Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence

Abstract

Simulations of elastoinertial turbulence (EIT) of a polymer solution at low Reynolds number are shown to display localized polymer stretch fluctuations. These are very similar to structures arising from linear stability (Tollmien-Schlichting (TS) modes) and resolvent analyses: i.e., critical-layer structures localized where the mean fluid velocity equals the wavespeed. Computation of selfsustained nonlinear TS waves reveals that the critical layer exhibits stagnation points that generate sheets of large polymer stretch. These kinematics may be the genesis of similar structures in EIT.Turbulent drag reduction is an important and puzzling phenomenon in the non-Newtonian flow of complex fluids. Addition of polymers or micelle-forming surfactants to a liquid can lead to dramatic reductions in energy dissipation during turbulent flow while having a negligible effect on laminar flow[1].In Newtonian channel or pipe flow, transition to turbulence occurs by a so-called subcritical or "bypass" transition mechanism as flow rate, measured nondimensionally by Reynolds number, Re, increases: turbulence is initiated by finite-amplitude perturbations to the laminar flow profile, while the laminar flow remains linearly stable. While channel flow exhibits a two-dimensional linear instability leading to so-called Tollmien-Schlichting (TS) waves, the critical Reynolds number Re = 5772 is much higher than that observed for transition, so these are not traditionally viewed as playing an important role in Newtonian transition.For flowing polymer solutions under some conditions (low concentration, short polymer relaxation times), transition to turbulence occurs via the usual bypass transition. With further increase in Re, drag reduction sets in, and the flow eventually approaches the so-called maximum drag reduction (MDR) asymptote, an upper bound on the degree of drag reduction that is insensitive to the details of the fluid.Under other conditions, flow transitions directly from laminar flow into the MDR regime, and can do so at a Reynolds number where the flow would remain laminar if Newtonian [2][3][4][5]. Recent experiments and simulations [6][7][8] suggest that turbulence in this regime has structure very different from Newtonian, denoting it as "elastoinertial turbulence" (EIT). Choueiri et al.[4] experimentally observed that at transitional Reynolds numbers and increasing polymer concentration, turbulence is first suppressed, leading to relaminarization, and then reinitiated with an EIT structure and a level of drag corresponding to MDR. Therefore, there are actually two distinct types of turbulence in polymer solutions, one that is suppressed by viscoelasticity, and one that is promoted.The present work reports computations and analysis that elucidate the mechanisms underlying EIT. We show that EIT at low Re has highly localized polymer stress fluctuations. Surprisingly, these strongly resemble linear Tollmien-Schlichting modes as well as the most strongly amplified fluctuations from the laminar state. Furthermore, the kinematic...

Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence

“…Numerical schemes based on the Kurganov-Tadmor solver have been employed in studies of both turbulent polymer solutions (e.g. Vaithianathan et al 2007;Perlekar, Mitra, Pandit 2010;Dallas, Vassilicos & Hewitt 2010;Robert et al 2010;Valente, da Silva & Pinho 2014;Gupta et al 2015;Shekar et al 2018) and elastic turbulence (Gupta & Pandit 2017;Plan et al 2017). Finally, the velocity field is obtained by solving the vorticity equation associated with (2.1a) in Fourier space.…”

Polymer-induced flow relaminarization and drag enhancement in spanwise-rotating plane Couette flow

“…Moreover, recent studies have shed light on the origin of the maximum drag reduction (MDR), namely, in this regime the flow dynamics is driven by an elasto-inertial instability (Dubief, Terrapon & Soria 2013;Samanta et al 2013;Li, Sureshkumar & Khomami 2015;Sid, Terrapon & Dubief 2018) that could even eliminate Newtonian turbulence (NT). Furthermore, flow relaminarization has recently been observed in channel and pipe flows of polymeric solutions as polymer concentration (elasticity level) is increased at the transition Re (Choueiri, Lopez & Hof 2018;Lopez, Choueiri & Hof 2019;Shekar et al 2019;Chandra, Shankar & Das 2020). Specifically, the MDR state is achieved via a reverse transition pathway from NT through a relaminarized state.…”

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 [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.…”