Article Validation of a Tool for the Initial Dynamic Design of Mooring Systems for Large Floating Wave Energy Converters

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1 Journal of Marine Science and Engineering Article Validation of a Tool for Initial Dynamic Design of Mooring Systems for Large Floating Wave Energy Converters Jonas Bjerg Thomsen *, Francesco Ferri and Jens Peter Kofoed Department of Civil Engineering, Aalborg University, Thomas Manns Vej 3, 9 Aalborg Ø, Denmark; ff@civil.aau.dk (F.F.); jpk@civil.aau.dk (J.P.K.) * Correspondence: jbt@civil.aau.dk; Tel.: Received: May 7; Accepted: 3 September 7; Published: September 7 Abstract: Mooring of floating wave energy converters is an important topic in renewable research since it highly influences overall cost of wave energy converter and reby cost of energy. In addition, several wave energy converter failures have been observed due to insufficient mooring systems. When designing se systems, it is necessary to ensure applicability of design tool and to establish an understanding of error between model and prototype. The present paper presents outcome of an experimental test campaign and construction of a numerical model using open-source boundary element method code NEMOH and commercial time-domain mooring analysis tool OrcaFlex. The work used wind/wave energy converter Floating Power Plant as a case study, which is defined as a large floating structure with a passive mooring system. The investigated mooring consists of a three-legged turret system with syntic lines, and it was tested for both operational and extreme events. In order to understand difference between model and experimental results, no tuning of model was done, besides adding drag elements with values found from a simplified methodology. This resembles initial design cases where no experimental data are available. Generally good agreement was found for tensions in lines when drag element was applied, with some overestimation of motions. The main cause of difference was found to be underestimation of linear damping. A model was tested with additional linear damping, and it illustrated that a final analysis needs to use experimental data to achieve best results. However, analyses showed that investigated model can be used without tuning in initial investigations of mooring systems, and it is expected that this approach can be applied to or similar systems. Keywords: wave energy; mooring; numerical; NEMOH; OrcaFlex; validation. Introduction During last few decades, large focus on renewable energy sources has led to suggestion of many different types of devices for harvesting energy. A number of se are wave energy converters (WECs), which use different principles for harvesting wave energy. Despite comprehensive research, wave energy sector is still not in a commercial state, and above all, re is a need to reduce levelized cost of energy (LCOE). WECs vary greatly in size and structure, with some of devices considered as being large floating structures. These form basis for present study, with examples of such structures being Floating Power Plant [], KNSwing, LEANCON Wave Energy [] and Wave Dragon [3]. Naturally, floating structures like se need a system to ensure station keeping, which is often solved by using mooring systems. Based on working principle of power take off (PTO) of WEC, mooring system can eir be considered passive, meaning that it does not take part in power absorption, or it can be considered active or reactive if it J. Mar. Sci. Eng. 7, 5, 45; doi:.339/jmse5445

2 J. Mar. Sci. Eng. 7, 5, 45 of 3 affects PTO [4]. Common for type of structures considered in this study is use of passive mooring systems. Moorings highly affect survivability and cost of floating WECs, since even a partial failure of this system can result in a total loss of device. In addition, cost of moorings has proven to take up a large part of total structural cost [5,6] and is, refore, vital to investigate and improve in order to lower LCOE. Despite a large experience in mooring design from or offshore sectors, a large number of WECs deployed offshore have failed due to insufficient moorings [5]. This can partly be explained by a tendency to apply mooring principles from traditional oil and gas sector with a catenary system of mooring chains. Studies like, e.g., [7 9] show not only that a chain results in a very stiff system with resulting high loads, but also that re could be a great potential for cost reduction in application of syntic lines. As a result of this, developers of mentioned WECs now consider this as a relevant mooring solution. Consequently, re is a great need for research into cost and reliability optimization of moorings. A method must be defined that can be used by similar WECs to make an initial investigation of mooring response. In order to secure survivability of mooring and structure, system must be designed to survive in all relevant conditions, and refore, design parameters like tensions and motions need to be evaluated. According to standards like, e.g., [ ], it is particularly important to ensure survival in extreme conditions, which is why extreme conditions are focus of this research. During se conditions, PTO of mentioned WECs will be in safety mode and is, refore, not necessary to consider in design. A method to identify parameters must be established eir by use of laboratory experiments or by numerical models. Commonly, a test campaign is initiated to provide data on motion and tension response of mooring, which is n used for validation of a numerical model. This allows for tuning of model so that good agreement between experiments and numerical model is achieved for tested sea states, mooring layout and model geometry. For instance, [3] presents a methodology for optimization of numerical model of a WEC, and a similar one is seen in, e.g., [4,5], which considers floating wind turbine platforms, aims to prove validity of numerical models and tunes m to available experimental tests. For many early stage WECs, however, experimental data are not available, and re is a need for understanding mooring system behavior prior to performing tests. It often happens that WECs experience changes during design phases, which gives a need for new and expensive tests. It is, refore, essential to have a model that can be used in initial studies of potential of different mooring layouts and materials, even without access to experimental data. Where studies like, e.g., [3 5] tune model to fit experimental results, present paper tends to validate a numerical tool according to definition of validation in [6] and identifies errors and ir magnitude without tuning it to experimental work. The focus is put on validating design values such as tensions and to some extent, motions, as se determine applicability of a certain mooring layout. This should justify use of an identical procedure for analyzing and designing initial mooring systems for or large floating WECs where no experimental data are available. For final design, it is still recommended to perform tests and to optimize model to get a better agreement with experiments. In order to illustrate this, an additional optimized model was produced and compared to experimental data. The research uses Floating Power Plant as a case study, cf. Figure. This device combines wind and wave energy absorption and has been undergoing comprehensive research in small-scale tests in laboratories followed by an offshore test campaign with a 37 m-wide model. In future research, two different models will be considered: a 6 m-wide model named P6 and a full-scale 8 m-wide model named P8. This paper will consider P6 device, illustrated in Figure, and sea states from expected deployment site at Belgian coast. The WEC is constructed from a floating foundation (indicated by red color in Figure ), a wind turbine and four wave energy absorbers (blue color), which utilizes principle of pitching bodies.

3 J. Mar. Sci. Eng. 7, 5, 45 3 of 3 PTO Figure. Illustration of Floating Power Plant P6 device. The red color indicates foundation, and blue color indicates floaters (power take off (PTO)). The paper uses laboratory experiments performed at The Hydraulic and Coastal Engineering Laboratory at Aalborg University, Denmark, for a structure resembling a simplified model of Floating Power Plant P6 where wave energy PTO and wind turbine are discarded. The structure is moored with compliant syntic lines, and acquired results are compared to numerical results found by using open source code NEMOH [7] and commercial software package OrcaFlex v.d (Orcina Ltd., Ulverston, UK) [8]. The paper is structured with five sections including this Introduction. The following section presents applied method in laboratory experiments and numerical model, and it is followed by a section presenting results from both. Section 4 includes a discussion of results, and Section 5 will present conclusions and discussion of future work.. Method This section and its subsections provide an introduction of method used for modeling of floating structure and its mooring system. It is followed by a short description of setup used during laboratory experiments, and more information, description and analysis of laboratory experiments can be found in [9]... Design and Modeling of Floating Structures with a Mooring System There are different design standards available with requirements and recommendations for design of mooring systems. Among most commonly recognized are DNV-OS-E3 [], API-RP-SK [] and ISO 99-7:5 []. IEC 66- [] has been developed for mooring design for marine energy devices, while DNV-OS-J3 [] deals with general design of floating wind turbines. The design procedure often requires evaluation of extreme response and validation according to extreme tensions in mooring lines. A time series of an extreme sea is evaluated and extremes identified, and data are fitted to a statistical distribution. The requirements of motions are not as defined as for tensions and must be decided based on given location, umbilical specifications, surrounding structures, etc. Different methods can be applied for generation of desired time series. One method includes use of experimental tests, which provide highly useful results, but are time consuming and potentially expensive. A design procedure is an iterative process and often implies investigation of many different configurations before most optimized solution is identified. A more common

4 J. Mar. Sci. Eng. 7, 5, 45 4 of 3 approach is to apply numerical models, as se are easier to automatize, more changeable and, hence, much less expensive to use. However, it is necessary to validate that extremes found in models resemble realistic values, for which experimental data are used. Model validation against experimental data has been done in [3] for a WEC and by several authors like, e.g., [4,5,,3] for floating wind turbine platforms, mainly considering waves and not coupled effect of wind and wave exposure. Different models can be used when simulating wave-structure and device response numerically. The most commonly-used models are Morison approach, boundary element method (BEM), computational fluid dynamics (CFD) or smooth particle hydrodynamics (SPH). Both CFD and SPH put high demands on computational effort; hence, BEM or Morison approach are more often used. Many of se models determine wave/structure interaction, while additional code is needed to simulate coupled response of mooring and structure. The BEM includes load contribution from diffraction and radiation, while Morison approach includes drag and inertia. The choice, refore, depends on sea states in relation to structure. Often, diagram by Chakrabarti [4] is used, cf. Figure 7c. This study uses a modeling procedure as shown in Figure. The open source BEM code NEMOH [7] is applied for calculation of wave-structure interaction in frequency domain, which implies linear potential ory with assumptions of an inviscid, incompressible and irrotational fluid. In addition, ory assumes incoming waves with low steepness and also structure motions with small amplitudes [7]. Particularly, two last assumptions are put under stress for a WEC with compliant mooring in extreme sea conditions. The output of BEM code is first order wave excitation force F exc (ω), added mass A(ω), radiation damping B(ω) and Kochin functions H(θ, ω). The latter is used to calculate second order drift force coefficients using far field formulation [5] and code available from [6]. The results from BEM code are coupled with dynamic analysis tool OrcaFlex [8], which solves coupled behavior of mooring system and floating structure in both time and frequency domain. The model includes first order wave excitation force and second order slowly-varying contribution. In this study, Newman approximation [7] is applied for calculation of second order motion, which implies that only mean drift force, calculated from first order quantities, is used to calculate second order response. The OrcaFlex package allows for using full quadratic transfer functions (QTFs), but this has not been considered in this study. It is stated in [8] that accuracy of Newman approximation decreases with shallow water depths and also if natural frequencies are within frequencies of wave spectrum. The latter does not cause any concerns as it will always be attempted to design a floating system to have natural frequencies outside wave spectrum of extreme seas. In present study where very large compliance is applied, this problem is even less considerable. Mesh geometri F exc (ω) A (ω) Frequency-dependent wave excitation force Frequencydependent added mass B (ω) Frequency-dependent radiation damping NEMOH Frequency-dependent hydrodynamic coefficients F exc (ω), A (ω), B (ω), H (θ, ω) BEM H (θ, ω) C D (ω) Frequency- and angle-dependent Kochin function Frequency-dependent mean drift force coefficient K hyd, M, H s, T p Drift force coefficient C D (ω) K hyd M H s Structure hydrostatic stiffness matrix Structure mass matrix Significant wave height OrcaFlex Time domain simulation T (t), x (t) T p T (t) x (t) Peak wave period Time-dependent line tension Time-dependent structure motions Figure. Illustration of numerical modeling procedure used in present study. OrcaFlex has potential to calculate response using eir a radiation/diffraction approach or Morison approach. It is expected that use of linear potential ory to include

5 J. Mar. Sci. Eng. 7, 5, 45 5 of 3 radiation/diffraction loads will provide a certain level of accuracy, but drag contribution will be needed, particularly at resonance frequencies. By combining two contributions by adding a drag element to radiation/diffraction calculation, it is possible to obtain a better description. This requires knowledge of drag coefficient C d, which can eir be obtained experimentally or by, e.g., CFD calculations. For cases where this is not possible, a coarse estimate must be suggested. In order to illustrate need and effect of this drag element, two configurations were defined for numerical model: Configuration : Radiation/diffraction without a drag element. Configuration : Radiation/diffraction with drag elements in surge, heave and pitch. The drag coefficients were estimated from a simplified methodology, where model was divided into a number of simpler shapes (cubes and ellipsoids), as shown in Figure 4e, for which drag coefficients are known and can be found in, e.g., [8]. The total drag coefficient for model was n determined by combining coefficients from each shape, which n provided a very coarse estimate, as it does not account for interaction between each shape. This methodology does not require use of experiments or advanced CFD simulations and is, refore, applicable for initial design. The numerical model allows for definition of drag in all degrees of freedom (DoF) by a drag coefficient in translational DoFs and a drag moment coefficient in rotational DoFs. The drag moment coefficient was found with respect to center of gravity using simplified shapes and corresponding moment arms. The drag coefficients and areas are defined in Table. Table. Definition of drag coefficients and areas used in numerical model. Parameter Surge Heave Pitch Drag coefficient, C d Drag area, A d m.9 3 m m 5.. al Setup The experiments were conducted in deep-water basin at The Hydraulic and Coastal Engineering Laboratory at Aalborg University, Denmark, in period of December 5 January 6. The wave basin was equipped with a snake-type wave maker at one end, controlled by software package AwaSys 7 [9], and a passive absorber at or end (gravel beach). Five resistant-type wave gauges were used for measurements of surface elevations. The array was located in front of model, and its layout allowed for 3D reflection analysis. Acquisition, post-processing and analysis of water surface elevation and mooring loads were performed with software package WaveLab 3 [3] and sampled at a frequency of 3 Hz. The motions of structure were measured using OptiTrack system [3], five reflective markers (cf. Figure 4) and four OptiTrack Flex 3 cameras. The Motive.9. software package was used for data acquisition and analysis. The choice of scale for model was based on specifications of basin. A range of full-scale sea states and a certain water depth were specified prior to test campaign, cf. Section... In order to satisfy all conditions, it was found feasible to use a Froude scale of :64.5. This corresponds well to recommendation in [3,33], which states that scale factors of :5 and up to :8 can be used when testing loadings under extreme conditions. The basin setup is illustrated in Figure 3.

6 J. Mar. Sci. Eng. 7, 5, 45 6 of 3 Wave maker Wave gauges.5 Model Absorbing beach.7 z x Figure 3. Illustration of experimental setup in wave basin. All measurements are in m. The laboratory model resembled a simplified geometry of Floating Power Plant P6. For simplification, it was decided to discard both wind turbine and floaters and instead apply ir mass at foundation. In extreme events, it is expected that loads from wind on turbine are negligible compared to wave loads, since wind turbine will be shut down, and effective area is much smaller compared to when it is in operational conditions. Despite large wind speeds, loads on structure will be smaller, justifying that turbine is neglected. Naturally, position of turbine mass will affect mass moment of inertia (MoI), giving larger values. Considering purpose of validating numerical model, it is merely important to ensure similarity between laboratory model and numerical model, hence discarding wind turbine and floaters do not affect overall purpose of study. Figure 4a,b illustrates dimensions of model in full scale, while Figure 4c shows constructed laboratory model. In numerical model, laboratory layout was adapted, and a panel mesh shown in Figure 4d was constructed and analyzed. A convergence analysis was performed in order to justify number of 768 panels (a) (b) (c) (d) Figure 4. (a) Side view of laboratory model at prototype scale (measurement in m); (b) front view of model; (c) picture of laboratory model; (d) illustration of mesh used in BEM code; (e) simplified geometry used for estimation of drag coefficients. (e)

7 J. Mar. Sci. Eng. 7, 5, 45 7 of 3 The structural parameters of lab model were measured in laboratory, and values were subsequently used in numerical model. In particular, model mass and mass moment of inertia (MoI) are of importance in order to model motion response correctly. Table lists measured and prototype values. Table. Model specification. Note that moment of inertia (MoI) is around center of gravity. Parameter Model-Scale Full-Scale Structure mass, m (kg) Moment of inertia, I xx (m kg) Moment of inertia, I yy (m kg) Moment of inertia, I zz (m kg) Mooring System The mooring was applied as a standard solution with three taut syntic lines installed as shown in Figure 5a. Despite a different shape of stiffness curve, linearized stiffness of lines corresponds approximately to, e.g., Ø mm Bridon Superline Nylon [34]. Three load cells of type FUTEK LSB 5/ lb. were installed at connection point between anchor and lines, and a VETEK 3 kg IP68 was positioned at connection point between lines and model, cf. Figure 5. A static test determined stiffness of lines where each line was gradually tensioned and elongation measured. The stiffness curve is plotted in Figure 5b, showing mild non-linearity. The mooring system in numerical model was defined with experimentally-measured values of line stiffness and layout. The drag and inertia coefficient of lines were chosen based on standard values from DNV-OS-E3 []. Table 3 provides data on mooring line characteristics found in laboratory and applied in numerical model. No structural damping in lines was defined in numerical model, as se values are unknown. The mooring lines in numerical model are divided into a number of segments and modeled as straight massless segments. All properties like mass, buoyancy, etc., are lumped to nodes at each end, while axial and torsional properties are modeled by segments. A higher number of segments, n, generally provides a higher level of accuracy to model, but is paid by higher computational time. In order to find number of segments that balances accuracy and computational time, a convergence analysis was performed and presented in Figure 6 with number of segments ranging from 5 3. The figure presents error between tensions found from each test and test with maximum number of segments. A relatively small error is found (less than %), and results clearly converge with n 5. The largest error is found for tension minimums where lines are slacked. However, minimum tensions are not of significant importance for design of moorings, and for n 5, error becomes less than 5%. Based on this, n = 5 was used in numerical model, resulting in a segment length of 3 m. Table 3. Mooring line specifications. Parameter Model-Scale Full-Scale Unstretched length (m) Nominal diameter d (m)..6 Mass (kg/m) Number of segments n (-) 5 Segment length (m) - 3 Drag coefficients (axial/normal) (-)./.6 Inertia coefficients (axial/normal) (-)./.

8 J. Mar. Sci. Eng. 7, 5, 45 8 of Rear 5 Starboard (-5.4, 36.4, -4.9) Portside (-5.4,., -4.9) Load (kn) 4 3 (-5.4, -36.4, -4.9) Extension (%) (a) (b) Figure 5. (a) Illustration of considered mooring layout. The green shapes illustrate load cells. (b) Mooring line stiffness curve determined during experiments. The values are presented at full scale. n = 5 n = n = 5 n = n = 5 n = T max Tension (kn) Tmax & Tmean error (%)..5 T mean T min 4 Tmin error (%) Time (s) (a) Number of segments (b) Figure 6. (a) Time series of segment convergence analysis with a zoom on maximum and minimum tensions; (b) error of each analysis compared to test with maximum segment number. Note different y-axes. The mooring lines were installed with an axial pretension of approximately 35 kn, cf. Figure 8a,b. This tension results from a relatively small extension of lines (cf. Figure 5b), which caused slacking of lines during wave exposure.... Environmental Conditions The tested sea states resemble conditions expected at deployment site of P6. Three operational (H s = m and T p = s) and six extreme (H s = m and T p = s) sea states were tested in order to ensure that expected range of wave frequencies and wave heights were covered; see Figure 7a. The sea states were simulated as long-crested waves (D) and with a JONSWAP spectrum (peak enhancement factor γ = 3.3). The duration of individual time

9 H s / (g T p ) J. Mar. Sci. Eng. 7, 5, 45 9 of 3 series was determined so that it allowed for a number of simulated waves according to recommendations in [33]. In addition to irregular sea states, 3 regular wave trains were tested. Considering application areas of wave ories as defined in [35] and plotted in Figure 7b, x-axis shows that waves primarily will be in intermediate water depths with some of tested waves in deep water conditions. The y-axis indicates variation of steepness of waves. It is seen that all sea states can be considered non-linear, hence stressing assumption of linear wave potential ory. As described, dominating force contribution is highly dependent on structure diameter in relation to wavelength. Considering boundaries defined in [4] and plotted in Figure 7c, it is seen that, when considering entire structure as one closed body, most of sea states are in load regime where diffraction is dominant. For longest waves, model will be in a regime where or load contributions have an effect. The investigated structure has a complex geometry where water can pass through body, which truly does not follow ory of [4]. Considering, e.g., just width of each of vertical columns (cf. Figure 4), force might be dominated or affected significantly by more than diffraction. Hs (m) Shallow Intermediate E6 E4 E Cnoidal ory H/h d =.78 5 th order stream function ory H = H B /4 H L /h 3 = 6 H/L =.4 Deep Stokes 4 th order Stokes 3 rd order E5E E3 Stokes nd order Linear ory f p (s) (a) h d / (g T p ) (b) (c) Figure 7. (a) Diagram of sea states simulated in wave basin; (b) sea states plotted against depth condition (x-axis), wave steepness (y-axis) and application areas of wave ories as defined in [35]; (c) sea states plotted against wave force regimes as defined in [4], with D being total width of structure and not considering open spaces.

10 J. Mar. Sci. Eng. 7, 5, 45 of 3 3. Results This section presents results obtained from numerical model and experimental work. These results will be compared to each or and used to investigate validity of numerical model. 3.. Quasi-Static Results A quasi-static test was carried out for validation of mooring layout and modeling of line tension. The model was displaced in surge DoF at a low velocity in order to avoid any dynamic effects. Due to low velocity, only restoring force present in system resulted from stiffness of mooring lines. Figure 8a,b plots measured loads in respectively starboard and rear mooring line. The experimental results show some scattering of results, which can be explained by fact that model was displaced manually. When model is displaced, mooring point will displace vertically as shown in Figure 8c, and this displacement is very sensitive to physical handling of model. For a perfect test with no displacement in any or DoF than surge, scatter would not be expected. Prior to measurement, one load cell was damaged; refore, results from port side line cannot be presented. It would have improved reliability of tests since both lines should have shown similar results. 3 Starboard Line 3 Rear Line 5 Exp. Num. 5 Exp. Num. Line Tension (kn) 5 5 Slacked Pretension Line Tension (kn) 5 5 Pretension Slacked Horizontal excursion (m) (a) Horizontal excursion (m) (b) Actual line layout during displacement Figure 8. Quasi-static test results for experimental (Exp.) and numerical (Num.) line tension in starboard (a) and rear (b) line; (c) illustration of line layout during surge motion. (c) When observing Figure 8, it is seen that numerical results are within scatter of experimental results, and refore, this illustrates similarity of mooring stiffness in two models. The difference, which is seen to be approximately constant, can be explained by tactile inaccuracy in physical handling of model as described previously. The most dominant difference is seen when lines are slacked where numerical tension is higher than experiments. In laboratory, no tension was measured in completely slacked lines, while some tension was found in

11 J. Mar. Sci. Eng. 7, 5, 45 of 3 numerical model. This is because lines are buoyant and give some tension in connection point. This effect was not seen in laboratory, possible due to presence of load cells. 3.. Decay Test A decay test was used to compare natural frequencies of and damping in two models. The test is performed by giving a displacement in one DoF, releasing model and allowing motion to decay. Due to complexity of model, it is difficult to activate only one DoF at a time, and hence, it is difficult to find natural frequencies for all DoF. The test presented a coupled frequency at.78 Hz where structure was activated in surge, heave and pitch. It was possible to activate only surge DoF in both numerical and experimental tests, even without applying any restraints on or DoFs. This means that even though primary motion was in surge DoF, some motions were also seen in heave and pitch, cf. Figure 9c. Since scale of experiments was :64.5, magnitudes of heave and pith motions are negligible compared to surge (less than 4 mm in laboratory). It was not possible to obtain any reliable results for heave and pitch only. The surge decay test is illustrated in Figure 9a for configurations with and without drag element. Num.: Config Num.: Config decay Config decay Config decay.5 Num.: Config Num.: Config linear regression Config linear regression Config linear regression Surge (m) - ( Tm log an ) a n Time (s) an 3 Tm (a) (b) Heave (m) & Pitch (deg) - Heave Pitch Time (s) Figure 9. (a) Free surge decay test from experiments and Configurations and (with and without drag element); (b) determination of linear and quadratic damping coefficients using linear regression [36]; (c) heave and pitch motion during surge decay test. (c)

12 J. Mar. Sci. Eng. 7, 5, 45 of 3 In decay test, structure moves at its natural frequency f n, and motion is dependent on structure mass M, added mass A, radiation damping B, hydrostatic stiffness K hyd and mooring stiffness K moor. The peaks and troughs of motion in Figure 9 were detected and used to calculate natural frequency as average of values. The first oscillation was not considered in order to avoid influence of releasing model. Since structure itself does not provide any hydrostatic stiffness in surge, natural frequency is mostly dependent on mass, added mass and mooring stiffness. The mass defined in numerical model is based on mass measured in laboratory and, refore, does not affect comparison. When considering quasi-static test, it was determined that re was good agreement between numerical and experimental stiffness. Therefore, difference in two natural frequencies mostly describes any inaccuracies in calculated added mass in BEM solver. Considering results in Table 4, it is however found that error is approximately 7% for Configuration, while it is 4% for Configuration, and as such, results can be considered acceptable. Table 4. Measured and calculated natural frequency, linear and quadratic damping in surge, toger with relative error. Parameter Num.: Config Num.: Config Value/Relative Error Value/Relative Error Natural surge frequency, f n.35 Hz.84 Hz/6.9%.93 Hz/3.9% Linear damping, p.64 s.4 s /97.6%.4 s /97.6% Quadratic damping, p.59 m.4 m /95.4%.378 m /7.% The decay test can additionally be used to illustrate damping of system, which is combination of a linear and quadratic contribution. Figure 9 clearly shows that numerical model highly underestimates this fact, with largest difference occurring for Configuration. In [36], Equation () is used to determine linear and quadratic damping coefficients p and p. T m log ( an a n+ ) = p a n T m p () where T m is natural period and a n is amplitude of n-th oscillation. When plotting left-hand side of equation against right-hand side, it is possible to use linear regression to calculate p and p. This is illustrated in Figure 9b, and results are listed in Table 4. Due to a limited number of oscillations in experimental decay test, linear fit is not as good as for numerical results. When considering Table 4, it is clear that numerical model in Configuration highly underestimates quadratic drag arising from viscous effects. An error of 95.4% is seen, which is reduced to 7.% in Configuration by adding drag element. Since no additional linear damping is added to model, similar results are obtained from two configurations with a relatively high error of approximately 98%. Section 3.5 presents an optimized model with additional linear damping in order to illustrate its influence on obtained results Regular Sea States A total of 3 regular sea states were tested (cf. Figure 7a) and used to determine response amplitude operators (RAOs) for motions, tensions and mean drift motion Motion Response The motion was measured in surge, heave and pitch. and ir RAOs are plotted in Figure, toger with numerical results.

13 J. Mar. Sci. Eng. 7, 5, 45 3 of 3 J. Mar. Sci. Eng. 7, 5, x 3 of 3 Considering results from Configuration (Figure a c), re is some agreement with Considering results from Configuration (Figure a-c), re is some agreement with experiments for most of frequency range in all DoFs, showing similar shape and amplitude experiments for most of frequency range in all DoFs, showing similar shape and amplitude of RAOs. Both numerical and experimental RAOs show peak at coupled motion frequency of RAOs. Both numerical and experimental RAOs show a peak at coupled motion frequency at at Hz, Hz, but but at at this this frequency, frequency, most most severe severe difference difference is is observed. observed. Due Due to to resonance resonance motion motion and and lack lack of of damping, damping, most most stress stress is is put put on on linear linear potential potential ory, ory, and and numerical numerical model model highly highly overestimates overestimates motion motionamplitude. For ForConfiguration (Figure d-f) d f) with withaa drag dragelement elementininall all DoFs, DoFs, better betteragreement agreementbetween between experimental and numerical results is isobtained, even evenat at peak peak of of RAOs. Still, Still, re reisisan an overestimation, but error is decreased. Num.: Config Num.: Config Configuration Surge RAO (m/m).5 Heave RAO (m/m).5 Pitch RAO (deg/m) Configuration Surge RAO (m/m).5 Heave RAO (m/m).5 Pitch RAO (deg/m) Figure. Measured and calculated motion response amplitude operators (RAOs) in surge, heave and Figure pitch.. Measured and calculated motion response amplitude operators (RAOs) in surge, heave and pitch Mean Drift Mean Drift Figure presents results for calculated and measured mean drift motion. In numerical Figure presents results for calculated and measured mean drift motion. In numerical and experimental model, mean drift during wave exposure is defined as mean displacement and experimental model, mean drift during wave exposure is defined as mean displacement from static position. Considering entire frequency range, both over- and under-estimations from static position. Considering entire frequency range, both over- and under-estimations are seen, and due to large error in motion amplitudes at peak frequency, Configurations are seen, and due to large error in motion amplitudes at peak frequency, Configurations provides paramount drift motion errors at this frequency. A very large underestimation is seen with provides paramount drift motion errors at this frequency. very large underestimation is seen with even negative drift, while drift at remaining frequencies shows a similar trend as for even negative drift, while drift at remaining frequencies shows a similar trend as for experiments. Despite better resemblance with experiments, Configuration also shows some experiments. Despite better resemblance with experiments, Configuration also shows some deviation from experimental results. Considering Figure, it is seen how drift motion is deviation from experimental results. Considering Figure, it is seen how drift motion is overestimated at lowest frequencies and underestimated for many of higher frequencies, overestimated at lowest frequencies and underestimated for many of higher frequencies, but with a trend following trend of results. Despite this error, motion amplitudes were

14 J. Mar. Sci. Eng. 7, 5, 45 4 of 3 shown in Figure to resemble experiments. Therefore, error in drift has proven not to affect motion amplitude significantly. Num.: Config Num.: Config Configuration Configuration.5.5 Mean drift (m/m) Figure. Measured and calculated drift motion RAOs for two configurations Tension Response Considering difference in measured and calculated motion response, especially in drift motion, some error was expected in calculated tensions, which are plotted in Figures and 3. Overall, numerical model shows good agreement with experiments, but with a high overestimation of tension around peak frequencies in Figure 3, a consequence of high overestimation of motions. As expected, this is most dominant for Configurations (Figure 3a,c). For low frequency waves, tension amplitudes are underestimated, but considering Figure, which presents a direct time series comparison between experiments and Configuration, peaks of tension time series are similar for both models, indicating that numerical model describes maximum values well. A difference can be observed between tension troughs in figure, which explains smaller amplitudes. 8 Num.: Config Starboard Tension (kn) Time (s) Figure. Direct comparison of measured and calculated tension time series for a regular sea state with H = 5. m and T = 8. s.

15 J. Mar. Sci. Eng. 7, 5, 45 5 of 3 J. Mar. Sci. Eng. 7, 5, x 5 of 3 Num.: Config Num.: Config Configuration Configuration Starboard Line tension RAO (MN/m) Rear Line tension RAO (MN/m) Figure 3. Measured and calculated tension RAOs in starboard and rear lines. Figure 3. Measured and calculated tension RAOs in starboard and rear lines Influence from Wave Height Influence from Wave Height As seen in Figure 7a a number of regular sea states covered a similar wave frequency with As seen in Figure 7a a number of regular sea states covered a similar wave frequency with varying wave heights in order to investigate non-linearities in response of structure. Figure 4 varying wave heights in order to investigate non-linearities in response of structure. Figure 4 illustrates motion RAOs and mean drift against wave height for se experiments and illustrates motion RAOs and mean drift against wave height for se experiments and Configuration. For surge DoF, numerical and experimental results show similar tendencies, Configuration. For surge DoF, numerical and experimental results show similar tendencies, but numerical model overestimates response. For shortest waves ( f =. Hz), re is but numerical model overestimates response. For shortest waves ( f =. Hz), re is good good agreement agreement independent independent of of wave wave height, height, but but a large large error error is is seen seen at at Hz Hz for for lowest lowest wave wave height. height. This This frequency frequency corresponds corresponds to to peak peak seen seen in in heave heave and and pitch pitch DoF DoF (cf. (cf. Figure Figure ). ). The The numerical numerical response responseisisseen seento tobe bealmost linear in surge, but but experiments experimentsshow showa anon-linear influence influencefrom fromwave waveheight. The Theresponse in in heave DoF illustrates non-linearity, andit itisis highly influencedbyby wave wave frequencies. The Thetendencies found in in experiments and numerical modelare are similar, and and magnitude of of difference seems independent of wave height. A similar observationisis foundfor for pitch DoF, with good agreement for shortest waves where smallest motionsare are present. More dominant errors are found at natural frequency and for longest waves wherea a large response will occur. The Thefigure clearly indicates that calculated RAOs are highly influencedby by incoming wave height, and andnot notlinearly dependent on it. The magnitude of deviation between numerical and and experimental results seems more dependent on wave frequency than wave height.

16 J. Mar. Sci. Eng. 7, 5, 45 6 of 3 J. Mar. Sci. Eng. 7, 5, x 6 of 3 f =. Hz f =.83 Hz f =.63 Hz Filled markers = Exp. Open markers = Num Surge RAO (m/m).5 Heave RAO (m/m).5 Pitch RAO (deg/m) Wave height (m) Wave height (m) Wave height (m]).8 Mean drift (m/m) Wave height (m) Irregular Irregular Sea Sea States States Figure Figure al al and and numerical numerical RAOs RAOs for for varying varying wave wave heights. heights. The The extreme values of of irregular sea states were found and presentedinin Figures 5 5 and and In this In this study, study, maximum simulated and measured valueisis considered toger with wi most most probable probable maximum, cf. cf. Equation (), (), which is commonly used for designin, in, e.g., e.g., []. []. T MPM () MPM = µ + σ ln(n) () where T MPM is most probable maximum (MPM) tension in waves, µ is mean tension and σ where T MPM is most probable maximum (MPM) tension in N waves, µ is mean tension and σ is standard deviation. This study uses MPM value in waves. is standard deviation. This study uses MPM value in waves. Since numerical and experimental wave time series are not identical, but have similar Since numerical and experimental wave time series are not identical, but have similar frequency domain parameters, it is not possible to compare maximum values directly. frequency Considering domain Figure parameters, 5, re is good it is agreement not possible in both to configurations compare for maximum two tests values with highest directly. Considering peak frequencies Figure(operational 5, re is good conditions). agreement Theseinalso both have configurations smallest wave for height twoand tests arewith most highest peaklinear frequencies waves. This (operational agreement conditions). is seen in both These also rear have and starboard smallest line. wave Forheight larger andsea arestates, most linear waves. error forthis Configurations agreementisbegins seen in to increase both significantly. rear and starboard For considered line. For sea states, largerit sea is not states, possible error fortoconfigurations show results forse begins twotoconfigurations increase significantly. for sea states For with considered frequencies sea lower states, thanit. is not possible Hz ( toextreme show results sea states). for se Under two se configurations conditions, for motions sea became statessowith largefrequencies that solver lower couldthan. Hz not ( find aextreme solution. sea The states). largestunder error isse foundconditions, for sea states motions with peak became frequencies so large around that. Hz. solver could Considering not find a solution. tested sea The states largest in Figure error7, isse found seafor states also sea correspond states withtopeak steepest frequencies sea states. around. Hz. Considering tested sea states in Figure 7, se sea states also correspond to steepest sea states. Still, maximum deviation for Configuration is 6% for T MPM for rear line, while it is only % for starboard line.

17 J. Mar. Sci. Eng. 7, 5, x 7 of 3 J. Mar. Still, Sci. Eng. maximum 7, 5, 45deviation for Configuration is 6% for T MPM for rear line, while it7 isof only 3 % for starboard line. Num.: Config Num.: Config Line tension (MN) Starboard T max Line tension (MN) Starboard T MPM Relative error (%) Starboard Relative Error Filled markers: T MPM Open markers: T max f p (Hz) f p (Hz) f p (Hz) Rear T max.5 Rear T MPM 6 Rear Relative Error Line tension (MN).5.5 Line tension (MN).5.5 Relative error (%) f p (Hz) f p (Hz) f p (Hz) Figure 5. Comparison of extreme tensions for irregular sea states. Figure 5. Comparison of extreme tensions for irregular sea states. The extreme motion of device is also of interest, and results are plotted in Figure 6. The extreme motion of device is also of interest, and results are plotted in Figure 6. Despite good agreement seen in previous figure, a larger deviation is found. The numerical Despite good agreement seen in previous figure, a larger deviation is found. The numerical model particularly overestimates pitch motion. Even though some quadratic damping is added model particularly overestimates pitch motion. Even though some quadratic damping is added in pitch DoF, it still appears that more damping is needed. For Configuration, relative error in pitch DoF, it still appears that more damping is needed. For Configuration, relative error exceeds %, with a maximum of 5%. The drag element in Configuration decreases error exceeds %, with a maximum of 5%. The drag element in Configuration decreases error to a maximum of 78%, which is still a significant overestimation. The smallest error is found for to a maximum of 78%, which is still a significant overestimation. The smallest error is found for operational sea conditions in deep water, with a smaller wave steepness. operational sea conditions in deep water, with a smaller wave steepness. The surge motion is overestimated with a maximum of 3% in most extreme situation. This sea The surge motion is overestimated with a maximum of 3% in most extreme situation. This sea state is also sea state in most shallow water and, according to Figure 7, also sea state where state is also sea state in most shallow water and, according to Figure 7, also sea state where diffraction contribution is smallest and drag and inertia most important. The surge maximums are diffraction contribution is smallest and drag and inertia most important. The surge maximums are underestimated for sea states with highest frequency. underestimated for sea states with highest frequency. The heave motion causes smallest relative error, with a maximum absolute value of 7%. The heave motion causes smallest relative error, with a maximum absolute value of 7%.

18 J. Mar. Sci. Eng. 7, 5, 45 8 of 3 J. Mar. Sci. Eng. 7, 5, x 8 of 3 Num.: Config Num.: Config Surge DOF 5 Heave DOF 4 Pitch DOF SurgeMPM (m) HeaveMPM (m) 4 3 PitchMPM (deg) f p (Hz) f p (Hz) f p (Hz) Surge DOF 6 Heave DOF 5 Pitch DOF 4 4 Relative error (%) Relative error (%) - Relative error (%) f p (Hz) f p (Hz) f p (Hz) Figure 6. Comparison of extreme motions for irregular sea states. Figure 6. Comparison of extreme motions for irregular sea states Optimized Model 3.5. Optimized Model As stated previously, objective of this paper is to validate that a numerical model can be As stated previously, objective of this paper is to validate that numerical model can be used in an initial design procedure, where no experimental data are available for optimization and used in an initial design procedure, where no experimental data are available for optimization and tuning of model. The results presented in previous sections indicate that structure can be tuning of model. The results presented in previous sections indicate that structure can be modeled with some overestimation of response compared to experiments. Considering Figure 9, modeled with some overestimation of response compared to experiments. Considering Figure 9, deviation appears to be caused by especially insufficient damping. Some quadratic damping deviation appears to be caused by especially insufficient damping. Some quadratic damping has been added by drag element, but figure showed significant underestimation of linear has been added by drag element, but figure showed significant underestimation of linear damping. Figure 7a illustrates a decay test where 37 m/s damping. Figure 7a illustrates a decay test where 37 m/s kn kn linear damping has been added in surge. linear damping has been added in surge. The additional damping clearly results in a better agreement between surge motion in The additional damping clearly results in better agreement between surge motion in experiment and model, which is also illustrated in Figure 7b, where linear regression now experiment and model, which is also illustrated in Figure 7b, where linear regression now indicates a minor difference between both linear and quadratic damping. For optimized model, indicates a minor difference between both linear and quadratic damping. For optimized model, additional linear damping results in a coefficient p =.7 s additional linear damping results in a coefficient p.7, which corresponds to a relative, which corresponds to relative error of 4.3% from experiments. error of 4.3% from experiments. Since no decay tests are available for heave and pitch, it is more difficult to tune se values. Since no decay tests are available for heave and pitch, it is more difficult to tune se values. The The work in [3] presented a method that can be used, but present study made a coarse sensitivity work in [3] presented a method that can be used, but present study made a coarse sensitivity analysis to find values of linear damping in heave and pitch, which improves model results for analysis to find values of linear damping in heave and pitch, which improves model results for regular tests. By adding kn knm m/s regular tests. By adding m/s kn and 4 rad/s in respectively heave and pitch, model showed knm and 4 rad/s in respectively heave and pitch, model showed better agreement with experiments. Figure 8 presents motion RAOs for optimized model. better agreement with experiments. Figure 8 presents motion RAOs for optimized model. Clearly, figure indicates that additional linear damping is main cause of difference between Clearly, figure indicates that additional linear damping is main cause of difference between Configuration and experiments. By adding damping, also mean drift is better estimated. Configuration and experiments. By adding damping, also mean drift is better estimated.

19 J. Mar. Sci. Eng. 7, 5, 45 9 of 3 J. Mar. Sci. Eng. 7, 5, x 9 of 3 Surge (m) Surge (m) Num.: Config Num.: Optimized Num.: Config decay Num.: Optimized Config decay decay Optimized decay Config decay Optimized decay ( Tm log an ( Tm log an an Time (s) 63anTm Time (s) 3 Tm (a) (b) (a) (b) Figure 7. (a) Decay test from experiments, model with drag elements (Configuration ) and Figure 7. (a) Decay test from experiments, model with drag elements (Configuration ) and optimized model with additional linear damping; (b) determination of p and p from experiments, optimized model with additional linear damping; (b) determination of p and p from experiments, Configuration Configuration and and optimized optimized model model using using linear linear regression. regression..5 ) ) a n+ a n Num.: Config Num.: Optimized Num.: Config linear regression Num.: Optimized Config linear regression linear regression Optimized linear regression Config linear regression Optimized linear regression Num.: Optimized Surge RAO (m/m).5 Heave RAO (m/m).5 Pitch RAO (deg/m) Mean drift (m/m) Figure Comparison of of optimized numerical model with experimental datafor forall all regular sea sea states.

20 J. Mar. Sci. Eng. 7, 5, 45 of 3 The results clearly indicate importance of tuning model. This, however, requires use of experiments, and as mentioned, this is not always available in initial design. The quadratic damping in this study has been added based on geometry of device and not experimental data, and refore, Configuration resembles a model that can be used initially to analyze mooring system before a final solution is chosen, experimental data or more sophisticated models are produced and numerical model is optimized. 4. Discussion This study has used a large set of experimental data to validate a numerical model to be used in initial design of mooring systems. It has been attempted to ensure similarity between model and laboratory in order to compare results, but sources of error are present during experiments. As stated previously, a small scale of :64.5 puts high demands on measurement precision, model manufacturing, anchor positioning, etc., and even minor uncertainties on measurements have high influence on full-scale values. Similarly, in some of tests, e.g., quasi-static test, model was displaced manually, which eventually will introduce some inaccuracy. The wave basin at Aalborg University is equipped with a passive absorber, and maximum reflection during test campaign was approximately % for longest waves. The reflective waves were not modeled in numerical model and could provide some divergence between model and experiment. Finally, it must also be mentioned that anchors used in test campaign were relatively large (cf. Figure 5) and could potentially have influenced wave field around model, at least for longest waves. During tests, it was attempted to minimize influence of all sources of error, and hence, y are assumed not to affect reliability of results. A quasi-static test was performed (cf. Figure 8) for validation of static behavior of numerical model, its capability of modeling mooring tension and stiffness and mooring layout. Good agreement was seen and proved that a good resemblance between numerical and experimental layout was present and that defined stiffness of lines had been achieved. This was additionally seen from decay test in Figure 9. Close values of surge natural frequency were achieved, also indicating that calculation of added mass was correct. Due to complex geometry, it was not possible to generate reliable decay tests for heave and pitch without activating more than one DoF at a time. The added mass can also affect natural frequencies, but since it is also indicated to be modeled correctly in surge, it is expected to show similar results in heave and pitch. Considering behavior found in dynamic tests, this seems to be correct. The decay highlighted a significant underestimation of damping in numerical model, both for linear and quadratic damping. By adding a drag element, error of quadratic damping was decreased, but naturally, linear damping still showed a significant error. Considering difference in Figure 9 and influence of adding a drag element, it is clear that CFD simulations and experiments are needed in order to determine drag coefficients and produce a better model of system. This was out of scope of this study, but is crucial to consider before a final mooring design can be achieved. The underestimation of linear damping in model was illustrated in Figures 7 and 8, where additional damping had been added and better agreement was found for RAOs and drift motion. A potential source of this error is presence of thin heave damper plates in model, which need to be solved using eir a very fine mesh or a thin plate approximation, which is not included in present version of NEMOH. This capability is included in or software packages like WAMIT [37] and will be implemented in next releases of NEMOH. The present study did not investigate this problem furr, but its influence will be investigated in future research. Based on a range of regular wave tests, RAOs were defined in Figure. Agreement between experimental and numerical results was found in most of frequency range for both model configurations. Some error was seen, particularly for heave and pitch at natural frequency, and most dominantly when no drag elements were applied. By introducing drag into pitch and heave DoF, significantly better results were obtained. At peak frequency, most outspoken motions will

21 J. Mar. Sci. Eng. 7, 5, 45 of 3 occur and hence put most demand on introduction of drag, but it is also at that frequency where most stress is put on assumptions of linear potential wave ory, which is assuming small amplitude wave and body motions. The drift motion showed largest error in model. The model uses Newman approximation, which is known to be poor in shallower water depths and when resonant motions are present. The use of full QTFs potentially could improve model and should be investigated in future research. The calculated drift coefficients are based on first order results from linear potential ory. Here, motions are used to calculate drift, and se are overestimated due to lack of drag and damping. From optimized model in Figure 8, it is seen that by adding more damping, motions are better described, and a similar observation can be made for drift. From irregular sea states, extreme tension and motions from experiments and numerical code were compared, and code showed a maximum relative error of approximately 6% for line tension. Considering that this paper focuses on applicability of numerical model at an initial design phase where no experimental data are available and no tuning performed, this error is within an expected and reasonable range. Based on objective of study, capability of code to model line tensions is, refore, validated. The motion of device was highly overestimated in pitch and probably needs more damping than what was introduced by drag element. This was particularly shown in Figure 7. The overestimation of extreme surge might be a result of overestimation of drift. Despite higher relative error of motion, relative error of tension was at an acceptable level. The study has shown that a relatively reliable numerical model can be constructed and used in initial analysis to model extreme design values for mooring lines, even without tuning it to experimental data, but only adding a drag element determined by a simplified method without use of experiments. The analysis provided an understanding of errors and limitations, which can be taken into account in future analysis of structures. It is expected that this approach can be used for or similar WECs as presented in a previous section. The results naturally need to be treated with caution, and best description of device is achieved by using experimental data to optimize model. Since model overestimates loads and motions, it could be highly beneficial to tune model to lower loads and, reby, decrease need for strength of lines. When considering that design standards like, e.g., [] or [] introduce safety factors in range of.4.67, much safety is now in system. From a survivability point of view, this can be desirable, but it will not help in reducing cost of moorings. For a final and complete design, it is refore desirable to optimize model as much as possible. For initial design, use of model in this paper will provide usable results that can be applied in furr investigation of mooring systems. 5. Conclusions The present paper presented outcome of an experimental test campaign and used results to validate a numerical model, constructed by use of BEM code NEMOH and time domain mooring analysis tool OrcaFlex. Focus was put on expected sea conditions for a specific deployment site and sea states covering expected frequency and wave height range. This included both operational and extreme conditions. The aim of paper was to investigate potential of codes to calculate extreme response for line tension in particular and, hence, ir applicability in initial mooring design for large WECs. In addition, work presented influence of applying drag elements with use of simplified ory, and not laboratory or CFD results, in order to improve BEM model. The focus was to achieve an understanding of obtained error when considering extreme response, in order to use model in initial design phases where, e.g., experimental data are not available. The main error was shown to be caused by underestimation of damping in model. By adding a drag element without use of experimental tuning, it was possible to improve quadratic damping significantly, but linear damping was still underestimated. The results are expected to be applicable

22 J. Mar. Sci. Eng. 7, 5, 45 of 3 to similar devices with passive mooring and where PTO is in safety mode during extreme events. The model showed an error that can be accepted in initial phases; however, study highlighted inaccuracies from parameters such as linear and quadratic damping, and se must be minimized before a complete and final mooring design can be achieved. Acknowledgments: The present study was funded by Energy Technology Development and Demonstration Program (EUDP) and its project Mooring Solutions for Large Wave Energy Converters (Grant Number ). The authors wish to acknowledge Floating Power Plant for input on experimental work. Author Contributions: J.B.T., F.F. and J.P.K. defined outline of study and experimental work in a shared effort. J.B.T. mainly performed experimental work with input from F.F. and J.P.K. J.B.T. analyzed data and performed numerical analysis. J.B.T. drafted paper, while F.F. and J.P.K. provided important input and review needed for finalization of paper. Conflicts of Interest: The authors declare no conflict of interest. References. Floating Power Plant. Available online: (accessed on 5 April 7).. LEANCON Wave Energy. Available online: (accessed on 5 April 7). 3. Wave Dragon. Available online: (accessed on 5 April 7). 4. Cruz, J. Ocean Wave Energy: Current Status and Future Perspectives; Springer: Berlin, Germany, Martinelli, L.; Ruol, P.; Cortellazzo, G. On mooring design of wave energy converters: The Seabreath application. Coast. Eng. Proc.,, doi:.9753/icce.v33.structures Fitzgerald, J. Position Mooring of Wave Energy Converters. Ph.D. Thesis, Chalmers Univerisity of Technology, Goteborg, Sweden, Thomsen, J.; Kofoed, J.; Delaney, M.; Banfield, S. Initial Assessment of Mooring Solutions for Floating Wave Energy Converters. In Proceedings of Twenty-Sixth (6) International Ocean and Polar Engineering Conference, Rhodes, Greece, 6 June July 6; Chung, J., Muskulus, M., Kokkinis, T., Wang, A., Eds.; International Society of Offshore & Polar Engineers: Cupertino, CA, USA, 6; Volume, pp Ridge, I.; Banfield, S.; Mackay, J. Nylon fibre rope moorings for wave energy converters. In Proceedings of OCEANS, Seattle, WA, USA, 3 September ; pp.. 9. Fitzgerald, J.; Bergdahl, L. Considering mooring cables for offshore wave energy converters. In Proceedings of 7th European Wave and Tidal Energy Conference, Porto, Portugal, 4 September 7.. Det Norske Veritas (DNV). Position Mooring; DNV Offshore Standard DNV-OS-E3; DNV: Høvik, Norway,.. API. Design and Analysis of Stationkeeping Systems for Floating Structures; American Petroleum Institute API-RP-SK; API: Washington, DC, USA, 5.. ISO. Stationkeeping Systems for Floating Offshore Structures and Mobile Offshore Units; ISO 99-7:5; ISO: Geneva, Switzerland, Harnois, V.; Weller, S.D.; Johanning, L.; Thies, P.R.; Le Boulluec, M.; Le Roux, D.; Soule, V.; Ohana, J. Numerical model validation for mooring systems: Method and application for wave energy converters. Renew. Energy 5, 75, Andersen, M.T.; Wendt, F.F.; Robertson, A.N.; Jonkman, J.M.; Hall, M. Verification and Validation of Multisegmented Mooring Capabilities in FAST v8. In Proceedings of 6th International Ocean and Polar Engineering Conference, Rhodes, Greece, 6 June July 6; International Society of Offshore and Polar Engineers: Cupertino, CA, USA, Wendt, F.F.; Andersen, M.T.; Robertson, A.N.; Jonkman, J.M. Verification and Validation of New Dynamic Mooring Modules Available in FAST v8. In Proceedings of 6th International Ocean and Polar Engineering Conference, Rhodes, Greece, 6 June July 6; International Society of Offshore and Polar Engineers: Cupertino, CA, USA, Oberkampf, W.L.; Trucano, T.G. Verification and validation in computational fluid dynamics. Prog. Aerosp. Sci., 38, Babarit, A.; Delhommeau, G. Theoretical and numerical aspects of open source BEM solver NEMOH. In Proceedings of th European Wave and Tidal Energy Conference (EWTEC5), Nantes, France, 6 September 5.

23 J. Mar. Sci. Eng. 7, 5, 45 3 of 3 8. Orcina Ltd. Orcaflex User Manual; Orcina Ltd.: Cumbria, UK, Thomsen, J.; Ferri, F.; Kofoed, J. al testing of moorings for large floating wave energy converters. In Progress in Renewable Energies Offshore; Soares, C., Ed.; CRC Press LLC: Boca Raton, FL, USA, 6; pp Assessment of Mooring System for Marine Energy Converters (MECs); IEC 66-; International Electrotechnical Commission (IEC): Geneva, Switzerland, 4.. DNV. Design of Floating Wind Turbine Structures; DNV Offshore Standard DNV-OS-J3; DNV: Høvik, Norway, 3.. Wehmeyer, C.; Ferri, F.; Andersen, M.T.; Pedersen, R.R. Hybrid Model Representation of a TLP including flexible topsides in non-linear regular waves. Energies 4, 7, Hall, M.; Goupee, A. Validation of a lumped-mass mooring line model with DeepCwind semisubmersible model test data. Ocean Eng. 5, 4, Subrata, K.C. Handbook of Offshore Engineering; Elsevier Science: Amsterdam, The Nerlands, Newman, J.T. The drift force and moment on ships in waves. J. Ship Res. 967,, Ecole Centrales Nantes. Available online: (accessed on 5 April 7). 7. Newman, J. Second-order, slowly-varying forces on vessels in irregular waves. In Proceedings of International Symposium on Dynamics of Marine Vehicles and Structures in Waves, London, UK, May DNV. Environmental Conditions and Environmental Loads; DNV Recommended Practice DNV-RP-C5; DNV: Høvik, Norway, AwaSys 7. Two and Three Dimensional Wave Generation, 6. Available online: civil.aau.dk/awasys/ (accessed on 5 April 7). 3. WaveLab 3. Data Acquisition and Analysis Software. Department of Civil Engineering, Aalborg University, 6. Available online: (accessed on 5 April 7). 3. OptiTrack. Motion Capture Systems. NaturalPoint, Inc., 6. Available online: com/ (accessed on 5 April 7). 3. Ingram, D.; Smith, G.; Bittencourt-Ferreira, C.; Smith, H. Protocols for Equitable Assessment of Marine Energy Convertes; Technical Report; University of Edinburgh: Edinburgh, UK, ; ISBN McCombes, T.; Johnstone, C.; Holmes, B.; Myers, L.; Bahaj, A.; Heller, V.; Kofoed, J.; Finn, J.; Bittencourt, C. Assessment of Current Practice for Tank Testing of Small Marine Energy Devices; Technical Report, EquiMar Deliverable; Aalborg University: Aalborg, Denmark,. 34. Bridon. Wire and Fibre Rope Solutions, 6. Available online: (accessed on 5 April 7). 35. Le Mehaute, B. An introduction to Hydrodynamics and Water Waves; Springer Science & Business Media: New York, NY, USA, Faltinsen, O. Sea Loads on Ships and Offshore Structures; Cambridge University Press: Cambridge, UK, 993; Volume. 37. Lee, C.H.; Newman, J.N. WAMIT User Manual; WAMIT, Inc.: Chestnut Hill, MA, USA, 6. c 7 by authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under terms and conditions of Creative Commons Attribution (CC BY) license (