Turbulent puffs in transitional pulsatile pipe flow at moderate pulsation amplitudes

TL;DR

This study investigates turbulent puffs in transitional pulsatile pipe flow at moderate amplitudes, revealing their localized nature, the role of linear instabilities, and extending a low-order model to capture these dynamics.

Contribution

The paper demonstrates the existence of localized turbulent puffs in pulsatile flow at moderate amplitudes and extends a low-order model to accurately reproduce these phenomena.

Findings

Turbulent puffs are localized structures similar to steady pipe flow.

Linear instabilities in the laminar profile aid puff survival.

Turbulence arises from mean shear and profile instabilities.

Abstract

We show that, in the transitional regime of pulsatile pipe flow, at moderate-to-high amplitudes 0.5 < A < 1, the first long-lived turbulent structures are localized and take the form of the puffs and slugs observed in statistically steady pipe flow. We perform direct numerical simulations at many pulsation frequencies, amplitudes and Re, and observe different dynamics of puffs and slugs. At certain flow parameters we find, using a causal analysis, that puffs actively make use of linear instabilities in the laminar Sexl-Womersley profile to survive the pulsation. Using all these lessons learned, we extend a low order model by Barkley et al., Nature (2015), to reproduce these dynamics. We find a good agreement between the extended model and our numerical results in a broad parametric space of pulsation amplitudes 0.5 < A < 1, frequencies Wo > 5 and 2100 < Re < 3000. With the help of our numerical results, causal analysis and model, we determine that turbulence production has two sources at these flow parameters: the mean shear as in statistically steady pipe flow, and the instabilities of the instantaneous pulsatile mean profile.