Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow

Abstract

The budgets of the Reynolds stress, turbulent kinetic energy and streamwise enstrophy are evaluated through direct numerical simulations for the turbulent channel flow of a viscoelastic polymer solution modeled with the Finitely Extensible Nonlinear Elastic with the Peterlin approximation (FENE-P) constitutive equation. The influence of viscoelasticity on the budgets is examined through a comparison of the Newtonian and the viscoelastic budgets obtained for the same constant pressure drop across the channel. It is observed that as the extensional viscosity of the polymer solution increases there is a consistent decrease in the production of Reynolds stress in all components, as well as in the other terms in the budgets. In particular, the effect of the flow elasticity, which is associated with the reduction in the intensity of the velocity-pressure gradient correlations, potentially leads to a redistribution of the turbulent kinetic energy among the streamwise, the wall-normal and the spanwise directions. In this work, we also show that in the presence of viscoelasticity there is a significant reduction in all components of the production of streamwise enstrophy. This is consistent with a proposed mechanism for polymer-induced drag reduction through the inhibition of vortex stretching by the high extensional viscosity of the polymer solution.