Impact of the Peterlin approximation on polymer dynamics in turbulent flows

Abstract

We study the impact of the Peterlin approximation on the statistics of the end-to-end separation of polymers in a turbulent flow. The finitely extensible nonlinear elastic (FENE) model and the FENE model with the Peterlin approximation (FENE-P) are numerically integrated along a large number of Lagrangian trajectories resulting from a direct numerical simulation of three-dimensional homogeneous isotropic turbulence. Although the FENE-P model yields results in qualitative agreement with those of the FENE model, quantitative differences emerge. The steady-state probability of large extensions is overestimated by the FENE-P model. The alignment of polymers with the eigenvectors of the rate-of-strain tensor and with the direction of vorticity is weaker when the Peterlin approximation is used. At large Weissenberg numbers, the correlation times of both the extension and of the orientation of polymers are underestimated by the FENE-P model.

Small scale dynamics of a shearless turbulent/non-turbulent interface in dilute polymer solutions

“…7 (b) present the pdf of the relative orientation between the largest polymer eigenvector 1 and the strain eigenvectors λ 1,2,3 respectively for the bulk of the flow and for the points on the TNTI. The polymers are preferentially aligned with λ 1 (Λ 1 > 0, stretching eigenvector) in the turbulent bulk again in agreement with the results from homogeneous isotropic turbulence with polymers 10,11,29 . At the interface the alignments with the eigenframe changes: there is an increase in λ 1 alignment and decrease of alignment with the compressing eigenvector λ 3 .…”

Polymer scission in turbulent flows

“…At large Reynolds numbers, polymers therefore experience strong straining events that can highly distort them. This has been confirmed in experiments and numerical simulations, both directly by examination of the probability distribution of polymer extensions (Vaithianathan & Collins 2003;Vincenzi et al 2007Vincenzi et al , 2015Jin & Collins 2008;Watanabe & Gotoh 2010) and indirectly through the observation of a strong polymer feedback on the flow (De Angelis et al 2005;Perlekar, Mitra & Pandit 2006, 2010Crawford et al 2008;Ouellette, Xu & Bodenschatz 2009;Xi, Bodenschatz & Xu 2013;Watanabe & Gotoh 2013a,b, 2014de Chaumont Quitry & Ouellette 2016). Furthermore, experimental measurements of polymer scission in different channel flows, by Vanapalli et al (2006), show that the majority of polymers reside, and therefore break up, in the bulk of the fluid, where the flow approximates isotropic turbulence, rendering the scission results independent of channel geometry.…”

Direct numerical simulations of turbulent viscoelastic jets

“…Therefore, the theoretical results described in the present work should also be valid in flows where the FENE-P model is known to give a poor representation of the polymer physics e.g. flows in the absence of solid walls with Wi η 7 (Watanabe & Gotoh 2010;Vincenzi et al 2015).…”