A FENE-P k–ε Viscoelastic Turbulence Model Valid up to High Drag Reduction without Friction Velocity Dependence

Abstract

A viscoelastic turbulence model in a fully-developed drag reducing channel flow is improved, with turbulent eddies modelled under a k–ε representation, along with polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model. The model performance is evaluated against a wide variety of direct numerical simulation data, described by different combinations of rheological parameters, which is able to predict all drag reduction (low, intermediate and high) regimes with good accuracy. Three main contributions are proposed: one with a simplified viscoelastic closure for the NLTij term (which accounts for the interactions between the fluctuating components of the conformation tensor and the velocity gradient tensor), by removing additional damping functions and reducing complexity compared with previous models; second through a reformulation for the closure of the viscoelastic destruction term, Eτp, which removes all friction velocity dependence; lastly by an improved modified damping function capable of predicting the reduction in the eddy viscosity and thus accurately capturing the turbulent kinetic energy throughout the channel. The main advantage is the capacity to predict all flow fields for low, intermediate and high friction Reynolds numbers, up to high drag reduction without friction velocity dependence.