Bird wings have been studied as prototypes for wing design since the beginning of aviation. Although wing tip slots, i.e. wings with distinct gaps between the tip feathers (primaries), are very common in many birds, only a few studies have been conducted on the benefits of tip feathers on the wing's performance, and the aerodynamics behind tip feathers remains to be understood. Consequently most aircraft do not yet copy this feature. To close this knowledge gap an extended lifting line model was created to calculate the lift distribution and drag of wings with tip feathers. With this model, is was easily possible to combine several lifting surfaces into various different birdwing-like configurations. By including viscous drag effects, good agreement with an experimental tip slotted reference case was achieved. Implemented in C++ this model resulted in computation times of less than one minute per wing configuration on a standard notebook computer. Thus it was possible to analyse the performance of over 100 different wing configurations with and without tip feathers. While generally an increase in wing efficiency was obtained by splitting a wing tip into distinct, feather-like winglets, the best performance was generally found when spreading more feathers over a larger dihedral angle out of the wing plane. However, as the results were very sensitive to the precise geometry of the feather fan (especially feather twist) a careless set-up could just as easily degrade performance. Hence a detailed optimization is recommended to realize the full benefits by simultaneously optimizing feather sweep, twist and dihedral angles.

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Unsteady power output and long-term loads (extreme and fatigue) drive wind turbine design.However, these loads are difficult to include in optimization loops and are typically only assessed in a post-optimization load analysis or via reduced-order methods. Both alternatives yield suboptimal results. The reason for this difficulty lays in the deterministic approaches to long-term loads assessment. To model the statistics of lifetime loads they require the analysis of many unsteady load cases, generated from many different random seeds-a computationally expensive procedure. In this paper, we present an alternative: a stochastic solution for the unsteady aerodynamic loads based on a projection of the unsteady Blade Element Momentum (BEM) equations onto a stochastic space spanned by chaos exponentials. This approach is similar to the increasingly popular polynomial chaos expansion, but with 2 major differences. First, the BEM equations constitute a random process, varying in time, while previous polynomial chaos expansion methods were concerned with random parameters (ie, random but constant in time or initial values). Second, a new, more efficient basis (the exponential chaos) is used. This new stochastic method enables us to obtain unsteady long-term loads much faster, enabling unsteady loads to become accessible inside wind turbine optimization loops. In this paper we derive the stochastic BEM solution and present the most relevant results showing the accuracy of the new method.

Abstract. Emerging stochastic analysis methods are of potentially great benefit for wind turbine power output and loads analysis. Instead of requiring multiple (e.g. 10 min) deterministic simulations, a stochastic approach can enable a quick assessment of a turbine's long-term performance (e.g. 20-year fatigue and extreme loads) from a single stochastic simulation. However, even though the wind inflow is often described as a stochastic process, the common spectral formulation requires a large number of random variables to be considered. This is a major issue for stochastic methods, which suffer from the curse of dimensionality leading to a steep performance drop with an increasing number of random variables contained in the governing equations. In this paper a novel engineering wind model is developed which reduces the number of random variables by 4–5 orders of magnitude compared to typical models while retaining proper spatial correlation of wind speed sample points across a wind turbine rotor. The new model can then be used as input to direct stochastic simulations models under development. A comparison of the new method to results from the commercial code TurbSim and a custom implementation of the standard spectral model shows that for a 3-D wind field, the most important properties (cross-correlation, covariance, auto- and cross-spectrum) are conserved adequately by the proposed reduced-order method.