Direct numerical simulation of drag reduction in rotating pipe flow up to

Direct numerical simulation (DNS) of rotating pipe flows up to $Re_\tau \approx 3000$ is carried out to investigate drag reduction effects associated with axial rotation, extending previous studies carried out at a modest Reynolds number (Orlandi & Fatica, J. Fluid Mech. , vol. 343, 1997, pp. 43–72; Orlandi & Ebstein, Intl J. Heat Fluid Flow , vol. 21, 2000, pp. 499–505). 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 approximately $70\,\%$ 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.