. With constant damping for power-takeoff, the DMSD system is found to have noticeably lower capture width in irregular waves than that in regular waves at a frequency that is the same as the peak wave frequency of the spectrum. Since excessive relative motion can occur in irregular-wave excitation, end-stops, modeled by a stiff spring and strong damper, are applied in the time-domain simulation. When properly designed, degradation of only 1–2% in the capture width in the irregular-wave environment is found when end-stops are applied. Highlights • Novel DMSD concept allows variable resonance-frequency capability to adapt to waves. • Capture width of WEC is optimized in the frequency domain with physical limitations. • Motion and power are analyzed and optimized in the time domain for irregular waves. • End-stop effect for internal mass is studied in the time domain for irregular waves. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to maximize the power-to-load ratio for asymmetric wave energy converters undergoing heave motion. Linear hydrodynamic theory is used to calculate bounds of the expected time-averaged power (TAP) and corresponding surge-restraining force, pitch-restraining torque, and power take-off (PTO) control force with the assumption of sinusoidal displacement. This paper formulates an optimal control problem to handle an objective function with competing terms in an attempt to maximize power capture while minimizing structural and actuator loads in regular and irregular waves. Penalty weights are placed on the surge-restraining force, pitch-restraining torque, and PTO actuation force, thereby allowing the control focus to concentrate on either power absorption or load mitigation. The penalty weights are used to control peak structural and actuator loads that were found to curb the additional losses in power absorption associated with a nonideal PTO. Thus, in achieving these goals, a per-unit gain in TAP would not lead to a greater per-unit demand in structural strength, hence yielding a favorable benefit-to-cost ratio. Demonstrative results for "The Berkeley Wedge" in the form of output TAP, reactive TAP needed to drive WEC motion, and the amplitudes of the surge-restraining force, pitch-restraining torque, and PTO control force are shown. Highlights • Review of "The Berkeley Wedge" an asymmetric wave energy converter/breakwater device. • Includes effect of power-take-off efficiency and force coefficients on power output. • Use of pseudo-spectral control theory while including structural and actuator loads. • Introduces a power-to-load ratio for evaluating wave energy converter performance. • Losses in power capture were exceeded by reductions in structural and actuator loads. [ABSTRACT FROM AUTHOR]

Significant reduction of steady-state resistance of a di-hull system with certain hull configurations (relative stagger and separation between the hulls) occurs because of interference effects between the two sets of ship-generated waves. The far-field wave interference and the resulting wave-resistance reduction of an asymmetric di-hull system, consisting of two distinct Series 60 hull models with various hull configurations are studied. The initial search for optimal configurations of the maximum prospective resistance reduction is conducted by an existing di-hull thin-ship computation. These theoretical results are then compared to the ones acquired by towing-tank measurements and those given by a semi-experimental approach. The latter approach obtains the wave resistance by combining experimental “wave-cut” data and analytical expressions developed for such a di-hull system. Experimental uncertainties are briefly discussed. Results of this study show that a considerable amount of wave-resistance reduction is indeed possible for the investigated hull configurations. However, beyond the far-field interference of the waves, near-field interactions of the two hulls are found to have non-negligible influence on the total resistance performance of the di-hull system. [ABSTRACT FROM AUTHOR]

The powering issue of a high-speed marine vehicle with multihulls and air-cushion support is addressed, since there is an often need to quickly evaluate the effects of several configuration parameters in the early stage of the design. For component hulls with given geometry, the parameters considered include the relative locations of individual hulls and the relative volumetric ratios. Within the realm of linearized theory, an interference-resistance expression for hull-to-hull interaction is first reviewed, and then a new formula for hull-and-pressure distribution interference is derived. Each of these analytical expressions is expressed in terms of the Fourier signatures or Kochin functions of the interacting component hulls, with the separation, stagger, and speed as explicit parameters. Based on this framework, an example is given for assessing the powering performance of a catamaran (dihull) as opposed to a tetrahull system. Also examined is the wave resistance of a surface-effect ship of varying cushion support in comparison with that of a base line catamaran, subject to the constraint of constant total displacement. [ABSTRACT FROM AUTHOR]

A point-absorber-type Wave-Energy Converter (WEC) consisting of a floating vertical inner cylinder and an annular outer cylinder that slides along the inner one is considered. The two cylinders heave differently under wave excitation, and wave energy can be harnessed from the relative heave motion between the two cylinders using a Permanent Magnet Linear Generator (PMLG) as the Power Take-Off unit. A mooring cable is attached to the bottom of the inner cylinder. This paper aims to examine the effect of the stiffness of the mooring cable on the performance of the coaxial-cylinder WEC system. The two limiting cases of no mooring cable (freely floating inner and outer cylinders) and an infinitely stiff mooring cable (fixed inner cylinder) were also considered. To perform the analysis, hydrodynamic and interference coefficients of the two heaving cylinders were computed semi-analytically using the method of matched eigenfunction expansions. Experimentally determined viscous corrections on damping were also included in the model in order to have more realistic predictions. The performance of the system in terms of motion responses and capture width were predicted and discussed for both regular and irregular waves. The results of the analysis indicate that both the freely floating design and the design with rigidly moored inner cylinder are viable. The two limiting cases show similar optimal performances, albeit with very different optimal generator damping. However, an ill-chosen mooring-cable stiffness may cause the inner and the outer cylinders to have the same resonance frequency, eliminating the relative heave motion and leading to almost no energy extraction. This situation needs to be avoided when designing the mooring system for a coaxial-cylinder WEC. [ABSTRACT FROM AUTHOR]

A point-absorber wave-energy extractor is developed, consisting of a dual coaxial-cylinder system, with the inner cylinder tension-tethered and an outer cylinder (floater) oscillating vertically. A permanent magnet linear generator (PMLG) is used as a power take-off (PTO) capturing wave energy from the relative motion of the two cylinders. The mathematical modeling of the system includes the coupling effects of the cylinder hydrodynamics and the PMLG behavior. It gives a rational and effective way of providing performance predictions and directions for optimization. The flat bottom shape of the floater is modified into a needle-like curved shape to minimize viscous losses, which leads to three-times increase in floater response, compared with the flat-bottom geometry and thus improved wave-energy capture. The behavior of the PTO in the presence of an appropriate supporting structure for the coaxial cylinders are investigated, and optimal operating conditions for energy extraction and mechanical to electrical conversion efficiency are determined. Experimental results of this coupled system in regular waves confirm the validity of the theoretical predictions and soundness of the engineering design. Optimizing the floater bottom shape and the operating conditions for energy extraction lead to a two-times increase in overall efficiency, even without any active control. [ABSTRACT FROM AUTHOR]

Abstract: This study proposes a ship weather-routing algorithm based on the composite influence of multi-dynamic elements for determining the optimized ship routes. The three-dimensional modified isochrone (3DMI) method utilizing the recursive forward technique and floating grid system for the ship tracks is adopted. The great circle sailing (GCR) is considered as the reference route in the earth coordinate system. Illustrative optimized ship routes on the North Pacific Ocean have been determined and presented based on the realistic constraints, such as the presence of land boundaries, non-navigable sea, seaway influences, roll response as well as ship speed loss. The proposed calculation method is effective for optimizing results by adjusting the weighting factors in the objective functions. The merits of the proposed method can be summarized as: (1) the navigability of the route can be analyzed dynamically to acquire the optimal route; (2) adopting multi-dynamic elements as weighting factors has the benefits in energy efficiency, time-saving and minimum voyage distance; and (3) an ability to enhance speed performance and to incorporate safety concern in a dynamic environment. [Copyright &y& Elsevier]

Abstract: An understanding of the fundamental system dynamics of wave energy converters (WECs) is required to safely and reliably benefit from the available wave energy resource to produce electricity. The effects of the geometry, mooring system, and mass distribution on the idealized power takeoff of a tethered wave energy absorber in irregular waves are examined. The effects on coupled pitch and sway motions are also considered using a linear frequency-domain method, based on potential flow theory, to obtain the hydrodynamic coefficients. Superposition is used to calculate the response in irregular waves. The objectives of this paper are to examine the characteristic system response of WECs, and to demonstrate the use of an efficient potential-based method for the optimization of a WEC to maximize the annual power takeoff while ensuring system safety at a given site. The analyses suggest that the idealized power takeoff damping increases with the size of the WEC, with the intensity of motion limited. A relatively light mooring system has little effect on the power takeoff, but it introduces a low-frequency coupled pitch-surge resonance that can cause system failure if subject to long-period swells. To mitigate the risk of coupled surge-pitch related failures, a low center of gravity and a low radius of gyration of the floater about the center of floatation are recommended. The results also demonstrate the importance of tuning the system for the site-specific probabilistic wave climate in order to maximize total energy capture and avoid potential failures. [Copyright &y& Elsevier]

The objective of this work is to develop and validate a coupled boundary element method-finite element method to simulate the transient fluid-structure interaction response of tidal turbines subject to spatially varying inflow. The focus is on tidal turbines, although the methodology is also applicable for the analysis and design of wind turbines. An overview of the formulation for both the fluid and solid domains, and the fluid-structure interaction algorithms, is presented. The model is validated by comparing the predicted thrust and power measurements, as well as cavitation patterns, with experimental measurements and observations for an 800 mm marine current turbine presented in the work of Bahaj et al. (2007, "Power and Thrust Measurements of Marine Current Turbines Under Various Hydrodynamic Flow Conditions in a Cavitation Tunnel and a Towing Tank," Renewable Energy, 32, pp. 407-426). Additional numerical results are shown for the same turbine, but scaled up to 20 m in diameter, operating in a tidal boundary layer flow with a water depth of 30 m. The results show that transient cavitation will develop near the blade tip when the blades are near the free surface at highly-loaded off-design conditions, and the blades will undergo excessive deformation because of the high fluid loading and slender blade profile. The results also show that the natural frequencies of the blades are significantly reduced when operating in water, as compared with when operating in air, because of added-mass effects. In addition to demonstrating the need for proper consideration for fluid cavitation and structural response, current design challenges for both wind and tidal turbines are discussed. [ABSTRACT FROM AUTHOR]