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Physics-based normalization for early leading-edge vortex circulation growth

Nathan Shumway*

  • *Contact author: nathan.shumway.ctr@afacademy.af.edu
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Phys. Rev. Fluids 10, 054701 – Published 15 May, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.054701

Abstract

Low Reynolds number flight frequently involves aggressive maneuvers or rotating wings at a high angle of attack. In these conditions a leading-edge vortex (LEV) forms, augmenting the force produced by the wing. To better understand how the LEV grows during its initial formation and to be able to compare across different conditions, it is important to have a normalization method that is grounded in the governing equations for vorticity. The result of an integral analysis of the vorticity equation for a general unsteady motion is a linear relationship between normalized circulation, Γu(t)c, and the number of chord lengths traveled. To determine the validity of this analysis, planar particle image velocimetry measurements of the flow on three different wing motions were analyzed. Surging wing data from prior work, an impulsively started rotating wing, and a pitching wing were the three cases used in this study. For all of these cases, the relationship derived in the integral analysis accurately described how the normalized circulation grows with the number of chords traveled for a period from 0.01 to at least 1.6 chords traveled, with a modification to the distance traveled normalization for pitching wings to include the effect of angle of attack.

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Phys. Rev. Fluids 10, 054701– Published 15 May, 2025
  • Received 4 December 2024
  • Accepted 29 April 2025
Article part of CHORUS
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