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Geometric-control formulation and averaging analysis of the unsteady aerodynamics of a wing with oscillatory controls

Published online by Cambridge University Press:  12 October 2021

Haithem E. Taha Open the ORCID record for Haithem E. Taha [Opens in a new window] ,
Laura Pla Olea Open the ORCID record for Laura Pla Olea [Opens in a new window] ,
Nabil Khalifa Open the ORCID record for Nabil Khalifa [Opens in a new window] ,
Cody Gonzalez Open the ORCID record for Cody Gonzalez [Opens in a new window]  and
Amir S. Rezaei Open the ORCID record for Amir S. Rezaei [Opens in a new window]
Haithem E. Taha*
Affiliation:
Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
Laura Pla Olea
Affiliation:
Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
Nabil Khalifa
Affiliation:
Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
Cody Gonzalez
Affiliation:
Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
Amir S. Rezaei
Affiliation:
Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
*
†Email address for correspondence: hetaha@uci.edu
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Abstract

Differential-geometric-control theory represents a mathematically elegant combination of differential geometry and control theory. Practically, it allows exploitation of nonlinear interactions between various inputs for the generation of forces in non-intuitive directions. Since its early developments in the 1970s, the geometric-control theory has not been duly exploited in the area of fluid mechanics. In this paper, we show the potential of geometric-control theory in the analysis of fluid flows, exemplifying it as a heuristic analysis tool for discovery of symmetry-breaking and unconventional force-generation mechanisms. In particular, we formulate the wing unsteady aerodynamics problem in a geometric-control framework. To achieve this goal, we develop a reduced-order model for the unsteady flow over a pitching–plunging wing that is (i) rich enough to capture the main physical aspects (e.g. nonlinearity of the flow dynamics at large angles of attack and high frequencies) and (ii) efficient and compact enough to be amenable to the analytic tools of geometric nonlinear control theory. We then combine tools from geometric-control theory and averaging to analyse the developed reduced-order dynamical model, which reveals regimes for lift and thrust enhancement mechanisms. The unsteady Reynolds-averaged Navier–Stokes equations are simulated to validate the theoretical findings and scrutinize the underlying physics behind these enhancement mechanisms.

JFM classification

Flow Control: Control theory Mathematical Foundations: General fluid mechanics Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A30
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© The Author(s), 2021. Published by Cambridge University Press

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References

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Taha et al. Supplementary Movie 1

Vorticity contours over the plunging cycle around mean angle of attack of 15◦, with reduced frequency k = 0.5 and plunging amplitude of 5◦ effective angle of attack. This low-amplitude, high-frequency plunging around the stall point (negative curvature of the steady lift curve) of NACA 0012 does not trigger a considerable leading edge vortex. A decrease in the mean lift coefficient is observed.

Download Taha et al. Supplementary Movie 1(Video)
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Taha et al. Supplementary Movie 2

Vorticity contours over the plunging cycle around mean angle of attack of 20◦, with reduced frequency k = 0.5 and plunging amplitude of 5◦ effective angle of attack. This low-amplitude, high-frequency plunging in the post-stall regime (positive curvature of the steady lift curve) of NACA 0012 triggers a considerable leading edge vortex, which leads to enhancement in the mean lift coefficient beyond the steady value.

Download Taha et al. Supplementary Movie 2(Video)
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