Generalized performance limits for propellers, windmills and lifting rotors with axes parallel to the undisturbed flow

Description

The report generalizes the classical momentum theory as usually applied to propellers, windmills and lifting rotors into a single unified treatment. It also extends the analysis to include the regime in which flow through part or all of the actuator disc is reversed with respect to the remote flow field. Dimensional analysis is used in a systematic manner to reduce the final results to their simplest and most significant forms. It is shown that the performance of these devices can always be represented by a single parameter family of curves in which the parameter expresses the extent to which the performance of the actual device falls short of the theoretical limit. Detailed algebraic solutions are derived in closed form for the performance of both the idealized zero torque and finite torque actuators; these represent performance limits which any comparable real device may approach but never exceed. A qualitative analysis is presented concerning the development of the vortex ring state. The fundamental dynamic stability of the ideal lifting rotor is also analyzed. While this paper deals with a classical topic in fundamental fluid mechanics, the approach employed is original and many of the results derived here are in a form that is essentially new. (Author)

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