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

Abstract

The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional 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 both two-and three-dimensional straight periodic channels. The Reynolds number is set to Reτ = 85 which is sub-critical for two-dimensional flows but beyond transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions and two moderate Weissenberg numbers, Wiτ = 40, 100, are considered. The simulation results show that sustained turbulence can be observed in two-dimensional sub-critical flows, confirming the existence of a bi-dimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional 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 (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. 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 (weakly diffusive polymers) is necessary to allow self-sustained turbulence to settle. Although EIT can withstand a low amount of diffusion and remains in a non-laminar chaotic state, adding a finite amount of GAD in the system can have an impact on the dynamics and lead to important quantitative changes, even for Schmidt numbers as large as 10 2 . * vincent.terrapon@ulg.ac.be arXiv:1710.01199v1 [physics.flu-dyn] 3 Oct 2017 2

Turbulence statistics and flow structure in fluid flow using particle image velocimetry technique: A review

“…This state is synonymous with reduced viscous stresses thereby increasing the potential for increased perturbation . The similarity between Newtonian laminar‐turbulent transitional flows and drag‐reduced turbulent flows led to the conjecture that viscous effects (Lumley's theory) was more pronounced than elastic effects in the complex mechanism of DR. Other numerical studies have highlighted the important role of polymer elasticity and a description of elastic‐inertia turbulence . Although, these investigations were based on numerical simulation, a validation of the findings by experiment such as the use of PIV technique could shed more light into the mechanism of DR.…”

“…19 The similarity between Newtonian laminar-turbulent transitional flows and drag-reduced turbulent flows led to the conjecture that viscous effects (Lumley's theory) was more pronounced than elastic effects in the complex mechanism of DR. Other numerical studies have highlighted the important role of polymer elasticity and a description of elastic-inertia turbulence. 7,11,15 Although, these investigations were based on numerical simulation, a validation of the findings by experiment such as the use of PIV technique could shed more light into the mechanism of DR. In the PIV oil-water flow drag-reduction studies of Edomwonyi-Otu and Angeli, 89 in horizontal pipe of 14 mmID, both HPAM and PEO were used as DRPs.…”

“…Extensive studies have been carried out on the numerical simulation of drag‐reducing fluid flow with the view of fully understanding the physics of the flow. These studies include those of Graham and coworkers and those of Dubief and coworkers . Numerical simulation of drag‐reducing flows has also been extended to curved conduits with reasonable success.…”

“…These studies include those of Graham and coworkers [4][5][6][7][8] and those of Dubief and coworkers. [9][10][11][12][13][14][15] Numerical simulation of drag-reducing flows has also been extended to curved conduits with reasonable success. These include the works of Mompean and coworkers on drag-reduced flows in straight and curved conduits.…”

Viscoelasticity-induced pulsatile motion of 2D roll cell in laminar wall-bounded shear flow

“…Recent studies have suggested the MDR phenomenon as a part of the EIT at the significant large Weissenberg number. Sid et al (2018) demonstrated through numerical simulation that at high enough additive concentration a twodimensional and chaotic flow can be sustained after sufficient perturbations have been introduced. This flow state was characterized by an energy injection from the additive to flow at medium and small scales.…”