Potential Flow Calculations of Axisymmetric Ducted Wind Turbines

An incompressible potential-flow vortex method has been constructed to analyze the flow field of a ducted wind turbine following that outlined by Lewis (1991). Attention is paid to balancing the momentum change in the flow to the total longitudinal forces acting on the duct-turbine combination: the pressure force on the actuator disk plus the pressure forces acting on the duct, which typically includes a negative component of drag due to high leading-edge suction. These forces are shown to balance the momentum changes in the flow, resulting in a model for power output from a ducted wind turbine over a wide range of pressure changes across the actuator disk. The results are compared to the Betz actuator disk model and it is shown that the maximum power output from a ducted turbine occurs at a lower value of pressure drop/momentum extraction than that for a bare turbine