On the Peterlin approximation for turbulent flows of polymer solutions

TL;DR

This study evaluates how the Peterlin approximation affects the statistical accuracy of polymer behavior predictions in turbulent flows, revealing qualitative agreement but notable quantitative discrepancies, especially at high Weissenberg numbers.

Contribution

It provides a detailed numerical comparison of the FENE and FENE-P models in turbulent flows, highlighting the limitations of the Peterlin approximation.

Findings

FENE-P overestimates large polymer extensions.

Weaker polymer alignment with flow eigenvectors under Peterlin approximation.

Underestimation of correlation times at high Weissenberg numbers.

Abstract

We study the impact of the Peterlin approximation on the statistics of the end-to-end separation of poly- mers in a turbulent flow. The FENE and FENE-P models 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 overesti- mated 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, both the correlation times of the extension and of the orientation of polymers are underestimated by the FENE-P model.