Introduction

With the increasing demands in energy and depletion of fossil fuels, the demand in renewable energy has grown significantly. In this regard, wind energy has become a popular source of renewable energy in recent years. To further meet the increasing demands of energy, the size of the wind turbine blades has also grown and these blades are tested to their limits structurally due to various loading and boundary conditions in different operating conditions. Usually, the safety factor approach is used to account for the uncertainties and unforeseen conditions; however, this leads to a conservative design which is heavier and cost ineffective. This demands for the implementation of a probabilistic approach so that the blades can manufactured by using less materials as possible while being robust the uncertainties.

In this regard, I developed a MATLAB based framework for aero-structural analysis of wind turbine blades during my post-doc within one year. The aero module was developed based on the blade element momentum theory using XFOIL for airfoil analysis, whereas the structural module was developed using the Ansys Parametric Language to create a fully parametric wind turbine blade made up of composites. The framework has the capability of estimating
the aerodynamic loads at different wind speed conditions, and then maps the aerodynamic load on the mesh of the finite element model of the blades for structural analysis.

The aero-structural framework was further incorporated to the stochastic optimization and uncertainty quantification framework based on PCE, Kriging, and SVMs to better understand the effects of uncertain parameters and obtain a more robust blade design that has a higher energy generation capability than the reference NREL 5 Megawatt wind turbine blade.
Duration: The framework for uncertainty quantification and stochastic optimization integrated with in-house aero-structural code was developed within one  year during my post-doc in 2020.

Parametric modeling of Wind Turbines Finite-element Code

Blade element momentum theory based aerodynamic Analysis for wind turbine blades

To aid the early design process of wind turbine blades, an efficient aerodynamic module based on the blade element momentum theory was developed. This module was written in MATLAB and integrates XFOIL for aerodynamic analysis. It also utilizes Kriging surrogate models for efficient mapping of the pressure loads from 2d airfoils to a three-dimensional pressure distribution over the wind turbine blades.

Stochastic Optimization of Wind turbine blades

In this research, a framework for stochastic optimization of horizontal-axis wind turbine composite blades was presented.
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It is well known that the structural responses of the wind turbines (e.g., natural frequency, blade tip displacement) are affected by uncertainties in, for instance, wind conditions and material properties. These uncertainties can have an undesirable impact on the performance and reliability of wind turbine blades, and therefore must be accounted for. However, performing the stochastic optimization of wind turbine blades is challenging because of the computational cost and the need to incorporate several disciplines. To make the stochastic problem tractable, a surrogate-based optimization framework using Kriging and support vector machines with adaptive refinement was developed. The framework is based on blade element momentum theory for aerodynamics coupled with a fully parameterized finite element structural model. The framework is used to find the optimal chord and twist distribution of a composite blade and, notably, the optimal control features such as tip-speed ratio and pitch angle with respect to operating wind speeds. The objective function considered is the ratio of mass to the expected value of the Annual Energy Production subjected to several probabilistic constraints on the blade tip deflection, natural frequencies, and failure indices. Uncertainties in material properties, as well as wind conditions are considered. The results of this industrial application demonstrate that the framework can lead, in a reasonable number of function calls, to an optimal composite blade with higher efficiency and robustness to uncertainty.
doi: doi.org/10.1007/s00158-021-03114-8

Example: The optimal chord, twist, and control features of a wind turbine blade by considering the widely used NREL 5MW wind turbine blade was calculated. The ratio of mass to the expected value of Annual Energy Production (AEP) was minimized while considering the structural failure constraints under the presence of uncertainties in material and geometric properties as well as wind conditions.
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The findings demonstrated the wind turbine blade thus obtained is more robust to uncertainties while generating more energy than the baseline NREL 5MW blade.

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Uncertainty Quantification and Global Sensitivity Analysis of Composite Wind turbine Blades

In this study, a framework for uncertainty quantification (UQ) and global sensitivity analysis (GSA) of composite wind turbine blades was presented.

​Because of the presence of uncertainties, the performance and reliability of wind turbine blades are adversely affected. Uncertainties must therefore be accounted for during the design phase. However, performing UQ of composite blades while considering a large number of random parameters is computationally intensive. To make the process tractable, this work is based on an approach referred to as polynomial chaos expansion (PCE) with l1-minimization. PCE also enables one to perform GSA to assess the relative importance of random parameters using Sobol Indices. This article also introduces an anisotropic formulation of PCE for dimension adaptive basis expansion. In addition, the UQ framework can handle random inputs with arbitrary distributions as well as spatial variations of material and geometric properties using Karhunen–Loève expansion. The presented framework was applied to three composite wind turbine blade problems – modal analysis, failure analysis, and buckling analysis – by considering the randomness in material and geometric parameters as well as loading conditions. The test case selected in this study is a blade from the National Renewable Energy Laboratory 5 Megawatt wind turbine. Results obtained with PCE were compared to Monte Carlo simulations. In addition, the influential random parameters were identified using Sobol Indices, obtained as an inexpensive sub-product of the PCE approximation.
doi: doi.org/10.1016/j.ress.2022.108354

Example: The effect of randomness in the thickness of the composite plies represented as random field was studied. The GSA was performed as post-processing and it was able to identify the influential material- Triax and Foam- that affected the buckling response of wind turbine blades substantially.