Kranz, Felix (2025): A dataset of energy-optimal driving waveforms in turbulent pipe flow [dataset]. PANGAEA, https://doi.org/10.1594/PANGAEA.986097
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Published: 2025-10-20 • DOI registered: 2025-11-19
Abstract:
We compute drag- and energy-optimal driving waveforms in turbulent pipe flow using direct numerical simulations combined with a gradient-free, black-box optimisation framework. Our results demonstrate that Bayesian optimisation significantly outperforms conventional gradient-based methods in terms of efficiency and robustness, owing to its ability to handle noisy objective functions that arise from the finite-time averaging of turbulent flows. Optimal waveforms are identified for three Reynolds numbers and two Womersley numbers. At a Reynolds number of 8600 and a Womersley number of 10, the optimal waveforms reduce total energy consumption by up to 22% and drag by up to 37%. This dataset includes the optimal waveforms, instantaneous and time-averaged velocity fields, as well as post-processing scripts.
Related to:
Morón, Daniel; Avila, Marc: Bayesian minimisation of energy consumption in turbulent pipe flow via unsteady driving. https://arxiv.org/pdf/2508.14593
Parameter(s):
| # | Name | Short Name | Unit | Principal Investigator | Method/Device | Comment |
|---|---|---|---|---|---|---|
| 1 | Binary Object | Binary | Kranz, Felix | Numerical simulated | ||
| 2 | Binary Object (File Size) | Binary (Size) | Bytes | Kranz, Felix | Numerical simulated | |
| 3 | Figure | Fig | Kranz, Felix | Numerical simulated | ||
| 4 | Title | Title | Kranz, Felix | Numerical simulated | ||
| 5 | File name | File name | Kranz, Felix | Numerical simulated | ||
| 6 | Variable | Variable | Kranz, Felix | Numerical simulated |
License:
Creative Commons Attribution 4.0 International (CC-BY-4.0)
Status:
Curation Level: Enhanced curation (CurationLevelC) * Processing Level: PANGAEA data processing level 2 (ProcLevel2)
Size:
59 data points
Data
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| 1 Binary | 2 Binary (Size) [Bytes] | 3 Fig | 4 Title | 5 File name | 6 Variable |
|---|---|---|---|---|---|
| fig1.zip | 279.2 MBytes | 1 | (a) Schematic description of the considered triangular waveforms in terms of the time variant Reynolds number or bulk velocity. (b) The evolution of the volume-integrated cross-stream turbulent kinetic energy. (c) The wall shear stress and power input over the last three periods of a four period run driven in the same manner as in (a). | fig1.zip | Python scripts to produce figure 1 along with .pkl files containing the underlying data |
| fig2.zip | 538.2 kBytes | 2 | (a) The relative standard error of the per-period wall shear stress versus the number of averaging periods. (b) The computational time to achieve a given standard error. | fig2.zip | Python scripts to produce figure 2 along with .pkl files containing the underlying data |
| fig3.zip | 850.8 kBytes | 3 | Best surrogates for the mean wall shear stress and power input | fig3.zip | Python scripts to produce figure 3 along with .pkl files containing the underlying data |
| fig4.zip | 31.7 MBytes | 4 | Optimal triangular waveforms at Re=5160 | fig4.zip | Python scripts to produce figure 4 along with .pkl files containing the underlying data |
| fig5.zip | 568.1 kBytes | 5 | Partial dependence for the wall stress and power input on acceleration time, minimum Reynolds number and maximum Reynolds number | fig5.zip | Python scripts to produce figure 5 along with .pkl files containing the underlying data |
| fig6.zip | 92.8 MBytes | 6 | Power-optimal waveforms obtained from three independent runs of the truncated Fourier approach at Re=5160 and Wo=10 | fig6.zip | Python scripts to produce figure 6 along with .pkl files containing the underlying data |
| fig7.zip | 152 MBytes | 7 | Power-optimal waveform at Re=8600 and Wo=10 | fig7.zip | Python scripts to produce figure 7 along with .pkl files containing the underlying data |
| fig8_9_13_14.zip | 49.9 GBytes | 8,9,13,14 | Time evolution of dissipation, production, spatial wall-shear stress distribution and turbulent kinetic energy for a (sub-)optimal waveform | fig8_9_13_14.zip | Python scripts to produce figure 8, 9, 13, 14 along with .pkl files containing the underlying data |
| fig10.zip | 627.1 kBytes | 10 | The evolution of the optimisation process for different choices of the admissible standard error | fig10.zip | Python scripts to produce figure 10 along with .pkl files containing the underlying data |
| fig11.zip | 12.5 MBytes | 11 | The power-optimal waveform obtained at Wo=10*2^0.5 | fig11.zip | Python scripts to produce figure 11 along with .pkl files containing the underlying data |
| fig12.zip | 135 MBytes | 12 | The evolution of the turbulent kinetic energy for waveforms 1-3 without forcing term | fig12.zip | Python scripts to produce figure 12 along with .pkl files containing the underlying data |
| utils.zip | 15 kBytes | Python scripts required to run the above | utils.zip | Python scripts required to run the above |