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

Abstract

Elastic turbulence is a chaotic regime that emerges in polymer solutions at low Reynolds numbers. A common way to ensure stability in numerical simulations of polymer solutions is to add artificially large polymer-stress diffusion. In order to assess the accuracy of this approach in the elastic-turbulence regime, we compare numerical simulations of the two-dimensional Oldroyd-B and FENE-P models sustained by a cellular force with and without artificial diffusion. We find that artificial diffusion can have a dramatic effect even on the large-scale properties of the flow and we show some of the spurious phenomena that may arise when artificial diffusion is used. †

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

“…Based on the recent work of Gupta & Vincenzi (2019) and Lopez et al (2019), the high-Re results discussed in the present study will not be significantly affected by a further increase in Sc. Specifically, Gupta & Vincenzi (2019) claimed that for Sc values that are not excessively small quantitative rather than qualitative changes in the numerical solutions of the high-Re or laminar flows are expected.…”

Linear instability of viscoelastic pipe flow

“…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). In this section, therefore, we 10 -2 10 -1…”

“…The recent work of Sid et al (2018) showed that the two-dimensional structures characteristic of EIT are suppressed for Sc < 9, which might explain the reason the EIT state was not observed in the aforementioned simulation efforts. A low Sc is known to affect structures even outside of those pertaining specifically to drag reduction, for instance, those related to low-Re elastic turbulence (Gupta & Vincenzi 2019). The recent DNS studies by Dubief and co-workers (Dubief, Terrapon & Soria 2013;Samanta et al 2013;Sid et al 2018) in the absence of stress diffusion (Sc → ∞) showed that the friction factor deviated from the laminar value at Re ∼ 750, whereas the Newtonian case remained laminar up to Re = 5000 for identical initial forcing.…”

Active open-loop control of elastic turbulence

“…Different numerical techniques were employed to solve equations modeling viscoelastic fluids and thereby also revealed the purely elastic instability in similar geometries. Articles address unbounded flows with sinusoidal forcing 6 , 46 , 47 , Kolmogorov flow 48 , 49 , as well as wall-bounded flows, including sudden-expansion flow 50 , channels with cross-slot geometry 51 or serpentines 52 and the Taylor–Couette geometry 53 – 55 . Thus, demonstrating the importance of numerical techniques in understanding the underlying physical principles in complex fluid flows.…”

“…Different numerical techniques were employed to solve equations modeling viscoelastic fluids and thereby also revealed the purely elastic instability in similar geometries. Articles address unbounded flows with sinusoidal forcing 6,46,47 , Kolmogorov flow 48,49 , as well as wall-bounded flows, including sudden-expansion flow 50 , channels with cross-slot geometry 51 open Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany. * email: r.vanbuel@tu-berlin.de or serpentines 52 and the Taylor-Couette geometry [53][54][55] .…”