The nonlinear actuator disk method as applied to open and ducted rotors

The thesis presents a generalized semi-analytical actuator disk model as applied to the analysis of the incompressible, axisymmetric and inviscid flow around open and ducted rotors. The method strongly couples the non-linear actuator disk method of Conway (J. Fluid Mech. 1998; 365: 235-267) and the vortex element method of Martensen (Arch. Rat. Mech. 1959; 3: 235-270) and it returns the exact solution, although in an implicit formulation, as superposition of ring vortices properly arranged along the duct surface and the wake region. The solution is made explicit through a semi-analytical procedure which is validated with the help of asymptotic relations. The model duly accounts for non-uniform load radial distribution, slipstream contraction, mutual nonlinear interaction between duct and propeller, wake rotation, and ducts of general shape. Furthermore, the method can be easily employed to simulate the flow around an open rotor with a finite hub. The thesis also presents an assessment of two existing numerical methods capable to simulate open and ducted rotors flow fields. The first is the aforementioned nonlinear and semi-analytical actuator disk method. The second is based on the introduction of an actuator disk model in a CFD package describing the effects of the rotor through radial profiles of blade forces distributed over a disk surface. A set of reference numerical data, providing the inviscid axisymmetric velocity and pressure field distributions, are generated with controlled accuracy. Owing to an in-depth analysis of the error generated by the semi-analytical method and to the exactness of the solution in its implicit form, the collected data are well-suited for code-to-code validation of existing or newly developed computational methods. Finally, thanks to its extremely reduced computational cost the semi-analytical procedure can easily be integrated into design systems based on the repeated analysis scheme of hierarchical type. The computer code is freely available on contacting the author at the following e-mail address: rodolfo.bontempo@unina.it