On the mechanism of elasto-inertial turbulence

Abstract

Elasto-inertial turbulence (EIT) is a new state of turbulence found in inertial flows with polymer additives. The dynamics of turbulence generated and controlled by such additives is investigated from the perspective of the coupling between polymer dynamics and flow structures. Direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 (based on the bulk and the channel height) are used to study the formation and dynamics of elastic instabilities and their effects on the flow. The flow topology of EIT is found to differ significantly from Newtonian wall-turbulence. Structures identified by positive (rotational flow topology) and negative (extensional/compressional flow topology) second invariant isosurfaces of the velocity gradient are cylindrical and aligned in the spanwise direction. Polymers are significantly stretched in sheet-like regions that extend in the streamwise direction with a small upward tilt. The cylindrical structures emerge from the sheets of high polymer extension, in a mechanism of energy transfer from the fluctuations of the polymer stress work to the turbulent kinetic energy. At subcritical Reynolds numbers, EIT is observed at modest Weissenberg number (, ratio polymer relaxation time to viscous time scale). For supercritical Reynolds numbers, flows approach EIT at large . EIT provides new insights on the nature of the asymptotic state of polymer drag reduction (maximum drag reduction), and explains the phenomenon of early turbulence, or onset of turbulence at lower Reynolds numbers than for Newtonian flows observed in some polymeric flows.

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

“…The existence of a sustained turbulent motion in two-dimensional flows demonstrates the ability of FENE-P fluid flows to generate turbulence for sub-critical (2D) Reynolds number in wall-bounded planar configurations. The physical mechanism behind the elasto-inertial instability observed is very similar to the one depicted in [4] for a similar range of Wi number in three-dimensional flows. Thin sheets of large polymer extension arise from the stretching and the advection of polymer macromolecules by the solvent.…”

“…Thus, an initial perturbation is necessary to trigger turbulence. The present methodology uses an alternated blowing-suction transervse excitation [4] added to the laminar viscoelastic Poiseuille flow during a short period of time to perturb the stable solution. After several flowthrough times, the external excitation is turned off and the flow naturally develops towards its turbulent statistically steady state.…”

“…One is the longstanding question of the nature, Newtonian or Non-Newtonian, of the maximum drag reduction (MDR) state, observed by Virk [2]. A second, possibly related to the first, is the role of a recently discovered turbulent state, elasto-inertial turbulence [3][4][5], in the dynamics of drag reduced flows. This letter first focuses on the latter through an investigation of the dimensionality and role of small scale dynamics of EIT in channel flows at a marginally supercritical Reynolds number for three-dimensional flows.…”

“…EIT [3][4][5] is a turbulent state driven by cyclic flow-polymer interactions, and can be found over a wide range of Reynolds numbers, from sub-critical to super-critical. This polymer-driven turbulence is akin to elastic turbulence [14][15][16], a chaotic state found in inertial-less polymer flows undergoing curved mean streamlines.…”

On the role of pressure in elasto-inertial turbulence

“…These seemingly contradictory effects of polymer additives can be explained by the interaction between elastic instabilities and the flow's inertia characterising elasto-inertial turbulence, hereafter referred to as EIT [6,7]. EIT is a state of small-scale turbulence driven by elastic instabilities that exists by either creating its own extensional flow patterns or by exploiting extensional flow topologies.…”