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


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 (

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 (


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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



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.

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Extended data

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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
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

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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).

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