Closed-form solution for the edge vortex of a revolving plate

TL;DR

This paper derives a simple analytical model for the edge vortex on a revolving plate at 90 degrees angle of attack, matching numerical Navier-Stokes solutions and highlighting key vortex formation mechanisms.

Contribution

It provides a novel closed-form solution for the circulation and position of the edge vortex on a revolving plate at high angle of attack.

Findings

Analytical expressions closely match numerical Navier-Stokes results.

Vorticity production at the sharp edge dominates vortex formation.

Transport effects are key to shaping the edge vortex.

Abstract

Flapping and revolving wings can produce attached leading edge vortices (LEVs) when the angle of attack is large. In this work, a low order model is proposed for the edge vortices that develop on a revolving plate at 90 degrees angle of attack which is the simplest limiting case, yet showing remarkable similarity with the generally known LEVs. The problem is solved analytically, providing short closed-form expressions for the circulation and the position of the vortex. A good agreement with the numerical solution of the Navier-Stokes equations suggests that, for the conditions examined, the vorticity production at the sharp edge and its subsequent three-dimensional transport are the main effects that shape the edge vortex.