Modeling and validation of a cross flow turbine using free vortex models and an improved 2D lift model

R. Urbina, M. L. Peterson, P. M. Bates, R. W. Kimball

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


A number of numerical methods have been developed to predict the performance and aerodynamic loads of the Darrieus turbine. Prior work by Reference [1] using blade element methods (BEM) and free vortex methods (FVM) [2] has produced reasonable models that predict the hydrodynamic performance of the Darrieus turbine. The validated models reasonably estimate the performance at low solidities (Nc/R≪1), but lose accuracy at higher solidity ratios. Dynamic stall and flow curvature has been recognized by [2] [3] and [4] to be significant modeling parameters which have limited the accuracy of prior models. The current numerical model extends the predictions of the FVM model to a higher solidity ratio range. An improved model is presented for the condition of high angles of attack and for dynamic stall,. Experimental data on a series of two (Nc/R≈.9) and four (Nc/R≈1.8) blade configurations are presented as validation of the modified analytical vortex model. Tidal Energy has the potential to be an important source to diversify and provide affordable renewable power to people near coastal areas. However, some of the best tidal currents available are near sensitive areas for fish spawning and feeding. For this reason, any device that is to be designed for installation in this environment has to minimize impact on these fragile ecosystems. The Darrieus turbine offers an attractive alternative design because of these environmental considerations. High solidity turbines are of interest since they operate at lower tip speed ratios and allow for lower pressure gradients along the blade. These characteristics have the potential to reduce environmental impact on marine fauna, as the conditions of excessive mechanical strike, cavitations, shear and large pressure gradients are minimized while maintaining reasonable power coefficient values. In order to analyze the performance of the high solidity Darrieus turbine, the FVM model was chosen to model the turbine and wake with discrete vortex segments, which were then used to determine the induced velocities at the blade. Although the computational expense is greater than with other methods, like BEM models, FVM models can better predict the turbine performance at higher tip to flow speed ratios and higher rotor solidities. These methods also have the advantage of providing information of the wake profile and can be extended to provide information on the interaction of different devices. The lifting line FVM model requires the lift and drag curves to be prescribed for a given hydrofoil profile. Experimental data have shown that the dynamic stall contribution is higher than expected at low tip speed ratios for high solidity Darrieus turbines. Because of the complex nature of the problem, an empirical lift model based on theoretical foundation is used. An approximation of the known asymptotic limit values was used to account for the dynamic stall behavior. In order to validate the empirical lift model for the FVM, a set of experiments was conducted using NACA 63018 blades at different toe angles, tip speed ratios, and free stream velocities. Results will be shown for a numerical model of high solidity Darrieus type cross flow turbines which have been experimentally validated. High solidity rotors (1 < Nc/R < 2) were tested and modeled for conditions of blade dynamic stall and other effects.

Original languageEnglish
Title of host publicationMTS/IEEE Seattle, OCEANS 2010
StatePublished - 2010
EventMTS/IEEE Seattle, OCEANS 2010 - Seattle, WA, United States
Duration: Sep 20 2010Sep 23 2010

Publication series

NameMTS/IEEE Seattle, OCEANS 2010


ConferenceMTS/IEEE Seattle, OCEANS 2010
Country/TerritoryUnited States
CitySeattle, WA

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Ocean Engineering


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