A simplified aerodynamic model for floating VAWTs

To ensure successful modeling of a floating wind turbine, its aerodynamic behaviour has to be investigated. At the time of writing, the only relevant studies on the topic are about VAWT in skewed flow. There is lack of experimental, numerical or theorical studies about floating turbines. In the following paper, the aerodynamic performance of a periodically oscillating VAWT is investigated through theorical and computational means. The complex dynamics of a floating turbine was simplified to a sinusoidal pitch motion, assuring simplicity without losing meaningfullness. A theory is given to predict the aerodynamic torque of an oscillating VAWT, obtaining it from the one of the same fixed axis turbine. A blade-element model was developed to achieve this result, taking into account the effect of oscillation on key parameters affecting the torque, that is angles of attack and relative wind speed. The core idea of the method, is to use blade element theory not as a prediction itself, but as a mean to correct the aerodynamic torque of the fixed axis turbine. The latter may be the result of both experiments, or numerical simulations. The simplest though most effective correction developed is To=Tf (1−k cos(ωot))2 , (1) where ωo is the frequency of oscillation in rad/s, and k is the ratio of the maximum oscillation speed for a certain section of the turbine over the freestream wind speed. Three different corrective functions were evaluated, that is one for the effect of the angles of attack, one for the relative wind speed and one considering both at the same time (Eq. (1)). Moreover, the correction may depend on just one representative section, the middle one in this case, or the entire rotor. Theorical predictions were compared against data from CFD simulations, for two different oscillation frequencies. These were chosen in the typical range of wave energy spectrum, in order to test representative conditions for floating applications. CFD simulations were also performed to obtain the torque of the fixed axis turbine, which was validated against experimental data from the 17m Darrieus-type rotor studied by SANDIA laboratories. CFD simulations showed aerodynamic forces are deeply affected by oscillation. As intuition suggests, torque increases when the turbine pitches in the opposite direction of the wind, and decreases when it pitches in the same direction. This periodic oscillation causes significative ripple and maximum torque increase. For the higher oscillation frequency, which represents the most extreme condition, maximum torque was about 2 times the one of the fixed turbine. Mean torque was found to be almost unaffected or slightly increased. For the higher oscillation frequency a 4.4% increase was observed. The theorical model was able to reproduce the behaviour of the oscillating turbine with satisfactory accuracy. To quantify the matching, absolute error was divided by the peak torque of the fixed axis turbine. For the lower oscillation frequency worst accuracy is 13.8%, while mean accuracy is 5.3%. As the frequency grows the hypothesis which the model is based on become less valid, so for the higher oscillation frequency precision decreases, in fact worst accuracy is 29.0% while mean is 9.1%. The theory proved to attain reasonably accurate results notwithstanding its simplicity, making it a cost-effective tool for quick analysis or optimization. Moreover, the theory could insight the way in which oscillation affects the torque. Considering relative wind speed separately showed that it has little influence, so it can be concluded that torque is affected by oscillation mainly by the change in the angles of attack. Finally, letting the correction depend on the entire rotor or just the middle section yielded almost identical results, proving the simpler model may be used without loss of precision.