Formation of a Rotor Tip Vortex

The origin of the tip vortex is described and important properties, such as core radius and circulation, as a function of these parameters, are calculated. Despite the fact that a large amount of computational and experimental work on the rotor wake has been published, little of a quantitative nature is known about the origin of the main component of the rotor wake, the tip vortex, as a function of the rotor speed, rotor blade geometry, and angle of attack. Experimental data by several workers have revealed little dependence on the Reynolds number. This lack of dependence on Reynolds number will hold only if the flow remains substantially unseparated, although it may be noted that drag coefficients of bluff bodies are remarkably constant over wide range of Reynolds number. The rotor blade is assumed to be of large aspect ratio, that is, to leading order in the blade aspect ratio, it appears infinite in length. In this limit case, the analytical solution for the bound circulation on a fixed wing is shown to be extendable to the rotary wing case when the blade is viewed as a lifting line. Lifting-surface results are obtained also, and these compare well with the lifting-line results for the bound circulation.