Analysis of Froude vortex wake,especially for 2D Giromill Vawt

Abstract

The purpose of this paper is to analyze the singular flow at the actuator disc’s rim joint to the wake tube to aid computing the wake. As the Froude wake vortex sheet issues from the perimeter of a windmill actuator of interference a, its vorticity is argued to build linearly from zero to asymptote to 2aV. The induction is integrated numerically for a parametric 2D sheet shape to find the flow direction and so slope ta at the perimeter. The vorticity build rate is simultaneously solved so that the axial velocity fraction at the disc averages to 1-a. At a = ⅓ the 2% deviation of the fraction is the rms error in localising the (2D) momentum equation. The extra induction of 0.18a just before the edge corrects the best local c_P to 0.49 versus ¹⁶/₂₇, whilst in 3D, swirl will zero the c_P in the center, wasting the lower central induction. Worse the leading edge t = 2.22 limits the Giromill’s overall C_P based on diameter to 0.49 at a = 0.27.