Finite Element Modelling and In Situ Modal Testing of an Offshore Wind Turbine
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Abstract
Purpose
Generating electricity from wind turbines is currently a viable option to meet the electric power requirements in many countries. The structure of offshore wind turbines is constantly subjected to external dynamic loads due to wind, waves and rotor loads due to the rotation of blades. The frequency content of these dynamic loads is in the range of natural frequencies of the wind turbine. Therefore, determining the in situ dynamic characteristics of a wind turbine is very beneficial, as it can lead to further improvements in its design, performance and safety.
Methods
In this paper, the dynamics of the structure of an offshore wind turbine is investigated numerically and experimentally. The finite element (FE) model of structural components is developed based on design specifications. The model takes the effect of rotor–nacelle assembly into account by considering its mass and moment of inertias relative to the top centre of the tower. In situ modal tests using impulse excitations were carried out on the actual wind turbine when the rotor blades were not rotating to identify the modal parameters.
Results
This paper presents predicted natural frequencies from the FE model based on design conditions and those identified from the modal and ambient excitation tests.
Conclusion
It was observed that the first two bending modes are close to the natural frequencies identified experimentally by the in situ modal tests. It was also observed that the in situ modal tests were not able to excite other higher natural frequencies of the structure.
Keywords
Offshore wind turbines In situ modal testing Structural dynamics Finite element modellingIntroduction
Developing and harvesting alternative sources of energy has become vital over the past few years due to concerns about global warming caused mostly by using fossil fuels for energy production. Some countries have set targets to produce a specific fraction of total required electricity from renewable sources for the next decade to gradually decrease their dependency on fossil fuels. Wind energy is one of the alternatives, which can be converted into electricity by installing wind turbines at locations with consistent winds. Offshore wind farms are rapidly being developed especially in Europe, mainly because larger wind turbines can be placed offshore leading to higher energy production capacity.
The structure of offshore wind turbines is constantly subjected to external dynamic loads due to wind and waves, as well as rotor loads due to the rotation of blades. The frequency content of these dynamic loads is in the range of natural frequencies of the wind turbine. Therefore, determining the dynamic characteristics of a wind turbine is very beneficial not only to improve the design and performance, but also to understand their sensitivity to different load cases for structural health monitoring purposes.
Zaaijer [1] investigated the accuracy of several simplified dynamic models for the foundation of offshore wind turbines. The first and second natural frequencies of the support structure for five different wind turbines were obtained from the finite element model and experimental data. The difference between computed and measured natural frequencies was in the order of 0.5–35% and 3–57% for the first and second natural frequencies, respectively. The dynamic responses of an offshore wind turbine with jacket foundation were studied by Ong et al. [2] through numerical simulations. Bisoi and Haldar [3] also conducted numerical studies to understand the dynamic behaviour of offshore wind turbines supported on monopiles in clay soil. The tower and monopile were modelled as Euler–Bernoulli beam elements, while the foundation was simulated using nonlinear Winkler model. Adhikari and Bhattacharya [4] also utilised Euler–Bernoulli beam theory to propose a model for characterisation of the dynamic behaviour of offshore wind turbines. Andersen et al. [5] obtained the probability density function of the first natural frequency of an offshore wind turbine with monopile foundation based on a simple model integrating a nonlinear p–y curve for calculation of pile displacement. Their model did not consider soil damping due to material dissipation or wave radiation.
Damgaard et al. [6] carried out experimental investigations to obtain the first bending frequency of an offshore wind turbine in the North Sea. Ten rotor stop tests were conducted to evaluate the dynamic properties of the wind turbine. They also developed a numerical model considering soil damping based on Winkler approach to perform modal analysis and presented the first bending frequency obtained from the numerical model and experiment. A comparison between dynamic responses of monopile, tripod and jacket foundation structures for an offshore wind turbine was made by Shi et al. [7]. In addition to natural frequencies, different responses such as displacement, bending moment and shear force were compared for all the foundations. The modal analysis results showed that marine growth has negligible effect on the natural frequencies. Ibsen [8] equipped a prototype of a bucket offshore wind turbine with accelerometers at different locations to obtain the natural frequencies of the wind turbine for three conditions: idle conditions, turbine without blades and turbine without blades and nacelle. The effect of different conditions on the first two natural frequencies was illustrated.
In this paper, the finite element (FE) model of structural components of an offshore wind turbine is developed based on design specifications to predict the natural frequencies and mode shapes. The model takes the effect of rotor–nacelle assembly into account by considering its mass and moment of inertias relative to the top centre of the tower. Nonlinear support springs obtained from a p–y curve are used to model the interaction between the monopile and the surrounding soil. Also presented in this paper are the results of in situ modal and ambient excitation tests carried out on the actual wind turbine.
Case Study
Specifications of the offshore wind turbine
Turbine name | SWT-2.3-93 |
Rotor diameter (m) | 93 |
Rated power (MW) | 2.3 |
Hub height (m) | 83.15 |
Water depth (m) | 12.52 |
Pile driven length (m) | 39.8 |
Structure diameter (conical) (m) | 2.5–4.6 |
Wall thickness (mm) | 16–90 |
Finite Element Analysis
This section describes how the components of the turbine shown in Fig. 1 are modelled and assembled together to build a complete FE model. The geometry of the components is created and meshed using open source software called Salome and the analysis is done in Code_Aster which is a mechanical solver.
Rotor–Nacelle Assembly
Mass properties of the RNA
Total mass (kg) | 134, 300 | ||
Mass moment of inertias (kg m^{2}) | I _{ xx} | I _{ yy} | I _{ zz} |
7.43 × 10^{6} | 1.21 × 10^{7} | 7.34 × 10^{6} |
Tower and Transition Piece
Euler–Bernoulli beam element is used to model the entire tower and a part of the transition piece which is above the grouted joint connection (Fig. 1). Each beam element consists of two nodes and each node has three translational and three rotational degrees of freedom and representing a section with constant wall thickness along the tower and transition piece. In total, 211 beam elements are used for modelling this section.
Point and distributed masses of appurtenances such as ladders, platforms and boat landing bumpers on the tower and transition piece are also incorporated into the model. Note that the stiffness contribution of these elements to the wind turbine tower is neglected in the FE model.
Grouted Joint Connection
Monopile and Surrounding Soil
Similar to the tower and the upper part of the transition piece, Euler–Bernoulli beam elements are used to construct the FE model of the monopile structure below the grouted joint connection. The hydrodynamic mass of water displaced by the submerged monopile and transition piece is calculated and included in the FE model by defining an equivalent density for each submerged element.
As recommended in DNV [9], the first discretisation point of the curve beyond the origin is localised at the relative displacement of \(\frac{y}{{y_{c} }} = 0.1\). The compressive strength for the mudstone layer is more than 6.9 MPa, which means the rocks are strong. Here, the p–y curve suggested by Reese [10] for strong rocks is used to calculate the stiffness of springs within the mudstone layer. The interaction between the monopile and the surrounding soil consists of 70 elements in the FE model.
Complete Assembly of the FE Model
Figure 3 shows the FE model of the complete wind turbine by assembling together all parts from Sects. “Rotor–Nacelle Assembly” to “Monopile and Surrounding Soil”. All the degrees of freedom of the node of the monopile at the bottom are restricted. As shown in Fig. 3(right), the nacelle was positioned at an angle of 20° with respect to the x direction during the in situ experiments; hence, this position of the nacelle is considered in the FE model. The 1-D beam models of the upper and lower parts of the turbine structure are connected to the 3-D model of the middle part through rigid links as shown in Fig. 3. The joint connection using LIAISON_ELEM command is used for these rigid links.
Modal Analysis
Computed natural frequencies from the FE analysis
FE model | x direction | y direction |
---|---|---|
1st bending mode (Hz) | 0.353 | 0.350 |
2nd bending mode (Hz) | 1.466 | 1.378 |
In Situ Modal Testing
Experimentally identified natural frequencies
Modal tests | x direction | y direction |
---|---|---|
1st bending mode (Hz) | 0.378 | 0.352 |
2nd bending mode (Hz) | 1.714 | 1.663 |
Ambient Excitation Test
Conclusion
The FE model of the wind turbine structure based on the design conditions is used to compute its natural frequencies and mode shapes. It was observed that the first two bending modes are close to the natural frequencies identified experimentally by the in situ modal tests. However, the initial FE model may need to be updated to match the computed natural frequencies to the experimental ones. This may provide better understanding of the turbine dynamics. It was also observed that the in situ modal tests were not able to excite higher natural frequencies of the wind turbine structure and this should be further investigated.
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