Structural Design Analysis of a novel Tidal Turbine Stefan Mieras1
Turaj Ashuri2
[email protected]
[email protected]
Peter Scheijgrond1
Gerard van Bussel2
[email protected]
[email protected]
Abstract Despite the large resource of tidal and wave energy, the marine energy industry is still lagging far behind the wind industry. Much of the knowledge required to develop reliable and profitable marine energy systems is available in the wind energy sector. A novel marine energy technology developed by Ecofys Netherlands BV, dubbed the C-Energy project, uses the knowledge of both vertical and horizontal axis wind turbines by combining a Darrieus and a Wells type rotor. The use of these two unidirectional rotor types enables the system to extract energy from both tidal currents and waves. During the summer of 2009 the 30kWp turbine was installed as a demonstration project in the Westerschelde River, The Netherlands. With use of blade element momentum theories for horizontal and vertical axis turbines, a hydrodynamic model has been developed for this turbine to predict its performance and the loads on the turbine blades. Measurements from the C-Energy demonstration project have been used to validate this computational model. A finite element model provides the strain data required for the validation process and is also used to estimate the fatigue life. The combination of the hydrodynamic model and the finite element model gives reliable estimates for the occurring stresses. With this result, the structural design of the turbine blades can be optimized for any site condition and expected life time. Keywords: Marine Energy, Tidal turbine, Wells blade, Darrieus blade, Structural design, Renewable energy, C-Energy project
1 Introduction
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for wave and tidal energy conversion. Until now it is not clear which of these techniques are most reliable and profitable. There is a number of advances required to develop economic and reliable marine energy technologies by 2020 [3] and many of these advances can be achieved by working more closely together with the offshore and wind industry. One of only a few grid-connected demo scale marine energy projects world wide was installed in 2009, in a free tidal flow (Figure 1). This project, dubbed the C_Energy project, uses the principles of both vertical and horizontal axis wind turbines by combining a Darrieus and a Wells type rotor. The blades of the Darrieus rotor extract energy from horizontal moving tidal currents that, in different geometrical set-up, also have the ability to use energy from moving wave particles. The Wells rotor blades are functioning as spokes in a tidal application and can be used
In Europe, the total long-term potential of tidal and wave energy is equal to the longterm potential of onshore wind energy [1]. Therefore, there is increasing interest in the development of tidal and wave energy conversion systems, but still the marine renewable energy industry is lagging far behind the wind industry. Most of the marine energy technologies are at the proof-of-concept or part-system R&D stage [2]. Where for the wind industry the horizontal axis turbine is by far the most commonly used system, many different techniques are still being developed 1
Ecofys Netherlands BV, PO BOX 8408, 3503 RK Utrecht, T. +31 30 662 34 47 2 Delft University of Technology, Faculty of Aerospace Engineering, Department of Aerodynamics & Wind Energy, Kluyverweg 1, 2629 HS Delft, T. +31 15 278 98 04
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rotor axis, is sent via a wireless connection from the rotor to a Programmable Logic Controller. For the validation process, a finite element model is developed to calculate the strain in the rotor blades subjected to the theoretical loads. The quasi static hydrodynamic model is based on aerodynamic models for wind turbines and uses the classical blade element momentum (BEM) theory, the double multiple streamtube theory and the Strickland modification for dynamic stall [9,10]. The finite element model is used to model the structural behaviour of the turbine blades based on the loads that follow from the hydrodynamic model. The 3D solid finite element model geometry is simplified and the mesh is optimized in order to quickly give strain results at the strain gauge locations in the Darrieus and Wells blades (Figure 2).
Figure 1: C-Energy Demonstration Project
to convert energy from the vertical moving water particles in waves. The Darrieus rotor has been used before in several demonstration projects for tidal energy production [4] and the Wells rotor has been applied in wave energy as part of oscillating water column systems [5, 6]. The C-Energy turbine integrates both rotor types creating a marine energy converter that is rotating independent of the direction of the waves and water currents. The 5 by 5 meters turbine is installed in open sea conditions for continuous operation. Earlier scale models up to 2.4m diameter have proven their performance in a laboratory set-up [7]. Based on these laboratory test results and theories from horizontal and vertical axis wind turbines, a hydrodynamic model was developed to calculate the forces acting on the rotor blades. This model can now be validated with strain measurements from the C-Energy project. After validation of the theoretical models, a load distribution will be generated to estimate the fatigue life of the rotor blades. The results of this research will be used for new turbines to be designed at lower structural costs, in order to be competitive in the emerging marine energy market..
Figure 2: Finite Element Model
2. Validation of the hydrodynamic model
The validation method is depicted in Figure 3, where the values of the water current velocity (U), the rotational speed (ω), the submergence (s) and the strain (ε) are most important. During the measurements for this validation, the turbine operates at a constant tip speed ratio.
The C-Energy demonstration project is equipped with strain gauges located in all three Darrieus blades, between the two spokes, and in the Wells blades close to the rotor axis. The 50Hz strain signal, which was calibrated before attaching the blades to the
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Figure 3: Validation Method
The strain measurement data (blue line) and computed (red line) values of the Darrieus and Wells blades are shown in Figures 4 and 5. The Darrieus strain has more or less the same pattern and magnitude as the theoretical (ANSYS) results predict. This is a first indication that the theoretical models used in
this model give reliable estimates of the stresses that occur in the Darrieus blade. The Wells strain fluctuates a bit more compared to the output of the finite element analysis, even though the order of magnitude seems to fit as well. The irregular disturbance is most likely caused by the impact of waves.
Figure 4: Darrieus Strain Validation (ANSYS results versus real data measurements from the CEnergy installation)
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Figure 5: Wells Strain Validation (ANSYS results versus real data measurements from the C-Energy installation)
Figures 6 and 7 show the strain measurement data for in total 15 minutes of operation. The red line indicates the value of the peaks of the theoretical model; the green lines are +/- 5% values. Based on these validation cases, there is high confidence in the accuracy of the model. Small deviation and
differences from the model predictions may be caused by local turbulence effects, influence of surface waves and non-uniformity of the water current velocity. The next step in the research is to apply the model to estimate the fatigue life for different load cases.
Figure 6: Darrieus Strain Validation
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Figure 7: Wells Strain Validation
3. Fatigue life estimation
parameter or average water current velocity and k shape parameter, in this case k = 3. From the Weibull curve, the number of rotor cycles and the corresponding fatigue damage can be estimated (Figure 9). The fatigue life is than calculated using the Miner rule [12]. For the C-Energy demonstration project, the allowable average water current velocity for an estimated fatigue life of 25 years is found to be 1.4 meters per second. Since the average water current velocity in the Westerschelde River is 0.6 m/s, this shows that the installation will not fail due to fatigue damage. With this result, the structural design of future turbines can be further optimized for any load spectrum.
The fatigue life of the C-Energy turbine blades is estimated by forecasting the stress cycles in certain water conditions. Figure 8 shows the histogram of 10 minute averaged velocities for 2 lunar periods (~60 days). Like it is done for wind speed distributions [11], the water current velocity distribution is approximated with a Weibull curve:
W=
k U ⋅ λ λ
k −1
⋅ e −(U λ )
k
U ≥0
where W is the number of occurrences for a given water current velocity U, λ is the scale
Figure 8: Water current velocity histogram with Weibull fit.
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Figure 9: Fatigue Damage Estimation
4. Conclusion
estimated using the Weibull distribution of the water current velocity. The major part of the fatigue damage is caused by high water current velocities that occur only a few times a year. Based on constraints for the total power output, design costs and expected life time of the rotor, one can optimize the rotor geometry for each specific site, using the developed model. The model is currently being used as a design tool for further upscaling of the turbine.
With use of theories from the wind industry a hydrodynamic BEM model has been developed and validated for a novel tidal turbine,. The combination of this hydrodynamic BEM model and a finite element model of the turbine blades gives reliable estimates for the occurring stresses. With this result, the structural design of the blades can be optimized for any site condition and expected life time. The maximum allowable site conditions for the current C-Energy turbine have been
[6] Clément A, McCullen P, Falcão A, Fiorentino A, Gardner F, Hammarlund K, Lemonis G, Lewis T, Nielsen K, Petroncini S, et al. Wave energy in Europe: current status and perspectives. Renewable and Sustainable Energy Reviews, 6(5):405–431, 2002. [7] Scheijgrond PC and Rossen EA. Development and model tests on a combined WellsDarrieus rotor. In 4th European Wave Energy Conference, Aalborg, 2000. [8] Raghunathan S. The Wells air turbine for wave energy conversion. Progress in Aerospace Sciences, 31(4):335–386, 1995. [9] Manwell JF, McGowan JG, and Rogers AL. Wind Energy Explained. 2002. [10] Paraschivoiu I. Wind turbine design: with emphasis on Darrieus concept. Presses intl Polytechnique, 2002. [11] Veritas D.N. Design of offshore wind turbine structures, Appendix K: Calculations by finite element method. Offshore Standard DNV-OS-J101, Hovik, Norway, 2007. [12] Mieras SA, Structural Design Analysis of a Sustainable Energy Wave Rotor, Master Thesis, February 2010
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