A species-transport model for circulation in a leading-edge vortex

Abstract

In this study, we propose a model to predict circulation growth along the span of a rotating wing, in which circulation transport is represented as species transport. Fluid particles entering the vortex shear layer at the leading edge are initialized as vorticity-containing mass and are advected by the flow along the span. A circulation budget is presented, consisting of a generation and transport term, the latter derived from the vorticity transport equation, which leaves only two unknowns for the modeller to determine: the shear-layer thickness and the spanwise flow distribution. We find that the model is insensitive to the value chosen for the shear-layer thickness, as varying the thickness by an order of magnitude only changes the output by a few percent. Meanwhile, we use Bernoulli equation in a rotating coordinates system as a basic model for spanwise flow. To verify the accuracy of the model, the predicted circulation values are compared against experimental circulation values and show good agreement to measurements close to the axis of rotation, which corresponds to the spanwise locations at which the spanwise flow model best matches experimental data. It is suggested, therefore, that this model produces accurate results subject to an appropriate spanwise flow model.