Statistics of polymer extensions in turbulent channel flow

TL;DR

This study uses direct numerical simulations to analyze the statistical behavior of passive polymers in turbulent channel flow, focusing on polymer extension, orientation, and the coil-stretch transition at a critical Weissenberg number.

Contribution

It provides a detailed statistical analysis of polymer behavior in turbulent flow, confirming theoretical predictions and exploring the effects of flow heterogeneity on polymer stretching and orientation.

Findings

Polymer stretching increases significantly near the wall for Wi>1.

The coil-stretch transition occurs at Wi≈1, consistent with theoretical predictions.

Polymers tend to align with the flow direction near the wall.

Abstract

We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elongation for both the Oldroyd-B model (for Weissenberg number $\Wi <1$) and the FENE model. We use the location of the minima of the Cramer's function to define the Weissenberg number precisely such that we observe coil-stretch transition at $\Wi\approx1$. We find agreement with earlier analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon and Lebedev [Phys. Rev. Lett., 84, 4765 (2000).] for linear polymers (Oldroyd-B model) with $\Wi<1$ and by Chertkov [Phys. Rev. Lett., 84, 4761 (2000).] for nonlinear FENE-P model of polymers. For $\Wi>1$ (FENE model) the polymer are significantly more stretched near the wall than at the center of the channel where the flow is closer to homogenous isotropic turbulence. Furthermore near the wall the polymers show a strong tendency to orient along the stream-wise direction of the flow but near the centerline the statistics of orientation of the polymers is consistent with analogous results obtained recently in homogeneous and isotropic flows.