COUPLED HYDRODYNAMIC AND STRUCTURAL BEHAVIOR OF SPAR BUOY FLOATING WIND TURBINES USING FAST

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1 8 th GRACM International Congress on Computational Mechanics Volos, 1 July 15 July 015 COUPLED HYDRODYNAMIC AND TRUCTURAL BEHAVIOR O PAR BUOY LOATING WIND TURBINE UING AT Evaggelos G. Karageorgopoulos 1 and Athanassios A. Dimas 1& Department of Civil Engineering University of Patras Patras, GR-500, Greece adimas@upatras.gr Keywords: wind turbine, spar buoy, fluid-structure interaction, AT. Abstract. The scope of the present wor is the coupled fluid-structure simulation of a floating wind turbine (spar buoy type) subject to hydrodynamic and aerodynamic loads using the aero-elastic simulator AT (atigue, Aerodynamics, tructures, Turbulence) Code. The diameter of the wind turbine tower is.5m, the height of the tower is 90m and the blade-tip diameter is 1m. Two different floating structures to support the wind turbine were examined; one with a draft of 10m and one with a draft of 100m. In both cases the floating wind turbines are anchored via 3 catenary lines. The simulations were performed for wind speeds (U 10) in the range from 0 to 11 Beaufort. The range of 0-8 Beaufort corresponds to the situation of normal wind turbine operation, while the wind turbine is pared in the range of 9-11 Beaufort. our different cases of incident irregular waves were examined with characteristic wave heights (Hs) of.5m, 3.8m, 4.5m and 8m which correspond to winds of 7, 8, 9 and 11 Beaufort, respectively, using the JONWAP spectrum. The results include the platform translational motions (urge, way and Heave), the rotational motions (Roll, Pitch, and Yaw), the corresponding accelerations and the corresponding tower base forces. Based on the results, we observed no substantial differences in the behavior of the two floating wind turbines; therefore, the use of the one with the smaller draft is preferable. 1 INTRODUCTION In recent years, the issue of offshore wind turbines, both fixed and floating, has gained importance due to their advantages with respect to land installations. pecifically for the floating wind turbines, there exist three types: the par-buoy, a vertical unitary cylindrical member which is anchored by cables, the emi-ubmersible Platform, a platform which consists of vertical columns and cross cylindrical members which is also anchored by cables, and the Tension Leg Platform (TLP), a floating platform which is anchored by cables under tension. The scope of the present wor is to use the coupled fluid-structure simulation of a floating wind turbine (par-buoy type) subject to hydrodynamic and aerodynamic loads, using the aero-elastic simulator AT (atigue, Aerodynamics, tructures, Turbulence) Code, in order to optimize the draft of the structure based on the environmental conditions prevailing in the Gree area. The environmental conditions for the simulations correspond to wind velocities up to 11 Beaufort with or without the effect of incident waves and for both possible conditions of the wind turbine as operational or pared. IMULATION PROGRAM AT.1 Operation of AT The simulation program AT is a product of the National Renewable Energy Laboratory (NREL). It is a complete aeroelastic simulator, capable to calculate fatigue loads (due to the incident wind and wave), displacements (translator and angular), as well as velocities and accelerations for the consisting members of two and three-bladed wind turbine type with horizontal axis (HAWTs). The operation of the AT program is facilitated by the use of appropriate modules and input files, which set the values of the parameters with respect to the geometry and the structural and hydrodynamic properties of the wind turbine structure, as well as the environmental conditions. The modules are: ElastoDyn (tructural Dynamics) BeamDyn (Nonlinear inite Element Dynamics ) AeroDyn (Aero Dynanics) ervodyn (Control and Electrical Dynamics)

2 HydroDyn (Hydro Dynamics) ubdyn (Multi-member ubstructural Dynamics) Map (Mooring tatics and Dynamics) EAMooring (Mooring Dynamics) Iceloe (Quasi_teady Ice Loading) IceDyn (Ice Dynamics) AT processes the input files and obtains results based on the selected type of wind turbine. The present wor focused on the study of cases using mainly the aerodynamic (AeroDyn) and hydrodynamic (HydroDyn) modules. [] igure 1. ummary of Input and Output iles for AT v a-bjj. HydroDyn In HydroDyn, the hydrodynamic loads are computed by a variety of approaches, i.e., potential flow theory, strip-theory or a combination of these two. The use of the strip-theory is based on the assumption that the construction or construction members have a small diameter compared to a typical wavelength. Parts of the strip-theory include the relevant form of Morison equation for the distributed fluid inertia, the additional mass of

3 the structure and the viscous-drag components. Additional parts are the axial loads from the conical members and buoyancy loads. The hydrodynamic loads are applied as concentrated loads at the ends of members, which are called joints in AT. It is also possible to include flood or ballasting of the members and the results of marine growth. The hydrodynamic coefficients which are required for this solution are derived through userspecified dynamic pressure, added mass and drag coefficient. The main HydroDyn input file defines the geometric infrastructure, the hydrodynamic coefficients, the inematic wave and current, the floods and the ballasting of the members of the structure, the development of plant microorganisms on the members of the structure (marine growth) and other parameters [4]. The equations of motion for a floating structure are M Tj t (.1) 1 d dt where j 1,...,, are the translatory motions for 1,, 3, i.e., surge, sway and heave along the x, y and z axes, respectively, are the angular motions for 4,5,, i.e., roll, pitch and yaw about the x, y and z axes, respectively, and Tj are the corresponding total forces ( j 1,,3 ) and moments ( j 4,5, ) acting on the structure. The total forces and moments on a floating structure are obtained as a sum of three components: The hydrodynamic forces and moments j on the structure when there are incident and diffracted waves and the structure is restrained from any motion. The wave excitation loads are composed of roude-kryloff and diffraction forces and moments j Ij Dj (.) The net hydrostatic forces and moments acting on the structure when there are no external waves but the structure is forced to oscillate in the six rigid-body motions. These loads are identified as restoring terms in the form Hj 1 C (.3) where C are the hydrostatic restoring force coefficients and give the net hydrostatic force acting on the structure in the jth direction due to a unit displacement in the th mode of motion. The hydrodynamic radiation forces and moments acting on the structure when there are no external waves but the structure is forced to oscillate in the six rigid-body motions. These loads are identified as added mass and damping in the form A d B d R j 1 dt dt (.4) A is the added mass in the jth direction due to a unit motion in the th mode, and where corresponding damping. Combining Eqs.(.1)-(.4), the equations of motions become B is the d d M A B C j D 1 dt dt (.5) Many of the mass, added mass, damping and restoring coefficients of Eq. (.5) become zero if the structure has one or more planes of symmetry. or ships, the x - z plane is usually a plane of symmetry, while floating wind turbines are usually axisymmetric about the z axis. The D component of the Morison equation is the drag forces and moments applied to node, x1 vector which occurs in the equation below. The resistance force is proportional to the square of the relative velocity between water-construction and scaled base transverse viscous-drag coefficient, C D.

4 where Evaggelos G. Karageorgopoulos, and Athanasios A. Dimas. ( ) ( ˆ) ˆ C ( ( ˆ) ˆ DW RtMG vrel vrel vrel vrel ) 0 D (.) 0 0 W is the water density, R the outer radius of structural member, t MG is marine-growth thicness, v rel relative velocity, 3x1 vector and ˆ the Unit vector along the local z-axis. or structures with lateral symmetry (symmetric about the x - z plane) and with the center of gravity at ( 0,0, z G ), the mass (inertia) matrix is M zg z 0 0 G zg 0 I44 0 I4 zg I I4 0 I (.7) where g and is the displaced volume of water. The restoring coefficient matrix is C C33 0 C C C53 0 C (.8) C ga (.9) 33 WP C C g xda (.10) A WP where respectively, A WP is the waterplane area, z B and C44 g z z g y da ggm (.11) B G T AWP C55 g z z g x da ggm (.1) B G L AWP z G are the z-coordinates of the centers of buoyancy and gravity, GM T and GM L are the transverse and longitudinal metacentric heights, respectively. The computation of the added mass and damping coefficients, under the assumption of potential flow, is based on the decomposition of the velocity potential of the flow induced by incident waves around a moving floating structure as follows I D 1 (.13) where I is the potential of incident waves, which results into the roude-kryloff forces and moments of Eq.(.), is the potential of the diffracted waves, which results into the diffraction forces and moments of D

5 Eq.(.), and are the radiation potential due to unit motion in the th mode, which result into the added mass and damping forces and moments of Eq.(.4). Under the assumption of linear wave theory, the generalized Bernoulli equation for the dynamic pressure is pi pd pr t (.14) Therefore, the corresponding forces are pnd nd (.15) I Ij I j j t p n d n d (.1) D Dj D j j t p n d n d (.17) Rj R j j t 1 where n j is the generalized unit vector normal to the structure surface with direction from the fluid into the surface. or j 1,, 3, the components correspond to the usual normal unit vector into the structure surface n n n n (.18) 1, ˆ, 3 while for j 1,, 3, the components correspond to moments of the usual normal unit vector according to n n n r n (.19) 4, ˆ 5, and r is the vector from the origin to the corresponding point on the structure surface. The incident potential is nown, therefore, the corresponding forces and moments are obtained by simple integration on the structure surface using Eq.(.15). The diffraction potential has to be obtained by simulation or approximation of the potential (irrotational) flow. or the radiation potentials, harmonic oscillations are assumed in the form (.0) e i t In linear theory, wave excitation and structure response have the same radial frequency. Therefore, Eqs. (.15)-(.17) become Ij e (.1) I i t j Dj e (.) D i t j e R Rj i t (.3) 1 where i n d (.4) R j The real and imaginary parts of R are separated as

6 where A Re R / and B Im R / Evaggelos G. Karageorgopoulos, and Athanasios A. Dimas. A ib (.5) R. The combination of Eqs. (.1)-(.5) results into I D M A ib C j j (.) 1 where the coefficients A and B depend on the radial frequency. rom the mass and restoring coefficients matrices, we note that they are symmetric and the cross-coupling values are zero when j 1, 3, 5 and, 4, and vice versa. The same is true for the added mass and damping coefficients A B A11 0 A13 0 A A 0 A4 0 A A31 0 A33 0 A A4 0 A44 0 A4 A51 0 A53 0 A A 0 A4 0 A B11 0 B13 0 B B 0 B4 0 B B31 0 B33 0 B B4 0 B44 0 B4 B51 0 B53 0 B B 0 B4 0 B (.7) (.8) which are also symmetric, i.e., A Aj andb B j. Therefore, the vertical-plane or longitudinal motions (surge, heave and pitch) are uncoupled from the horizontal-plane or transverse motions (sway, roll and yaw). Note that for structures axisymmetric about the z axis or with the y - z plane as a plane of symmetry and zero mean velocity, the inertia coefficients I4 I4 0 in Eq.(.7), the restoring coefficients C35 C53 0 in Eq.(.8), while the added mass and damping coefficients become A A A A11 0 A A A4 0 A A A (.9) B B B B11 0 B B B4 0 B B B (.30) Then, the heave motion becomes uncoupled from surge and pitch, and the yaw motion become uncoupled from sway and roll.

7 .4 Turbim Turbim is a stochastic, turbulent-wind simulator which uses statistical models in order to simulate (numerical) time series for the three vector components of the wind speed at points in a -D vertical rectangular space fixed grid. The outputs of AeroDyn are used as inputs into the AT simulator. The module which AeroDyn s Inflow Wind module uses is the Taylor s frozen turbulence hypothesis in order to acquire the local wind speeds by using interpolation to the Turbim generated fields for both time and space. [3] In particular, through Turbim is given the opportunity to define the parameters for the runtime options, the turbine/model specifications, the meteorological boundary conditions, the non-international Electrotechnical Commision (IEC) conditions and finally for the coherent turbulence scaling parameters..4 AeroDyn AeroDyn is a plug-in type code, which is interfacing with a number of dynamic programs such as AT program for wind turbines. The AeroDyn is a data level routine, which refers to the analysis of wind turbines. AeroDyn requires information about the condition of a wind turbine from the dynamic analysis routine and returns the aerodynamic loads on each element of the blade of the wind turbine in the dynamic routine. [1] Through AeroDyn are defined very important parameters such as the hub height, the air density, the inematic viscosity and some parameters of the blades which the will be used. 3 REULT The behavior of a floating wind turbine is similar to the behavior of a ship. The movements consist of three translatory (urge, way and Heave) and three rotational (Roll, Pitch and Yaw) displacements, as you can see in ig.. igure. Geometry of the wind turbine The geometry of the wind turbine tower is.5m diameter, 90m height and the blade-tip diameter is 1m.There were examined two different floating structures of the wind turbine; one with draft of 10m and one with draft of 100m, while both of them are anchored via 3 catenary lines, as you can see in igs and 3. In both supporting structures the diameter at the upper part is.5m for 4m deep, equal to the diameter of the wind turbine in order to connect with it. At the depth of 4m the diameter increases until the depth of 1m where it reached the 9.4m and 10.4m, respectively, for the 10m and the 100m draft structure, and then continues with the same diameter for the rest 108m and 88m respectively, of the depth.

8 igure 3. Τhe submerged floating platform 3.1 The Cases The simulation cases which were performed were for wind speeds, U 10, in the range from 0 to 11 Beaufort. The range of 0-8 Beaufort corresponds to the situation of normal wind turbine operation, while in the range of 9-11 Beaufort the wind turbine is pared. our different incoming JONWAP irregular wave cases were examined with wave heights, Hs, of.5m, 3.8m, 4.5m and 8m which are induced by winds of 7, 8, 9 and 11 Beaufort, respectively. The results are presented through eight diagrams, igs. 4-7, for the two different types of floating wind turbines and two operating status cases. The first two diagrams (ig. 4) show the three translatory and three angular displacements respectively, for the limiting case of operation of the wind turbine with a draft of 10m while the next two (ig. 5) represent the respective displacements for the case where the wind turbine is pared (switched off). The next four graphs (igs. -7) correspond to the case of the 100m draft wind turbine. igure 4. Translational and rotational displacements for the limiting case of operation (U 10= 7 Bft, H s=.5m and T =.1sec) of the wind turbine with a draft of 10m

9 igure 5. Translational and rotational displacements for the pared case of operation (U 10= 11 Bft, H s= 8m and T = 8sec) of the wind turbine with a draft of 10m According to igs 4 and 5, it appears that in the case where the wind turbine is operating normally, the blowing wind speed is 7Bft and the contributing wave has wave height, H,.5m and period, T,.1 sec, the translational and rotational motions have greater range in contrast to the range of values of the corresponding movements in the case when the wind turbine is pared due to the high wind strength. This is because when the wind turbine is set as pared, the rotor is turned off thus the resistance which the blades receive, i.e., the force which the structure receives, is smaller. igure. Translational and rotational displacements for the limiting case of operation (U 10= 7 Bft, H s=.5m and T =.1sec) of the wind turbine with a draft of 100m igure 7. Translational and rotational displacements for the pared case of operation (U 10= 11 Bft, H s= 8m and T = 8sec) of the wind turbine with a draft of 10m imilarly, according to igs. -7, it appears that in the case where the wind turbine is operating normally, the blowing wind speed again is 8Bft and the contributing wave has wave height, H,.5m and period, T,.1 sec, the translational and rotational motions have greater range in contrast to the range of values of the corresponding movements in the case when the wind turbine is pared. This is because when the wind turbine is set as pared, the rotor is turned off thus the resistance which the blades receives i.e. the force which the structure receives is smaller.

10 4 CONCLUION The coupled fluid-structure interaction of a spar-buoy wind turbine, wind forcing and incident waves was examined for typical wave conditions in the Aegean ea using the modular program AT. Two different sparbuoy platforms were used to support the same wind turbine, and it was found that the platform with the smaller draft (100m) had no substantial operational deficiencies than the one with the larger draft (10m). ACKNOWLEDGEMENT This research has been co-financed by the European Union (European ocial und - E) and Hellenic national funds through the Operational Program "Competitiveness and Entrepreneurship" of the National trategic Reference ramewor (NR ) - Research unding Program: Bilateral R&D Cooperation between Greece and China , under project EAWIND with code 1CHN184. REERENCE [1] Laino, D.J. and Hansen, A.G. (00), ReadMe User s Guide to the Wind Turbine Aerodynamics Computer oftware AeroDyn, Windward Engineering LC, alt Lae City,UA. [] Jonman, J.M., Marshall, L. and Buhl, Jr. (005), AT User s Guide, National Renewable Energy Laboratory, UA. [3] Jonman, B.J., and Kilcher, L. (01), Turbim User's Guide: Version , National Renewable Energy Laboratory, UA. [4] Jonman, J.M., and Hayman, G. (013), ReadMe ile for HydroDyn v.00.0a-gjh, National Renewable Energy Laboratory, UA.