Aerodynamic Force Modelling of Free and Shrouded Propellers in Incidence for Low Subsonic VTOL Operations

Abstract Growing market demand for urban aerial mobility has led to the rise of electric Vertical Take-off and Landing (eVTOL) aircraft. Tiltrotors, an increasing preference for urban applications, have a unique characteristic of rotors operating in a large range of incidence angles while transitioning from take-off to cruise. During such operation, the non-axisymmetric inflow leads to uneven loading over the rotating blades and additional forces in the tilted rotational plane. The current study presents existing low-order analytical models in the literature for the calculation of such aerodynamic forces for free propellers. Starting with Glauert’s deflected momentum theory for in-plane force gradient, the various limitations and modifications in the theory over the years are explored. Some of the limitations are then improved by adding models for the rotor induced velocity components in incidence for more precise estimation of in-plane forces. A scarcity of such models for shrouded propellers in the literature is observed and addressed to help with preliminary design of VTOL aircraft. A similar analytical model to that of the free propeller is thus developed for shrouded propellers operating in incidence, to consider both the modified rotor flow field in the presence of a shroud and the additional loads on the shroud in incidence. The analytical models are compared against available experimental data in the literature, as well as numerical simulation results using designed propellers representative of a typical VTOL aircraft. The calculated results from the analytical models follow the observed trend of variation of in-plane force gradient with varying incidence, while the exactitude to the observed value varies with changing advance ratio. This is owing to the increasing flow separation that sets in with increasing incidence, especially for the shrouded propeller, that introduces additional losses in the flow. While further improvements are recommended, the goal of a low-order analytical model for estimation of in-plane forces for free and shrouded propeller is satisfactorily reached.