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Active attenuation of a trailing vortex inspired by a parabolized stability analysis

Published online by Cambridge University Press:  19 September 2018

Adam M. Edstrand Open the ORCID record for Adam M. Edstrand [Opens in a new window] ,
Yiyang Sun Open the ORCID record for Yiyang Sun [Opens in a new window] ,
Peter J. Schmid Open the ORCID record for Peter J. Schmid [Opens in a new window] ,
Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]  and
Louis N. Cattafesta III Open the ORCID record for Louis N. Cattafesta III [Opens in a new window]
Adam M. Edstrand
Affiliation:
Department of Mechanical Engineering, Florida Center for Advanced Aero-Propulsion, Florida State University, Tallahassee, FL 32310, USA
Yiyang Sun
Affiliation:
Department of Mechanical Engineering, Florida Center for Advanced Aero-Propulsion, Florida State University, Tallahassee, FL 32310, USA
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Kunihiko Taira
Affiliation:
Department of Mechanical Engineering, Florida Center for Advanced Aero-Propulsion, Florida State University, Tallahassee, FL 32310, USA
Louis N. Cattafesta III*
Affiliation:
Department of Mechanical Engineering, Florida Center for Advanced Aero-Propulsion, Florida State University, Tallahassee, FL 32310, USA
*
†Email address for correspondence: lcattafesta@fsu.edu
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Abstract

Designing effective control for complex three-dimensional flow fields proves to be non-trivial. Often, intuitive control strategies lead to suboptimal control. To navigate the control space, we use a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack $\unicode[STIX]{x1D6FC}=5^{\circ }$ and a chord-based Reynolds number $Re=1000$. The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode does not. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Relative to the uncontrolled case, the controlled flows show increased attenuation of circulation and peak streamwise vorticity, with the fifth-mode-based control set-up outperforming the principal-mode-based set-up. From these results, we conclude that a rudimentary linear stability analysis can provide key insights into the underlying physics and help engineers design effective physics-based flow control strategies.

JFM classification

Flow Control: Flow Control Flow Control: Instability control Vortex Flows: Vortex instability
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , R2
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Copyright
© 2018 Cambridge University Press 

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