Hydrodynamic Loading of Compact Structures and the Effect on Foundation Design

Transcription

1 Hydrodynamic Loading of Compact Structures and the Effect on Foundation Design. A. R. Henderson, BSc (Hon), MSc, PhD; M.B. Zaaijer, MSc Delft University of Technology, The Netherlands SYNOPSIS Gravity base foundations for wind turbines in deeper water at exposed sites will experience significant wave loading. The compact nature of these structures and the likely occurrence of non-linear extreme waves make it more difficult to calculate the hydrodynamic loading. This paper addresses various methods to calculate wave loading on compact structures and the effect of hydrodynamic loading on the foundation design solution, based on a case study of a 3 MW turbine at a Baltic site. It suggests that the simplified methods utilised here are conservative for the deepwater concepts and makes recommendations for improving the accuracy without increasing the complexity beyond what is appropriate for a design-optimisation model. The stability of the gravity base foundation is dominated by the ratio between surge and heave forces, which varies enormously during passing of the wave. INTRODUCTION Gravity base foundations have been a popular foundation concept for offshore wind turbines in sheltered and iceinfested waters. As wind turbines increase in size and move to deeper and more exposed sites, the hydrodynamic loading on the large gravity base structures becomes an ever more important contribution. The determination of hydrodynamic loads on a gravity base structure is more complicated than on slender monopiles, due to the irregular geometry and the complicated effect that the structure has on the wave field (termed diffraction). Furthermore, the design of gravity base structures with a large contribution of hydrodynamic loading will be more susceptible to inaccuracies in the determination of the hydrodynamic loading. The hydrodynamic loading on the gravity base structure itself is part of the design loop with respect to its load bearing function. On the other hand, the geo-technical design of a pile foundation can be performed directly using the hydrodynamic loading on the structure above the seabed as a priori knowledge. HYDRODYNAMIC LOADING The traditional approach to wave load calculation for gravity base structures in the offshore industry has been to use diffraction analysis. In the deep waters, in which such structures are located, the wave height is relatively low compared with the water depth. Therefore the use of linear wave theory (also called Airy theory), upon which the most commonly implemented form of diffraction theory is based, is applicable. On the other hand, offshore windfarms are located in much shallower seas, where highly non-linear waves are a more frequent phenomenon. Breaking waves also become more frequent and the balance of the type of breaking shifts from the relatively benign spilling breaker (which can be modelled using the appropriate non-breaking method) to include cases of the more severe plunging breakers (which impose significantly higher loads than the non-breaking case). A comprehensive evaluation of the impactsforces due to breaking waves is beyond the scope of this paper, however the effect of non-linearities in the wave field (i.e. the asymmetry in the vertical direction) and the structural geometry (i.e. the departure from simple cylindrical columns) is examined. Of particular interest is the effect of the ice-cone, which is located at the water surface, where wave kinematics and hence wave load effects are greatest. The hydrodynamic loads are also assessed in the perspective of all loads on the offshore wind-turbine, since although the non-linearities in shallow waters are higher, the hydrodynamic loads themselves will be lower, because of the shallowness.. Authors Biographies Dr. Andrew Henderson is presently Assistant Professor in Offshore Wind Energy at Section Wind Energy, Delft University of Technology. His research currently focuses on wave loading and floating support structures issues. He is working on, among others, the OWTES-Blyth project, which includes work on the development of design methods for windturbines in exposed seas and evaluating the performance of the Blyth offshore windfarms, of which this paper forms a part, and was co-ordinator of the Concerted Action on Offshore Wind Energy in Europe project. Previously, he worked as Research Fellow in the Mechanical Engineering Department of University College London on a research project / Ph.D. on floating wind energy. Michiel Zaaijer is presently Assistant Professor in offshore wind energy at Delft University of Technology. His research focuses on dynamic behaviour of offshore turbines and integrated wind farm design methods. After his M.Sc. in physics in 993 he has worked for several years as a researcher in the field of aircraft navigation.

2 In general, the modelling of wave loadings can be divided into three stages: (i) selection of the wave model, (ii) selection of the load-calculation model and (iii) examining the response of the structure (i.e. structural dynamics). For a rigid structure, such as a GBS, the small magnitude of the structural dynamics do not affect the wave loads and hence this stage can be ignored. The choice of wave models for engineering application has converged on to two main theories: (i) the linear Airy model, with or without modifications and (ii) the non-linear stream function model. Regarding the load calculation method: three approaches are applicable according to the type of structure: (i) Morrison theory, a slender body theory and (ii) Diffraction theory and (iii) Froude-Krylov method, both for massive structures, such as the gravity base structures (GBS) being considered within this paper. Of the second and third methods, both have particular weaknesses, in the case of diffraction it is in the application of non-linear wave models and in the case of Froude-Krylov it is in the modelling of the effect of the structure on the flow field (i.e. diffraction). In the longer term, computational fluid dynamics (CFD) promises the benefits of being able to model all aspects of interest, though the current penalties of complexity for the user and computational costs necessary will need to be reduced. Figure and Figure 2 show the two candidate GBS support structures analysed in this paper; the first is suitable for shallow waters and similar to that used at Middelgrunden, while the second is the optimised design from the Opti- OWECS research project [5], which assumed a deeper water depth of 5m. Note also that the shallow water design includes an ice-cone; ice is a frequent phenomenon in the Baltic Sea but does not occur in the North Sea at the latitudes of interest. Table I gives the design conditions used in this paper; the values for the deep-water concept are again taken from the Opti-OWECS study [5]. Of the following example calculations in this paper, most are for the deeper-water concept, to tie in with the subsequent geotechnical analysis; exceptions are when the analysis of the shallow-water concept leads to different conclusions, for example due to the presence of the ice-cone. Figure : Shallow Water (6m) Gravity Base Support Structure Figure 2: Deep Water (5m) Gravity Base Support Structure Table I: Design Conditions Parameter Shallow Water Concept Deep Water Concept Water Depth 6 m 5 m Return Period 5 years Extreme Height 4 m 9.7 m Wave Period 8 s s The Selection of the Wave Kinematics Model Currently, the two most widely used wave models are: (i) Airy [] and (ii) stream function [4] theories. Stokes [8] theory has been commonly used in the past but has been superseded for non-linear applications, since its analytical nature means that extending to each subsequent order becomes progressively more difficult, fifth being the highest that the theory was commonly applied. Since stream function theory is numerical, higher orders take longer to solve but can be done so using the same algorithm. The airy theory is linear and hence, in its original formulation, does not include surface effects. It does however have advantages due to its simplicity, in that it can be applied to diffraction theory and in the frequency domain and is relatively easy to apply to the modelling of stochastic seas. In addition, numerous empirical methods have been developed to model the effect of wave height: stretching the wave field up to the actual surface. These methods can be applied to both regular waves and to stochastic seas and the versions to have been developed include Wheeler [] and

3 Chakrabarti stretching [3] (where the wave kinematics field is stretched up or down to the actual surface), extrapolation (where the wave kinematics are extrapolated from the mean water level up to free surface) and constant crest (where the wave kinematics are assumed to be constant at the mean-water-level value, from the mean-water-level up to surface). The extrapolation and constant crest methods tend to over-estimate the kinematics, however the stretching methods are generally superior to the basic formulation and hence are widely used. However, they can over and underestimate the kinematics severely in the shallowest water depths. Wave tank experiments have shown that for small waves in deep water, all wave theories are adequate but in shallow water or with steep waves, the most accurate wave kinematics model is the non-linear stream function. The conditions where traditional offshore oil and gas gravity base structures are installed fall within the first group, hence the utilisation of only diffraction theory for the design of such structures. The Selection of the Wave Load Calculation Method As described above, both diffraction and Froude-Krylov methods suffer from substantial weaknesses when calculating the wave loads on massive structures. However, the weaknesses of each method are different from each other, see Table II, and hence the obvious approach is to use both methods together: diffraction theory to estimate the effect of the structure on the flow field and Froude-Krylov to calculate the wave loads using non-linear waves. Since GBS structures tend to be fairly simple, i.e. consisting of a round base, a tower section and possible an ice-cone at the water surface, in many cases, it should also be possible to estimate the diffraction coefficients by comparing with other similar structures. Table II: Comparison of Wave Load Calculation Methods for Massive Structures Wave Load Calculation Method Morison Diffraction Froude-Krylov CFD Inertia Transverse Drag X X Forces Lateral (drag) X X Pressure X Diffraction X 2 X 4 Geometry Surface D X Effects 3 3D X X Wave Non-Linear X Models Stochastic (Linear) X 5 X 5 Commercially Available *** *** ** * Applicability Ease of Use *** *** ** * Speed of Calculations *** ** ** * = can be modelled relatively easily by adding an extra term 2 = can be modelled using MacCamy-Fuchs [6] correction 3 = non-linear surface effects between the structure and the wave-field: D = in vertical direction only (i.e. wave height considered only at the vertical-axis of the structure) 3D = full geometric field (i.e. wave height at each surface element of the structure) 4 = must be estimated 5 = excessive demands on computation power Sources of Error in Wave Load Calculations for GBS Structures Accepting that diffraction and Froude-Krylov offer the most appropriate paths for calculating wave loads on GBS structures, this section attempts to evaluate the relative size of the different sources of error. Starting with diffraction, Table II shows that this is unable to include the effect of (i) viscous effects (transverse and lateral drag), (ii) surface effects (D and 3D) and (iii) non-linear waves. Likewise, the Froude-Krylov method is also unable to include transverse drag, (i) viscous effects plus (iv) diffraction effects. It is possible to examine the effect of drag (i) by examining the Keulegan-Carpenter number, K, equation and (ii) utilising the Morison equation. UˆT K = () D The Keulegan-Carpenter number depends on the peak fluid velocity, U, the wave period, T, and the structure diameter, D and, for this deepwater GBS structure under this design wave, will be approximately 2.5 and 5 for the base and tower respectively. Values of K below 5 mean that the flow is inertia dominated while above 25 indicates flow is drag dominated; hence drag forces may have some importance for the load calculations on the tower but can be ignored for

4 the base. From Figure 3 we can infer that the shear loads occur predominantly on the base-slab (since changes in the C m value of the tower have relatively little effect on the overall loads), hence it can be concluded that drag can be ignored. The same conclusion applies to the drag force on the upper surface of the base, which can be shown to be insignificant [7].,,5 8, 6,, Base Shear Loads [kn] 4, 2, -2, -4, -6, Base Shear Loads [kn] 5-5 -, -8, -, Time [s] CM=.25 (all) CM=.25 (base) 2 (tower) CM=2 (all) Diffraction -, Time [s] Airy (linear) wave Stream Function (non-linear) Wheeler Stretching (Airy) Figure 3: Effect of C m Values on Deep Water Structure and Evaluation Against Diffraction Figure 4: Effect of Wave Model / Surface Geometry on Shallow Water Structure The importance of surface effects depends on the size of the structure at the water surface, i.e. the presence and dimensions of the ice-cone. Even with an ice-cone, for the deepwater GBS the loads calculated using the unmodified Airy & Wheeler methods give similar results: Figure 5. This is not the case for the shallow water GBS, as can be seen in Figure 4. Note that the variation with time as well as the extreme values is important. Figure 5 shows how important an appropriate wave model selection is, again with respect to the variation with time and the extreme values. For this example, linear theory results in a conservative design but this may not be correct for all cases, see Figure 4. Note that if non-linear theory is selected, the erratic shape of the curve means that the timeresolution needs to be higher to ensure that peak loads are detected. 6, 2, Base Shear Loads [kn] 4, 2, -2, -4, -6, Time [s] Airy (linear) wave Stream Function (non-linear) Wheeler Stretching (Airy) Base Heave Loads [kn] 5,, 5, -5, -, -5, -2, Time [s] Airy (linear) wave Stream Function (non-linear) Wheeler Stretching (Airy) Figure 5: Effect of Wave Model on Deep Water Structure The importance of diffraction effects is also evaluated in Figure 3, where it can be seen that they significantly reduce the shear forces. Accurate results from Froude-Krylov require an appropriate C m value, for this geometry around.25 for the base. (A similar curve would show that heave is unaffected and a pressure coefficient of is applicable for all cases where there is no flow around the base in the vertical direction). Whether this value is applied to the base only or the whole structure including the tower is not important in this case but becomes more so when surface effects are included. It should be noted that the accuracy of the Morison formula is heavily dependant on the appropriate selection of coefficients in a very similar manner; however Morison is generally applied only to relatively simple geometries, such as cylinders, for which the coefficients are easier to estimate. The coefficient C m is composed of two parts: the first, which always has a value of, represent the inertia due to the displaced fluid while the second can be visualised as the mass of the surrounding water influenced by the structures presence. For simple geometries, such as the deepwater structure, the relationship is fairly straight-forward and it is possible to develop a simple function relating the added inertia coefficient, for the base slab, to the slab height, B and diameter, D, such as equation 2, with k.5. B C m = + k (2) D

5 If possible, different values of C m should be used for the base, tower and ice-cone, with a value of 2 being utilised for the tower, though the effect of this was shown to be small. For the ice-cone, it is suggested to use a value of.5, which is derived from a potential flow analysis of a sphere. On a practical note, the base shear force, which is shown to be a design driver below, can be reduced by (i) partly burying the structure (this may introduce additional bed-preparation costs though a soft topsoil would make it necessary anyway) and by (ii) coning the base slab. RESISTANCE FACTORS The gravity base structure (GBS) must provide sufficient resistance against sliding and sufficient vertical bearing capacity. Evidently, the hydrodynamic heave force may not lift the entire structure, in which case sliding resistance reduces to zero. The structure may also not be tilted by the overturning moment of the wind loads and hydrodynamic pitch, but before that point is reached the vertical bearing capacity will be reduced to zero. This will be shown below, when the calculation of bearing resistance is explained. Sliding resistance and bearing resistance are determined according to [2] and [9], assuming cohesionless, sandy soil. When the horizontal force on the structure equals F X and the vertical force equals F X and the z-axis is taken positive upward, the criterion for the sliding resistance becomes ( F ) tan( ϕ ) F Φ (3) x SS z with: Φ SS = resistance factor for sliding, taken equal to.8, ϕ = friction angle of the soil, taken equal to 3º. This equation is based on Coulomb s relation for frictional material, which gives a linear relation between the normal force and the shear force. Equation 3 can be interpreted as a criterion for the maximum inclination of the combined forces with respect to the vertical. Bearing capacity is calculated according to the theory developed by Prandtl, Terzaghi and Brinch Hansen. Only the contribution of the soil weight is taken into account, because this is commonly the largest contribution to bearing capacity for an offshore GBS. The bearing capacity is corrected for inclined loading and overturning moment according to ( F ) Φ i s m N ' D πd (4) z SB GBS GBS with: Φ SB = resistance factor for bearing, taken equal to.67, i s m = inclination factor, = shape factor, taken equal to.7 for a circular gravity base, = reduction factor of effective area, N = empirical dimensionless function of ϕ, ' = submerged unit weight of the soil, taken equal to 9 N/m 3 D GBS = diameter of the gravity base. Equation 4 appears to give an upper limit for the downward vertical force, but the inclination factor and reduction factor of the effective area are functions of F X that lead to lower limits. The inclination and reduction of the effective area are illustrated in Figure 6 below. Top view of contact surface: Horizontal force at effective height Vertical force Reduced bearing area in grey Intersection point Inclination Combined force Figure 6 Inclination and reduced bearing area of combined loading

6 The intersection of the combined force with the soil-structure contact plane is the centre of the reduced area. The gravity base would be tilted when the intersection reaches the edge of the contact surface, but as can be seen the effective bearing area is then already reduced to zero. Thus, the soil would fail near the rim of the base well before the structure topples from a geometrical point of view. The inclination factor reduces from to zero between vertical loading and the inclination at which sliding occurs. Because the correction factors reduce to zero at tilting and sliding the bearing criterion is an all-embracing criterion. LOAD AND RESISTANCE FACTOR ANALYSIS A case study is performed to assess the various parameters that affect the gravity base stability. A simple circular gravity base is designed for a 3 MW turbine in the conditions listed in Table I. An operational load case has also been considered, but this appeared to be less demanding. A previous design study for the same location and turbine resulted in a gravity base with a 25 m diameter and a mass of 3 t [5]. In that study linear diffraction theory was applied to calculate the wave loading for 4 phases of the wave period. Weak to firm soil conditions were assumed, with soil shear strength of 5 kpa. The current case study assumes cohesionless soil, with a friction angle of 3º. The current design is made using linear wave theory without diffraction to calculate hydrodynamic loading at 5 phases of the wave period. The pressure distribution according to Bernoulli s equation is integrated over the horizontal surface of the gravity base and horizontal loading is calculated with Morison s equation with C m = 2. and C d =.7. Under these conditions a gravity base with the same 25 m diameter is designed. The minimum required mass in this case equals 42 t, with a height of 2.5 m. The different mass of the previous study and this design will be addressed later. This section analyses the loading, capacity and stability of the reference design during different phases of the extreme wave, in order to get insight in the design drivers. The various relevant parameters are combined in the plots of Figure 7. The horizontal axis is positive in downwind direction and the vertical axis is positive upward. Pitch is related to the centre of the gravity base at the contact surface and positive for the wind force. The utilisation is the ratio between the loading and the capacity. E+7 (N) E+ -E+7 Surge E+8 4E+7 (N) Weight tower+nacelle (Nm) Pitch due to heave Wind E+ Heave Bouyancy Wind E+ Weight nacelle Total Total Weight GBS Pitch due to surge Total -E+8-4E+7 Horizontal Vertical Overturning moment Load contributions 4E+7 (N) 2E+7 Capacity Utilisation 6E+8 (N) Effective area correction Utilisation Inclination correction -Load Capacity E+ (m) 5E- Intersection E+ Abs(Load) Utilisation E+ E Sliding Bearing Tilting stability Utilisations Figure 7 Loads and utilisations of 25 m x 2.5 m GBS (linear wave model with Morison equation and integrated horizontal surface pressure) (Horizontal axis is wave phase) During the extreme wave the horizontal wind loading on the idle turbine is insignificant. The submerged weight and hydrodynamic heave force are of the same order of magnitude and therefore nearly cancel at wave phase.5. Pitch due to heave and surge partially cancel and are slightly larger than pitch due to wind loading. Both capacity against sliding and bearing capacity vary enormously during passing of the wave. The heave reduces the normal force at the contact surface and the effect on sliding capacity is clearly visible. The inclination correction, which depends on surge and heave, clearly dominates the variation of the bearing capacity. The effective area correction is nearly equal to, because the offset of the total force from the centre of the contact surface is small as can be seen in the lower-right plot. The offsets between the extremes of loading and capacity result in a maximum utilisation of sliding and bearing capacity just before and just after maximum heave occurs. The maximum bearing utilisation at wave phase.4 is not detected in the previous design study, because of the low number of wave phases, and this is probably the most important reason why the previous study resulted in a lighter GBS.

7 EFFECTS OF HYDRODYNAMIC MODELLING ON DESIGN SOLUTION Design optimisation Often the design of a GBS will be optimised toward smallest dimensions and lowest weight. To determine how the optimum solution is affected by hydrodynamic modelling the stability of gravity bases with a range of diameters and heights is tested. The result for the hydrodynamic model used for the design in the previous section is shown in Figure 8 (however, here 24 phases of the wave are used, instead of 5). Gravity bases with dimensions within the shaded area are stable, while other dimensions might fail. For different failure mechanisms the boundaries are given, with the instable area directed away from the shaded area. As stated before, the bearing criterion is all-embracing and hence the shaded area is on the stable-side of all boundaries. The bearing capacity without surge and pitch is the fictitious capacity that is obtained when the inclination correction and effective area correction are omitted in Equation 4. The lightest stable structure according to this model is found in the lower-left corner of the shaded area. Stability boundaries GBS height (m) 5 Instable Stable GBS diameter (m) Bearing Sliding Tilting Bearing (no surge and pitch) Lifting Figure 8 Dimensions of stable and instable gravity bases with stability boundaries The lower boundary of the stable area is close to the boundary below which the structure is lifted. Therefore, a good prediction of heave forces is a first essential step toward finding this lower boundary. The sliding boundary is even closer to the stable area, indicating that this criterion incorporates the most important effect of the relation between surge and heave on the lower stability boundary. The upper bound and particularly the related left boundary of the stable area are farther away from the other stability boundaries. This demonstrates the importance of the correction factors for the combined loading. Since the correction factors depend on the relative magnitudes of the loading contributions, proper determination of these contributors during several stages of the passing of the wave is crucial to find the correct lightest possible structure. Influence of modelling on optimisation The main question of the design study is how the area with stable gravity bases changes when different hydrodynamic models are used, particularly in the region of low diameters. Figure 9 plots the stability area for several alternatives to the reference of the previous section. GBS height (m) 5 Instable Stable Reference Linearised pressure 4 wave phases Cd and Cm % reduced GBS diameter (m) Figure 9 Stability boundaries for several alternative hydrodynamic models When the pressure on the horizontal surface of the GBS is linearised around the centre an analytic solution of the heave and pitch can be obtained, which is convenient in early design phases. This model has only a small conservative difference with the reference model, since the wavelength of 89 m is much larger than the analysed diameters. Only for larger diameters the deviation is visible. Reduction of the number of wave phases to 4 lowers the lower boundary approximately to the boundary where the structure is lifted by the heave. Simultaneously, smaller diameters appear to be possible. This approach clearly underestimates the required minimum diameter and height. The underestimation of the minimum height is nearly the same as the difference observed between the two 25 m diameter designs mentioned

8 earlier. Reduction of C m and C d also results in a significant reduction of minimum required diameter and height, even though this doesn t affect the heave force. The effect is caused by the change in correction factors for the bearing capacity. Diffraction and non-linear wave theory are not implemented in the used design tool. However, when linear diffraction is considered, surge, heave and pitch amplitudes will be affected differently, but their variation in time will remain the same. Therefore, the effect on the stability diagram will be similar to that of changing C m and C d, although numerically somewhat different. Since diffraction will particularly result in reduced surge, omission of a diffraction model is likely to result in a conservative design solution. The use of non-linear wave theory will not only change the amplitudes of the loading, but also the shape of the variation in time. Because the instantaneous relation between the load contributions is so important for the capacity correction factors, this may have a larger effect on the stability diagram. For the water depth and extreme wave height of this study non-linearity can be significant. It is not known a priori whether omission of non-linearity will result in a conservative or underestimated design. CONCLUSIONS AND RECOMMENDATIONS Examination of the results from the above hydrodynamic analyses suggests that diffraction is necessary to determine the added mass coefficient of the support structure, in particular of the base. For simple structures, such as the deepwater GBS examined here, a simple relationship can be determined using a handful of diffraction analysis. The loads should then be checked using the Froude-Krylov method, to allow the implementation of non-linear wave theory, utilising the added mass coefficients calculated using diffraction analysis previously. For the deepwater geometry examined here, it was found that linear theory was conservative, since using linear theory gives both a higher maximum lifting force, and a higher base shear (surge) force at that critical moment in the phase of the wave. Due to the variation of the combined loading on the structure the sliding and bearing capacity of the gravity base foundation varies as well when the wave passes. As a consequence, the variation of the utilisations is erratic and doesn t resemble the shape of the variation of any of the loadings. Therefore, the highest utilisation is only found when sufficient phases of the wave are tested. Two design studies were compared and an underestimation of the GBS mass in one of the designs by nearly 3% could be explained from the difference in tested wave phases (4 and 24, respectively). The correction of the bearing capacity due to the inclination of the combined loading is a dominant factor in the bearing utilisation. Therefore, hydrodynamic load calculations must not only lead to correct prediction of load amplitudes, but the shape of the variation during passing of the wave must also be accurate. Although not investigated numerically, the results point in the direction that both modelling of non-linearity and of (linear) diffraction are important to obtain a safe lightweight design solution. In early phases of the design emphasis of the hydrodynamic modelling should be on the variation of the load contributions during passing of the wave. Sensitivity to variation in shape and amplitude of the load contributions can reveal the necessity to apply diffraction or non-linear theory for the particular design conditions. ACKNOWLEDGEMENT The author would like to acknowledge the contributions made by the partners in the OWTES project and John Brown Hydrocarbons Limited to this paper. The project Design methods for Offshore Wind Turbines at Exposed Sites is being funded by the European Commission under contract number JOR3-CT98-284, with co-funding of NOVEM under contract REFERENCES Airy, Sir G. B., Tides and waves, Encycl. Metrop., Art 92, API, RP 2A-LRFD: API Recommended Practices for Planning, Designing and Constructing Fixed Offshore Platforms Load and Resistance Factor Design, July, Chakrabarti, S.K., Hydrodynamics of Offshore Structures, WIT Press, Dean, R.G., Stream Function Representation of Nonlinear Ocean Waves, J. Geophys. Res., Vol 7, No. 8, pp , Ferguson, M.C. et al. Opti-OWECS Final Report Vol. 4: A Typical Design Solution for an Offshore Wind Energy Conversion System, Institute for Wind Energy, Delft, MacCamy, R.C. and Fuchs, R.A., Wave Forces on Piles: a Diffraction Theory, Tech. Memo No. 69, US Army Corps of Engineers, Beach Erosion Board, Massey, B.S., Mechanics of Fluids 5 th Edition, Van Nostrand Reinhold, Stokes, G. 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