Contents lists available at ScienceDirect Journal of Non-Newtonian Fluid Mechanics journal homepage: www.elsevier.com/locate/jnnfm Modeling and numerical simulations of polymer degradation in a drag reducing plane Couette flow Anselmo S. Pereira a , Gilmar Mompean b , Edson J. Soares ⁎ ,c a MINES ParisTech, Centre de mise en forme des matériaux (CEMEF), PSL Research University, CNRS UMR 7635, CS 10207 rue Claude Daunesse, Sophia-Antipolis 06904, France b PolytechLille, and Unité de Mécanique de Lille (UML), Université de Lille 1 - Sciences et Technologies, Cité Scientifique, Villeneuve dAscq 59655, France c LabReo, Department of Mechanical Engineering, Universidade Federal do Espírito Santo, Avenida Fernando Ferrari, 514, Goiabeiras, Vitória, ES 29075-910, Brazil ABSTRACT Mechanical molecular scission is the main problem of polymeric drag reducers. The ability to reduce the drag is notably decreased as the molecules break down step by step as time goes on. A number of researchers have given a large part of their time to attempts to further understand the role that some important features play in polymer degradation. Until now, all efforts have been in experimental approaches. This paper is the first attempt to take into account the effect of molecular scission on a drag reducing flow by a direct numerical simulation. We analyse a turbulent plane Couette flow of a FENE-P fluid. Our degradation model is based on the maximum polymer extension length L. Unlike the standard FENE-P model, in which L is a constant, the polymer extension here is a spatio-temporal field L(x, y, z, t). When the molecules are highly stretched, which is measured by the trace of the conformation tensor, their maximum length is locally reduced and, consequently, so is their ability to reduce drag. The degraded L spreads within the domain by means of a transport equation. We show here that with such a simple idea we are able to predict the main aspects of mechanical degradation in the flow, such as the change of the turbulent structures and velocity field, and, consequently, the fall of the drag reduction over time. 1. Introduction Drag reducing polymers have been studied for over 70 years. The number of their practical uses is enormous, including the transport of liquid in pipelines, firefighting operations, and medical applications. The main aspects of the phenomenon, as the role played by the polymer concentration, molecular weight, temperature, Reynolds number, and the quality of the solvent, have been much analysed (see [12,26]). Researchers have also devoted a lot of time to attempts to describe the mechanism of drag reduction (DR). The two main ideas were first proposed by Lumley [11] (the viscous theory) and Tabor and de Gennes [22] (the elastic theory). Recently, some authors have used both the viscous and elastic concepts in an effort to describe in detail the me- chanism of DR based on a coil–stretch cycle of the polymer near the wall (see [6,7,9,15,17–19]). However, many aspects of the problem are still under investigation, such as the role played by mechanical de- gradation in such a coil–stretch cycle. Perhaps a new mechanism should consider a cycle consisting of a coil–stretch followed by a scission, i.e. a coil–stretch–scission cycle. The focus here is the polymer degradation. It is the consensus that the mechanical molecular scission is the main problem in the attempt to conceive a highly efficient drag reducer. Such a problem has received deserved attention over the years and many authors have contributed to interpreting the role played by the many features of the problem in the polymer degradation in turbulent flows. The role played by the con- centration, molecular weight, temperature, Reynolds number, and quality of the solvent in the resistance of the solution can be found in [1,14,16,20,21], who conducted a detailed analysis of degradation using different water soluble materials (PEO, PAM and XG) and showed that the shear resistance increases with the concentration and mole- cular weight. It is worth noting that the molecules break step by step in a drag reducing flow, but this process stops after a long enough time, when the polymer mean molecular weight reaches an asymptotic value. Hence, it is also to be expected that there will be a certain steady state of a DR larger than zero, [10,16,21,25]. Obviously, here we are not considering biological degradation, which can take the DR to zero, see [4]. As far as we know, our paper is the first attempt to provide a computer model of mechanical molecular scission in drag reducing flows. In fact, there have been a number of important numerical https://doi.org/10.1016/j.jnnfm.2018.03.007 Received 24 May 2017; Received in revised form 5 December 2017; Accepted 10 March 2018 ⁎ Corresponding author. E-mail addresses: anselmo.soeiro_pereira@mines-paristech.fr (A.S. Pereira), gilmar.mompean@polytech-lille.fr (G. Mompean), edson.soares@ufes.br (E.J. Soares). Journal of Non-Newtonian Fluid Mechanics 256 (2018) 1–7 Available online 12 March 2018 0377-0257/ © 2018 Elsevier B.V. All rights reserved. T