Inviscid Wind-Turbine Analysis Using Distributed Vorticity Elements

Open Access
Basom, Blair J.
Graduate Program:
Aerospace Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • Mark David Maughmer, Thesis Advisor
  • wind turbine
  • horizontal axis
  • vortex lattice
  • wake modeling
  • relaxed wake
  • inviscid analysis
  • prescribed wake
  • Goldstein rotor
With the recent push for green energy technologies by governments around the world, interest in wind energy has skyrocketed. From 2006 to 2009 worldwide wind power production has doubled. To continue the pace of wind-turbine innovation, more advanced design and analysis methods are needed. The primary tool currently used for wind-turbine design is the blade element momentum method, which lacks a detailed wake model and relies on an assumption of non-interacting streamtubes. These simplifications limit the designer’s ability to tailor the blade shape to minimize the induced power loss of the rotor. Improved prediction of the induced velocity distribution on the blades can be achieved through the use of potential flow models. This thesis presents the implementation of one such model featuring the use of distributed vorticity elements. Distributed vorticity elements are quadrilateral elements with vortex filaments of equal and opposite strength along their leading and trailing edges connected by a sheet of distributed vorticity. The circulation of the filaments varies quadratically with the local spanwise coordinate, while the strength of the sheet varies linearly. Both the rotor and its wake are paneled using these elements. Because the wake has a strong influence on the flow at the rotor, the accurate prediction of its geometry is highly important. To this end a force-free relaxed wake model is presented, as well as fixed wake and hybrid wake models that are less numerically intensive than the relaxed wake model. Comparison is made to Goldstein’s theoretical solution for the ideal lightly-loaded rotor, as well as to the blade element momentum method.