In this paper, we emphasize the dynamical-systems aspect of unsteady aerodynamics.
That is, we consider the unsteady aerodynamics problem of a two-dimensional airfoil as a
dynamical system whose input is the angle of attack (or airfoil motion) and output is the lift
force. Based on this view, we discuss the lift evolution from a purely dynamical perspective
through the step response, frequency response, transfer function, etc. In particular, we
point to the relation between the high-frequency gain and the physics of circulatory lift
and circulation. Based on this view, we show the circulatory lift dynamics is different
from the circulation dynamics. That is, we show that the circulatory lift is not lift due to
circulation. In fact, we show that the circulatory-non-circulatory classification is arbitrary.
By comparing the steady and unsteady thin airfoil theory, we show that the circulatory lift
possesses some added-mass contributions. Finally, we perform high-fidelity simulations of
Navier Stokes equations to show that a non-circulatory maneuver in the absence of a free
stream induces viscous circulation over the airfoil.
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This content will become publicly available on March 1, 2025
Geometric control analysis of the unsteady aerodynamics of a pitching–plunging airfoil in dynamic stall
Geometric control theory is the application of differential geometry to the study of nonlinear dynamical systems. This control theory permits an analytical study of nonlinear interactions between control inputs, such as symmetry breaking or force and motion generation in unactuated directions. This paper studies the unsteady aerodynamics of a harmonically pitching–plunging airfoil in a geometric control framework. The problem is formulated using the Beddoes–Leishman model, a semi-empirical state space model that characterizes the unsteady lift and drag forces of a two-dimensional airfoil. In combination with the averaging theorem, the application of a geometric control formulation to the problem enables an analytical study of the nonlinear dynamics behind the unsteady aerodynamic forces. The results show lift enhancement when oscillating near stall and thrust generation in the post-stall flight regime, with the magnitude of these force generation mechanisms depending on the parameters of motion. These findings demonstrate the potential of geometric control theory as a heuristic tool for the identification and discovery of unconventional phenomena in unsteady flows.
more » « less- Award ID(s):
- 1846308
- PAR ID:
- 10524865
- Publisher / Repository:
- AIP
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 36
- Issue:
- 3
- ISSN:
- 1070-6631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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