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Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit. (English) Zbl 1419.76040
Summary: Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so-called state of ‘maximum drag reduction’ (MDR), is to a good approximation 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 at low Reynolds numbers $$(Re)$$ using minimal sized channels appeared to support this view and reported long ‘hibernation’ periods where turbulence is marginalized. In simulations of pipe flow at $$Re$$ near transition 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 relaminarizes, 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 at these low$$Re$$ from a separate instability and the underlying dynamics corresponds to the recently proposed state of elasto-inertial turbulence.

##### MSC:
 76A10 Viscoelastic fluids 76F06 Transition to turbulence 76F70 Control of turbulent flows
##### Keywords:
drag reduction; turbulent transition; viscoelasticity
Openpipeflow
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