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

  • Adam M. Edstrand (a1), Yiyang Sun (a1), Peter J. Schmid (a2), Kunihiko Taira (a1) and Louis N. Cattafesta (a1)...

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.

Copyright

Corresponding author

Email address for correspondence: lcattafesta@fsu.edu

References

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Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134150.
Crouch, J. 2005 Airplane trailing vortices and their control. C. R. Phys. 6 (4–5), 487499.
Devenport, W. J., Rife, M. C., Liapis, S. I. & Follin, G. J. 1996 The structure and development of a wing-tip vortex. J. Fluid Mech. 312, 67106.
Edstrand, A. & Cattafesta, L. N. 2015 Topology of a trailing vortex flow field with steady circulation control blowing. In 53rd AIAA Aerospace Sciences Meeting, AIAA-2015-1706. American Institute of Aeronautics and Astronautics.
Edstrand, A. M., Davis, T. B., Schmid, P. J., Taira, K. & Cattafesta, L. N. 2016 On the mechanism of trailing vortex wandering. J. Fluid Mech. 801, R111.
Edstrand, A. M., Schmid, P. J., Taira, K. & Cattafesta, L. N. 2018 A parallel stability analysis of a trailing vortex wake. J. Fluid Mech. 837, 858895.
Ham, F. & Iaccarino, G. 2004 Energy Conservation in Collocated Discretization Schemes on Unstructured Meshes, pp. 314. Annual Research Brief, Center for Turbulence Research, Stanford University.
Ham, F., Mattsson, K. & Iaccarino, G. 2006 Accurate and Stable Finite Volume Operators for Unstructured Flow Solvers, pp. 243261. Annual Research Brief, Center for Turbulence Research, Stanford University.
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245283.
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Proc. of the Summer Program, pp. 193208. Center of Turbulence Research.
Jacquin, L., Fabre, D., Geffroy, P. & Coustols, E. 2001 The properties of a transport aircraft wake in the extended near field: an experimental study. In 39th AIAA Aerospace Sciences Meeting, AIAA-2001-1038. American Institute of Aeronautics and Astronautics.
Khorrami, M. R. 1991 On the viscous modes of instability of a trailing line vortex. J. Fluid Mech. 225, 197212.
Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39 (1), 383417.
Margaris, P. & Gursul, I. 2006 Wing tip vortex control using synthetic jets. Aeronaut. J. 110 (1112), 673681.
Margaris, P. & Gursul, I. 2010 Vortex topology of wing tip blowing. Aerosp. Sci. Technol. 14, 143160.
Matalanis, C. G. & Eaton, J. K. 2007 Wake vortex alleviation using rapidly actuated segmented Gurney flaps. AIAA J. 45 (8), 18741884.
Mayer, E. & Powell, K. 1992 Viscous and inviscid instabilities of a trailing vortex. J. Fluid Mech. 245, 91114.
Paredes, P., Theofilis, V., Rodríguez, D. & Tendero, J. 2011 The PSE-3D instability analysis methodology for flows depending strongly on two and weakly on the third spatial dimension. In 6th AIAA Theoretical Fluid Mechanics Conference, AIAA-2011-3752. American Institute of Aeronautics and Astronautics.
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656 (10), 528.
Spalart, P. R. 1998 Airplane trailing vortices. Annu. Rev. Fluid Mech. 30 (1), 107138.
Streett, C. L., Lockard, D. P., Singer, B. A., Khorrami, M. R. & Choudhari, M. M. 2003 In search of the physics: the interplay of experiment and computation in airframe noise research: flap-edge noise. In 41st Aerospace Sciences Meeting and Exhibit, AIAA-2003-0979. American Institute of Aeronautics and Astronautics.
Taira, K. & Colonius, T. 2009 Effect of tip vortices and low-Reynolds-number poststall flow control. AIAA J. 47 (3), 749756.
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