A nonlinear and semi-analytical actuator disk method accounting for general hub shapes. Part 1. Open rotor

The paper presents a newly developed method for the analysis of the flow around open rotors characterised by hubs of general shape. The exact and implicit solution of the axysimmetric, inviscid and incompressible flow is represented as the superposition of infinite ring vortices properly arranged along the hub surface and the rotor wake. The solution is made explicit through a semi-analytical and iterative procedure. The proposed semi-analytical approach can deal with hubs of arbitrary shape and with quite general rotor load distributions. The method strongly couples the flow induced by the rotor and the hub. Moreover, the contraction/divergence and the rotation of the wake can be fully taken into account. The results of the semi-analytical method are also compared with those obtained with a widely diffused actuator disk model based on computational fluid dynamics (CFD) techniques. Finally, in comparison with more advanced methods, such as those relying on a CFD approach, this method is characterised by an extremely reduced computational cost. The computer code is freely available on contacting the authors.