Active attenuation of a trailing vortex inspired by a parabolized stability analysis
Abstract
Designing effective control for complex threedimensional flow fields proves to be nontrivial. 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 halfwing at an angle of attack $$\unicode[STIX]{x1D6FC}=5^{\circ }$$ and a chordbased 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. Furthermore, relative to the uncontrolled case, the controlled flows show increased attenuation of circulation and peak streamwise vorticity, with the fifthmodebased control setup outperforming the principalmodebased setup. From these results, we conclude that a rudimentary linear stability analysis can provide key insights into the underlying physics and help engineers design effective physicsbased flow control strategies.
 Authors:

 Florida State Univ., Tallahassee, FL (United States)
 Imperial College London, London, (United Kingdom)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 ONR; USDOE
 OSTI Identifier:
 1477439
 Report Number(s):
 SAND20186492J
Journal ID: ISSN 00221120; 664491
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Fluid Mechanics
 Additional Journal Information:
 Journal Volume: 855; Journal ID: ISSN 00221120
 Publisher:
 Cambridge University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING
Citation Formats
Edstrand, Adam M., Sun, Yiyang, Schmid, Peter J., Taira, Kunihiko, and Cattafesta, Louis N. Active attenuation of a trailing vortex inspired by a parabolized stability analysis. United States: N. p., 2018.
Web. https://doi.org/10.1017/jfm.2018.701.
Edstrand, Adam M., Sun, Yiyang, Schmid, Peter J., Taira, Kunihiko, & Cattafesta, Louis N. Active attenuation of a trailing vortex inspired by a parabolized stability analysis. United States. https://doi.org/10.1017/jfm.2018.701
Edstrand, Adam M., Sun, Yiyang, Schmid, Peter J., Taira, Kunihiko, and Cattafesta, Louis N. Wed .
"Active attenuation of a trailing vortex inspired by a parabolized stability analysis". United States. https://doi.org/10.1017/jfm.2018.701. https://www.osti.gov/servlets/purl/1477439.
@article{osti_1477439,
title = {Active attenuation of a trailing vortex inspired by a parabolized stability analysis},
author = {Edstrand, Adam M. and Sun, Yiyang and Schmid, Peter J. and Taira, Kunihiko and Cattafesta, Louis N.},
abstractNote = {Designing effective control for complex threedimensional flow fields proves to be nontrivial. 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 halfwing at an angle of attack $\unicode[STIX]{x1D6FC}=5^{\circ }$ and a chordbased 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. Furthermore, relative to the uncontrolled case, the controlled flows show increased attenuation of circulation and peak streamwise vorticity, with the fifthmodebased control setup outperforming the principalmodebased setup. From these results, we conclude that a rudimentary linear stability analysis can provide key insights into the underlying physics and help engineers design effective physicsbased flow control strategies.},
doi = {10.1017/jfm.2018.701},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 855,
place = {United States},
year = {2018},
month = {9}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Viscous and inviscid instabilities of a trailing vortex
journal, December 1992
 Mayer, Ernst W.; Powell, Kenneth G.
 Journal of Fluid Mechanics, Vol. 245, Issue 1
Effect of Tip Vortices in LowReynoldsNumber Poststall Flow Control
journal, March 2009
 Taira, Kunihiko; Colonius, Tim
 AIAA Journal, Vol. 47, Issue 3
On the viscous modes of instability of a trailing line vortex
journal, April 1991
 Khorrami, Mehdi R.
 Journal of Fluid Mechanics, Vol. 225
Parabolized Stability Equations
journal, January 1997
 Herbert, Thorwald
 Annual Review of Fluid Mechanics, Vol. 29, Issue 1
Dynamic mode decomposition of numerical and experimental data
journal, July 2010
 Schmid, Peter J.
 Journal of Fluid Mechanics, Vol. 656
A Linear Systems Approach to Flow Control
journal, January 2007
 Kim, John; Bewley, Thomas R.
 Annual Review of Fluid Mechanics, Vol. 39, Issue 1
Wing tip vortex control using synthetic jets
journal, October 2006
 Margaris, P.; Gursul, I.
 The Aeronautical Journal, Vol. 110, Issue 1112
Airplane trailing vortices and their control
journal, May 2005
 Crouch, Jeffrey
 Comptes Rendus Physique, Vol. 6, Issue 45
A parallel stability analysis of a trailing vortex wake
journal, January 2018
 Edstrand, Adam M.; Schmid, Peter J.; Taira, Kunihiko
 Journal of Fluid Mechanics, Vol. 837
Vortex topology of wing tip blowing
journal, April 2010
 Margaris, P.; Gursul, I.
 Aerospace Science and Technology, Vol. 14, Issue 3
The structure and development of a wingtip vortex
journal, April 1996
 Devenport, William J.; Rife, Michael C.; Liapis, Stergios I.
 Journal of Fluid Mechanics, Vol. 312
Airplane Trailing Vortices
journal, January 1998
 Spalart, Philippe R.
 Annual Review of Fluid Mechanics, Vol. 30, Issue 1
Optimal disturbances and bypass transition in boundary layers
journal, January 1999
 Andersson, Paul; Berggren, Martin; Henningson, Dan S.
 Physics of Fluids, Vol. 11, Issue 1
Wake Vortex Alleviation Using Rapidly Actuated Segmented Gurney Flaps
journal, August 2007
 Matalanis, Claude G.; Eaton, John K.
 AIAA Journal, Vol. 45, Issue 8
On the mechanism of trailing vortex wandering
journal, July 2016
 Edstrand, Adam M.; Davis, Timothy B.; Schmid, Peter J.
 Journal of Fluid Mechanics, Vol. 801
Works referencing / citing this record:
Modal Analysis of Fluid Flows: Applications and Outlook
journal, March 2020
 Taira, Kunihiko; Hemati, Maziar S.; Brunton, Steven L.
 AIAA Journal, Vol. 58, Issue 3
Figures / Tables found in this record: