The stacking axis locations for twist and taper distributions along the span of a wind turbine blade are optimized to maximize the rotor torque and/or to minimize the thrust. A neural networks (NN)-based model is trained for the torque and thrust values calculated using a computational fluid dynamics (CFD) solver. Once the model is obtained, constrained and unconstrained optimization is conducted. The constraints are the torque or the thrust values of the baseline turbine blade. The baseline blade is selected as the wind turbine blade used in the National Renewable Energy Laboratory (NREL) Phase VI rotor model. The Reynolds averaged Navier–Stokes (RANS) computations are done using the FINE/turbo flow solver developed by NUMECA International. The k-epsilon turbulence model is used to calculate the eddy viscosity. It is observed that achieving the same torque value as the baseline value is possible with about 5% less thrust. Similarly, the torque is increased by about 4.5% while maintaining the baseline thrust value.

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The common approach to wind energy feasibility studies is to use Weibull distribution for wind speed data to estimate the annual energy production (AEP). However, if the wind speed data has more than one mode in the probability density, the conventional distributions including Weibull fail to fit the wind speed data. This highly affects the technical and economic assessment of a wind energy project by causing crucial errors. This paper presents a novel way to define the probability density for wind speed data using splines. The splines are determined as a solution of constrained optimization problems. The constraints are the characteristics of probability density functions. The proposed method is implemented for different wind speed distributions including multimodal data and compared with Weibull, Weibull and Weibull and Beta Exponentiated Power Lindley (BEPL) distributions. It is also compared with two other nonparametric distributions. The results show that the spline-based probability density functions produce a minimum fitting error for all the analyzed cases. The AEP calculated based on this method is considered to have high fidelity, which will decrease the investment risk.

The taper distribution along the span of a helicopter blade is defined using a novel method applied for the first time and considered as the main contribution of this work. This method uses cubic splines to generate modified blade shapes. The thrust and the torque values, computed by a 3-D Reynolds Average Navier Stokes solver, are used to train a Neural Networks based model. After that a constrained optimization is conducted based on this model for two different rotor speeds under hover condition. The optimization variables are the chord lengths at three different span locations: root, mid-span and tip. The optimization constraints are the torque or thrust values of the original blade and the practical limits for the chord lengths. Two optimum cases are investigated: maximum Figure of Merit with greater thrust and maximum Figure of Merit with less torque than the baseline. The major challenge of this work is to use the taper distribution as the only design parameter to obtain comparable results to other studies in literature in which more than one parameter is used. The results show that the Figure of Merit can improve by around 5% and the torque can be reduced by around 20%.

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