Direct numerical simulation of drag reduction in rotating pipe flow up to $Re_{\tau} \approx 3000$

TL;DR

This study uses direct numerical simulations to analyze how axial rotation affects drag reduction in pipe flow at high Reynolds numbers, revealing up to 70% drag reduction and proposing new scaling laws and predictive formulas.

Contribution

It extends previous research by exploring higher Reynolds numbers and provides new scaling laws, a predictive friction factor formula, and insights into turbulent structure modifications due to rotation.

Findings

Drag reduction up to 70% observed.

Scaling laws for velocity profiles proposed.

Outer layer contributes most to drag reduction at high Re.

Abstract

Direct numerical simulations (DNS) of rotating pipe flows up to $Re_{\tau} \approx 3000$ are carried out to investigate drag reduction effects associated with axial rotation, extending previous studies carried out at a modest Reynolds number (Orlandi & Fatica 1997; Orlandi & Ebstein 2000). The results show that the drag reduction, which we theoretically show to be equivalent to net power saving assuming no mechanical losses, monotonically increases as either the Reynolds number or the rotation number increases, proportionally to the inner-scaled rotational speed. Net drag reduction up to about $70\%$ is observed, while being far from flow relaminarisation. Scaling laws for the mean axial and azimuthal velocity are proposed, from which a predictive formula for the friction factor is derived. The formula can correctly represent the dependency of the friction factor on the Reynolds and rotation numbers, maintaining good accuracy for low-to-moderate rotation numbers. Examination of the turbulent structures highlights the role of rotation in widening and elongating the small-scale streaks, with subsequent suppression of sweeps and ejections. In the core part of the flow, clear weakening of large-scale turbulent motions is observed at high Reynolds numbers, with subsequent suppression of the outer-layer peak in the pre-multiplied spectra. The Fukagata-Iwamoto-Kasagi decomposition indicates that, consistent with a theoretically derived formula, the outer layer yields the largest contribution to drag reduction at increasingly high Reynolds numbers. In contrast, both the inner and the outer layers contribute to drag reduction as the rotation number increases.