Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit

Abstract

Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so-called state of ‘maximum drag reduction’ (MDR), is to a good approximation independent of the type of polymer and solvent used. Until recently, the consensus was that, in this limit, flows are in a marginal state where only a minimal level of turbulence activity persists. Observations in direct numerical simulations at low Reynolds numbers ( $Re$ ) using minimal sized channels appeared to support this view and reported long ‘hibernation’ periods where turbulence is marginalized. In simulations of pipe flow at $Re$ near transition we find that, indeed, with increasing Weissenberg number ( $Wi$ ), turbulence expresses long periods of hibernation if the domain size is small. However, with increasing pipe length, the temporal hibernation continuously alters to spatio-temporal intermittency and here the flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an increase in $Wi$ , the flow fully relaminarizes, in agreement with recent experiments. At even larger $Wi$ , a different instability is encountered causing a drag increase towards MDR. Our findings hence link earlier minimal flow unit simulations with recent experiments and confirm that the addition of polymers initially suppresses Newtonian turbulence and leads to a reverse transition. The MDR state on the other hand results at these low $Re$ from a separate instability and the underlying dynamics corresponds to the recently proposed state of elasto-inertial turbulence.

Linear instability of viscoelastic pipe flow

“…Importantly, the instability continues to exist for the experimentally relevant values of Dλ/R 2 ∼ 10 −9 -10 −7 , but would be suppressed at much larger values of Dλ/R 2 ∼ 10 −4 -10 −2 (or, equivalently, Sc < 1000, for E ∼ 0.1) used in earlier DNS studies FIGURE 27. The effect of stress diffusion (characterized by Dλ/R 2 ) on the threshold Re required for onset of instability at different E, β and k. (Sureshkumar & Beris 1995;Sureshkumar et al 1997;Lopez et al 2019). Thus, consistent with the results of Sid et al (2018), the results of figure 27 reinforce the importance of using simulation techniques, which avoid an artificially enhanced diffusivity, to access the axisymmetric structures associated with the centre-mode instability.…”

“…It is worth emphasizing that all of the experiments on viscoelastic transition (with the exception of Srinivas & Kumaran 2017) pertain to the pipe geometry. Further, and importantly, recent simulations in both the channel (Samanta et al 2013;Sid et al 2018) and pipe (Lopez et al 2019) geometries have found analogous (span-wise oriented) coherent structures, suggesting a common underlying mechanism for elasto-inertial transition.…”

“…In § 4.3, we examine the role of stress diffusion in the constitutive relation to show that the unstable centre mode persists for physically realistic values of the diffusion coefficient. Our theoretical predictions are compared (in a parameter-free manner) with the experimental observations of Samanta et al (2013) and Chandra et al (2018) in § 4.4; herein, we also compare our predictions with the recent DNS results for viscoelastic pipe flow by Lopez et al (2019). Finally, in § 5, we summarize the salient findings of this study, and provide a discussion on how the discovery of a linear instability in viscoelastic pipe flow can play a pivotal role in clarifying the pathway to the MDR regime from the laminar state.…”

“…As discussed in the introduction, artificial stress diffusion is often used for regularization in DNS studies of viscoelastic flows (Sureshkumar & Beris 1995;Sureshkumar et al 1997;Lopez et al 2019). Recently, it has been shown that this additional diffusivity can qualitatively affect the stress dynamics (Gupta & Vincenzi 2019), even to the extent of suppressing signatures associated with EIT (Sid et al 2018).…”

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.…”