Stochastic methods for unsteady aerodynamic analysis of wings and wind turbine blades




Fluck, Manuel

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Advancing towards `better' wind turbine designs engineers face two central challenges: first, current aerodynamic models (based on Blade Element Momentum theory) are inherently limited to comparatively simple designs of flat rotors with straight blades. However, such designs present only a subset of possible designs. Better concepts could be coning rotors, swept or kinked blades, or blade tip modifications. To be able to extend future turbine optimization to these new concepts a different kind of aerodynamic model is needed. Second, it is difficult to include long term loads (life time extreme and fatigue loads) directly into the wind turbine design optimization. This is because with current methods the assessment of long term loads is computationally very expensive -- often too expensive for optimization. This denies the optimizer the possibility to fully explore the effects of design changes on important life time loads, and one might settle with a sub-optimal design. In this dissertation we present work addressing these two challenges, looking at wing aerodynamics in general and focusing on wind turbine loads in particular. We adopt a Lagrangian vortex model to analyze bird wings. Equipped with distinct tip feathers, these wings present very complex lifting surfaces with winglets, stacked in sweep and dihedral. Very good agreement between experimental and numerical results is found, and thus we confirm that a vortex model is actually capable of analyzing complex new wing and rotor blade geometries. Next stochastic methods are derived to deal with the time and space coupled unsteady aerodynamic equations. In contrast to deterministic models, which repeatedly analyze the loads for different input samples to eventually estimate life time load statistics, the new stochastic models provide a continuous process to assess life time loads in a stochastic context -- starting from a stochastic wind field input through to a stochastic solution for the load output. Hence, these new models allow obtaining life time loads much faster than from the deterministic approach, which will eventually make life time loads accessible to a future stochastic wind turbine optimization algorithm. While common stochastic techniques are concerned with random parameters or boundary conditions (constant in time), a stochastic treatment of turbulent wind inflow requires a technique capable to handle a random field. The step from a random parameter to a random field is not trivial, and hence the new stochastic methods are introduced in three stages. First the bird wing model from above is simplified to a one element wing/ blade model, and the previously deterministic solution is substituted with a stochastic solution for a one-point wind speed time series (a random process). Second, the wind inflow is extended to an $n$-point correlated random wind field and the aerodynamic model is extended accordingly. To complete this step a new kind of wind model is introduced, requiring significantly fewer random variables than previous models. Finally, the stochastic method is applied to wind turbine aerodynamics (for now based on Blade Element Momentum theory) to analyze rotor thrust, torque, and power. Throughout all these steps the stochastic results are compared to result statistics obtained via Monte Carlo analysis from unsteady reference models solved in the conventional deterministic framework. Thus it is verified that the stochastic results actually reproduce the deterministic benchmark. Moreover, a considerable speed-up of the calculations is found (for example by a factor 20 for calculating blade thrust load probability distributions). Results from this research provide a means to much more quickly analyze life time loads and an aerodynamic model to be used a new wind turbine optimization framework, capable of analyzing new geometries, and actually optimizing wind turbine blades with life time loads in mind. However, to limit the scope of this work, we only present the aerodynamic models here and will not proceed to turbine optimization itself, which is left for future work.



wind energy, bird wings, lifting line models, vortex models, wind interpolation, stochastic models, wind modelling, Blade Element Momentum, chaos expansion, extreme loads, fatigue loads