Kinetic Energy Budget in Turbulent Flows of Dilute Polymer Solutions

Direct numerical simulation of a turbulent pipe flow of a realistic solution of 108\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^8$$\end{document} polymers, modelled as finitely extensible nonlinear elastic (FENE) dumbbells, and directly momentum coupled with the incompressible Navier–Stokes equations, are performed by means of an Eulerian-Lagrangian approach. Besides the drag reduction, the polymers significantly modify mean and turbulent kinetic energy budgets. The polymer backreaction to the solvent reduces the Reynolds stress and thus decreases the turbulent production and, at large Weissenberg number, the polymers act as a source of turbulent kinetic energy for y+>40\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y^+> 40$$\end{document}, leading to an increase in the dissipation. This effect is peculiar to large Weissenberg polymers and it is particularly apparent at a small Reynolds number. At a smaller Weissenberg number, the effect of the polymers remains confined in the buffer layer, with the kinetic energy budget not significantly altered elsewhere.