Abstract
The paper presents a free-wake actuator disk model as applied to uniformly loaded propellers without slipstream rotation. The wake vorticity, originating from the disk edge, is represented by the superposition of a ring vortex sheet and a semi-infinite cylindrical vortex tube modelling the far wake. The shape and the density strength of the sheet are iteratively evaluated using two conditions. Firstly, the vortex sheet stability condition is strongly enforced, that is the static pressures just above and beneath the sheet are required to be equal. Secondly, the vortex sheet is constrained to align with the overall induced flow field, namely it is compelled to be a streamsurface. By doing so, the contraction of the wake is naturally accounted for in the model and no assumptions on its shape are made. The first part of this work deals with the theoretical foundations of the model and with the description of its discrete counterpart. The characteristics of the flow singularities used to model the flow induced by the wake are also presented.
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