A Meta-Learning based Aerodynamic Analysis Framework for Wind Turbine Design Applications

Abstract

Design testing and analysis is a major bottleneck in the design process of wind turbine applications, mainly due to the computational cost of analysis tools like computational fluid dynamics (CFD). Furthermore, the accuracy of the state-of-the-art turbulence models is low in flows with high adverse pressure gradients such as airfoils operating at high angles of attack. This study aims to develop an aerodynamic analysis framework for wind turbine airfoils with both improved cost and improved accuracy to use in design applications.

An artificial neural network-based data-driven surrogate model is developed to predict the aerodynamic performance quantities of lift coefficient, lift-to-drag ratio, and pitching moment coefficient for wind turbine airfoils. An efficient geometric space exploration strategy is used to generate a representative database of wind turbine airfoils and their corresponding performance quantities. The developed surrogate model shows a uniform accuracy across a wide range of wind turbine airfoil geometries, with an L2 error estimates of 0.03 in lift coefficient, 0.4 in lift-to-drag ratio, and 0.003 in pitching moment coefficient. These errors correspond to less than 2% magnitudes of the corresponding performance quantities at the design point. With a benefit of more than six orders of magnitude in computational cost compared to CFD, the surrogate model has the capabilities to be embedded in uncertainty quantification (UQ) and multidisciplinary design analysis and optimization (MDAO) frameworks.

To reduce the model development cost, various parameter space exploration and reduction strategies are tested to benchmark the impact of reducing the training data on the accuracy of the surrogate model. With uniform data puncturing style, the accuracy level of the surrogate model is maintained even with up to a 50% reduction in the training data.

The propagation of uncertainty from the geometric parameters of the airfoils to the airfoil performance quantities is quantified using the surrogate model coupled with a Monte-Carlo-based UQ framework. The performance quantities show an uncertainty of about 3% of their magnitude for a 5% geometric uncertainty near the operational angle of attack and more than 10% magnitude of uncertainty near the stall angle of attack.

Secondly, field inversion machine learning (FIML) methodology is applied on multiple airfoils to arrive at a model consistent correction to the turbulence model for improved airfoil stall predictions. The corrected turbulence model shows a consistent improvement of the stall lift predictions with an improvement in stall angle of attack by more than 35% and stall lift coefficient by more than 40%. Besides the lift coefficient, the corrected turbulence model predicts the surface pressure and flow separation point more accurately.

A meta-learning model is developed using the corrected turbulence model on the database of wind turbine airfoils, which is both computationally inexpensive and closer to the experimental data. The model is integrated with an evolutionary optimization framework and tested on various airfoil design problems, including airfoil drag minimization by 5% and stall delay by 1 degree.