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Turbulence suppression by cardiac-cycle-inspired driving of pipe flow

Nature volume 621, pages 71–74 (2023)Cite this article

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Abstract

Flows through pipes and channels are, in practice, almost always turbulent, and the multiscale eddying motion is responsible for a major part of the encountered friction losses and pumping costs1. Conversely, for pulsatile flows, in particular for aortic blood flow, turbulence levels remain low despite relatively large peak velocities. For aortic blood flow, high turbulence levels are intolerable as they would damage the shear-sensitive endothelial cell layer2,3,4,5. Here we show that turbulence in ordinary pipe flow is diminished if the flow is driven in a pulsatile mode that incorporates all the key features of the cardiac waveform. At Reynolds numbers comparable to those of aortic blood flow, turbulence is largely inhibited, whereas at much higher speeds, the turbulent drag is reduced by more than 25%. This specific operation mode is more efficient when compared with steady driving, which is the present situation for virtually all fluid transport processes ranging from heating circuits to water, gas and oil pipelines.

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Fig. 1: Decay of turbulence in aortic flow.
Fig. 2: Friction reduction in pulsating flow and the effect of three different cycles on wall shear stress.
Fig. 3: Optimization of power savings.

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Data availability

The datasets generated and analysed during the current study are freely available in the Zenodo repository (https://doi.org/10.5281/zenodo.7828996)35.

Code availability

The numerical simulations were conducted with the open-source code nsPipeFlow, distributed under the terms of the GNU General Public License v.3. A detailed description of the code and user guide are provided in ref. 30. The code version used in this study and an initial condition to start the simulations are openly available in the Zenodo repository (https://doi.org/10.5281/zenodo.7828996)35.

References

  1. Kühnen, J. et al. Destabilizing turbulence in pipe flow. Nat. Phys. 14, 386–390 (2018).

    Article  Google Scholar 

  2. Davies, P. F., Remuzzi, A., Gordon, E. J., Dewey, C. F.Jr & Gimbrone, M. A. Turbulent fluid shear stress induces vascular endothelial cell turnover in vitro. Proc. Natl Acad. Sci. USA 83, 2114–2117 (1986).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  3. DePaola, N., Gimbrone, M. A. Jr, Davies, P. F.Jr & Dewey, C. F. Vascular endothelium responds to fluid shear stress gradients. Arterioscler. Thromb. J. Vasc. Biol. 12, 1254–1257 (1992).

    Article  CAS  Google Scholar 

  4. Davies, P. F. Hemodynamic shear stress and the endothelium in cardiovascular pathophysiology. Nat. Clin. Pract. Cardiovasc. Med. 6, 16–26 (2009).

    Article  CAS  PubMed  Google Scholar 

  5. Gimbrone, M. A.Jr & García-Cardeña, G. Endothelial cell dysfunction and the pathobiology of atherosclerosis. Circ. Res. 118, 620–636 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Frenning, L. Pump Life Cycle Costs: A Guide to LCC Analysis for Pumping Systems (Hydraulic Institute, Europump, and the US Department of Energy’s Office of Industrial Technologies, 2001).

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

    Article  ADS  CAS  PubMed  MATH  Google Scholar 

  8. Ku, D. N. et al. Blood flow in arteries. Annu. Rev. Fluid Mech. 29, 399–434 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  9. Stalder, A. F. et al. Assessment of flow instabilities in the healthy aorta using flow-sensitive MRI. J. Magn. Reson. Imaging 33, 839–846 (2011).

    Article  PubMed  Google Scholar 

  10. Nerem, R. M., Rumbergerr, J. A. Jr, Gross, D. R., Hamlin, R. L. & Geiger, G. L. Hot-film anemometer velocity measurements of arterial blood flow in horses. Circ. Res. 34, 193–203 (1974).

    Article  CAS  PubMed  Google Scholar 

  11. Brunton, S. L. & Noack, B. R. Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67, 050801 (2015).

    Article  ADS  Google Scholar 

  12. Karniadakis, G. & Choi, K.-S. Mechanisms on transverse motions in turbulent wall flows. Annu. Rev. Fluid Mech. 35, 45–62 (2003).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. 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 

  14. Nakanishi, R., Mamori, H. & Fukagata, K. Relaminarization of turbulent channel flow using traveling wave-like wall deformation. Int. J. Heat Fluid Flow 35, 152–159 (2012).

    Article  Google Scholar 

  15. 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 

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

    Article  ADS  MATH  Google Scholar 

  17. García-Mayoral, R. & Jiménez, J. Drag reduction by riblets. Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 369, 1412–1427 (2011).

    ADS  Google Scholar 

  18. Virk, P. S., Mickley, H. S. & Smith, K. A. The ultimate asymptote and mean flow structure in Toms’ phenomenon. J. Appl. Mech. 37, 488–493 (1970).

    Article  ADS  CAS  Google Scholar 

  19. Choueiri, G. H., Lopez, J. M. & Hof, B. Exceeding the asymptotic limit of polymer drag reduction. Phys. Rev. Lett. 120, 124501 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  20. He, S. & Jackson, J. D. A study of turbulence under conditions of transient flow in a pipe. J. Fluid Mech. 408, 1–38 (2000).

    Article  ADS  MathSciNet  CAS  MATH  Google Scholar 

  21. Greenblatt, D. & Moss, E. A. Rapid temporal acceleration of a turbulent pipe flow. J. Fluid Mech. 514, 65–75 (2004).

    Article  ADS  MATH  Google Scholar 

  22. He, S., Ariyaratne, C. & Vardy, A. E. Wall shear stress in accelerating turbulent pipe flow. J. Fluid Mech. 685, 440–460 (2011).

    Article  ADS  MATH  Google Scholar 

  23. He, S. & Seddighi, M. Turbulence in transient channel flow. J. Fluid Mech. 715, 60–102 (2013).

    Article  ADS  MathSciNet  CAS  MATH  Google Scholar 

  24. He, K., Seddighi, M. & He, S. DNS study of a pipe flow following a step increase in flow rate. Int. J. Heat Fluid Flow 57, 130–141 (2016).

    Article  Google Scholar 

  25. Mathur, A. et al. Temporal acceleration of a turbulent channel flow. J. Fluid Mech. 835, 471–490 (2018).

    Article  ADS  CAS  Google Scholar 

  26. Cheng, Z., Jelly, T. O., Illingworth, S. J., Marusic, I. & Ooi, A. S. H. Forcing frequency effects on turbulence dynamics in pulsatile pipe flow. Int. J. Heat Fluid Flow 82, 108538 (2020).

    Article  Google Scholar 

  27. Ariyaratne, C., He, S. & Vardy, A. E. Wall friction and turbulence dynamics in decelerating pipe flows. J. Hydraul. Res. 48, 810–821 (2010).

    Article  Google Scholar 

  28. Kobayashi, W., Shimura, T., Mitsuishi, A., Iwamoto, K. & Murata, A. Prediction of the drag reduction effect of pulsating pipe flow based on machine learning. Int. J. Heat Fluid Flow 88, 108783 (2021).

    Article  Google Scholar 

  29. Foggi Rota, G., Monti, A., Rosti, M. E. & Quadrio, M. Saving energy in turbulent flows with unsteady pumping. Sci. Rep. 13, 1299 (2023).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  30. Bürk, J. et al. Evaluation of 3D blood flow patterns and wall shear stress in the normal and dilated thoracic aorta using flow-sensitive 4D CMR. J Cardiovasc. Magn. Reson. 14, 84 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  31. Stein, P. D. & Sabbah, H. N. Turbulent blood flow in the ascending aorta of humans with normal and diseased aortic valves. Circ. Res. 39, 58–65 (1976).

    Article  CAS  PubMed  Google Scholar 

  32. López, J. M. et al. nsCouette—a high-performance code for direct numerical simulations of turbulent Taylor–Couette flow. SoftwareX 11, 100395 (2020).

    Article  Google Scholar 

  33. Blasius, H. in Mitteilungen über Forschungsarbeiten auf dem Gebiete des Ingenieurwesens Vol. 131, 1–41 (Springer, 1913); https://doi.org/10.1007/978-3-662-02239-9_1.

  34. Tanaka, M., Girard, G., Davis, R., Peuto, A. & Bignell, N. Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports. Metrologia 38, 301 (2001).

    Article  ADS  CAS  Google Scholar 

  35. Scarselli, D., Lopez, J. M., Varshney, A. & Hof, B. Turbulence suppression by cardiac cycle inspired pulsatile driving of pipe flow: datasets and numerical code used to perform the simulations. Zenodo https://doi.org/10.5281/zenodo.7828996 (2023).

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Acknowledgements

We acknowledge the assistance of the Miba machine shop and the team of the ISTA-HPC cluster. We thank M. Quadrio for the discussions. The work was supported by the Simons Foundation (grant no. 662960) and by the Austrian Science Fund (grant no. I4188-N30), within Deutsche Forschungsgemeinschaft research unit FOR 2688.

Author information

Authors and Affiliations

  1. Institute of Science and Technology Austria, Klosterneuburg, Austria

    D. Scarselli, J. M. Lopez, A. Varshney & B. Hof

  2. Universidad de Málaga, Málaga, Spain

    J. M. Lopez

  3. School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar, India

    A. Varshney

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Contributions

B.H. supervised the project. D.S. and A.V. designed and performed the experiment. D.S. analysed the experimental data. J.M.L. designed and performed the computer simulations of the Navier–Stokes equations and analysed the numerical results. D.S., J.M.L., A.V. and B.H. wrote the paper.

Corresponding author

Correspondence to B. Hof.

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The authors declare no competing interests.

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Nature thanks Yongyun Hwang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Extended data

is available for this paper at https://doi.org/10.1038/s41586-023-06399-5.

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Extended data figures and tables

Extended Data Fig. 1 Sketch of the experimental setup.

Drawing not to scale.

Extended Data Fig. 2 Waveform, pressure and power signal.

Signals from the optimal cycle (Fig. 2c) measured in experiments. (a) Waveform based on the linear piston speed and (b) pressure drop Δp measured over the test section. The signal from all the 100 cycles measured is shown in blue, while the phase average is represented in orange. The number of samples per cycles is N = 325. For comparison, we report also the pressure drop computed with the DNS for the same cycle (gray dotted line). In this case the signal is obtained by phase-averaging the available 8 cycles. (c) The power input for the same waveform. The values for the 100 cycles in experiments are shown in blue, the ensemble average in red and the power input in DNS is given by the grey doted line.

Extended Data Fig. 3 Comparison of the values of (a) R and (b) S between experiments (blue histogram) and DNS.

For the optimal cycle (Fig. 2c, main text) the histogram shows the distribution of the values obtained from 100 runs. The orange, dashed line shows the mean of the available corresponding DNS cycles.

Extended Data Fig. 4 Definition of the flow cycle used in the experiments of Fig. 2 and Fig. 3

.

Extended Data Table 1 Parameters used in the direct numerical simulations
Full size table
Extended Data Table 2 Comparison between the values of R and S in percentage for the waveforms of Fig. 2 obtained from experiments and DNS
Full size table

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Scarselli, D., Lopez, J.M., Varshney, A. et al. Turbulence suppression by cardiac-cycle-inspired driving of pipe flow. Nature 621, 71–74 (2023). https://doi.org/10.1038/s41586-023-06399-5

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