Skip to main content
SpringerLink
Log in

Experimental and Theoretical Sensitivity Analysis of Turbulent Flow Past a Square Cylinder

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

We assess experimentally and theoretically the ability of a small control cylinder to alter vortex shedding in turbulent flow past a square cylinder at R e = 22,000. Results are presented in terms of sensitivity maps showing the flow regions where the shedding frequency and amplitude are most affected by the control cylinder. Experimental results are obtained for a ratio 0.02 of the cylinder diameters, over an extended domain covering the wake, the shear layers and the free stream. The shedding frequency can be either decreased or increased, the largest effects being obtained placing the control cylinder at the outer edge of the detached shear layers (associated with frequency decrease) or upstream of the square cylinder (associated with frequency increase, in contrast with previous results obtained for a D-shaped geometry of the main cylinder). In contrast, the oscillation amplitude is rarely decreased, meaning that any variation of the shedding frequency comes at the expense of more intense vortex shedding. These findings are revisited in the frame of a theoretical, linear sensitivity analysis of the time-averaged mean flow, performed using adjoint methods in the frame of Reynolds-averaged Navier–Stokes modeling. We show that the retained approach carries valuable information in view of guiding efficient control strategy, as it allows identifying the main regions yielding either a decrease or an increase of the shedding frequency in striking agreement with the experiments. This is a tremendous timesaving in so far as the controlled states need not be computed, the overall computational cost being roughly that of computing the mean flow. In contrast, performing the sensitivity analysis on the underlying unstable steady state yields flawed predictions, hence stressing the need to encompass some level of mean coherent-coherent perturbations interaction in the linear model.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Notes

  1. See Eq. 40 herein.

  2. Source code and official documentation available at http://www.openfoam.org.

References

  1. Mathis, C., Provansal, M., Boyer, L.: J. Physique Lett. 45, 483 (1984)

    Article  Google Scholar 

  2. Provansal, M., Mathis, C., Boyer, L.: J. Fluid Mech. 182, 1 (1987)

    Article  Google Scholar 

  3. Dušek, J., Le Gal, P., Fraunié, P.: J. Fluid Mech. 264, 59 (1994)

    Article  MathSciNet  Google Scholar 

  4. Jackson, C.P.: J. Fluid Mech. 270, 23 (1987)

    Article  Google Scholar 

  5. Kelkar, M., Patankar, S.: Int. J. Numer. Meth. Fluids 14, 327 (1992)

    Article  Google Scholar 

  6. Noack, B., Eckelmann, H.: J. Fluid Mech. 270, 297 (1994)

    Article  Google Scholar 

  7. Williamson, C.: Annu. Rev. Fluid Mech. 28, 477 (1996)

    Article  Google Scholar 

  8. Strykowski, P., Sreenivasan, K.: J. Fluid Mech. 218, 71 (1990)

    Article  Google Scholar 

  9. Mittal, S.: J. Fluids Struct. 15, 291 (2001)

    Article  Google Scholar 

  10. Mittal, S., Raghuvanshi, A.: Int. J. Numer. Methods Fluids 35(4), 421 (2001)

    Article  Google Scholar 

  11. Morzynski, M., Afanasiev, K., Thiele, F.: Comput. Meth. Appl. Mech. Engng. 169, 161 (1999)

    Article  Google Scholar 

  12. Dalton, C., Xu, Y., Owen, J.: J. Fluids Struct. 15, 617 (2001)

    Article  Google Scholar 

  13. Yildirim, I., Rindt, C., Steenhoven, A.: Phys. Fluids 22(9), 094101 (2010)

    Article  Google Scholar 

  14. Kuo, C.H., Chiou, L.C., Chen, C.C.: J. Fluids Struct. 23, 938 (2007)

    Article  Google Scholar 

  15. Igarashi, T.: J. Wind Eng. Ind. Aerodyn. 69-71, 141 (1997)

    Article  Google Scholar 

  16. Sakamoto, H., Tan, K., Haniu, H.: J. Fluids Eng. 113(2), 183 (1991)

    Article  Google Scholar 

  17. Sakamoto, H., Haniu, H.: J. Fluids Eng. 116(2), 221 (1994)

    Article  Google Scholar 

  18. Parezanović, V., Cadot, O.: Phys. Fluids 21(7), 071701 (2009)

    Article  Google Scholar 

  19. Parezanović, V., Cadot, O.: J. Fluid Mech. 693, 115 (2012)

    Article  Google Scholar 

  20. Cadot, O., Thiria, B., Beaudoin, J.F.: In: Braza, M., Hourigan, K. (eds.) IUTAM Symposium on Unsteady Separated Flows and their Control, IUTAM Bookseries, vol. 14, pp 529–537. Springer (2009)

  21. Hill, D.C.: AIAA 92-0067, See also NASA technical memorandum No. 103858 (1992)

  22. Giannetti, F., Luchini, P.: J. Fluid Mech. 581, 167 (2007)

    Article  MathSciNet  Google Scholar 

  23. Luchini, P., Giannetti, F.: J. Pralits, AIAA, 2008–4227 (2008)

  24. Marquet, O., Sipp, D., Jacquin, L., Chomaz, J.M.: AIAA, 2008–4228 (2008)

  25. Marquet, O., Sipp, D., Jacquin, L.: J. Fluid Mech. 615, 221 (2008)

    Article  MathSciNet  Google Scholar 

  26. Meliga, P., Sipp, D., Chomaz, J.M.: Phys. Fluids 22(5), 054109 (2010)

    Article  Google Scholar 

  27. Pralits, J., Brandt, L., Giannetti, F.: J. Fluid Mech. 650, 513 (2010)

    Article  MathSciNet  Google Scholar 

  28. Alizard, F., Robinet, J.C., R.U.: Phys. Fluids 22, 014103 (2010)

  29. Sipp, D., Marquet, O., Meliga, P., Barbagallo, A.: App. Mech. Rev. 63, 030801 (2010)

    Article  Google Scholar 

  30. Brandt, L., Sipp, D., Pralits, J., Marquet, O.: J. Fluid Mech. 687, 503 (2011)

    Article  MathSciNet  Google Scholar 

  31. Boujo, E., Ehrenstein, U., Gallaire, F.: Phys. Fluids 25(12), 124106 (2013)

    Article  Google Scholar 

  32. Boujo, E., Gallaire, F.: J. Fluid Mech. 742, 618 (2014)

    Article  MathSciNet  Google Scholar 

  33. Meliga, P., Boujo, E., Pujals, G., Gallaire, F.: Phys. Fluids 26, 104101 (2014)

    Article  Google Scholar 

  34. Meliga, P., Pujals, G., Serre, E.: Phys. Fluids 24, 061701 (2012). See supplementary material at 10.1063/1.4724211 for provision of the theoretical formalism and detailed equations solved in the paper

    Article  Google Scholar 

  35. Mettot, C., Sipp, D., Bézard, H.: Phys. Fluids 26(4), 045112 (2014)

    Article  Google Scholar 

  36. Barkley, D.: Europhys. Lett. 75, 750 (2002)

    Article  MathSciNet  Google Scholar 

  37. Meliga, P., Gallaire, F., Boujo, E.: Accepted for publication in J. Fluid Mech (2016)

  38. Rodi, W.: J. Wind Eng. Ind. Aerodyn. 69–71, 55 (1997)

    Article  Google Scholar 

  39. Rodi, W., Ferziger, J., Breuer, M., Pourquié, M.: J. Fluid Eng. 119, 248 (1997)

    Article  Google Scholar 

  40. Minguez, M., Brun, C., Pasquetti, R., Serre, E.: Int. J. Heat Fluid Fl. 32, 558 (2011)

    Article  Google Scholar 

  41. Hussain, A., Reynolds, W.: J. Fluid Mech. 41, 241 (1970)

    Article  Google Scholar 

  42. Pier, B.: J. Fluid Mech. 458, 407 (2002)

    Article  Google Scholar 

  43. Meliga, P., Sipp, D., Chomaz, J.M.: Phys. Fluids 21, 054105 (2009)

    Article  Google Scholar 

  44. Camarri, S., Fallenius, B., Fransson, J.: J. Fluid Mech. 715, 499 (2013)

    Article  MathSciNet  Google Scholar 

  45. Noack, B., Afanasiev, K., Morzynski, M., Tadmor, G., Thiele, F.: J. Fluid Mech. 497, 335 (2003)

    Article  MathSciNet  Google Scholar 

  46. Stuart, J.: J. Fluid Mech. 4, 1 (1958)

    Article  MathSciNet  Google Scholar 

  47. Stuart, J.: Annu. Rev. Fluid Mech. 3, 347 (1971)

    Article  Google Scholar 

  48. Lyn, D.A., Einav, S., Rodi, W., Park, J.H.: J. Fluid Mech. 304, 285 (1995)

    Article  Google Scholar 

  49. Spalart, P., Allmaras, S.: Rech. Aerosp. 1, 5 (1994)

    Google Scholar 

  50. Giles, M.B., Duta, M.C., Müller, J.D., Pierce, N.A.: AIAA J 41, 198 (2003)

    Article  Google Scholar 

  51. Boukir, K., Maday, Y., Métivet, B., Razafindrakoto, E.: Intl. J. Numer. Meth. Fluids 25, 1421 (1997)

    Article  Google Scholar 

  52. Iaccarino, G., Ooi, A., Durbin, P.A., Behnia, M.: Int. J. Heat Fluid Flow 24, 146 (2003)

    Article  Google Scholar 

  53. Bao, Y., Zhou, D., Wu, Q., Chen, X.Q.: J. Comput. Struct. 89, 325 (2011)

    Article  Google Scholar 

  54. Lee, B.: J. Fluid Mech. 69, 263 (1975)

    Article  Google Scholar 

  55. Sohankar, A., Davidson, L., Norberg, C.: ASME Trans. J. Fluids Eng. 122, 39 (2000)

    Article  Google Scholar 

  56. Sipp, D., Lebedev, A.: J. Fluid Mech. 593, 333 (2007)

    Article  Google Scholar 

  57. Chomaz, J.M.: Annu. Rev. Fluid Mech. 37, 357 (2005)

    Article  MathSciNet  Google Scholar 

  58. Henderson, R.: Phys. Fluids 7, 2102 (1995)

    Article  Google Scholar 

  59. Roshko, A.: J. Wind Eng. Ind. Aerodyn. 49(1-3), 79 (1993)

    Article  Google Scholar 

  60. Åkervik, E., Brandt, L., Henningson, D., Hœpffner, J., Marxen, O., Schlatter, P.: Phys. Fluids 18, 068102 (2006)

    Article  Google Scholar 

  61. Maurel, A., Pagneux, V., Wesfreid, J.: Europhys. Lett. 32, 217 (1995)

    Article  Google Scholar 

  62. Zielinska, B., Goujon-Durand, S., Dušek, J., Wesfreid, J.: Phys. Rev. Lett. 79, 3893 (1997)

    Article  Google Scholar 

  63. Mantič-Lugo, V., Arratia, C., Gallaire, F.: Phys. Rev. Lett. 113, 084501 (2014)

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the Investissements d’Avenir French Government program, managed by the French National Research Agency (ANR) through the A*MIDEX grant (ANR-11-IDEX-0001-02) and the LABEX MEC project (ANR-11-LABX-0092). P.M. is grateful to G. Pujals at PSA Peugeot-Citroën for his expertise in OpenFoam simulations.

Author information

Authors and Affiliations

  1. Aix-Marseille Université CNRS, Ecole Centrale Marseille, Laboratoire M2P2, Marseille, France

    P. Meliga & E. Serre

  2. Unité de Mécanique, Ecole Nationale Supérieure de Techniques Avancées de ParisTech, Palaiseau, France

    O. Cadot

Authors
  1. P. Meliga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Cadot
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Serre
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Meliga.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meliga, P., Cadot, O. & Serre, E. Experimental and Theoretical Sensitivity Analysis of Turbulent Flow Past a Square Cylinder. Flow Turbulence Combust 97, 987–1015 (2016). https://doi.org/10.1007/s10494-016-9755-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-016-9755-0

Keywords

Search

Navigation