Feedback control of vortex shedding from an inclined flat plate

  • Won Tae JoeEmail author
  • Tim Colonius
  • Douglas G. MacMynowski
Original Article


Open- and closed-loop control of vortex shedding in two-dimensional flow over a flat plate at high angle of attack is numerically investigated at a Reynolds number of 300. Unsteady actuation is modeled as a body force near the leading or trailing edge and is directed either upstream or downstream. For moderate angles of attack, sinusoidal forcing at the natural shedding frequency results in phase locking, with a periodic variation of lift at the same frequency, leading to higher unsteady lift than the natural shedding. However, at sufficiently high angles of attack, a subharmonic of the forcing frequency is also excited and the average lift over the forcing period varies from cycle-to-cycle in a complex manner. It is observed that the periods with the highest averaged lift are associated with particular phase differences between the forcing and the lift, but that this highest-lift shedding cycle is not always stably maintained with open-loop forcing. We design a feedback algorithm to lock the forcing with the phase shift associated with the highest period-averaged lift. It is shown that the compensator results in a stable phase-locked limit cycle for a broader range of forcing frequencies than the open-loop control, and that it is able to stabilize otherwise unstable high-lift limit cycles that cannot be obtained with open-loop control. For example, at an angle of attack of 40°, the feedback controller can increase the averaged magnitude of force on the plate by 76% and increase the averaged lift coefficient from 1.33 to 2.43.


Flow control Vortex shedding Post stall Feedback control Flat plate 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amitay M., Glezer A.: Role of actuation frequency in controlled flow reattachment over a stalled airfoil. AIAA J. 40(2), 209–216 (2002)CrossRefGoogle Scholar
  2. 2.
    Bearman P.W.: On vortex street wakes. J. Fluid Mech. 28, 625–641 (1967)CrossRefGoogle Scholar
  3. 3.
    Colonius T., Taira K.: A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions. Comput. Methods Appl. Mech. Eng. 197(25–28), 2131–2146 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Colonius, T., Rowley, C.W., Tadmor, G., Williams, D.R., Taira, K., Dickson, W.B., Gharib, M., Dickinson, M.: Closed-loop control of leading-edge and tip vortices for small UAV. In: Conference on Active Flow Control, DFG, Berlin, 27–29 (2006)Google Scholar
  5. 5.
    Glezer A., Amitay M.: Synthetic jets. Annu. Rev. Fluid Mech. 34, 503–529 (2002)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Glezer A., Amitay M., Honohan A.M.: Aspects of low- and high-frequency actuation for aerodynamic flow control. AIAA J. 43(7), 1501–1511 (2005)CrossRefGoogle Scholar
  7. 7.
    Greenblatt D., Wygnanski I.J.: The control of flow separation by periodic excitation. Prog. Aerosp. Sci. 36(7), 487–545 (2000)CrossRefGoogle Scholar
  8. 8.
    Griffin O.M.: Universal strouhal number for locking-on of vortex shedding to vibrations of bluff cylinders. J. Fluid Mech. 85, 591–606 (1978)CrossRefGoogle Scholar
  9. 9.
    Huang L., Huang P.G., LeBeau R.R.P., Hauser T.: Numerical study of blowing and suction control mechanism on NACA0012 airfoil. J. Aircr. 41(5), 1005–1013 (2004)CrossRefGoogle Scholar
  10. 10.
    Miranda S., Vlachos P.P., Telionis D.P.: Flow control of a sharp-edged airfoil. AIAA J. 43(4), 716–726 (2005)CrossRefGoogle Scholar
  11. 11.
    Pastoor M., Henning L., Noack B.R., King R., Tadmor G.: Feedback shear layer control for bluff body drag reduction. J. Fluid Mech. 608, 161–196 (2008)zbMATHCrossRefGoogle Scholar
  12. 12.
    Roshko A.: Experiments on the flow past a circular cylinder at very high reynolds number. J. Fluid Mech. 10(3), 345–356 (1961)zbMATHCrossRefGoogle Scholar
  13. 13.
    Rullan J.M., Vlachos P.P., Telionis D.P., Zeiger M.D.: Post-stall flow control of sharp-edged wings via unsteady blowing. J. Aircr. 43(6), 1738–1746 (2006)CrossRefGoogle Scholar
  14. 14.
    Seifert A., Bachar T., Koss D., Shepshelovich M., Wygnanski I.: Oscillatory blowing: a tool to delay boundary-layer separation. AIAA J. 31(11), 2052–2060 (1993)CrossRefGoogle Scholar
  15. 15.
    Tadmor G.: Observers and feedback control for a rotating vortex pair. IEEE Trans Control Syst. Technol. 12(1), 36–51 (2004)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Tadmor, G., Noack, B.R., Morzynski, M., Siegel, S.: Low-dimensional models for feedback flow control. Part II: control design and dynamic estimation. AIAA Paper 2004-2409 (2004)Google Scholar
  17. 17.
    Taira K., Colonius T.: The immersed boundary method: a projection approach. J. Comput. Phys. 225(2), 2118–2137 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Taira K., Colonius T.: Effect of tip vortices in low-reynolds-number poststall flow control. AIAA J. 47(3), 749–756 (2009)CrossRefGoogle Scholar
  19. 19.
    Wu J.Z., Lu X.Y., Denny A.G., Fan M., Wu J.M.: Post-stall flow control on an airfoil by local unsteady forcing. J. Fluid Mech. 371, 21–58 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Zhang M.M., Zhou Y., Cheng L.: Control of poststall airfoil aerodynamics based on surface perturbation. AIAA J. 46(10), 2510–2519 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Won Tae Joe
    • 1
    Email author
  • Tim Colonius
    • 1
  • Douglas G. MacMynowski
    • 2
  1. 1.Department of Mechanical Engineering, MC104-44California Institute of TechnologyPasadenaUSA
  2. 2.Department of Controls and Dynamical Systems, MC107-81California Institute of TechnologyPasadenaUSA

Personalised recommendations