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

Abstract

The goal of the present study is: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bi-dimensional instability in three-dimensional EIT flows and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of FENE-P fluid flows are performed in two- and three-dimensional channels. The Reynolds number is set to $\mathrm{Re}_τ= 85$ which is sub-critical for 2D flows but beyond transition for 3D ones. The polymer properties correspond to those of typical dilute polymer solutions and two moderate Weissenberg numbers, $\mathrm{Wi}_τ= 40, 100$, are considered. The simulation results show that sustained turbulence can be observed in 2D sub-critical flows, confirming the existence of a bi-dimensional elasto-inertial instability. The same type of instability is also observed in 3D simulations where both Newtonian and elasto-inertial turbulent structures co-exist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of the typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of the small elastic scales is investigated by introducing global artificial diffusion in the hyperbolic transport equation for polymers. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed turbulence, eventually leading to the flow laminarization. A sufficiently high Schmidt number is necessary to allow self-sustained turbulence to settle.