Approximate actuator disk model of a rotor in hover or axial flow based on potential flow equations

An actuator disk model of a rotor in hover or axial flow is derived based on an approximate solution of the equations of an incompressible and inviscid flow through the disk. For the case of a fast axial flow the equations have the same form as the equations of the dynamic-inflow model and under certain assumptions both models may even be identical. For hover it is shown that it is very important to include in the derivations the influence of the radial component of the induced velocity. Moreover, when the disk moves, rolls or pitches, it is very important to note that a reference system that is attached to the disk is not an inertial system. Since the derivation is carried out using such a system, the influence of all the accelerations present in such a case should be considered. If all the effects are taken into account, an actuator disk model is obtained that includes all the elements of the original dynamic-inflow model, but on the other hand also includes the wake distortion effects that are obtained as an integral part of the derivation. The new model is discussed and compared to other models from the literature.