Wind turbine tip-loss corrections

  • Branlard, Emmanuel Simon Pierre (Project Participant)

Project Details


The focus of this study is the use of a lifting-line free wake vortex code to derive tip-loss corrections that could be implemented in Blade Element Momentum (BEM) codes. The different theories and three dimensional effects that are related to tip-losses are progressively introduced: lifting-line concepts, wake dynamics and its vortex modeling, far-wake analysis. The different tip-loss corrections found in the literature are reviewed with a focus on the main theories, namely the work of Betz, Prandtl, Goldstein and Theodorsen, and the different implementations in BEM codes found in the literature are presented. The method of Okulov to compute Goldstein’s factor at a reasonable computational cost is provided with details. The computation of Goldstein’s factor being accessible, a method to use this factor in the BEM method is presented. Various form of Prandtl’s tip-loss factor are also listed for reference. Tip-losses are investigated using a free wake vortex code and with Computational Fluid Dynamics(CFD), and results from both approaches are compared and discussed. For the use of CFD data, the question of definition of the local induction factor on the blade is risen and different method to define it are investigated. The author introduces the naming of “performance tip-loss” factor, which is a correction to the airfoil coefficients due to the tri-dimensionality of the flow at the tip. A preliminary model for the performance tip-loss function is introduced. For the representation of various circulation shapes, a new method using the formulation of Bézier curves is described and developed. Such method can be widely used to describe curves such as lift, circulation or chord distribution. Last, a method to determine tip-losses using a vortex code is described and implemented. From this method, a new tip-loss model is implemented in a BEM code in order to reproduce the 3D effects inherently present in a vortex code.
Effective start/end date16/04/201130/09/2011