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Scaling the circulation shed by a pitching panel

Published online by Cambridge University Press:  31 October 2011

James H. J. Buchholz*
Department of Mechanical and Industrial Engineering / IIHR – Hydroscience & Engineering, University of Iowa, Iowa City, IA 52242, USA
Melissa A. Green
Laboratories for Computational Physics and Fluid Dynamics, Naval Research Laboratory, Washington, DC 20375, USA
Alexander J. Smits
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Email address for correspondence:


A new scaling parameter is developed for the circulation shed by a rigid, rectangular panel pitching periodically about its leading edge. This parameter is the product of a kinematic and a geometric component. The kinematic component describes the relationship between the mean vorticity flux from the panel surface and the panel motion. The geometric component depends on the ratio of pitching amplitude to the span of the panel. The kinematic component is developed based on the connection between the surface pressure distribution and the resulting surface vorticity flux, which are supported in a stroke-averaged sense by pressure measurements on the surface of the panel. The parameter gives a robust scaling for the total spanwise circulation shed in a half-cycle by the panel. It provides a useful predictive tool, in that it can be either complementary to the formation number or provide an alternative scaling parameter when vortex saturation and pinch-off do not occur.

Copyright © Cambridge University Press 2011

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