Dynamics of viscoelastic pipe flow in the maximum drag reduction limit

TL;DR

This study investigates the complex flow dynamics in viscoelastic pipe flow near the maximum drag reduction limit, revealing the transition from turbulence suppression to relaminarization and the emergence of elasto-inertial turbulence.

Contribution

It uncovers the transition from turbulence hibernation to spatio-temporal intermittency and links minimal flow simulations with experimental observations at the MDR limit.

Findings

Long hibernation periods in small domains at high Wi

Flow relaminarizes with increasing Wi in larger pipes

Emergence of elasto-inertial turbulence at high Wi

Abstract

Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so called "maximum drag reduction" (MDR) asymptote is universal, i.e. independent of the type of polymer and solvent used. Until recently, the consensus was that, in this limit, flows are in a marginal state where only a minimal level of turbulence activity persists. Observations in direct numerical simulations using minimal sized channels appeared to support this view and reported long "hibernation" periods where turbulence is marginalized. In simulations of pipe flow we find that, indeed, with increasing Weissenberg number (Wi), turbulence expresses long periods of hibernation if the domain size is small. However, with increasing pipe length, the temporal hibernation continuously alters to spatio-temporal intermittency and here the flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an increase in Wi, the flow fully relaminarises, in agreement with recent experiments. At even larger Wi, a different instability is encountered causing a drag increase towards MDR. Our findings hence link earlier minimal flow unit simulations with recent experiments and confirm that the addition of polymers initially suppresses Newtonian turbulence and leads to a reverse transition. The MDR state on the other hand results from a separate instability and the underlying dynamics corresponds to the recently proposed state of elasto-inertial-turbulence (EIT).