Assessment of low-order theories for analysis and design of shrouded wind turbines using CFD

The use of a shroud around the rotor of a wind turbine has been known to augment the airflow through the rotor plane and hence result in improved performance. This work uses Computational Fluid Dynamics (CFD) to assess the validity of several simple theories which attempt to extend Betz theory to shrouded turbines. Two CFD models are employed and compared to predictions of previously published models. The first makes use of a fixed pressure-drop actuator disk, while the second incorporates the twist and chord distribution of the turbine blade as well as an airfoil polar using a technique much like the classical blade element momentum (BEM) method. Calculations are performed for a sweep of turbine loadings using the fixed pressure-drop model and a sweep of tip speed ratios using the BEM model for both an open and shrouded turbine. Power is computed using a control volume approach for the fixed pressure-drop model and by integrating tangential forces for the BEM model. Information including mass flow ratio, power coefficient ratio, axial induction, and shroud force is extracted from the solution fields and compared against the predictions of low-order theories. Finally, the blade element model is used to redesign the turbine twist distribution to achieve greater performance across a range of tip speed ratios.