Hydrodynamic Module Coupling In The Offshore Wind Energy Simulation .
Proceedings of the ASME 2014 33rd International Conference on Ocean, Offshore and Arctic EngineeringOMAE2014June 8-13, 2014, San Francisco, California, USAOMAE2014-24175Hydrodynamic Module Coupling in the Offshore Wind Energy Simulation (OWENS) ToolkitMatthew J. FowlerUniversity of MaineOrono, Maine, U.S.A.Brian OwensSandia National LaboratoriesAlbuquerque, New Mexico, U.S.A.Diana BullSandia National LaboratoriesAlbuquerque, New Mexico, U.S.A.Andrew J. GoupeeUniversity of MaineOrono, Maine, U.S.A.John HurtadoTexas A&M UniversityCollege Station, Texas, U.S.A.D. Todd GriffithSandia National LaboratoriesAlbuquerque, New Mexico, U.S.A.Marco AlvesWave Energy CenterLisbon, Portugal.ABSTRACTWhen considering the future of offshore wind energy,developing cost effective methods of harnessing the offshorewind resource represents a significant challenge which mustbe overcome to make offshore wind a viable option. As themajority of the capital investment in offshore wind is in theform of infrastructure and operation and maintenance costs,reducing these expenditures could greatly reduce the cost ofenergy (COE) for an offshore wind project. Sandia NationalLaboratory and its partners (TU Delft, University of Maine,Iowa State, and TPI Composites) believe that vertical axiswind turbines (VAWTs) offer multiple advantages over otherrotor configurations considering this new COE breakdown.The unique arrangement of a VAWT allows the heavygenerator and related components to be located at the base ofthe tower as opposed to the top, as is typical of a horizontalaxis wind turbine (HAWT). This configuration lowers thetopside CG which reduces the platform stability requirements,leading to smaller and cheaper platforms. Additionally thislocates high maintenance systems close to the ocean surfacethus increasing maintainability. To support this project andthe general wind research community, the Offshore WindENergy Simulation (OWENS) toolkit is being developed inconjunction with Texas A&M as an open source, modularaero-elastic analysis code with the capability to analyzefloating VAWTS. The OWENS toolkit aims to establish arobust and flexible finite element framework and VAWTmesh generation utility, coupled with a modular interface thatallows users to integrate easily with existing codes, such asaerodynamic and hydrodynamic codes.Current efforts to include a hydrodynamic module arefocused on coupling WavEC2Wire with OWENS.WavEC2Wire is a wave-to-wire numerical model developedby Marco Alves at the Insituto Superior Tecnico for theanalysis of wave energy converter devices. It has beenadapted from its original form and restructured for use as ahydrodynamic module capable of providing OWENS withnecessary floating platform dynamics. Hence, WavEC2Wirefunctions as a rigid-body solver designed to calculate theplatform motion due to wave loads, moorings, and theinfluence of the attached VAWT and tower. This paperpresents the WavEC2Wire module and details the OWENScoupling method. Additionally, planned improvements in theWavEC2Wire module as well as future development inOWENS are presented.INTRODUCTIONAlthough offshore wind resources make offshore windenergy an attractive opportunity, the cost of energy (COE) ofoffshore wind projects must be reduced to make offshore winda viable option. As over half of the capital investment inoffshore wind is in the balance of station costs (Figure 1),reducing these expenditures could greatly reduce the COE forthese projects. For a land based wind farm the turbinecontributes 68% of the installed cost, whereas it is only 32%of the total for an offshore wind project [15]. Therefore, it ismore important to consider turbine designs that lower thebalance of station costs rather than trying to decrease the costof the turbine itself.1Copyright 2014 by ASME
Figure 1 - Offshore wind farm, installed capital costs [15]Horizontal-axis wind turbines have gained muchpopularity for land-based wind energy. Unlike VAWTs,HAWT designs have undergone much development over thepast 20 years, which has led to lowered COE. As a result,further significant reduction in COE, which is necessary forfuture offshore wind energy, is not likely in the foreseeablefuture with HAWT configurations. Moreover, the high CGtogether with gearbox and generator placement at the top ofthe tower exacerbates installation, logistics, and other O&Mcost concerns of offshore wind. Generally speaking, reducingthese costs is often considered to have the greatest potentialfor lowering COE for off-shore wind.Figure 2 - Comparison of VAWTs and HAWTs for offshoreapplications [14]Vertical-axis wind turbines held significant interest in theearlier days of wind energy technology during the 1980s. Inthe early 1990s, this configuration lost its popularity and theHAWT was adopted as the primary wind turbineconfiguration. However, when considering the primary COEdrivers for offshore wind, the VAWT configuration offerssome unique opportunities to significantly lower the supportstructure, installation, and O&M costs (Figure 2) [14]. Thesepotentials for COE reduction are primarily due to theplacement of the gearbox and generator at the bottom of thetower. This not only reduces platform cost by lowering the CGof the turbine, but also reduces O&M costs by having highmaintenance components readily accessible near water level.The insensitivity of the VAWT to wind direction and theability to scale the machines to large sizes will increase energyproduction and further reduce COE.The advantages that VAWT technologies offer foroffshore wind development are offset by the lack ofdevelopment in the past years. Modular aero-hydro-elasticanalysis software capable of accurately predicting design loadsfor a floating VAWT system need to be developed andvalidated. This paper details the development of a frameworkcapable of predicting coupled loading on offshore windstructures.OWENS FRAMEWORKTo facilitate the development of VAWT technology,robust design tools must be developed to assess innovativedesign concepts for offshore wind energy technology.Therefore, an aeroelastic design tool is being developed formodeling large offshore VAWT configurations [11], [12],[13]. The Offshore Wind ENergy Simulation toolkit will beable to explore a wide array of offshore VAWT configurationsvia modal and transient analysis. This tool is developed inMATLAB [8] and is a modular framework that will interfacewith aerodynamics, platform & mooring dynamics(hydrodynamics), and drivetrain/generator modules to predictthe response of a VAWT of arbitrary configuration under avariety of conditions. The formulation also allows for stabilityanalysis to identify potential resonance and flutter issues. Thecore of the analysis tool is a robust and flexible finite elementframework capable of considering the dynamics of large,flexible, rotating structures.The fundamental requirements of the aero-elastic analysistool for offshore VAWTs necessitate a flexible frameworkcapable of considering arbitrary configuration geometries,arbitrary loading scenarios, and the ability to interface withvarious modules that account for the interaction of theenvironment and power generation hardware with motions ofthe turbine. Figure 3 shows the analysis framework and theassociated flow of information between the core OWENSanalysis tool, aerodynamic, hydrodynamic, generator, andcontroller modules. The general finite element formulation iseasily adaptable to transient analysis for investigation of startup and shut-down procedures as well as turbulent wind andwave loadings. This implementation is also adaptable to modalanalysis to assess stability of VAWT configurations andidentify potential instabilities.2Copyright 2014 by ASME
Figure 3 - Analysis framework for the OWENS toolkitWhile existing commercially available multi-bodydynamics software could be adapted for the required VAWTanalyses, OWENS is developed to address the need for amodular, open source VAWT aero-elastic code to serve thewind research community. The modularity of the presentapproach also allows re-use of many existing analysis codecomponents, such as existing aerodynamics andhydrodynamics codes.The blades may be rotated into an arbitrary orientation atarbitrary locations about the tower. Therefore configurationswith swept blades may be considered. The VAWTconfiguration will be discretized from continuous structuralcomponents into a finite number of beam elements. Theimplementation also allows for concentrated structuralcomponents to be considered, and constraints of various jointsmay be imposed between structural components.VAWT MESH GENERATORA VAWT rotor consists of a tower, blades, and possiblysupport members (or struts). The blades may be affixed to thetower at their ends as in the Darrieus and V-VAWTconfigurations or via struts (H-VAWT). Struts may alsoprovide a connection between the tower and blades at anyposition along the tower and blade spans. The VAWTGenmesh generator has been created and is capable of generatingVAWTs of arbitrary geometry, including H-type, V-type, andDarrieus configurations (see Figure 4, from left to right: sweptDarrieus, Darrieus with struts, V-VAWT, and H-VAWT).FINITE ELEMENT IMPLEMENTATIONVAWTs are typically constructed of relatively slenderstructural components. Accordingly, Timoshenko beam theoryhas been utilized to characterize the motions of structuralcomponent. The equations of motion are developed for a beamelement of arbitrary orientation in a rotating reference frame.This reference frame is allowed to translate in order to accountfor platform or foundation effects. Rotational effects ofCoriolis and spin softening phenomenon are included in theformulation. More details of the finite element implementationas well as initial verification efforts are discussed inReferences [10] and [12] respectively.Figure 4 - VAWT configurations produced by VAWTGenWAVEC2WIRE MODULEFor a floating VAWT, the overall system dynamics aresignificantly influenced by the interaction of the platform withthe aquatic environment. To properly capture this interactionit is necessary to incorporate a hydrodynamic analysis codeinto the OWENS toolkit. With the goal being to develop anopen-source and modular toolkit, WaveEC2Wire was used asthe hydrodynamic module for this study. WaveEC2Wire is aMATLAB based numerical tool developed by Marco Alves atthe Wave Energy Center for the analysis of wave energyconverters (WECs) Error! Reference source not found. In3Copyright 2014 by ASME
order to interface with OWENS, WaveEC2Wire has beenmodified and restructured such that it functions as the platformhydrodynamics/mooring module shown in Figure 3.Additionally, to use WaveEC2Wire, results from a 3Dradiation-diffraction analysis are required for many of theanalysis steps. In this study WAMIT was used but anysufficiently capable analysis code is acceptable.As the hydrodynamic module of OWENS, WavEC2Wirecalculates the platform dynamics of the floating VAWT. Thisis done by applying Newton’s second law and equating thebody inertial force with the forces acting on the device (Eq. 1).̈( )( )( )( )( )( )( ) ( )](2)Then, a parametric model of the transfer function iscalculated using the least squares method. This model iscomputed in the frequency domain to eliminate additionalerrors introduced in calculation of the impulse responsefunctions. For each convolution in the convolution integral, astate-space representation is created using Eq. 3. These statesare used in the global state space system defined later. ) ̇( )(̃ ̇(1)where M is the platform inertia matrix, ̈ the platformaccelerations, Fpe are forces due to pressure differences on therigid body platform (i.e. purely wave-structure interactionforces), Fpto are forces from the power take-off conversionchain (PTO) which interact with the structure to produceelectrical power, Fm are mooring forces, Ff are friction forces,and Fapp are user defined applied forces. For use withOWENS, the PTO terms are removed and Fapp is defined asthe VAWT tower reaction forces which are provided fromOWENS through the coupling interface. WaveEC2Wireimplements a rigid body assumption for the platform andretains only DOF relating to rigid body motion. This isconsistent with other analysis codes [5] and consideredadequate as the turbine tower is significantly more flexiblethan the platform, rendering platform deformations negligible.The user defines the active DOF (eg. surge, sway, heave, roll,pitch, yaw) to be considered in the analysis.WaveEC2Wire utilizes a fully linear approach todetermine the wave-structure interaction forces. For offshoreplatforms in operating conditions, meaning non-storm seastates with low to medium amplitude waves, the linearassumption holds true and is consistent with other platformanalysis codes [5]. Utilizing the linear assumption, thecomplex amplitudes of the hydrodynamic diffraction (waveexcitation) and radiation forces are determined due to a unitaryamplitude incident wave as a function of frequency using a 3Dradiation-diffraction solver (WAMIT [16]). The excitationcomplex amplitude is then applied to the wave time history forthe desired incident environment to obtain the excitation forcetime history. WaveEC2Wire can calculate wave time historiesfor definitions of regular waves, JONSWAP or PiersonMoskowitz spectrums (directional or non-directional), and seawave measurements.The radiation force is calculated using a state-spaceapproach and is represented by a small number of first orderlinear differential equations with constant coefficients. Thisapproach uses the frequency dependent added mass anddamping coefficients as well as the infinite added masscomputed from WAMIT to calculate the frequency dependentradiation transfer function K(ω), (Eq. 2).[ ( )̇( )( )( )(3)The buoyancy force is calculated through the use of thehydrostatic coefficients which are provided by a 3D radiationdiffraction code (WAMIT). The inertia matrix is defined asshown in Eq. 4 below and can be either calculated by WAMITor input by the user.(4)[]where m is the mass of the platform; xg, yg, and zg coordinatesof the platform CG, and I## the moments of inertia of theplatform. All quantities are calculated for the platform onlyand contributions from the attached VAWT and tower areintroduced through the coupling interface.Other force terms consist of forces imposed by the PTOequipment, mooring system, and friction/drag. As mentionedearlier, the PTO system is deactivated and will not bediscussed here. Mooring forces and drag forces are calculatedusing user defined polynomial functions of platform positionand velocity. For this study, simple linear springs were usedto simulate the mooring stiffness as a function of platformdisplacement and drag was neglected. The mooring and dragforce calculations are currently an area of improvement andmore robust modules are being developed, as discussed in theFuture Work section.To solve the equation of motion, a global state-spacemodel is created. The size of the model depends on thenumber of convolution states and the number of active DOF inthe solution as shown below (Eq. 5).̇( )( )( )( )( )( )[[](5)[] [ ] [ ̇ ]]where xr1-rn are the convolution states, and ̇ are thedisplacement and velocity vectors respectively and Fapp areapplied forces. M’ is the mass matrix (Eq. 6).4Copyright 2014 by ASME
(6)[[]]where M is the mass matrix defined in Eq. 4 andis theinfinite added mass from WAMIT. A, B, and C are the statespace coefficient matrices (Eq. 7).[[[]][[]][][][][ ( )( )] [[][][ ]( ̇ )]](7)[ ]where ff and fm are the coefficients for the friction drag andmooring forces respectively. The system of ODEs representedin Eq. 5 is then solved using the MATLAB explicit ODE45Runge-Kutta ODE solver with initial conditions and time stepsdefined by OWENS. The solution contains state-space terms,as well as platform position, velocity, and acceleration whichare output from the WaveEC2Wire module to OWENS. Allresults are calculated in the platform body coordinate systemand transformed to the tower base in order to send to OWENS.Similarly, the external force from OWENS is transformedfrom the tower base to the platform CG for inclusion in theplatform equation of motion. As the transformation capabilitywas under development at the time of this study, it was chosento attach the tower to the platform CG, thus requiring notransformation.This was adequate to demonstrate thecoupling between codes and a finalized transformation routinehas been developed for future work. Results for each time stepare computed and sent to OWENS according to the couplingmethodology, described in the next section.COUPLING METHODOLOGYThe OWENS toolkit has been designed with ability tointerface with arbitrary modules that provide forcing during astructural dynamics simulation. There are a number of ways toconsider incorporating external forcing in the analysisframework. One approach, which has been termed“monolithic” [4] incorporates the solution for both the externalloads and the structural responses into a single system ofequations to be solved at each time step. Whereas thispotentially allows for structural dynamics and loadingcalculations to be performed simultaneously, the modularity ofthe framework is severely limited. This approach requires alldetails of loading calculations be implemented alongside thestructural dynamics code under a single framework, which canpotentially limit code development and collaboration efforts.Another approach considers “loose” coupling of modulesor sub-systems and provides a greater degree of flexibility andmodularity in the framework. The framework is no longermonolithic and knowledge of details of external modules isnot required by the core analysis framework. Instead, only thedata flow between the module and core analysis frameworkmust be defined. This approach has been illustrated in Figure 3for the OWENS toolkit. A specific example is that reactionforce at the base of a turbine will be provided to aplatform/hydrodynamics module that calculates the rigid bodymotions (translational and rotational) of a floating platformunder the influence of an attached, flexible turbine structure.The core analysis has no knowledge of the hydrodynamicscalculations being performed, and only requires the rigid bodymotions of the platform system to perform the coupledsimulation.The drawback of the loosely coupled approach is thatanalysis occurs in a staggered manner with motions/forces atprevious time steps being utilized to calculate solutions at acurrent time step. This can lead to potential stability concernsin the coupling procedure, and critical time step sizes must beconsidered to maintain a stable solution procedure.Furthermore, a loose coupling approach may have significantstability concerns for modules coupled through acceleration(mass matrix coupling).An improvement over the loose coupling procedureconsiders iteration at each time step, using a “predictorcorrector” approach. A popular approach is the Gauss-Seideliterative method [9], which is used to integrate WavEC2Wirewith OWENS. In this implementation, OWENS operates as adriver code and requests solutions from WavEC2Wire atspecified time increments.To maintain the modularenvironment, even though both codes are written inMATLAB, they are run in separate instances. To passinformation between the two MATLAB instances, networksockets are used as this approach is straight-forward andefficient for the transmission of small amounts of data. Uponstart-up OWENS launches WavEC2Wire with appropriateinputs (platform details, environment, file locations, etc) forWavEC2Wire to define the problem and pre-process anyrequired information. Once initialized, WavEC2Wire waits fora request from OWENS to solve an increment of thehydrodynamics problem. To request a solution, OWENSwrites the required input parameters (requested time step andinitial conditions) to the network socket, which is then read byWavEC2Wire. For each call, WavEC2Wire solves the systemof equations over the requested time step (Eq. 5) and reportsback the platform motions and accelerations to OWENS usinga similar network socket call. In OWENS, this information iscompared with the predicted results using a convergencetolerance to determine if iteration is required.If so,WavEC2Wire is called with a corrected set of inputs and theprocess repeats. If not, the solution is stored and OWENSmoves to the next time increment.5Copyright 2014 by ASME
PLATFORM AND MOORING DESIGNTo perform an initial platform design, topsidecharacteristics for a non-optimized 5MW Darrieus VAWT arecalculated by scaling existing Darrieus designs. The topsidemass is determined to be 973 mt, with a CG of 54.9m abovethe still water line. The roll and pitch moments of inertiaabout the CG are 1.35 x 10 9 kg-m2. The operating thrust loadon the turbine is 550.0 kN with a center of pressure 67.0 mabove the still water line. With these topside specifications,the following considerations are taken into account to size theinitial platform.1) The desired mean pitch angle is to be 5 deg2) The desired roll/pitch natural period is to be greaterthan 20 sec and less than 40 secUsing the OC3 Hywind spar as a baseline, a platform wasscaled to meet the desired performance criteria [3].The preliminary mooring design is based on the mooringfor the OC3 Hywind spar [6]. This system uses three equallyspaced catenary lines attached using a delta connection(Figure 6) to increase the mooring yaw stiffness. Each line ismade of varied segments and a clump weight.Mooring DetailPlan ViewTable 1 – Spar-buoy designSpar-Buoy DesignMass (with ballast)9050 mtDraft80 mMajor/Minor Diameter8.0/13.0 mCG below SWL63.5 mPitch/Roll Inertia about CG3.4 x 109 kg-m2Yaw Inertia about CG2.0 x 108 kg-m2With the given topside information, the performance ofthe unmoored spar-buoy is as follows. The mean pitch underthe 550 kN aerodynamic load is 4.4 deg. As the naturalperiods are influenced by the addition of a mooring system,they are described later.To perform the WAMIT analysis for this spar design, aquarter symmetric surface model mesh was prepared inMultiSurf [1] and is shown in Figure 5. The model wascreated using low-order geometry representation with 672waterline panels and 64 free surface panels to remove irregularfrequencies.Figure 5 - Spar geometry and surface mesh for WAMIT analysisFigure 6 – Spar-buoy mooring attachmentsThe mooring system was linearized using a mooringmodel in FAST by independently exciting a platform DOF andmeasuring the resulting mooring loads [6]. Results for all 6DOF are presented as the matrix of coefficients below.(8)[]In WavEC2Wire this matrix is multiplied by the platformDOF to determine the mooring forces for a given positiondisplacement. The inclusion of the mooring stiffnessinfluences the natural periods of the system, most notably dueto the strong coupling in surge/pitch and sway/roll. For themoored floating platform, the rigid body natural period inpitch/roll is 22.8 sec (0.044 Hz) and 29.0 sec (0.034 Hz) inheave.This linear mooring model represents a baseline for initialplatform design. More advanced mooring representations arecurrently under development including catenary equation andfinite element models. These capabilities will be integratedinto WavEC2Wire and allow more realistic simulations of theplatform and mooring configurations. Additionally, themooring system will be updated and tailored to the specificplatform and environmental conditions as detailed in FutureWork.6Copyright 2014 by ASME
PLATFORM DYNAMICS SIMULATIONThe topside is represented by a flexible tower structurewith the aforementioned rigid body properties (Figure 7). Forsimplicity, the tower is assumed to be mounted at the center ofmass of the platform via a fixed/clamped connection. Theflexibility of the tower will also influence the natural periodsof the system. In particular, the pitch/roll period will shortenslightly, as demonstrated in the next section.u3 (heave, yaw)Topsideu1 (surge, roll)u2 (sway, pitch)PlatformFigure 7 - Representative system for verification proceduresA Newmark-Beta implicit time integration method wasconsidered in the structural dynamics simulation with a timestep size of 0.1 seconds. To expedite the analysis, nonlineareffects were deactivated in the structural dynamics simulation.Furthermore, a reduced order model was employed in thestructural dynamics simulation which included only the first10 flexible modes of the tower structure. Although, the linearnature and reduced order of this structural model introducecertain approximations, the goal of this exercise is to verifycoupling between a structural dynamics module and platformhydrodynamics module regardless of the fidelity of theindividual modules.employed to couple the two simulations together, and aconvergence criterion of 1e-8 was enforced at each time stepfor iterations of the coupled structural dynamics and platformanalysis. Gravity was deactivated in these initial verificationprocedures.Additional tests were conducted that examined thecombined sway/roll (surge/pitch) response of the coupledplatform and structural dynamics analysis. Buoyancy effectswere verified by examining a coupled platform/structuraldynamics analysis under gravity and buoyant loads to confirmthe platform design behaved as intended under self-weight andweight of the attached structure. Finally, a full six-degree offreedom platform analysis was also considered with waveloading active. This exercise sought to verify the effect ofhydrodynamic forcing on the platform was also evident in thetower motion. Selected results are shown in the next sections.PLATFORM ROLL/PITCHThe roll and pitch motions of the platform were isolatedand all other rigid body motions of the turbine wereconstrained. Due to the axisymmetric nature of the platformand attached representative topside, roll and pitch verificationtests are identical. First, the platform step relaxation inroll/pitch was considered. Second, an excitation force wasapplied in the sway/surge direction (u2/u1) to the tower top fora configuration with an initially stationary platform. Theplatform and structural motions were inspected for consistencyin frequency content as well as periodicity, indicating energyis being conserved during the coupling scheme.To perform the step relaxation, the platform wasdisplaced at a roll angle of 0.1 radians with all other rigid bodymodes of the platform deactivated. The attached flexibleturbine structure was initially at rest. At t 0 the platform wasreleased and hydrodynamic restoring/mooring forces resultedin harmonic motion of the platform as well as the attachedtower structure. The response of the simulation is simulatedfor two minutes. Figure 8 shows the time history and FFT ofplatform roll motion and tower tip displacement in the u2direction.VERIFICATION PROCEDURESVerification procedures considered the isolated motion ofindividual platform surge, sway, heave, roll, pitch, and yawrigid body degrees of freedom. First, step relaxations of eachplatform mode were considered and the influence of platformmotion on the response of the flexible structure attached to theplatform was observed. Next, an excitation force was appliedto the flexible structure, and the response of the platform wasobserved. Fast Fourier Transforms (FFTs) of the platform andstructural response were observed in each case and thefrequency content of platform and structure were checked forconsistency. Furthermore, all damping mechanisms weredeactivated from the platform module (radiation damping,drag, etc.) and no structural damping was applied to theflexible structure. This verified energy was not beingdissipated by the numerical time integration schemes or thecoupling procedure. The Gauss-Seidel iterative method wasFigure 8 - Roll/Pitch Step Relaxation Results7Copyright 2014 by ASME
Periodicity of the platform motion as well as the towermotion is observed, indicating the coupling scheme andnumerical integration schemes are not spuriously dissipatingenergy. Frequencies of 0.050 and 0.41 Hz are observed in thetower motion, the former being representative of the lowfrequency platform motion and the latter being representativeof the tower structural vibration. Furthermore, a frequency ofthe 0.050 Hz is observed in the platform motion. Closerinspection of the FFT of platform motion reveals a smallirregularity in the smooth FFT distribution around 0.41 and1.59 Hz. This suggests there is some impact of the structuralmotion on the frequency content of the tower although theforcing as a result of structural vibration is minimal comparedto restoring forces acting on the platform.For the second test the tower structure was excited byapplying a force of 1e7 N for 1 second to the tower top in thesway direction to excite a roll rotation of the platform. Theplatform was initially stationary in this verification exercise.After 1 second, the excitation force was removed and thenatural response of the system was observed. Figure 9 showsthe time history and FFT of platform roll motion and tower tipdisplacement in the u2 direction.restoring forces acting on the platform and the lowerfrequency platform motion.COMBINED SWAY AND ROLLThe combined sway/roll and surge/pitch motions of theplatform were isolated and all other rigid body motions of theturbine were constrained. First, a platform step relaxation insway was considered. Second, an excitation force beingapplied in the sway/surge direction (u2/u1) to the tower top fora configuration with an initially stationary platform. Resultsfrom the step relaxation test are shown below.The platform was displaced in sway/surge a distance of 1meter with all other rigid body modes of the platformconstrained to zero. The attached flexible tower was initiallyat rest. At t 0 the platform was released and hydrodynamicrestoring/mooring forces resulted in harmonic motion of theplatform swa
energy an attractive opportunity, the cost of energy (COE) of offshore wind projects must be reduced to make offshore wind a viable option. As over half of the capital investment in offshore wind is in the balance of station costs (Figure 1), reducing these expenditures could greatly reduce the COE for these projects.
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