Skip to main content
SpringerLink
Log in
Book cover

Advances in Fluid-Structure Interaction pp 335–348Cite as

Cylinder Wake Stabilization Using a Minimal Energy Compensator

  • Conference paper
  • First Online:

  • 1526 Accesses

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 133))

Abstract

In the present work a linear feedback control strategy is used to control and suppress the cylinder vortex-shedding at low Reynolds numbers. The classical minimal control energy or small gain solution of the optimal control and estimation problems is exploited in order to design a full-dimensional stabilizing compensator of the linearized Navier–Stokes equations. Both feedback and observer gains are efficiently computed based solely on the knowledge of the unstable adjoint and direct global modes, respectively. In our control setup, the actuation is realized by means of angular oscillations of the cylinder surface while a single velocity sensor is employed for the state estimation. For \(\text {Re}=50\) the derived compensator is shown to be able to drive the flow from the natural limit cycle to the unstable steady state which is finally restored. Then the sensitivity of the control performance to the sensor placement and the Reynolds number is investigated.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    \(\mathcal {E}\{\cdot \}\) is employed here to denote the expectation operator.

References

  1. Ahuja, S., Rowley, C.W.: Feedback control of unstable steady state of flow past a flat plate using reduced-order estimators. J. Fluid Mech. 645, 447–478 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Amodei, L., Buchot, J.-M.: A stabilization algorithm of the Navier-Stokes equations based on algebraic Bernoulli equation. Numer. Linear Algebra Appl. 19, 700–727 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barbagallo, A., Sipp, D., Schmid, P.-J.: Closed-loop control of an open cavity flow using reduced-order models. J. Fluid Mech. 641, 1–50 (2009)

    Article  MATH  Google Scholar 

  4. Bergmann, M., Cordier, L., Brancher, J.P.: Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced-order model. Phys. Fluids 17(097101), 1–21 (2005)

    MATH  Google Scholar 

  5. Bewley, T.R., Pralits, J.O., Luchini, P.: Minimal-energy control feedback for stabilization of bluff-body wakes. In: Proceeding FEDSM2002-31048. In BBVIV5, Fifth Conference on Bluff Body Wakes and Vortex-Induced Vibrations, Bahia, Brazil, December 2007

    Google Scholar 

  6. Burl, J.B.: Linear Optimal Control: \(\cal {H}_2\) and \(\cal {H}_\infty \) Methods. Addison-Wesley Longman Publishing Co., Boston (1998)

    Google Scholar 

  7. Choi, H., Jeon, W., Kim, J.: Control of flow over bluff body. Annu. Rev. Fluid Mech. 40, 113–139 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Davis, T.A.: Algorithm 832: UMFPACK, an unsymmetric-pattern multifrontal method. ACM Trans. Math. Software 30(2), 196–199 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Fujisawa, N., Nakabayashi, T.: Neural network control of vortex shedding from a circular cylinder using rotational feedback oscillations. J. Fluids Struct. 16, 113–119 (2002)

    Article  Google Scholar 

  10. Giannetti, F., Luchini, P.: Structural sensitivity of the first instability of the cylinder wake. J. Fluid. Mech. 581, 167–197 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. He, J.-W., Glowinski, R., Metcalfe, R., Nordlandelr, A., Periaux, J.: Active control and drag optimization for flow past a circular cylinder: I. Oscillatory cylinder rotation. J. Comput. Phys 163, 83–117 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kim, J., Bewely, T.R.: A linear system approach to flow control. Annu. Rev. Fluid Mech. 39, 383–417 (2007)

    Article  Google Scholar 

  13. Lauga, E., Bewley, T.R.: The decay of stabilizability with Reynolds number in a linear model of spatially developing flows. Proc. R. Soc. Lond. A 459, 2077–2095 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lehoucq, R.B, Sorensen, D.C., Yang, C.: ARPACK Users Guide (siam edn). (1998)

    Google Scholar 

  15. Lewis, F.-L., Syrmos, V.L.: Optimal Control. Wiley, New York (1995)

    Google Scholar 

  16. Marquet, O., Sipp, D., Jacquin, L.: Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221–252 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Park, D.S., Ladd, D.M., Hendricks, E.W.: Feedback control of von Kármán vortex shedding behind a circular cylinder at low Reynolds numbers. Phys. Fluids 6, 2390–2405 (1994)

    Article  MATH  Google Scholar 

  18. Protas, B.: Linear feedback stabilization of laminar vortex shedding based on a point vortex model. Phys. Fluids 16, 4473–4488 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Protas, B., Styczek, A.: Optimal rotary control of the cylinder wake in the laminar regime. Phys. Fluids 14, 2073–2087 (2002)

    Article  MATH  Google Scholar 

  20. Roussopoulos, K.: Feedback control of vortex shedding at low Reynolds numbers. J. Fluid Mech. 248, 267–296 (1993)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20158, Milano, Italy

    Marco Carini

  2. Dipartimento di Ingegneria Civile, Chimica e Ambientale, Università degli Studi di Genova, via Montallegro 1, 16145, Genova, Italy

    Jan Oscar Pralits

  3. Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, via Ponte don Melillo 1, 84084, Fisciano (SA), Italy

    Paolo Luchini

Authors
  1. Marco Carini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Oscar Pralits
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paolo Luchini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marco Carini .

Editor information

Editors and Affiliations

  1. Fluides de Toulouse, Institut de Mécanique des, Toulouse, France

    Marianna Braza

  2. Università di Genova, Genova, Italy

    Alessandro Bottaro

  3. Mechanical & Aerospace Engineering, Monash University, Victoria, Victoria, Australia

    Mark Thompson

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Carini, M., Pralits, J.O., Luchini, P. (2016). Cylinder Wake Stabilization Using a Minimal Energy Compensator. In: Braza, M., Bottaro, A., Thompson, M. (eds) Advances in Fluid-Structure Interaction. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-319-27386-0_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27386-0_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27384-6

  • Online ISBN: 978-3-319-27386-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation