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Destabilizing turbulence in pipe flow

Nature Physics volume 14, pages 386–390 (2018)Cite this article

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Abstract

Turbulence is the major cause of friction losses in transport processes and it is responsible for a drastic drag increase in flows over bounding surfaces. While much effort is invested into developing ways to control and reduce turbulence intensities1,2,3, so far no methods exist to altogether eliminate turbulence if velocities are sufficiently large. We demonstrate for pipe flow that appropriate distortions to the velocity profile lead to a complete collapse of turbulence and subsequently friction losses are reduced by as much as 90%. Counterintuitively, the return to laminar motion is accomplished by initially increasing turbulence intensities or by transiently amplifying wall shear. Since neither the Reynolds number nor the shear stresses decrease (the latter often increase), these measures are not indicative of turbulence collapse. Instead, an amplification mechanism4,5 measuring the interaction between eddies and the mean shear is found to set a threshold below which turbulence is suppressed beyond recovery.

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Fig. 1: Perturbing turbulence.
Fig. 2: Laminarization mechanisms.
Fig. 3: Drag reduction.

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References

  1. Lumley, J. & Blossey, P. Control of turbulence. Ann. Rev. Fluid Mech. 30, 311–327 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  2. Kasagi, N., Suzuki, Y. & Fukagata, K. Microelectromechanical systems-based feedback control of turbulence for skin friction reduction. Ann. Rev. Fluid Mech. 41, 231–251 (2009).

    Article  ADS  MATH  Google Scholar 

  3. Kim, J. & Bewley, T. R. A linear systems approach to flow control. Ann. Rev. Fluid Mech. 39, 383–417 (2007).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. Hydrodynamic stability without eigenvalues. Science 261, 578–584 (1993).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Brandt, L. The lift-up effect: The linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. B 47, 80–96 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  6. Avila, K. et al. The onset of turbulence in pipe flow. Science 333, 192–196 (2011).

    Article  ADS  Google Scholar 

  7. Bewley, T. R., Moin, P. & Temam, R. DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 447, 179–225 (2001).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Högberg, M., Bewley, T. R. & Henningson, D. S. Relaminarization of Reτ = 100 turbulence using gain scheduling and linear state-feedback control. Phys. Fluids 15, 3572–3575 (2003).

    Article  ADS  MATH  Google Scholar 

  9. Auteri, F., Baron, A., Belan, M., Campanardi, G. & Quadrio, M. Experimental assessment of drag reduction by traveling waves in a turbulent pipe flow. Phys. Fluids 22, 115103 (2010).

    Article  ADS  Google Scholar 

  10. Lieu, B., Moarref, R. & Jovanović, M. Controlling the onset of turbulence by streamwise travelling waves. Part 2. Direct numerical simulation. J. Fluid Mech. 663, 100–119 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Moarref, R. & Jovanović, M. Controlling the onset of turbulence by streamwise travelling waves. Part 1. Receptivity analysis. J. Fluid Mech. 663, 70–99 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Quadrio, M., Ricco, P. & Viotti, C. Streamwise-traveling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161–178 (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Hof, B., De Lozar, A., Avila, M., Tu, X. Y. & Schneider, T. M. Eliminating turbulence in spatially intermittent flows. Science 327, 1491–1494 (2010).

    Article  ADS  Google Scholar 

  14. Rathnasingham, R. & Breuer, K. Active control of turbulent boundary layers. J. Fluid Mech. 495, 209–233 (2003).

    Article  ADS  MATH  Google Scholar 

  15. Willis, A. P., Hwang, Y. & Cossu, C. Optimally amplified large-scale streaks and drag reduction in turbulent pipe flow. Phys. Rev. E 82, 036321 (2010).

    Article  ADS  Google Scholar 

  16. Du, Y. & Karniadakis, G. E. Suppressing wall turbulence by means of a transverse traveling wave. Science 288, 1230–1234 (2000).

    Article  ADS  Google Scholar 

  17. Min, T., Kang, S. M., Speyer, J. L. & Kim, J. Sustained sub-laminar drag in a fully developed channel flow. J. Fluid Mech. 558, 309–318 (2006).

    Article  ADS  MATH  Google Scholar 

  18. Park, J. & Choi, H. Effects of uniform blowing or suction from a spanwise slot on a turbulent boundary layer flow. Phys. Fluids 11, 3095–3105 (1999).

    Article  ADS  MATH  Google Scholar 

  19. Sumitani, Y. & Kasagi, N. Direct numerical simulation of turbulent transport with uniform wall injection and suction. AIAA J. 33, 1220–1228 (1995).

    Article  ADS  Google Scholar 

  20. Fukagata, K., Iwamoto, K. & Kasagi, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, 73–76 (2002).

    Article  ADS  MATH  Google Scholar 

  21. Fransson, J. H. M. & Alfredsson, P. H. On the disturbance growth in an asymptotic suction boundary layer. J. Fluid Mech. 482, 51–90 (2003).

    Article  ADS  MATH  Google Scholar 

  22. Matisse, P. & Gorman, M. Neutrally buoyant anisotropic particles for flow visualization. Phys. Fluids 27, 759–760 (1984).

    Article  ADS  Google Scholar 

  23. Willis, A. P. The Openpipeflow Navier–Stokes solver. SoftwareX 6, 124–127 (2017).

    Article  ADS  Google Scholar 

  24. Avila, M., Willis, A. P. & Hof, B. On the transient nature of localized pipe flow turbulence. J. Fluid Mech. 646, 127–136 (2010).

    Article  ADS  MATH  Google Scholar 

  25. Barkley, D. et al. The rise of fully turbulent flow. Nature 526, 550–553 (2015).

    Article  ADS  Google Scholar 

  26. Willis, A. & Kerswell, R. Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized ‘edge’ states. J. Fluid Mech. 619, 213–233 (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Jimenez, J. & Pinelli, A. The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359 (1999).

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

We acknowledge the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 306589, the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 737549) and the Deutsche Forschungsgemeinschaft (Project No. FOR 1182) for financial support. We thank our technician P. Maier for providing highly valuable ideas and greatly supporting us in all technical aspects. We thank M. Schaner for technical drawings, construction and design. We thank M. Schwegel for a Matlab code to post-process experimental data.

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Author notes

  1. Jakob Kühnen and Baofang Song contributed equally to this work.

Authors and Affiliations

  1. Nonlinear Dynamics and Turbulence Group, IST Austria, Klosterneuburg, Austria

    Jakob Kühnen, Baofang Song, Davide Scarselli, Nazmi Burak Budanur, Michael Riedl & Björn Hof

  2. Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, Bremen, Germany

    Baofang Song & Marc Avila

  3. Center for Applied Mathematics, Tianjin University, Tianjin, China

    Baofang Song

  4. School of Mathematics and Statistics, University of Sheffield, Sheffield, UK

    Ashley P. Willis

Authors
  1. Jakob Kühnen
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  2. Baofang Song
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  4. Nazmi Burak Budanur
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  6. Ashley P. Willis
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  7. Marc Avila
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  8. Björn Hof
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Contributions

J.K. and B.H. designed the experiments. J.K. and D.S. carried out the experiments and post-processed the data. M.R. carried out the rotor experiments. J.K., D.S. and B.H. analysed the experimental results. J.K. and B.H. supervised the experimental work. B.S. and N.B.B. performed the computer simulations of the Navier–Stokes equations. B.S., M.A. and N.B.B. analysed the numerical results. M.A., A.P.W. and B.H. supervised the computer simulations. D.S., A.P.W., M.A. and B.S. performed the theoretical analysis. J.K., B.S., D.S., M.A. and B.H. wrote the paper.

Corresponding authors

Correspondence to Jakob Kühnen or Björn Hof.

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The authors declare no competing financial interests.

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Supplementary information

Supplementary Information

Destabilizing turbulence in pipe flow.

Videos

Supplementary Movie

Relaminarization by vigorously stirring a turbulent pipe flow with four rotors.

Supplementary Movie

Relaminarization by impulsive movement of a pipe segment.

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Kühnen, J., Song, B., Scarselli, D. et al. Destabilizing turbulence in pipe flow. Nature Phys 14, 386–390 (2018). https://doi.org/10.1038/s41567-017-0018-3

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