[Paper Review] Beyond the maximum drag reduction asymptote: the pseudo-laminar state

Anselmo Soeiro Pereira, Roney L. Thompson+1 more|arXiv (Cornell University)|Nov 1, 2019

Rheology and Fluid Dynamics Studies1 references4 citations

TL;DR

This study reveals a transient pseudo-laminar state in viscoelastic turbulent flows where drag reduction exceeds the Maximum Drag Reduction Asymptote (MDR), sustained by minimal polymer energy injection. Despite laminar-like mean velocity profiles and wall shear stress, nonlinear polymer-flow interactions trigger weak core-like turbulent structures that evolve into elastoinertial turbulence (EIT), with the flow cycling between active and hibernating states.

ABSTRACT

Recent experiments indicated that polymers can reduce the turbulent drag beyond the asymptotic limit known as the MDR, leading to a laminar flow. In this Letter, we show through direct numerical simulations that, when the MDR is exceeded, the flow can remain in a laminar-like regime for a very long period without being truly laminar. During this period called pseudo-laminar state, a transient behavior is observed as a consequence of a small rate of polymer energy injected into the flow. Later on, flow instabilities develop across the channel, finally triggering elastoinertial turbulence.

Motivation & Objective

• To investigate the behavior of viscoelastic turbulent flows when drag reduction exceeds the Maximum Drag Reduction Asymptote (MDR), a regime previously thought to mark the transition to laminar flow.
• To understand the physical mechanisms sustaining a laminar-like state beyond MDR, despite the presence of weak instabilities.
• To characterize the role of polymer energy injection and elastic stress in initiating and sustaining transient turbulent structures leading to elastoinertial turbulence (EIT).
• To examine the dynamic cycle between active and hibernating states in the flow, and how this cycle relates to the MDR and log-law profiles.
• To clarify whether the observed laminar-like behavior is truly laminar or a metastable state preceding EIT.

Proposed method

• Direct numerical simulations (DNS) of incompressible turbulent plane Couette flows with dilute polymer solutions using a FENE-P kinetic model for viscoelasticity.
• Wall-unit normalization applied using total zero-shear viscosity and friction velocity, with dimensionless momentum equations incorporating polymer extra-stress tensor components via the FENE-P model.
• The polymeric conformation tensor evolves according to a FENE-P model with Peterlin approximation, accounting for finite extensibility and Weissenberg number effects.
• Energy transfer between flow and polymers is quantified via the polymer work term $ E^{+} = u_i' rac{ abla au_{ij}'}{ abla x_j} $, tracking energy injection and fluctuation dynamics.
• Simulations were conducted at high Weissenberg numbers (Wi_h = 10, 40, 80) to probe the regime beyond MDR, with analysis of velocity profiles, wall shear stress, and polymer stretching.
• Flow states were classified into three phases: strong activation (S-Act), moderate activation (M-Act), and hibernation (Hib), based on wall shear stress oscillations and energy transfer patterns.

Experimental results

Research questions

• RQ1 Can drag reduction exceed the Maximum Drag Reduction Asymptote (MDR) while maintaining a laminar-like mean velocity profile?
• RQ2 What physical mechanisms sustain a laminar-like state beyond MDR, despite the presence of weak turbulent fluctuations?
• RQ3 How does polymer energy injection influence the development of instabilities leading to elastoinertial turbulence (EIT)?
• RQ4 What are the dynamic characteristics of the flow cycle between active and hibernating states in the pseudo-laminar regime?
• RQ5 Is the MDR truly the edge between laminar and turbulent regimes in viscoelastic flows, as suggested by the observed oscillations between log-law and MDR profiles?

Key findings

• The flow exhibits a long-lived pseudo-laminar state beyond the MDR, with mean velocity profiles and wall shear stress matching laminar behavior, despite the absence of true laminar stability.
• Very weak core-like turbulent structures emerge due to a small but sustained rate of polymer energy injection into the near-wall region, primarily in the $ z^+ < 30 $ range.
• The polymer work term $ E^{+} $ is positive in the very near-wall region ($ z^+ < 30 $) during the pseudo-laminar state, indicating energy transfer from polymers to the mean flow.
• During the S-Act and M-Act states, $ ar{E}^{+} $ and $ ar{E'^+} $ are negative, indicating energy storage by polymers and damping of fluctuations, while in Hib state, $ E^{+} $ becomes positive, releasing energy and reactivating EIT.
• The flow cycles between three states: strong activation (S-Act), moderate activation (M-Act), and hibernation (Hib), with the mean velocity profile oscillating between the log-law (S-Act) and MDR (Hib) profiles.
• The MDR and log-law profiles are consistently observed during the active and hibernating phases, reinforcing the idea that the MDR acts as the edge between laminar and non-laminar regimes in viscoelastic flows.