Novel Curvature-Based Airfoil Parameterization for Wind Turbine Application and Optimization

Abstract

The direct proportionality of streamline curvature to the pressure gradient normal to it causes the dependence of surface pressure loading on geometry curvature. This allows for the use of geometry curvature as a direct and aerodynamically meaningful interface to modify and improve performance of wind turbine sections. A novel blade parameterization technique driven by specification of meanline second derivative and a thickness distribution is presented. This technique is implemented as T-Blade3 which is an already existing in-house open-executable. The second derivative which is indicative of curvature, is used, enabling exploration of a large design space with minimal number of parameters due to the use of B-spline control points, capable of producing smooth curves with only a few points. New thickness and curvature control capabilities have been added to TBlade3 for isolated and wind turbine airfoils. The parameterization ensures curvature and slope of curvature continuity on the airfoil surface which are critical to smooth surface pressure distribution. Consequently, losses due to unintentional pressure spikes are minimized and likelihood of separation reduced. As a demonstration of the parameterization capability, Multi-Objective optimization is carried out to maximize wind turbine efficiency. This is achieved through an optimization tool-chain that minimizes a weighted sum of the drag-to-lift ratios over a range of angles of attack and sectional Reynolds numbers using a Genetic Algorithm. This allows for radial Reynolds number variation and ensures efficiency of wind turbine blade with twist incorporated. The tool-chain uses XFOIL to evaluate drag polars. This is implemented in MATLAB and Python in serial and in parallel with the US Department of Energy optimization system, DAKOTA. The Python and DAKOTA versions of the code are fully open-source. The NREL S809 horizontal axis wind turbine laminar-flow airfoil which is 21% thick has been used as a benchmark for comparison. Hence, the optimization is carried out with the same thickness-to-chord ratio. Drag coefficient improvement ranging from 17% to 55% for Cl between 0.3 and 1 was achieved.