Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear  Interaction
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Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear Interaction

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An offshore wind turbine can be considered as a relatively complex structural system ...

An offshore wind turbine can be considered as a relatively complex structural system
since several environmental factors (e.g. wind and waves) affect its dynamic
behavior by generating both an active load and a resistant force to the structure’s
deformation induced by simultaneous actions. Besides the stochastic nature, also
their mutual interaction should be considered as nonlinear phenomena could be
crucial for optimal and cost-effective design. Another element of complexity lies in
the presence of different parts, each one with its peculiar features, whose mutual
interaction determines the overall dynamic response to non-stationary environmental
and service loads. These are the reasons why a proper and safe approach to the
analysis and design of offshore wind turbines requires a suitable technique for
carrying out a structural and performances decomposition along with the adoption of
advanced computation tools. In this work a finite element model for coupled windwaves
analysis is presented and the results of the dynamic behavior of a monopiletype
support structure for offshore wind turbine are shown.

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    Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear  Interaction Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear Interaction Document Transcript

    • Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves NonlinearInteractionManenti S., Petrini F.University of Rome Sapienza, via Eudossiana, 18 – 00184 Rome (Italy)Phone: +39 06 44 585 265Fax: +39 06 48 848 52e-mail: sauro.manenti@uniroma1.it - francesco.petrini@uniroma1.itABSTRACTAn offshore wind turbine can be considered as a relatively complex structural systemsince several environmental factors (e.g. wind and waves) affect its dynamicbehavior by generating both an active load and a resistant force to the structure’sdeformation induced by simultaneous actions. Besides the stochastic nature, alsotheir mutual interaction should be considered as nonlinear phenomena could becrucial for optimal and cost-effective design. Another element of complexity lies inthe presence of different parts, each one with its peculiar features, whose mutualinteraction determines the overall dynamic response to non-stationary environmentaland service loads. These are the reasons why a proper and safe approach to theanalysis and design of offshore wind turbines requires a suitable technique forcarrying out a structural and performances decomposition along with the adoption ofadvanced computation tools. In this work a finite element model for coupled wind-waves analysis is presented and the results of the dynamic behavior of a monopile-type support structure for offshore wind turbine are shown.INTRODUCTIONOwing to the major regularity and power of the wind forcing, open-sea turbinescould be an advantageous alternative with respect to analogous inland plants;furthermore they could become competitive with respect to other conventional,exhaustible and high environmental impact sources of energy if a proper designapproach is established assuring a good compromise between safety and costs relatedaspects.Anyway boundary conditions (i.e. loads and constraints) are highly time- andspace-dependent, along with mechanical properties of the materials that are subjectto significant variation over the structural life owing to fatigue, marine growth,corrosion etc. Furthermore different configurations must be handled, passing fromcomplete functionality to rotor stop.2014Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • As a consequence these structures can be defined “complex” and this requiresa critical revision of the design procedure according to a systemic approach(Bontempi, 2008b), i.e. a systemic decomposition of the relevant elements bothphysical (e.g. the constituting parts) and environmental related (i.e. identification ofthe structural loads and constraints).Different aspects and various performances under several load conditionshave to be investigated for this type of structures. Referring to all possible systemconfigurations that can be assumed by the blades and then by the rotor, one needexplicitly:1. to ensure that the components are designed for the extreme loadsallowing a fair survivability;2. to assure that the fatigue life of the components is guaranteed forthe service life;3. to define component stiffness with respect to vibrations andcritical deflections in a way that the behavior of the turbine cankeep under control by a careful matching of stiffness.In this context an important task concerns the proper definition of nonlinearinteraction between the forcings (e.g. wind and wave) that can influence significantlythe numerical prediction of the dynamic response and, consequently, the durabilityand the cost-effectiveness of the turbine (OWTES, 2003).Since an offshore wind turbine is generally planned for installation inintermediate depth water (with respect to a representative design wave length), itsdynamic characteristics are fairly different from an offshore platform for oil industry:the latter usually has a design natural frequency higher than the wave excitation,while the former is wedged between the wind and wave frequency; so in the last casenonlinear interaction between the environmental forcings should be properlyconsidered during the design phase as it can led to a beneficial aerodynamic dampingby lowering the structural stiffness of the turbine’s support: this would lead to bothan increase fatigue life and reduce the cost of the support.Relevant codes and standards (BSH, DNV, GL, IEC) provides an accuratedescription of the analytical methods for estimating the random action by wind andwaves separately; anyway nonlinear interaction phenomena still requires an in depthand careful investigation with the aim to give reliable estimate of the loads: such anaspect could play a crucial role in the calculation procedure of economical and safeoffshore wind turbines.This work is part and continues an early study on the modeling and design ofoffshore wind turbines (Bontempi, 2009); its approach follows structural andperformances decomposition in order to organize the qualitative and quantitativeassessment in various sub-problems, which can be faced by sub-models of differentcomplexity both for structural behavior and load scenarios.In the present work the dynamic analysis of a turbine and its monopilesupport structure in the frequency domain is carried out by means of the ANSYSfinite element model. Initially the loading induced by wind and random waves actingseparately is considered; subsequently the nonlinear effects by their mutual2015Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • interaction are accounted with the aim of pointing out the implication on the designprocedure.The outline of the paper is as follow:• the main features of both the ANSYS finite element and theanalytical models for the wind and wave random forcingare illustrated;• the results of the analyses carried out are discussed bypointing out the nonlinear effect induced by wind-wavesinteraction;• final conclusions concerning the study are then illustrated atthe end of the paper.MODEL DESCRIPTIONIn the present work a 5MW 3-bladed offshore wind turbine with monopile-typesupport is considered for carrying out the coupled wind-wave spectral analysis: itrepresents a structure of interest for possible planning of an offshore wind farm in theMediterranean Sea near the south-eastern cost of Italy.Tab. 1. Main geometrical characteristics of the structure.Monopile type supportZY XAerodynamicFluid-dynamicGeotechnicalFoundationSubmergedEmergentdlfoundHmud line ZY XZY XAerodynamicFluid-dynamicGeotechnicalFoundationSubmergedEmergentdlfoundHmud lineH = 100md=35mlfound=40mD =5mtw=0.05mDfound=6mD = diameter of the tubular tower;tw = thickness of the tower tubularmember;The main geometrical characteristics are summarized in Tab. 1: a Vestas-V90turbine with rotor diameter of 100m; the hub height is positioned 100m above meansea level (m.s.l.); the tower, with a steel tubular section, has a diameter of 5m with a2016Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • thickness of 50mm; water depth is 35m. At this stage of investigation the effect offoundation medium has been neglected and the lower node of the pile is assumedfixed at the sea bottom.Even if such an hypothesis looks like far from the actual behavior of thestructure, it has been possible, during an early phase, to check the numerical modelby comparing the numerical results with the analytical solution for an equivalentone-degree of freedom body. Additional investigations have to be carried out forintroducing the effect of marine soil on the dynamic response of the wind turbine andthe support (here after the structure).The monopile support has been selected as it appear economically convenientfor intermediate water depth purposes: according to the DNV (2004) classification itsrange of application is around 25m water depth and it would be a possible designsolution for planning an offshore wind farm in the southern Adriatic Sea.Moreover it is a relatively simple support structure and this allow to reducethe uncertainties related to the wave-induced loads estimation on submerged slopingmembers (Chakrabarti et al., 1975).In this work the analysis is performed by considering typical wind and wavesforcing with relatively small recurrence period (i.e. exercise load condition) thatcould be crucial for fatigue-induced long term damage; an early investigation basedon extreme events for monopile-type and other support structure has been yet carriedout in Bontempi (2008a).In the following subsections a description of the main features relevant to thefinite element model is provided; then the analytical models for the estimate of windand waves random loads are shown separately.zyx,x’z’y’Water level (medium)Mud lineWavesMediumwindCurrentP(t)vP(t)wP(t)uPTurbulentwind Vm(zP)PWater level (medium)Mud lineHub levelRHhvw(z’)Vcur(z’)zyzyx,x’z’y’x,x’z’y’Water level (medium)Mud lineWavesMediumwindCurrentP(t)vP(t)wP(t)uPP(t)vP(t)wP(t)uPTurbulentwind Vm(zP)PWater level (medium)Mud lineHub levelRHhvw(z’)Vcur(z’)Fig. 1 Problem sketch and actions configuration.2017Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • Model Features. The finite element model is realized with the ANSYS finiteelement code by adopting beam elements (BEAM4) for simulating the tower, whilethe blades and nacelle have been represented by a concentrated mass Mtop on thetower top by means of MASS21 element on which is applied the random horizontalforce caused by the wind trust. The tower base is assumed to be fixed for the reasonsexplained above.A suitable discretization of the exposed structure is carried out for loadapplication; at each node a spectral force is specified which corresponds to the effectof random waves (for nodes below the mean sea level) or wind excitation acting onthe corresponding area of pertinence.Calculation of the force spectrum for both environmental factors has beencarried out by applying the analytical models described in the following. Tab. 2summarizes the principal mechanical parameters for calculation of the random loads:E is the elastic modulus, ρ is the density, cD is the drag coefficient, cM is thehydrodynamic added mass coefficient and cL is the lift coefficient.Tab. 2. Summary of the most relevant model parameters.Vm10 [m/s] 14.5Esteel [kg/m2] 2.059E+11Eblade [kg/m2] 3.100E+20ρsteel [kg/m3] 7.980E+3ρwater [kg/m3] 1.024E+3cD hydr 1.05cM hydr 1.00cD tow 0.50cD blade 0.15cL blade 1.00Mtop [kg] 1.1E+5Wave Forcing. In the present work a Pierson-Moskowitz wave spectrum (for fullydeveloped sea condition) is adopted for dynamic analysis of the support structure forthe offshore wind turbine (Kamphuis, 2000):4445274.0,45,0081.0exp2)(⎟⎠⎞⎜⎝⎛===⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛−⋅⋅=VggSPMpPMPMpPMPMβωβαωωβωαπωηη(1)with ω =2π/T=2π f angular frequency, ωp spectral peak angular frequency, η(t) localfree surface elevation with respect to the mean sea level (m.s.l.), V intensity ofcharacteristic wind speed at the reference height of 19.5m above m.s.l. (see Eq. (12)for variation of the mean wind sped over the height).2018Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • According to the linear wave theory and making use of complex algebra thetime evolution of the free surface elevation η and of the horizontal components ofthe water particles velocity x& and acceleration x&& for each spectral wave componentof angular frequency ω are respectively:),(),()(sinhcosh),()exp()( 0tzxitzxtkdkztzxtiat&&&&ωηωωη−=⋅=−=; (2)By applying the Fourier transform and its conjugate to the variable x& , thespectrum of the horizontal velocity component of the water particles can be obtained:)(sinhcosh),(2ωωω ηηSkdkzzS xx ⋅⎟⎠⎞⎜⎝⎛=&&; (3)where from Sηη is defined by Eq. (1); the standard deviation of the water particlesvelocity component is then given by:∫∫∞∞⋅⎟⎠⎞⎜⎝⎛==0202)(sinhcosh),()( ωωωωωσ ηη dSkdkzdzSz xxx &&&. (4)In this work the Morison et al. (1950) empirical formula for evaluating theforce induced by a regular surface non-breaking wave on a slender and partiallysubmerged vertical cylinder is adopted.d|z|zxd+zdF(z,t)dzA A Sect. A-ADtwdzxdF(z,t)dzA ASect AADtwFig. 2 Specific force induced by regular wave on a partially submerged cylinder.2019Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • According to the scheme in Fig. 2 the force per unit length on the column is:),(),(),(),( tzxtzxCtzxCtzdF DI &&&& += (5)which is the sum of two distinct contributions: i) inertial force, also called virtualmass force, that is proportional to the horizontal component of the water particleacceleration; ii) drag force, proportional to the square of the water particle horizontalvelocity.The expression (5) implies that the axis of the cylinder is orthogonal to thedirection of wave advance; the horizontal components of both water particle velocityand acceleration are evaluated at the column axis as if it was absent by adopting thelinear wave theory (Dean & Dalrymple, 1991).The inertia and drag coefficients in Eq. (5) has the following expression for acylinder having circular section of diameter D:DcCCCADcC WDDAMWWMI ρρπρ2142=+=+= . (6)The inertia coefficient is made up of two contribution: the former is due tohydrodynamic mass and the latter pertains the variation of the pressure gradientwithin the accelerating fluid.The added mass coefficient cM is tabulated for the geometries of technicalinterest (Hooft, 1978); the drag coefficient cD is a function of the Reynolds number.Moreover both coefficients depends also on the Keulegan-Carpenter number definedas:DTxKC max&= , (7)with maxx& the maximum horizontal component of the water-particle velocity, T is thewave period and D is the cylinder diameter (Chakrabarti et al., 1976).Assuming that the velocity of the fluid particles is a Gaussian process withzero mean it is possible to eliminate nonlinearity from the drag term in Eq. (11)5 andwrite the linearized Morison force per unit length as follows:),(),(8),(),( tzxtzCtzxCtzdF xDI&&& &σπ+= , (8)being x&σ the standard deviation of the water-particle velocity component in xdirection given by Eq. (4).The Eq. (5) holds for a vertical cylinder (not necessary circular); whendealing with certain structures containing some members forming an angle with thevertical direction, such as steel lattice type, there is no general agreement on how theMorison Eq. should be extended to deal with. A method has been proposed inChakrabarti et al. (1975) that generalize the formulation given in (5) for a verticalcylinder.2020Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • The force dF acting per unit length on the wet part of the support structureassociated to a random sea state with spectral energy density Sηη as defined by Eq.(1) can be obtained by considering the expression of η, xx &&& and in (8) and substitutinginto Eq. (5):)()()cosh(8)cosh(sinh),( tzkzCkziCkdtzF xDI ησπωω⎥⎦⎤⎢⎣⎡+−= &, (9)being k=2π/L the wave number and L the wave length; note that the complexresponse method is adopted for representation of the harmonic variables (i denotesthe imaginary unit).By making the Fourier transform of such an expression the force spectrum isobtained as a function of the wave energy spectral density:[ ] )()()cosh(8)cosh()sinh(),(222ωσπωωω ηηSzkzCkzCkdzS xDIFF ⋅⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎥⎦⎤⎢⎣⎡+⎥⎦⎤⎢⎣⎡= &, (10)where the expression between braces in Eq. (10) is the force transfer function.Wind Forcing. Concerning the wind modeling for computing the aerodynamicactions, a Cartesian three-dimensional coordinate system (x,y,z), with origin at waterlevel and the z-axis oriented upward is adopted as shown in Fig. 1.Focusing on a short time period analysis the three components of the windvelocity field Vx(j), Vy(j), Vz(j) at each spatial point j (the variation with time isomitted for simplicity) can be expressed as the sum of an averaged (time-invariant)value Vm and the turbulent components u(j), v(j), w(j) with zero mean.Assuming that Vm is non zero only in x direction, the three components of thetotal velocity are given by:)()();()();()()( jwjVjvjVjujVjV zymx ==+= . (11)The mean velocity Vm(j) can be determined by a database of values recordedat or near the site, and evaluated as the record average over a proper time interval(e.g. 10 minutes).The variation of the mean velocity Vm with z over an horizontal surface ofhomogeneous roughness can be described, as usual, by an exponential law:α⎟⎟⎠⎞⎜⎜⎝⎛=hubhubmzzVzV )( . (12)In this expressions, Vhub is the reference wind velocity at the rotor elevationzhub, α=0.14 for extreme wind conditions; Vhub it is usually obtained as the mean ofthe wind velocity on a 10 minutes time period V10.2021Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • The turbulent components of the wind velocity are modeled as zero-meanGaussian ergodic independent processes; by adopting an Eulerian description and adiscretization of the spatial domain in N points representing the locations where thewind acts on the structure, each Gaussian process is completely characterized by thepower spectral density matrix [S]i, (i = u, v, w). The diagonal terms Sijij(n, z) (i = u, v,w and j = 1,2,…,N) of [S]i are given by the normalized half-side von Karman’spower spectral density (Solari and Piccardo, 2001):[ ] 652287014/iiijij(z)n.nσ(n,z)nSi+= , (13)where n is the current frequency (in Hz), z is the height (in m), σi2is the variance ofthe velocity fluctuations, given by (Solari and Piccardo, 2001):( )[ ] 202751logarctan116 *i u.)(zg.-σ += , (14)with z0 is the roughness length, u* is the friction or shear velocity (in m/s), given by:(0.006)1/2Vm(z=10), while ni(z) is a non-dimensional height dependent frequencygiven by:)()()(zVznLznmii = . (15)The integral scale Li(z) of the turbulent component can be derivedrespectively for i = u, v, w according to the procedure given in ESDU (2001).The out of diagonal terms Sijik(n, z) (k = 1,2,…,N) of [S]i are given by:))(exp()()()( nfnSnSnS jkikikijijijik −= , (15)being:( ))()(2)()(22kmjmkjzjkzVzVzzCnnf+−=π, (16)where Cz represents the decay coefficient, that is inversely proportional to the spatialcorrelation of the process.By considering a drag and lift force produced by undisturbed wind velocityacting on exposed turbine parts, the proposed model allows to estimate the forcespectrum at the j-point of the structure. When considering mobile structural partssuch as the rotor blades, relative wind speed (in a frame of reference moving with theblade) should be assumed for drag and lift force computation. For more details aboutsuch topics refers to Bontempi et al. (2008a).2022Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • DISCUSSION OF RESULTSIn the following results for the analyses carried out are discussed: first wave andwind forcing are treated separately and then their mutual interaction is investigated;the values adopted for the most relevant model parameters are summarized in Tab. 2.Fig. 3 shows the input spectra to the finite element model: both have beenplotted for a mean wind speed of 14.5m/s at 10m elevation above m.s.l. directed in x-direction and correspond to the parametric formulation given in previous Sections.1.0E-011.0E+011.0E+031.0E+051.0E+071.0E+091.0E+111.E-04 1.E-02 1.E+00 1.E+02 1.E+04freq [Hz]Forcespectra[N2/Hz]WindWaveFig. 3 Wind and wave force energy density spectra.Wave Forcing. Fig. 4 shows the results for the case of wave forcing acting alone onthe structure.1.0E-031.0E-021.0E-011.0E+001.0E+011.E-04 1.E-03 1.E-02 1.E-01 1.E+00freq [Hz]Responsespectra[m2/Hz]X directionFig. 4 Response spectra for wave forcing only.2023Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • The frequency of the first relative peak corresponds to the peak frequency ofthe wave force spectrum (about 0.1Hz); the maximum of the structural responseoccurs however at about 0.2Hz which is very close to the first vibration mode of thestructure.Wind Forcing. Fig. 5 shows the results for the case of wind forcing acting alone onthe structure.1.0E-031.0E-021.0E-011.0E+001.0E+011.E-04 1.E-03 1.E-02 1.E-01 1.E+00freq [Hz]Responsespectra[m2/Hz]X directionY directionFig. 5 Response spectra for wind forcing only.In this case the structural response in y-direction (i.e. orthogonal with respectto the mean wind direction) is non-zero since the two speed turbulent components arecorrelated as explained above.The spectral response is however higher along the x-direction as expectedsince the wind energy distribution is greater.In both cases a maximum peak appear for the peak frequency of the windspectrum and close to the first mode frequency of the structure.Combined Wind-Wave. When considering the effects of both wind andwave on the structure, the increasing roughness length of the sea surface owing to thepresence of propagating waves has been modeled according to an iterative processfollowing Holmes 2001.Fig. 6 shows calculated response spectra in each coordinate horizontaldirection.While along the y-axis the results are not affected by the presence of wavespropagating in the orthogonal direction, when considering the x-oriented responsespectrum it shows, in addition to the case of wind only (Fig. 5), the characteristicrelative maximum at the wave peak frequency (about 1Hz); furthermore, at thestructure’s natural frequency (i.e. 0.2Hz) the curve is above the value of 1.0m2/Hzbut it is not exactly the summation of those related to the wind and the wave alone(Fig. 4 and 5).2024Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
    • 1.0E-031.0E-021.0E-011.0E+001.0E+011.E-04 1.E-03 1.E-02 1.E-01 1.E+00freq [Hz]Responsespectra[m2/Hz]X directionY directionFig. 6 Response spectra for combined wind-wave forcing.The phenomenon described above is the result of a destructive interferencebetween wind and wave forcings: the resultant energy density of the response spectraat the structure’s natural frequency is less than the sum of the corresponding valuesrelated to the wind and wave acting separately.CONCLUSIONSIn this work a finite element model for the dynamic analysis of a monopile-typesupport structure for offshore wind turbine has been presented.The structural response in the frequency domain has been analyzed for bothwind and wave spectral forcings obtained starting from a characteristic wind velocitywhich is representative of the exercise condition to be adopted for fatigue-damageanalysis.These forcings have been considering as acting separately in the first phase,and then their mutual interaction has been simulated.Obtained results have shown that the response spectrum at the naturalfrequency of the structure exhibit a destructive interference between wind and waveforcings acting simultaneously.As a consequence, nonlinear interaction should be considered in the designphase of a safe and cost-effective offshore wind turbine as the actual load on thestructure could be lower than that extrapolated from the linear superposition of theeffects produced by the single forcings acting separately.ACKNOWLEDGEMENTSThe present work has been developed within the research project“SICUREZZA ED AFFIDABILITA DEI SISTEMI DELLINGEGNERIA CIVILE:IL CASO DELLE TURBINE EOLICHE OFFSHORE", C26A08EFYR, financed byUniversity of Rome La Sapienza Fruitful discussions with Prof. Franco Bontempi arealso acknowledged2025Earth and Space 2010: Engineering, Science, Construction,and Operations in Challenging Environments © 2010 ASCE
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