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performance is carried out, in order to organize the qualitative and quantitative assessment in various sub-problems. These can be faced by sub-models of different complexity both for the structural behavior and for the load models. Numerical models are developed to assess the safety performance under aerodynamic and hydrodynamic actions. In the structural analyses, three types of turbine support structures have been considered and compared: a

monopile, a tripod and a jacket.

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- 1. Structural Design and Analysis of Offshore Wind Turbines from a System Point of View by Francesco Petrini, Sauro Manenti, Konstantinos Gkoumas, Franco Bontempi R EPRINTED FROM WIND ENGINEERING VOLUME 34, N O . 1, 2010 M ULTI -S CIENCE P UBLISHING C OMPANY 5 WATES WAY • B RENTWOOD • E SSEX CM15 9TB • UK T EL : +44(0)1277 224632 • FAX : +44(0)1277 223453 E-MAIL: mscience@globalnet.co.uk • WEB SITE: www.multi-science.co.uk
- 2. W IND E NGINEERING VOLUME 34, N O . 1, 2010 PP 85–108 85 Structural Design and Analysis of Offshore Wind Turbines from a System Point of View Francesco Petrini1, Sauro Manenti2, Konstantinos Gkoumas3, Franco Bontempi*,4 1Department of Structural and Geotechnical Engineering, University of Rome “La Sapienza”, via Eudossiana, 18 - 00184 Rome, Italy (francesco.petrini@uniroma1.it) 2Department of Hydraulics Transportation and Roads, University of Rome “La Sapienza”, via Eudossiana, 18 - 00184 Rome, Italy (sauro.manenti@uniroma1.it) 3Department of Hydraulics Transportation and Roads, University of Rome “La Sapienza”, via Eudossiana, 18 - 00184 Rome, Italy (konstantinos.gkoumas@uniroma1.it) 4Department of Structural and Geotechnical Engineering, University of Rome “La Sapienza”, via Eudossiana, 18 - 00184 Rome, Italy (franco.bontempi@uniroma1.it) ABSTRACT Offshore wind turbines are relatively complex structural and mechanical systems located in a highly demanding environment. In this study, the fundamental aspects and major issues related to the design of such structures are inquired. The system approach is proposed to carry out the design of the structural parts: in accordance with this philosophy, a decomposition of the system (environment, structure, actions/loads) and of the structural performance is carried out, in order to organize the qualitative and quantitative assessment in various sub-problems. These can be faced by sub-models of different complexity both for the structural behavior and for the load models. Numerical models are developed to assess the safety performance under aerodynamic and hydrodynamic actions. In the structural analyses, three types of turbine support structures have been considered and compared: a monopile, a tripod and a jacket. 1. INTRODUCTION Offshore wind turbines (OWT) emerge as an evolution of the onshore plants for which the construction is a relatively widespread and consolidated practice providing a renewable power resource [1]. In order to make the wind generated power more competitive with respect to conventional exhaustible and high environmental impact sources of energy, the attention has turned toward offshore wind power production [2]. Besides being characterized by a reduced visual impact, since they are placed far away from the coast, OWTs can take advantage from more constant and intense wind forcing, something that can increase the amount and regularity of the productive capacity and make such a resource more cost-effective if the plant is lifelong and operates with minimum interruption through its lifespan. From a general point of view, an OWT is formed by both mechanical and structural elements. Therefore, it is not a “common” civil engineering structure; it behaves differently according to different circumstances related to the specific functional activity (idle, power *Corresponding author
- 3. S TRUCTURAL D ESIGN 86 AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A Blades – Rotor – Nacelle Tower Transition platform MONOPILE TRIPOD JACKET Water level Substructure Support structure Sea floor Foundation Seabed Foundation Figure 1: Main parts of an offshore wind turbine for different support structures. production, etc), and it is subject to highly variable loads (wind, wave, sea currents loads, etc.). In the design process, different structural schemes for the supporting structure can be adopted (Figure 1), mainly depending on the water depth, which determines the hydrodynamic loads acting on the structure and drives the choice of the proper techniques for the installation and maintenance of the support structure. Moreover, since the structural behavior of OWTs is influenced from nonlinearities, uncertainties and interactions, they can be defined as complex structural systems [3]. The above considerations highlight that a modern approach to study such structures has to evolve from the idea of “structure” itself, intended as a simple device for channeling loads, to the one of “structural system”, intended as “a set of interrelated components which interact one with another in an organized fashion toward a common purpose” [4]. This system approach includes a set of activities which lead and control the overall design, implementation and integration of the complex set of interacting components [5,6]. In this study, the original definition by NASA [4] has been extended in such a way that the “structural system” organization contains also the actions and loads. The latter derive from, and are strictly related to, the environment (Figure 2). A certain amount of complexity arises from the lack of knowledge and from the modeling of the environment in which the turbine is located. In this context two main design issues can be individuated: the consideration of the uncertainty deriving from the stochastic nature of the environmental forcings (in particular aerodynamic and hydrodynamic) and the proper
- 4. W IND E NGINEERING VOLUME 34, N O . 1, 2010 87 PERFORMANCE Structural system ENVIRONMENT Interaction STRUCTURE ACTIONS Figure 2: Structural system organization. Wind and wave flow ENVIRONMENT ZONE EXCHANGE ZONE Aerodynamic and aeroelastic phenomena Wind site basic parameters Structure Wave site basic parameters Site-specific environment Structural (nonenvironmental) system Wind, wave and sea current actions Nonenvironmental solicitations Other environmental agents Hydrodynamic phenomena Types of uncertainties Propagation 1. 2. 3. Aleatoric Epistemic Model Propagation 1. 2. 3. Aleatoric Epistemic Model 1. 2. 3. Aleatoric Epistemic Model Figure 3: Generic depiction of the uncertainties and the interaction mechanisms in the design of an offshore wind turbine structure. modeling of the possible presence of non linear interaction phenomena between the different actions and between the actions and the structure. In general, uncertainties can spread during the various analysis phases that are developed in a cascade. The incorrect modeling of the involved uncertainty can lead to an incorrect characterization of the structural response from a stochastic point of view and, thus, to an improper quantification of the risk for a given structure subjected to a specific hazard. Having as a goal the schematization of the problem and the individuation of the uncertainty propagation mechanisms, reference can be made to the Figure 3, where the process of the environmental actions generation is qualitatively represented also with considerations on the involved uncertainties. Following the wind and the hydrodynamic flows impacting on the structure, it is possible to distinguish two zones: • Environment zone: it is the physical region sufficiently close to the structure to assume the same environmental site parameters of the structure, yet far enough to neglect the flow field perturbations (in terms of particle’s trajectories, pressure field, etc.) induced by the presence of the structure itself. In the environment zone, the wind and the hydrodynamic flows can interact with each other and with other environmental agents, changing their basic parameters. The physical phenomena and uncertainties in the environment zone propagate in the neighborhood regions.
- 5. S TRUCTURAL D ESIGN 88 AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A • Exchange zone: it is the physical region adjoining the structure. In this zone, the structure itself, the wind and the hydrodynamic field experience the mechanical interchange (aerodynamic and hydrodynamic phenomena) from which the actions arise. In the exchange zone, some non-environmental solicitations are present; these solicitations may change the dynamic or aerodynamic characteristics of the original structure; so the actions are generated considering this structural sub-system (original structure combined with non-environmental solicitations) instead of regarding only the original structure itself. By definition, physical phenomena and uncertainties cannot propagate from the exchange zone to the environment zone. In general, the uncertainties can be subdivided in three basic typologies: • aleatory uncertainties (arising from the unpredictable nature of the magnitude, the direction and the variance of the environmental actions); • epistemic uncertainties (deriving from the insufficient information and the errors in measuring the previously mentioned parameters); • model uncertainties (deriving from the approximations in the models). Regarding for example the wind model and considering the turbulent wind velocity field as a Gaussian stochastic process, an uncertainty related to the hypothesis of Gaussianity is introduced. The aleatory uncertainties can be treated by carrying out a semi-probabilistic (looking for the extreme response) or a probabilistic analysis (looking for the response probabilistic distribution) analysis. A possible way to reduce the model uncertainties is given by differentiating the modeling levels. This can be carried out not only for the structural models, but also for the action and interaction phenomena models; for this reason different model levels are adopted (for the sake of simplicity, the epistemic uncertainties are not considered in this study). A suitable tool to govern the complexity is given from the structural system decomposition, represented by the design activities related with the classification and the identification of the structural system components, and by the hierarchies (and the interactions) between these components. As mentioned before, the decomposition regards not only the structure, but also the environment and the actions and loads, and it is the subject of the first part of this study. Furthermore, due to the complexity, the design of these structures has to be carried out under a Performance-Based Design philosophy: different aspects and performance under different loading conditions (with reference to all possible system configurations that can be assumed by the blades and the rotor) have to be investigated for this type of structures. Additional design issues related to the structural aspects are mentioned below with some proper references: • Aerodynamic optimization [7]. • Foundation design and soil-structure interaction [8, 9, 10]. • Fatigue calculations [11, 12]. • Vessel impact and robustness [13]. • Life Cycle assessment [14, 15]. • Marine scour [16, 17]. • Possible floating supports [18, 19]. • Standards certification [20, 21, 22, 23, 24, 25].
- 6. W IND E NGINEERING VOLUME 34, N O . 1, 2010 89 Figure 4: Different views of the jacket support structure adopted after the numerical analyses. Finally, an important issue for offshore wind turbines is the choice of the support structure, related principally to the water depth, the soil characteristics and economic issues. If the water depth (h) is considered as the principal parameter, according to the DNV-OS-J101 [22], the following rough classification can be made: monopile, gravity and suction buckets (h < 25m); tripod, jacket and lattice tower (20m < h < 40–50m); low-roll floaters and tension leg platform (h > 50m). In this study focus is given to monopile, tripod and jacket support structures. The paper starts with the description of the system approach applied to OWT design: while the system point of view is a consolidated practice in many engineering fields (e.g. aerospace engineering), in the case of OWTs, it is not fully established and represents an ongoing process. In the second part of the paper, the system point of view is applied to the numerical modeling of a case study. More precisely, numerical analyses are carried out on different OWT support structures. The obtained results justify the adoption of a jacket structure for the specific case (Figure 4). 2. STRUCTURAL SYSTEM DECOMPOSITION As previously stated the decomposition of the structural system is a fundamental tool for the design of complex structural systems, and it has to be performed together with the decomposition of the performance the structure has to fulfill (Figure 5). The decomposition is carried out focusing the attention on different levels of detail: starting from a macro-level vision and moving on towards the micro-level details (for more details see Bontempi et al. [26]). 2.1. Decomposition of the Environment The first step of the structural system decomposition concerns the environment. This is due to the fact that, in a global approach, the structure is considered as a real physical object placed on an environment where a variety of conditions, strictly related to the acting loads, should be taken into consideration. Their decomposition is performed in the first column of Figure 5.
- 7. S TRUCTURAL D ESIGN 90 AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A ENVIRONMENT STRUCTURE ACTIONS/LOADS Main structure Gravitational / Inertial Wind conditions Normal wind conditions Rotor–nacelle assembly Extreme wind conditions Marine conditions Junctions/bearings Waves Junctions/bearings Extreme wave conditions Junctions/bearings Water level Actuation Tower Seabed movement and scour Torque control Junctions Other conditions Yaw and pitch actuator loads Substructure Mechanical breaking loads Junctions Air temperature Other Foundations Humidity Wake loads Junctions Solar radiation Impact loads Secondary structure Rain, hail, snow, ice Wave Current Support structure Marine growth Aerodynamic Hydrodynamic Blades Sea currents Aviation Seismic activity Rotor Normal wave conditions Gravity Braking Nacelle Chemically active substances Mechanically active substances Tsunami Energy production Energy transfer Auxiliary structure Environmental aggressiveness Seismicity Operation Water density Maintenance Water temperature Emergency Lighting Maritime traffic PERFORMANCE Serviceability Safety Service Limit States –SLS Reliability Ultimate Limit States –ULS_1 Deflections/Displacements Stress limit Vibrations Strain limit Buckling Ultimate Limit States –ULS_2 Degradation effects Fatigue Limit States –FLS Robustness Accidental Limit States –ALS Impact Explosion Fire Figure 5: Structural system and performance decomposition of an offshore wind turbine. 2.2. Decomposition of the Structure The second step of the decomposition relates to the offshore wind turbine structure. This is organized hierarchically, considering all the structural parts categorized in three levels (second column of Figure 5): • Macroscopic (macro-level), related to geometric dimensions comparable with the whole construction or parts with a principal role in the structural behavior; the parts so considered are called macro components which can be divided into: – – the main structure, that has the objective to carry the main loads; the secondary structure, connected with the structural part directly loaded by the energy production system; – the auxiliary structure, related to specific operations that the turbine may normally or exceptionally face during its design life: serviceability, maintainability and emergency.
- 8. W IND E NGINEERING VOLUME 34, N O . 1, 2010 91 Focusing the attention on the main structure, it consists in all the elements that form the offshore wind turbine. In general, the following segments can be identified: a. b. • support structure (the main subject of this study); rotor-nacelle assembly. Mesoscopic (meso-level), related to geometric dimensions still relevant if compared to the whole construction but connected with specialized role in the macro components; the parts so considered are called meso-components. In particular the support structure can be decomposed in the following parts: a. foundation: the part which transfers the loads acting on the structure into the seabed; b. substructure: the part which extends upwards from the seabed and connects the foundation to the tower; c. • tower: the part which connects the substructure to the rotor-nacelle assembly. Microscopic (micro-level), related to smaller geometric dimensions and specialized structural role: these are simply components or elements. 2.3. Decomposition of the Actions and Loads The next step of the structural system decomposition is the one regarding the actions related to the environmental conditions. These are decomposed as shown in the third column of Figure 5, from which the amount of the acting loads can be comprehended. It is important to underline that, since the environmental conditions in general are of stochastic nature, the magnitude of the actions involved is usually characterized, from a statistical point of view, by a return period TR: lower values of TR are associated with the so called “normal conditions”, while higher values of TR are associated with “extreme conditions”. 2.4. Performance Decomposition As a final step, the performance requirements are identified and decomposed as follows (lower part of Figure 5). • Assurance of the serviceability (operability) of the turbine, as well as of the structure in general. As a consequence, the structural characteristics (stiffness, inertia, etc.) have to be equally distributed and balanced along the structure; • Safety assurance with respect to collapse, in plausible extreme conditions; this is applicable also to the transient phases in which the structure or parts of it may reside (e.g. transportation and assembly), and that have to be verified as well; • Assurance of an elevated level of reliability for the entire life-span of the turbine. As a consequence, a check of the degradation due to fatigue and corrosion phenomena is required; • Assurance of sufficient robustness for the structural system, that is to ensure the proportionality between an eventual damage and the resistance capacity, independently from the triggering cause, ensuring at the same time the survival of the structure under a hypothetical extreme condition. The following performance criteria can be identified for the structural system, leading eventually to the selection of appropriate Limit States: • Dynamic characterization of the turbine as defined by the functionality requirements, regarding the: – natural vibration frequencies of the whole turbine, including the rotor-nacelle assembly, the support structure and the foundations;
- 9. S TRUCTURAL D ESIGN 92 AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A – compatibility of the intrinsic vibration characteristics of the structural system with those of the applied forces and loads; – compatibility of the displacement and the acceleration of the support system with the functionality requirements of the turbine. • Structural behavior with respect to serviceability (SLS- Serviceability Limit State), regarding the: – – • limitation of deformations; prevention of any loosening of the connections. Preservation in time of the structural integrity, regarding the: – – • durability for corrosion; structural behavior with respect to fatigue (FLS-Fatigue Limit State). Structural behavior under near collapse conditions (ULS-Ultimate Limit State), regarding the: – assessment of the stress state for the whole structure, its parts, elements and connections; – – • assessment of the global resistance of the structural system; assessment of the resistance for global and local instability phenomena. Structural behavior in presence of accidental scenarios (ALS-Accidental Limit State), regarding the: – provisions for the decrease in the load bearing capacity proportional to the damage (the concept of structural robustness- see for example Starossek [27] and Bontempi et al. [28]); – provisions for the survival of the structural system in presence of extreme and/or unforeseen, situations; these include the possibility of a ship impacting the structural system (support system or blades), with consequences accounted for specific risk scenarios. 3. ENVIRONMENT AND ACTION MODEL From all the loads indicated in Paragraph 2.3, in this study attention is focused on the aerodynamic and the hydrodynamic ones. Typically, an environmental action, when observed during a short time period, is made of two components: a mean (or slowly variable) component, and a stochastic one. For the aerodynamic and the hydrodynamic actions, the mean component is generated respectively by the mean wind velocity and by the sea current, while the stochastic component is generated respectively from the turbulence wind velocity and from the linear waves. The definition of “mean” has to be specified with reference to a specified “short time period” (usually less than 1 hour); in contrast, the so called “mean component” varies in a stochastic manner during long time periods. For this reason, in what follows the mean components will be considered as constant only for short periods of analyses. The generic environmental configuration is shown in Figure 6, where the macrogeometric parameters defining the problem are also represented. These are the local mean water depth (h), the hub height above the mean water level (H) and the blade length (or rotor radius, R). Correct prediction of the structural response under extreme and normal load conditions requires the definition of their probability distribution and statistical
- 10. W IND E NGINEERING VOLUME 34, N O . 1, 2010 93 WP (t) P uP (t) VP (t) Turbulent wind W ate r le ve l (m P Vm (zP) Mean wind ea n) R Hub Waves Mu level z dl ine H y Vw (z′) y′ x, x′ Current z′ Vcur (z′) vel ter le n) (mea Wa h e d lin Mu Figure 6: Problem statement and configuration of the actions. parameters; these are site specific, and have to be estimated by carrying out statistical analyses of the measurements database. In particular two kinds of investigations are usually carried out: short term statistics for fatigue analysis, and long term statistics, for ultimate limit state analysis. Finally, the definition of the extreme load cases requires an estimation of the probability distribution for: (i) the extreme 10-min average wind velocity at the reference height, and (ii) the significant wave height estimated in a 3-hour reference period along with the associated spectral peak period. When no information is available for defining the long term joint probability distribution of extreme wind and waves, it shall be assumed that the extreme 10-min mean wind speed with a 50-year recurrence period occurs during the extreme sea state with a 50-year recurrence period (IEC 64100-3 [25]) adopting appropriate reduced values. 3.1. Aeolian and Hydrodynamic Fields Model Concerning the wind modeling for the computation of the aerodynamic action, a Cartesian three-dimensional coordinate system (x,y,z), with origin at the mean water level and the zaxis oriented upward is adopted. Focusing on a short time period analysis, the three components of the wind velocity field Vx ( j ), Vy ( j ), Vz ( j ) at each spatial point j (the variation with time is omitted for the sake of simplicity) can be expressed as the sum of a mean (timeinvariant) value and a turbulent component u(j ), v(j), w(j) with mean value equal to zero.
- 11. S TRUCTURAL D ESIGN 94 AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A Assuming that the mean value of the velocity is non-zero only in x direction, the three components are given by: Vx (j) = Vm(j) + u(j ); Vy ( j ) = v(j ); Vz ( j ) = w(j) (1) The mean velocity Vm(j) can be determined by a database of values recorded at or near the site, and evaluated as the record average over a proper time interval (e.g. 10 minutes), while the variation of the mean velocity Vm with the height z over a horizontal surface of homogeneous roughness can be described by an exponential law. Finally, the turbulent components of the wind velocity are modeled as zero-mean Gaussian ergodic independent processes. By using the proposed model, it is possible to generate samples of the wind action exerted at each point j of the structure. Concerning the hydrodynamic actions, as previously stated, they are due to currents and waves. For what concerns the sea currents induced by the tidal wave propagation in shallow water condition (i.e. the ratio between water depth h and wave length L is lower than 0.05), in general they are characterized by a sub-horizontal velocity field, while their intensity decreases slowly with the depth. Waves act on the submerged structural elements and on the transition zone above the water-air interface; in the first case actions are the result of the alternative motion of fluid particles, induced by the fluctuating perturbation of the liquid surface; in the second case the action is the consequence of the breaking waves, which may occur in shallow water condition. In general the short period water surface fluctuation, with respect to the mean sea level, is a time-dependent stochastic variable, and can be described by means of statistical parameters: • the significant wave height HS ; it is defined as four times the mean square root of the sea elevation process. It represents a statistical measure of the intensity of the wave climate as well as of the variability in the arbitrary wave heights. • the spectral peak period TP ; it is related to the mean zero-crossing period of the sea elevation process. For extreme events analysis, in general the significant wave height is defined with respect to a proper return period TR (DNV-OS-J101 [22]). For fatigue analysis the sea state is characterized through the wave energy spectral density, defined upon the domain of frequency and geographic direction of the wave components: usually this is obtained by multiplying the calculated one-dimensional spectrum S(f) by a function of directional spreading, symmetric with respect to the principal direction of the wave propagation [29]. 3.2. Aerodynamic and Hydrodynamic Actions Model In general, the components of the actions could be calculated separately for all structural elements adopting a common frame of reference and then superimposed by a vector sum in a phase-correct manner. The aerodynamic force can be decomposed, as usual, in a drag (parallel to the mean wind velocity) and a lift (orthogonal to the mean wind velocity) component, while moments have been neglected in the present paper. These can be computed for each structural component from the specific wind velocity field and for each structural configurations (for example, extreme wind and parked turbine configurations), by using well known expressions, as shown in Bontempi et al. [30] and Petrini et al. [31]. The equivalent static load can be derived through peak factors, based on the probabilistic characteristics of the wind velocity modeled as a stochastic process [32].
- 12. W IND E NGINEERING VOLUME 34, N O . 1, 2010 95 Concerning the hydrodynamic loads on a structural slender cylindrical member (D/L < 0.2, with: D member diameter normal to the fluid flow, L wave length), both wave and (stationary) current generate the following two components: • A force per unit length acting in the direction perpendicular to the axis of the member and parallel to the orthogonal (with respect to the member) components of the water particle velocity (wave vw plus current Vcur induced) and acceleration (wave only); it can be estimated by means of Morison equation: ρ πD 2 · 1 dF ( z ',t ) = ci wat vw ( z ',t ) + cd ρwat D vw ( z ',t ) +Vcur ( z ',t )⋅ vw ( z ',t ) +Vcur ( z ',t ) dz ' 4 2 (2) where ρwat is the water density, ci and cd are the inertia (including added mass for a moving member) and drag coefficient respectively, which are related to structural geometry, flow pattern and surface roughness: superposed dot indicates the time derivate, in the Eq. (2). Periodic functions are adopted for both the wave velocities and accelerations [33]. • A non-stationary (lift) force per unit length acts in the direction perpendicular both to the axis of the slender member and to the water current. This component is induced by vortex shedding past the cylinder and inverts its direction at the frequency fl of eddies separation which is related to flow field and structural geometry through Strouhal number St = Dfl /Vcur ; fl should be kept far from the structure’s natural frequency to avoid resonances. In the case of static analysis, equivalent static forces are applied considering the amplitude of the fluctuating actions and, eventually, applying proper load amplification factors. 4. NUMERICAL MODELING OF THE STRUCTURE As stated in Section 1, a differentiation of the modeling level is adopted to reduce the uncertainties. The level of a generic model of the structure is here identified by means of two parameters: the maximum degree of detail and the scale of the model; if the finite element method is adopted, at each model level it is possible to associate a certain typology of finite element, which is mainly used to build the model. In general, four model levels are defined for the structure: 1. System level (S): the model scale comprises the whole wind farm and can be adopted for evaluating the robustness of the overall plant; highly idealized model components are used in block diagram simulators. 2. Macro level or Global modeling (G): in these models, the scale reduces to the single turbine structure, neglecting the connections between different structural parts. The component shapes are modeled in an approximate way, the geometric ratios between the components are correctly reproduced; beam finite elements are mainly adopted; 3. Meso-level or Extended modeling (E): these models are characterized by the same scale of the previous level but with a higher degree of detail: the actual shape of the structural components is accounted for and the influence of geometrical parameters on the local structural behavior is evaluated. Shell elements are adopted for investigating the internal state of stress and strain (e.g. for fatigue life and buckling analysis) inside the structure extrapolated from previous models;
- 13. S TRUCTURAL D ESIGN 96 AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A 4. Micro level or Detail modeling (D): this kind of models are characterized by the highest degree of detail and used for simulating the structural behavior of specific individual components, including connecting parts, for which a complex internal state of stress has been previously pointed out e.g. due to the presence of concentrated loads. Shell or even solid finite elements are used. The features for different structural model levels are resumed in Table 1; a similar distinction can be made regarding the specification of the external loads. According to what said above, at the initial stage of investigation structural analyses have been carried out with macro-level and meso-level models of the three offshore wind turbine structure types previously described. With reference to Figure 7 some of the developed macro-level structural models are shown for the monopile (left part), tripod (middle) and jacket (right part) support structure. Model Level System level Macro-level Meso-level Micro level Table 1: Definition of the model levels Maximum Detail Level Main Adopted Finite Elements wind farm approximate shape of the BLOCK elements structural components single turbine approximate shape of the BEAM elements structural components, correct geometry single turbine detailed shape of the SHELL, SOLID elements structural components individual detailed shape of the SHELL, SOLID elements components connecting parts Scale (a) (b) (c) Emergent Transition Z X Y Immersed Foundation Figure 7: Macro-level finite element models: monopile (a), tripod (b) and jacket (c).
- 14. W IND E NGINEERING VOLUME 34, N O . 1, 2010 97 The effect of foundation medium should be simulated with a full non-linear model in order to account for possible plastic effects and load time-history induced variation of the mechanical properties. At this level of investigation, an idealized soil has been simulated by means of both: • Linear springs: such technique has been adopted for the macro-level models. Springs are applied at the pile surface and acts in the two coordinate horizontal directions: the corresponding mechanical parameters have been set up on the basis of available soil characteristic and simulates its lateral resistance at the pile interface; • Solid elements: used for meso-level models. These three-dimensional elements simulate the linear mechanical behavior of the soil. The extension of the foundation medium included in the model has been selected in order to minimize boundary effects. Both kinds of models have been used for evaluating the modal response of the structural system. The decomposition of both the structural system and the performance, and the differentiation of the model levels can be used to guide and optimize the numerical analysis efforts in this design phase. In this sense, focusing on a certain structural component and selecting the specific performance, the choice of both model level and type of analysis to adopt can be done, in such a way, to give the best efficiency of the analysis (deriving from a suitable balance between the required detail level of outputs and the computational efforts needed). For example, focusing the attention on the tower with a steel tubular section, the maximum stresses for Ultimate Limit State analysis can be preliminary obtained by adopting a macro-level model and by carrying out a static extreme analysis (characterized by extreme values of the environmental loads). However, if the local buckling phenomena need to be assessed, a more detailed meso-level structural model and a static incremental analysis is required. These considerations are summarized in Table 2. Structural Component Table 2: Model and analysis type selection Performance Model Level Analysis Type Macro Stress safety (ULS) Static extreme Meso Macro Global Buckling (ULS) Static incremental Meso Tower Meso Local Buckling (ULS) Static incremental Micro Macro (poor) Fatigue (FLS) Meso Micro Dynamic
- 15. S TRUCTURAL D ESIGN 98 AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A 5. NUMERICAL ANALYSES The numerical analyses have been conducted for three different support structures: monopile, tripod and jacket. The principal geometrical and structural features adopted for the analyses are as follows: • hub height positioned 100 m above the mean sea level (m.s.l.); • tower with a steel tubular section, with a diameter of 5 m and a thickness of 0.05 m; • water depth of 35 m; • foundations depth of 40 m; • foundation diameter of 6 m (monopile), 2.5 m (tripod and jacket). For the tripod substructure, the tubular tripod arm diameter and thickness is respectively of 2.5 m and 0.05 m. For the jacket substructure, the diameter (thickness) of the vertical, horizontal and diagonal tubular members, is respectively of 1.3 m (0.026 m), 0.6 m (0.016 m) and 0.5 m (0.016 m). Finally, the tower supports a Vestas-V90 turbine [34] with a rotor diameter of 90 m. 5.1. Modal Analysis The preliminary task of the dynamic analysis is to assess the natural modes of vibration in order to avoid that non-stationary load (e.g. wind and wave induced) could cause the system resonance when excitation and natural frequencies are closer. Geometrical parameters of the three support structures have thus been selected with the aim of maintaining the corresponding natural frequency far from that of the non-stationary external forcing (wind and wave). The finite element modal analysis provided the deformed shapes given in Figure 8, where only odd modes are displayed since modes i and i +1 (with i = 1, 3) have the same frequency but vibration occurs in orthogonal planes, according to the axial symmetry of the tower (the eccentric mass of the blades is neglected). In Figure 9, the two x-parallel dashed lines correspond, respectively, to the mean rotor frequency (1P) and the frequency of a single blade passing (3P), which is triple with respect to the former one for a three bladed turbine. These frequencies determine the sampling period of the wind turbulent eddies and, as a consequence, the characteristics of the induced non-stationary actions. Therefore, they (a) 1st (b) M0 3rd M0 1st (c) M0 3rd M0 1st M0 3rd M0 Z X Y Z X Y Figure 8: Modal analysis (macro-level models). Natural mode shapes for the monopile (a), tripod (b) and jacket (c) support structures.
- 16. W IND E NGINEERING VOLUME 34, N O . 1, 2010 99 2.0 Freq. [Hz] 2.5 Monopile Tripod Jacket 1.5 1.0 3P 0.5 1P 0.0 1 3 Mode number 5 Figure 9: Comparison of the natural frequencies. assume importance when performing dynamic analysis and are generally compared with respect to the first natural frequency fnat in order to classify the structural behavior: • if fnat falls below 1P the structure is called “soft-soft”; for this type of structure the wave load could be dominant with respect to the wind load, and the fatigue effects can be significant; • if fnat is between 1P and 3P the structure is called “soft-stiff”; for this type of structure the wind action frequency could be considerable higher than the one due to waves, and the fatigue effects can be still significant; • if fnat is greater than 3P the structure is called “stiff-stiff”; for this type of structure the fatigue effects in general are not significant. From the results plotted in Figure 9 it can be seen that the structural system falls in the softstiff range only if the jacket support type is adopted. In the same figure, it can be noted that for the first couple of modes the dynamic behavior of the jacket is stiffer than the one of the other types, but the trend inverts from the third mode on. 5.2. Static Analysis Under Extreme Loads Steady loads have been assumed for the principal environmental actions and no functional loads are present (parked condition). The external forcing has been characterized by assuming prudentially a return period larger than the one prescribed by Codes and Standards. The numerical analysis for the selected support structure types has been carried out considering the three load cases summarized in Table 3, where: • Vhub represents the wind velocity at the hub height; • VeN (with N = 1 or 100) represents the maximum wind velocity with a return period TR equal to N years, derived from the reference wind velocity associated with the same return period VrefN multiplied by a certain peak factor; • VredN represents the reduced wind velocity with a return period TR equal to N years and it is derived from the previous one by applying a reduction factor;
- 17. 100 S TRUCTURAL D ESIGN AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A Table 3: Load cases Design Situation Load Factors γF Gravitational Inertial Combination Name Wind Condition Marine Condition Environmental 6.1b Vhub=Ve100 H=Hred100 1.35 1.1 1.25 Vhub=Vred100 H=Hmax100 Vhub=Ve1 H=Hred100 1.35 1.35 1.1 1.1 1.25 1.25 Parked (standstill or idling) 6.1c 6.3b In the same table HmaxN and HredN represent respectively the design maximum wave height and the design reduced wave height associated whit a return period TR equal to N years. Steady wind field has been assumed along with stationary and regular wave actions; both actions have been assumed to act in the same direction. The design wind exerts a force distribution that is dependent on the undisturbed flow pattern: the resultant action on the rotor blades has been concentrated at the hub height while the drag forces acting on the support are distributed along the tower and the exposed piece of the substructure (jacket type only). The immersed part of the support structure is subject to combined drag and inertia forces induced by the undisturbed wave and the current induced flow field. In Figure 10, the calculated vertical profiles of the aerodynamic and hydrodynamic actions induced per unit length on the tower and the substructure respectively are shown for the monopile case. The analyses carried out through macro-level models allowed for evaluation of both the reactions at the mud line (shear and overturning moment) and the induced displacement at the hub height. Results obtained with macro-level models are summarized in Figure 11. The maximum shear stress at the mud line is reached for the load case 6.1c, i.e. the one characterized by maximum wave height and reduced wind speed (see Table 3); on the other hand, the combination giving the maximum bending moment at the mud line corresponds to extreme wind and reduced wave height (combination 6.1b). From what above follows that wave and current exert much more influence on the resultant shear force, while the wind appears to be more critical for the overturning moment, being distributed at a higher distance from the base. Aerodynamic Hydrodynamic Hydrodynamic 40 120 35 Height above sea level [m] 100 40 35 30 30 Height above mud line [m] 80 25 20 15 10 10 5 40 20 15 60 Height above mud line [m] 25 5 20 Action [N/m] 0 0 0 5000 Comb 6.1b Action [N/m] Action [N/m] 0 10000 Comb 6.1c 0 100000 Comb 6.1b 200000 Comb 6.1c 0 100000 Comb 6.1b Figure 10: Environmental actions (monopile type support). 200000 Comb 6.1c
- 18. W IND E NGINEERING VOLUME 34, N O . 1, 2010 101 400000 7000 350000 6000 300000 5000 250000 4000 200000 3000 150000 100000 2000 50000 1000 0 [KN*m] Monopile Tripod 6.1b 6.1c 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 [m] 0 [KN] Jacket Monopile 6.1b 6.3b Monopile Tripod 6.1b 6.1c Tripod 6.1c Jacket 6.3b Jacket 6.3b Figure 11: Overturning moment, total shear reaction at the mud line and hub displacements, for three different load cases. Moreover, from the same figure it can be seen that the three structural types experience approximately the same resultant shear and moment under each load combination. Concerning the horizontal displacement at hub height, it can be seen an increasing stiffness of the support structure moving from the monopile to the jacket type under each load combination. Maximum displacement occurs always for load case 6.1b giving rise to the higher overturning moment; for the jacket type it is almost one-third the one of the monopile. In Table 4 the applied loads and the numerical results obtained for the more severe combination (6.1b) are reported, where the maximum stress in the tower has been computed by the combination of compression (or tension) and bending stresses. Table 4: Applied loads and the numerical results (loads combination 6.1b) Actions Reactions at mud line Structural checks Wind on rotor [KN] Wind on tower [KN] Wave and current [KN] Overturning moment [KN*m] Shear reaction at mud line [KN] Vertical reaction at mud line [KN] Maximum stress in the tower [N/mm2] Nacelle displacement [m] Monopile 1663 740 3372 350456 5775 Tripod 1663 740 3372 350456 5775 Jacket 1663 428 3500 337087 5591 10714 286 10356.3 (max in pile =15018) 230 13768 (max in pile =9929) 151 4.66 3.72 1.82
- 19. 102 S TRUCTURAL D ESIGN AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A Figure 12: Detailed jacket support structure meso-level model. From the previous results, it can be deduced that the jacket support type is the best choice for what concerns the structural response under extreme loads (above all for the maximum stress in the tower and for the nacelle displacement). A meso-level model has been prepared for this type of support, after the exploration of a number of tentative models (the model is shown in detail in Figure 12). The meso-level model of the OWT structure is shown in Figure 13 (left part), while the right part of Figure 13 shows the foundation medium (five substrates with different mechanical characteristics), modeled using brick finite elements. This level of detail allows the designer to investigate the internal state of stress for critical parts (Figure 14). The connection between the tower (shell elements) and the jacket is modeled using rigid beams elements (middle part of Figure 14). The meso-model is subjected to the load case referred to as 6.1b in Table 3 (most severe); the result gives a nacelle displacement equal to 2 m and a maximum stress in the tower equal to 178 MPa (at the jackettower connection). This is in good agreement with the result of the macro-level. The small differences are probably related to the variation in the tower diameter (ranging from 5.0 meters at the tower base to 3.4 meters at the top) along the vertical direction and to the
- 20. W IND E NGINEERING VOLUME 34, N O . 1, 2010 103 Figure 13: Meso-level structural model of the jacket and corresponding deformed shape under static aerodynamic and hydrodynamic loads. Figure 14: Elastic internal state of stress at critical zones, jacket-tower connection and tower thickness transition. varying thickness of the tubular member at a fixed transition section (right part of Figure 14). These features are properly reproduced in the meso-level model, while in the macro-level model they are set equal to their maximum values. 5.3. Buckling Analysis Another important aspect concerns the stability problem. A static incremental analysis has been conducted in order to assess the buckling load; in this case, the hydrodynamic actions
- 21. S TRUCTURAL D ESIGN 104 AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A Figure 15: Results of the buckling analysis. have been schematized by using of single force acting on the jacket at the mean water level (Figure 15). The analysis gives a multiple of 1.17 for the extreme load case referred to as 6.1b in Table 3. It is important to outline that the first buckling mode shows a local instability of the tower tubular section, an effect that cannot be accounted for with the macro-models. 6. CONCLUSIONS In this paper, the system approach has been proposed as a conceptual method for the design of offshore wind turbine structures. In this sense, a structural system decomposition has been performed, with a specific view on the structural analysis and performance. The presented considerations aim at the organization of the framework for the basis of design of offshore wind turbines, as a support to the decision making, with specific reference to the structural safety, serviceability and reliability for the entire lifespan. Furthermore, numerical analyses have been performed to compare the safety performance of three different support structure types, generally adopted for a water depth lower than 50m: monopile, tripod and jacket support structures. Extreme loads with a recurrence period of 100-years have been applied at this stage of investigation. Well-known analytical formulations have been summarized for correct characterization of both the aerodynamic and hydrodynamic actions, whose contribution is crucial for assessing the structural behavior. An early analysis has been carried out for the investigation of the dynamic response for each one of the three support structures. Thus, the natural modes of vibration have been determined in relation with the principal geometrical design parameters. This is essential for avoiding the occurrence of resonance when the frequencies of the external forces could excite the structure’s natural modes. A subsequent static analysis has been carried out simulating three different load combinations as prescribed by International Standards: the relative influence of aerodynamic and hydrodynamic loads has been assessed, focusing on the resultant shear force and the overturning moment at the mud line, and on the horizontal displacement at the hub height. This step is introductory for the selection of the jacket structure as the appropriate support type. Moreover, the internal state of stress under the abovementioned steady extreme loads has been evaluated by means of two different levels of detail for the numerical models (macroand meso-level). The analyses have confirmed that macro-level model results can predict the basic aspects of the structural response, yet the meso-level model provides an additional and more detailed picture of the structural behavior due both to the major capabilities of the
- 22. W IND E NGINEERING VOLUME 34, N O . 1, 2010 105 adopted finite elements (shell and brick instead of beam elements) and to the higher geometrical resolution of the models. Finally, an incremental analysis has been carried out to assess the buckling load of the examined offshore wind turbine: this occurs in the tower tubular section for a multiplier equal to 1.17 for the more severe extreme loads. Starting from the results presented here, future and more refined studies can take into account for other relevant effects influencing the dynamic response of the structure (e.g. scour, coupling with foundation medium, non-stationary loads, non-linear interactions etc.) by performing transient analyses. ACKNOWLEDGEMENTS The present work has been developed within the Wi-POD Project (2008-2010) and other research projects in the field of wind engineering, partially financed by the Italian Ministry for Education, University and Research (MIUR). Fruitful discussions with Prof. Pier Giorgio Malerba of the Politecnico di Milano, Prof. Marcello Ciampoli of the Sapienza – Università di Roma, Professor Hui Li of the Harbin Institute of Technology and Dr. Ing. Gaetano Gaudiosi of the OWEMES association are gratefully acknowledged. Finally, Prof. Jon McGowan is acknowledged, for inspiring part of this work. REFERENCES [1] Hau, E., Wind Turbines: Fundamentals, Technologies, Application, Economics, 2nd edn., Springer-Verlag Berlin, Heidelberg, 2006. [2] Breton, S.-P. and Moe, G., Status plans and technologies for offshore wind turbines in Europe and North America, Renewable Energy, 2009, 34 (3), 646–654. [3] Bontempi, F., Basis of Design and expected Performances for the Messina Strait Bridge, Proceedings of the International Conference on Bridge Engineering – Challenges in the 21st Century, Hong Kong, 1-3 November, 2006. [4] NASA (National Aeronautics and Space Administration), Systems Engineering Handbook, 1995. Available online on 10/2009 at: www.nasa.gov. [5] Simon, H.A, The Sciences of the Artificial, The MIT Press, Cambridge, 1998. [6] Bontempi, F., Gkoumas, K. and Arangio, S., Systemic approach for the maintenance of complex structural systems, Structure and infrastructure engineering, 2008, 4, 77–94. [7] [8] Snel, H., Review of Aerodynamics for Wind Turbines, Wind Energy, 2003, 6 (3), 203–211. Westgate, Z.J. and DeJong, J.T., Geotechnical Considerations for Offshore Wind Turbines, 2005, Report for MTC OTC Project, Available online on 10/2009 at: http://www.masstech.org/IS/Owec_pdfs/GeotechOffshoreFoundations-MTCOWC.pdf. [9] Ibsen, L. B. and Brincker R., Design of a New Foundation for Offshore Wind Turbines, Proceedings of the IMAC-22: A Conference on Structural Dynamics, Michigan, 26–29 January, 2004. [10] Zaaijer, M. B., Foundation modelling to assess dynamic behaviour of offshore wind turbines, Applied Ocean Research, 2006, 28 (1), 45–57. [11] Veldkamp, D., A probabilistic approach to wind turbine fatigue design, Proceedings of the European wind energy conference and exhibition, Milan, 7–10 May, 2007. [12] Tempel, J. van der, Design of support structures for offshore wind turbines, PdD Thesis, Technische Universiteit Delft, 2006.
- 23. 106 S TRUCTURAL D ESIGN AND A NALYSIS OF O FFSHORE W IND T URBINES S YSTEM P OINT OF V IEW FROM A [13] Biehl, F. and Lehmann, E., Collisions of Ships and Offshore Wind Turbines: Calculation and Risk Evaluation, Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, 4–9 June, 2006. [14] Martìnez, E., Sanz, F., Pellegrini, S., Jiménez, E. and Blanco, J., Life cycle assessment of a multi-megawatt wind turbine, Renewable Energy, 2009, 34 (3), 667–673. [15] Weinzettel, J., Reenaas, M., Solli, C. and Hertwich, E.G., Life cycle assessment of a floating offshore wind turbine, Renewable Energy, 2009, 34 (3), 742–747. [16] Sumur, B.M. and Fredsøe, J., The mechanics of scour in the marine environment, World Scientific Publishing Co., Singapore, 2002. [17] Tempel, J. van der, Zaaijer, MB. and Subroto, H., The effects of scour on the design of offshore wind turbines, Proceedings of the 3 rd International conference on marine renewable energy, Blyth, July 6–9, 2004. [18] Henderson, A.R. and Patel, M.H., On the modeling of a floating Offshore Wind Turbines, Wind Energy, 2003, 6 (1), 53–86. [19] Jonkman, J.M. and Buhl Jr., M.L., Loads Analysis of a Floating Offshore Wind Turbine Using Fully Coupled Simulation, Proceedings of the WindPower Conference and exhibition, Los Angeles: California, June 3–6, 2007. [20] API (American Petroleum Institute), Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms–Load and Resistance Factor Design (RP 2A-LRFD), 1993 (suppl. 1997). [21] BSH (Bundesamt für Seeschifffahrt und Hydrographie), Standard: Design of Offshore Wind Turbines, 2007. [22] DNV (Det Norske Veritas), Offshore Standard: Design of Offshore Wind Turbine Structures (DNV-OS-J101), 2004. [23] GL (Germanischer Lloyd) Wind Energie GmbH, Richtlinie zur Erstellung von technischen Risikoanalysen für Offshore-Windparks, 2002. [24] GL (Germanischer Lloyd) Wind Energie GmbH, Guideline for the Certification of Offshore Wind Turbines, 2005. [25] IEC (International Electrotechnical Commission), Wind Turbine Generator Systems – part 3: Design requirements for offshore wind turbines (IEC 61400-3), 2009. [26] Bontempi, F., Li, H., Petrini, F. and Gkoumas, K., Basis of Design of Offshore Wind Turbines by System Decomposition, Proceedings of the 4th International Conference on Advances in Structural Engineering and Mechanics, Jeju, Korea, 26–28 May, 2008. [27] Starossek, U., Progressive Collapse of Structures, Thomas Telford Publishing, London, 2009. [28] Bontempi, F., Giuliani, L. and Gkoumas, K., Handling the exceptions: dependability of systems and structural robustness, Proceedings of the 3rd International Conference on Structural Engineering, Mechanics and Computation, Alphose Zingoni (Ed.), Millpress, Rotterdam, 2007. [29] Polnikov, V.G., Manenti S., Study of relative role of nonlinearity and depth refraction in wave spectrum evolution in shallow water, Journal of Engineering Applications of Computational Fluid Mechanics, 2009, 3 (1), 42–55.
- 24. W IND E NGINEERING VOLUME 34, N O . 1, 2010 [30] 107 Bontempi, F., Li, H., Petrini, F. and Manenti, S., Numerical modeling for the analysis and design of offshore wind turbines, Proceedings of the 4th International Conference on Advances in Structural Engineering and Mechanics, Jeju, Korea, 26–28 May, 2008. [31] Petrini, F. Giuliano, F. and Bontempi, F., Comparison of time domain techniques for the evaluation of the response and the stability in long span suspension bridges, Computer & Structures, 2007, 85, 1032–1048. [32] Van Binh, L., Ishihara, T., Van Phuc, P. and Fujino, Y., A peak factor for non-Gaussian response analysis of wind turbine tower, Journal of Wind Engineering and Industrial Aerodynamics, 2008, 96 (10–11), 2217–2227. [33] Brebbia, C.A. and Walker Newnes, S., Dynamic analysis of offshore structures, Butterworth, London, 1979. [34] www.vestas.com.

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