Dynamics of viscoelastic pipe flow in the maximum drag reduction limit

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).

arXiv comment18 pages, 5 figures

References in corpus (10)

• Elasto-inertial turbulence
• The rise of fully turbulent flow
• Exceeding the asymptotic limit of polymer drag reduction
• On the mechanism of elasto-inertial turbulence
• Drag Reduction by Polymers in Wall Bounded Turbulence
• Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids
• Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction
• The Openpipeflow Navier--Stokes Solver
• Critical-layer structures and mechanisms in elastoinertial turbulence
• A Hybrid MPI-OpenMP Parallel Implementation for pseudospectral simulations with application to Taylor-Couette Flow

Cited by in corpus (19)

• Turbulent drag reduction by polymer additives: Fundamentals and recent advances
• Understanding viscoelastic flow instabilities: Oldroyd-B and beyond
• A continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow
• Linear instability of viscoelastic pipe flow
• Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers
• Self-sustained elastoinertial Tollmien-Schlichting waves
• Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia
• Tollmien-Schlichting route to elastoinertial turbulence in channel flow
• Nonasymptotic elastoinertial turbulence for asymptotic drag reduction
• Suppression of turbulence and travelling waves in a vertical heated pipe
• Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows
• Vortex merging and splitting events in viscoelastic Taylor Couette flow
• nsCouette -- A high-performance code for direct numerical simulations of turbulent Taylor-Couette flow
• Inertia-driven and elastoinertial viscoelastic turbulent channel flow simulated with a hybrid pseudo-spectral/finite-difference numerical scheme
• Role of elasto-inertial turbulence in viscoelastic drag-reducing turbulence
• Vortex dynamics in low- and high-extent polymer drag reduction regimes revealed by vortex tracking and conformation analysis
• Viscoelastic laminar drag bounds in pipe flow
• Experimental observation of the origin and structure of elasto-inertial turbulence
• Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions