Evaluation of Offshore Wind Turbine Tower Dynamics with Numerical Analysis

A dynamic behaviour of a cylindirical wind tower with variable cross section is investigated under environmental and earthquake forces. ,e ground acceleration term is represented by a simple cosine function to investigate both normal and parallel components of the earthquake motions located near ground surface. ,e function of earthquake force is simplified to apply Rayleigh’s energy method. Wind forces acting on above the water level and wave forces acting on below this level are utilized in computations considering earthquake effect for entire structure.,e wind force is divided into two groups: the force acting on the tower and the forces acting on the rotor nacelle assembly (RNA). ,e drag and the inertial wave forces are calculated with water particle velocities and accelerations due to linear wave theory. ,e resulting hydrodynamic wave force on the tower in an unsteady viscous flow is determined using theMorison equation.,e displacement function of the physical system in which dynamic analysis is performed by Rayleigh’s energy method is obtained by the single degree of freedom (SDOF) model. ,e equation of motion is solved by the fourth-order Runge–Kutta method.,e two-way FSI (fluid-structure interaction) technique was used to determine the accuracy of the numerical analysis.,e results of computational fluid dynamics and structural mechanics are coupled in FSI analysis by using ANSYS software. Time-varying lateral displacements and the first natural frequency values which are obtained from Rayleigh’s energy method and FSI technique are compared.,e results are presented by graphs. It is observed from these graphs that the Rayleigh model can be an alternative way at the prelimanary stage of the structural analysis with acceptable accuracy.


Introduction
During the last decades, world energy demand is constantly increasing on a global scale.is increase encourages to start exploring new directions in energy production.Renewable energy has become a mainstream subject of these investigations.e production of electrical energy from the wind energy is one of the most cost-effective and feasible projects to reduce the emissions of carbonic gas, preserve the environment, and earn carbon credits [1,2].Wind plays a predominant role on the scene of clear energy production.Wind turbines can be efficiently used at offshore sites where the higher wind speeds are available compared to those on land [3].An additional 50% of electricity can be generated by the same turbine in offshore, compared to that in onshore [4].However, it is essential that the offshore turbine towers are designed for severe environmental conditions.Wind is considered as design force for onshore structures [5] while wave force is dominant in the offshore environment [6].Approximately, 70% of the total environmental forces is composed of wave and current forces affecting the dynamic response [7].e wave forces can be used as decisive in the design of offshore wind towers [8,9].e combination of wind and wave forces is a common study field, and these investigations are used to design offshore wind towers more stable [10].On the other hand, the effect of earthquake force on dynamic behaviour of wind turbine structures is investigated as well as the wave and wind forces [11][12][13].
A typical modern wind turbine can be broken down into its major parts, which are the blade, cabin, and tower.Dynamic analyses of the blade, cabin, and tower are investigated separately by many researchers [14].e tower that should safely carry both dead loads of equipments and additional loads caused by the environmental forces is the critical part of the wind turbine.e tapered, tubular steel towers are the simplest and the most common technical solutions in the last decade [15].
e o shore structures under various environmental force patterns are examined with using numerous analysis techniques in the past [16][17][18].
Nowadays, it is possible to solve complicated uidstructure interaction (FSI) problems due to the rapid development of computer software.FSI analyses can be classi ed as one-way and two-way coupling models.In the one-way coupling type, only the uid pressure is transferred to the structure solver, and in the two-way coupling type, the displacement of the structure is also transferred to the uid solver [19].
e one-way FSI analysis in wind turbines is being researched actively [20][21][22], and the two-way FSI model is being performed [23,24] to analyze structural stability, deformation, and stress due to environmental forces.In addition, semi-empirical models are developed as alternative applications to examine the dynamic behaviour.Rayleigh's energy method is one of the available techniques for vibration analysis.
e basic concept of Rayleigh's energy method is single degree of freedom (SDOF).Rayleigh's energy method is used to estimate the natural frequency corresponding to the rst mode of vibration by Kim and Han [25], Ward [26], and Cruz and Miranda [27] as in this study.
In this study, the e ect of environmental forces and seismic loads on the o shore wind tower behaviour is performed with two various approaches.Wind force is divided into force acting on the tower and equipments.e tower subjected to wave forces represented by the linear wave theory.e Morison equation is employed to obtain lateral wave forces.In the rst approach, the displacement function of the wind tower is determined by the SDOF model.Dynamic vibration is investigated with Rayleigh's energy method by using this displacement function.e equation of motion that is representing dynamic behaviour is integrated by using the fourth-order Runge-Kutta method.e values of displacements, stresses, and natural frequencies are established under wind, wave, and earthquake forces.In the second approach, numerical simulations are also utilized in a 3D nite element model in the framework of ANSYS by evaluating FSI.Two-way FSI analysis is performed by connecting the mechanical system and another participant Fluent system to a system coupling component system [28].e variations of displacements and natural frequency values are compared for the results of the nite element model (FEM) and Rayleigh model.

Description of Structure
e wind tower is selected as similar to the one used in Van der Woude and Narasimhan [13] for this study, consisting of uniform and homogeneous material that is planned to be xed to the seabed.e outside diameter of the tower is 4.00 m at the base and 1.50 m at the top and the constant wall thickness of 30 mm. e material properties are chosen to represent the steel, with Young's modulus of 21 × 10 7 kN/m 2 , Poisson's ratio of 0.3, and density of 78.50 kN/m 3 .For steel, it is assumed that the material will comply with the associated Prandtl-Reuss ow rule and von Mises yield criterion [29].e reinforced berglass polyester material is used for the blades which are xed on pitched bearings that can be feathered 90 °for shutdown purposes.
e hub height of the wind turbine is 65 m.Fixed and free supports are placed at the boundaries.
e tower construction carries the weight of the nacelle, hub, and the rotor blades which is 83,000 kg.Young's modulus of the blade material is 65×10 6 kN/m 2 , and the value of density is 21.00 kN/m 3 .e blade length is 24 m, hub diameter is 6 m, and swept area of the blades is 624 m 2 .e structural model is presented in Figure 1.
Apart from the equipment, only the wind tower is considered in the structural analysis.e dead weight of the equipment (hub, nacelle, and blade) is implemented at the top of the tower.e dead weight, earthquake, wind, and wave forces in the global x direction are taken into account in the solutions.

Description of Forces Acting on Structure
e structural modal is designed by considering dead loads (N) as well as wind (F w and F aero ), wave (F H ), and earthquake forces (F eqk ) as given in Figure 2. When determining the dynamic behaviour of the wind tower, two di erent strategies are used.
e environmental forces (wind and wave) and earthquake force are externally assigned to the tower in Rayleigh's energy method.Advances in Civil Engineering In the nite elements analysis, velocity pro les that de ned as boundary conditions are used to compute these mentioned forces.e e ect of environmental forces and earthquake force in designing is explained in the other sections.

Wind Forces.
e wind forces acting on the Rotor Nacelle Assembly (RNA) and associate instrumentation can be considered as a concentrated force [30] and can be determined with an equation similar to that for the calculation of hydrodynamic forces: where F aero is the wind force acting on the structure, ρ air is the density of air, C aero is the aerodynamic coe cient (shape, surface and dependent) which is considered as 0.50 for the cylindrical sections, A (y) is the exposed area of the section, and V air(y,t) is the wind velocity which is presented by the following equation [31]: where V ref is the basic parameter called as reference wind velocity.e values of time-dependent wind velocity are presented in Figure 3.
e mean value of wind velocity is determined as 18 m/s.e roughness coe cient describes the e ect terrain roughness and is de ned by a logarithmic law [32].In this study, the terrain factor k r is assumed as 0.17 and the length of roughness z 0 is considered as 0.01.

Wave Forces.
e wave parameters were utilized to compute the hydrodynamic wave forces acting on the wind tower.e wave height H, wave length L, and wave period Tare the major wave parameters [33,34].Moreover, di erent environmental conditions were characterized by using water depth d which is applicable to determine the wave theories [35].
In this study, the o shore environment conditions are modelled in the numerical analysis by the linear wave theory.e parameters are considered as H 1.80 m, T 5 s, L 38.90 m, and d 20 m.As seen in Figure 4, the wave surface is determined based on the potential ow approach, by linear wave theory.e sea water characteristics were chosen as uid properties, with a density of 1025 kg/m 3 and a dynamic viscosity of 0.0015 Ns/m 2 .
e orbital motion of the water particle is signi cant for the horizontal hydrodynamic force.
e force consists of two components: a drag force (F D ) and an inertial force (F I ) [36].
e drag force and the inertial force are proportional to the uid particle velocity and uid particle acceleration, respectively.e equations of uid particle velocity (u) and acceleration ( _ u) according to linear wave theory are given as follows: where θ (2π/L)x − (2π/L)t and is called as the phase angel.e total lateral hydrodynamic force (F H ), which

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includes drag and inertial forces, is obtained by the Morison equation as follows: ese two components are added together to give the Morison equation: where ρ w is the salty water density, D is represented as the diameter of the tower.As seen in ( 4) and ( 5), the drag force coefficient C d and inertial force coefficient C M are needed to calculate the force components.In this study, the values of C d and C M are assumed as 2.4 and 0.7, respectively [37].

Earthquake Forces.
e dynamic analyses predicting the behaviour of the tower to either wind, wave, or seismic excitation are complicated due to the fact that the structure is partially immersed in water.
e acceleration, or the rate of change of the velocity of the waves setting the structure in motion, determines the percentage of the structure mass or weight that must be dealt with as a horizontal force [38].Because of the inertial force formula, acceleration is a key factor in determining the forces on a tower, but a more significant measure is acceleration combined with duration, which takes into account the impact of earthquake forces over time.In this study, the acceleration of earthquake is considered as follows: Because sine and cosine acceleration pulses are physically realizable and resemble in several occasions, the fault parallel and the fault normal component of motions are recorded near the source of strong earthquakes [39].A forcing function is derived for the earthquake model by writing the equations of motion in an accelerating frame of reference coincident with the base motion.

Analysis of the Wind Tower Response
Rayleigh's energy method and ANSYS FSI analysis are utilized to obtain natural frequencies neglecting the dynamic effects of blades on the tower [13].e weight of the nacelle and the rotor blades and wind loads acting on these equipments are implementing on the top of the turbine tower.
All problems in structural dynamics can be formulated based on the above equation of motion [40]: where Z is the coordinate vector, m is the mass, c and k are the coefficients of damping and stiffness, respectively.e external force is equalized to the inertial, damping, and restoring forces.Moreover, _ Z(t) is the velocity, € Z(t) is the acceleration, and F(t) is the total force.(•) denotes derivative with respect to time d/dt.

Displacement Function.
When motion is analyzed in a specific direction, the dynamic system is processed as a SDOF.Accordingly, we can define the displacement function as where ψ(y) is a shape function and Z(t) is the displacement.By substituting ( 9) into ( 8), the equation of motion of the tower can be reconstructed and thus can be given as follows: e dynamic analysis is performed considering the external forces acting on the wind tower when t � 0 by using SAP software.And the initial shape function is obtained in accordance with the displacement curve as e examination of the exact solution of linear ordinary differential equations is carried out utilizing the associated classical boundary conditions.
Fixed support is considered as the bottom condition and free support is assumed at the top of the tower.e boundary conditions are defined as follows: e equation of motion of the SDOF system is determined by substituting the shape function as below: � 140732 − 33.92 sin(1.26t)+ 2.59 cos(1.26t) 4

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where the length of the turbine tower is L, Young's modulus of the material is E, the axial force is N, the damping coe cient of the system is c and are assumed as 65 m, 2.1 × 10 e fth-order Runge-Kutta method is used to solve (14).e initial conditions are considered as when t 0 at y 0 ⇒ Z(0) 0 and _ Z(0) 0, e displacement function based on time-varying, Z(t), is generated with boundary conditions.en, the displacement function based on locationvarying, v(y, t), is obtained as where Z 0 is the value of the maximum displacement and ω is the natural frequency.e displacement function (16) described above is used in Rayleigh's energy method to derive the natural frequency.

Rayleigh's Energy Method.
e dynamic behaviour of the o shore structures can be characterized in terms of one or more natural frequencies.Rayleigh's energy method is one of the available techniques for determining the natural frequency [41]. is method, which requires a displacement function, reduces the dynamic system to a single degree of freedom (SDOF) system.
Rayleigh's energy method is a technique for nding natural frequencies by equating the maximum kinetic energy of a system with the maximum potential (often strain) energy.e potential energy of the wind tower can be given as e maximum potential energy is attained when the mass reaches its maximum displacement as follows: e kinetic energy of nonuniform mass distribution is presented as e maximum kinetic energy is attained when the mass passes the equilibrium position as given below: Advances in Civil Engineering e natural frequency is obtained by equalizing kinetic and potential energy e method described above is checked with the computer-aided FSI method (ANSYS FSI).In this study, the modelling process starts in ANSYS Workbench multi eld when the simulation is performed between transient structural (ANSYS Mechanical) and uid ow (ANSYS Fluent).Both models are developed independently.Independent mesh, boundary conditions, analysis options, and output options are used for each model.Initial analysis is performed for the structural part with the speci ed fundamental properties (density, Young's modulus, and Poisson's ratio) for the structure.
e ow chart for multi eld simulations with ANSYS is given in Figure 5.
In the mechanical application, the structural part is meshed and the uid part is suppressed.Appropriate names are assigned to all inlet, outlet, and side surfaces and symmetry planes in Fluent.e ANSYS mapping is done to interpolate loads between dissimilar meshes on either side of the coupling interface.is model will be used to transfer the displacement applied at the boundary surface to the other nodes.
e e ect of wave and wind forces on structural behaviour of the wind tower is considered with a nonlinear numerical model based on the nite volume method with the ANSYS Fluent analysis program [40].
e dimensions of the air domain are 20 × 20 × 45 m and the water domain is 20 × 20 × 20 m in directions x, y, and z, respectively (Figure 6).e wind tower is surrounded by a box with 5 × 5 × 65 m which is created to make a re ned mesh around the structural members.
e CFD mesh of this study is a hybrid mesh combination of tetrahedral and prism layers.e mesh distance of the uid model in the box is taken as 0.01 m. e mesh distance is 0.30 m in the remaining parts of the model.To calculate deformation of the boundary between uid and solid, the displacement di usion algorithm is used.e connections between the nodes are modelled as springs. is sti ness can change from node to node; near boundaries, though, the mesh sti ness is set very high.e mesh distance of the uid model is taken as 0.02 m in contact surfaces with the solid model.e computational structural mechanics (CSM) nite element mesh is used for the tower.e same value of wall thickness (0.035 m) is selected for node distances in the solid model.e uid (water and air) and solid domains contain approximately 2.12 million and 51.000 cells, respectively.
Five meshes with di erent resolution as shown in Figure 7 has been created in order to perform a mesh convergence study.Re ned mesh sizes (RMSs) are considered as 0.01 m, 0.02 m, 0.05 m, 0.07 m, and 0.10 m. Figure 7 shows Advances in Civil Engineering the comparison of horizontal hydrodynamic forces (F H ). e maximum di erence of 8% is observed between the peak values.So, it can be concluded from the comparison that the solution (force) is reasonably independent of the mesh resolution.
e ow involves the free surface between air and water that is solved using VOF (volume of uid) formulation [40].
e VOF model depends on the Euler-Euler approach.e general form of the transport equation can be given as where ρ is the density and u and S are the velocity and momentum source terms, respectively.e variable φ can be replaced by any scalar quantity, and Γ is the di usion coe cient [42].e e ects of turbulence are modelled using RANS (Reynolds-averaged Navier-Stokes) simulation.e realizable k-ε turbulence model is represented by the transport equations as follows [43]: where k is the turbulent kinetic energy, ε is the turbulence dissipation rate, μ t is the turbulent viscosity, e calculations for the structure side are based on the impulse conservation.e model utilizes the equation of motion presented in (8).e earthquake force is considered besides the environmental forces in structural dynamic analysis.e vibration characteristics of a structure while it is being designed are investigated by modal analysis.In a mathematical sense, the computation of natural frequencies and mode shapes is equivalent with the solution of an eigenvalue problem [42].In this study, the QR damped method is used as an eigensolver in ANSYS to compute natural frequencies.
At the boundary between uid and solid, the uidstructure interface, information for the solution is shared between the uid solver and structure solver.
e information of pressures and displacements is exchanged between the domains dependent on the coupling method.For two-way coupling calculations, uid and wind pressure is transferred to the structure and the displacement of the structure is also transferred to the uid solver [19].e properties of steel material are employed for the wind tower.Salty water and air properties are de ned for uid domain.e system is solved iteratively until the changes in the ow forces and the structural displacements fall below a prescribed amount.

Numerical Results
e examination of the exact solution of the linear ordinary di erential equation is carried out by the Runge-Kutta method utilizing the associated boundary conditions.
Hence, the time-varying displacement values which are obtained by using Rayleigh's energy method and FEM are compared in Figure 8. Analyses are observed during 40 seconds, and the time step size is assumed as 0.01 second.
As seen in Figure 8, the maximum value of the displacement is obtained as 0.412 m for the FEM method and 0.382 m for Rayleigh's energy method.e maximum displacement is obtained at the top of the cylindrical structure.
e von Mises stress and displacement values according to the FEM analysis are presented in Figure 9.
e maximum von Mises stress value is 1.1639 × 10 10 Pa. ese gures illustrate that the stress values on the tower surface are found to be higher closer to the seabed.e hydrodynamic wave and wind velocities calculated by the CFD analysis are shown in Figure 10 for 10 seconds.
Hydrodynamic forces that are transferred from the uid domain to the solid domain are determined by analysis program according to these hydrodynamic velocities.e natural torsional frequency values and vibration modes are computed by eigenvalue analysis.e dominant vibration modes are given in Figure 11.ere is a predominance of translational displacements towards the "x" axis in the first vibration mode.e first torsional natural frequency value is determined as 9.012 Hz (bending frequency as 0.691 Hz) by ( 21) and 9.440 Hz (bending frequency as 0.711 Hz) by FEM analysis.Environmental forces effect on the behaviour of the structure is investigated by several researchers, similar to our study [44,45].e transfer matrix method was used for dynamic analyzing of the large-scale wind turbine steel tower and the natural frequency value was obtained as 0.9765 for the first mode by Meng and Zhangqi [45].Zhao et al. investigated the influence of the diameter, thickness, taper angle, nacelle and rotor mass, and offset of mass on the inherent characteristic of the tower on the dynamic behaviour.e basic bending frequency and torsional frequency values were obtained as 0.529 Hz and 5.142 Hz, respectively, by the Rayleigh method.e proposed methods in this paper showed good agreements with dynamic analysis results by the published literatures.

Conclusions
e dynamic behaviour of the wind tower when it is subjected to environmental and seismic loads is investigated utilizing two various approaches.Environmental forces consist of regular wind and wave loads.Wind force acting on the tower is determined due to Eurocode velocity.Linear wave theory is adopted to design marine conditions.e Morison equation is employed to obtain lateral wave forces.e tower is designed by using the single degree of freedom (SDOF) model.In the first approach, Rayleigh's energy method which is the most popular analytical method for vibration analysis of a single degree of freedom system is used.Rayleigh's energy method is based on the principle of conservation of energy.Dynamic vibration is investigated by using the displacement function in presence of the fourthorder Runge-Kutta method.
e values of displacements and natural frequency are established under wind, wave, and earthquake forces.In the second approach, numerical simulations are applied with the framework of ANSYS via FSI.Two-way FSI analysis is performed to compare the results.e forces from fluid to structure and displacements from structure to fluid are considered with the two-way FSI analysis.
When the first natural frequency values of the tower were investigated, it was established that differences are not exceeding 4.77%.
e natural frequency value which is obtained from the approximate shape function converges to its real value from top.e displacement values decrease as the FEM analysis results.
e maximum displacement is calculated at 2.53 sec.While the maximum wave velocity value is 1.78 m/s, wind velocity reached 27.25 m/s in the peak point of the tower.e results of the investigation for the FEM analysis showed that the highest value of von Mises stresses is 1.1639 × 10 10 Pa for 2.53 sec.
High structures cannot be modelled easily by the FEM because of node and elements number.In the present paper, it is observed that the Rayleigh model can be an alternative practical way of structural analysis.

Figure 1 :
Figure 1: e model of the wind turbine.

Figure 2 :
Figure 2: e forces acting on the wind tower.

Figure 5 :
Figure 5: Flow chart for multi eld simulations with ANSYS.

Figure 9 :
Figure 9: e distribution of the von Mises stress values.

t = 1 Figure 10 :
Figure 10: Velocity vectors of uid domain around the wind tower.

C 1 ,
C 1ε , and C 2 are the constants, and σ k and σ ε are the Prandtl numbers.G k represents the generation of turbulence kinetic energy due to the mean velocity gradients, G b represents the generation of turbulence kinetic energy due to buoyancy, Y M is the contribution of uctuating dilation, and i, j are the tensor indices.e Fluent CFD code and ANSYS transient structural FEM code are applied concurrently for the following boundary conditions as illustrated in Figure 6.e transport equations are discretized in both space and time.Explicit time integration is used for temporal discretization.

Figure 11 :
Figure 11: First three vibration modes of the wind tower.