Drag on flat plates of arbitrary porosity*

An analytical model for the prediction of the drag on a plate of arbitrary porosity (actuator disk) is introduced. The flow kinematics are determined using potential flow theory, along with several conditions to render the flow field realistic. Drag is then calculated under the constraints of mass, momentum and energy balance. The predictions exhibit convincing agreement with experimental observations over a wide range of porosities, including the solid plate case, as long as shedding is absent or suppressed. The developed model offers better predictions of the drag and wake velocities compared to the classical Betz model, and therefore can replace the latter in blade element momentum theory (BEM) algorithms, widely used for the prediction of wind-turbine loads and power generation.