Bayesian minimisation of energy consumption in turbulent pipe flow via unsteady driving

TL;DR

This paper demonstrates that Bayesian optimisation can efficiently identify unsteady driving waveforms that significantly reduce energy consumption and drag in turbulent pipe flow, outperforming traditional gradient-based methods.

Contribution

The study introduces a Bayesian optimisation framework to find energy-efficient pulsatile waveforms in turbulent pipe flow, showing substantial energy savings over steady driving.

Findings

Optimal waveforms reduce energy consumption by 22%.

Drag is reduced by 37% with optimal waveforms.

Bayesian optimisation outperforms gradient-based methods in noisy turbulent flow scenarios.

Abstract

Turbulence accounts for most of the energy losses associated with the pumping of fluids in pipes. Pulsatile drivings can reduce the drag and energy consumption required to supply a desired mass flux, when compared to steady driving. However, not all pulsation waveforms yield reductions. Here, we compute drag- and energy-optimal driving waveforms using direct numerical simulations and a gradient-free black-box optimisation framework. Specifically, we show that Bayesian optimisation is vastly superior to ordinary gradient-based methods in terms of computational efficiency and robustness, due to its ability to deal with noisy objective functions, as they naturally arise from the finite-time averaging of turbulent flows. We identify optimal waveforms for three Reynolds numbers and two Womersley numbers. At a Reynolds number of 8600 and a Womersley number of 10, optimal waveforms reduce total energy consumption by 22 % and drag by 37 %. These reductions are rooted in the suppression of turbulence prior to the acceleration phase, the resulting delay in turbulence onset, and the radial localization of turbulent kinetic energy and production toward the pipe centre. Our results pinpoint that the predominant, steady operation mode of pumping fluids through pipes is far from optimal.