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

Michael McDermott,David Harbottle,Pedro Resende,Alexandre Afonso,Gregory de Boer,Thibaut Charpentier,Mark Wilson

doi:10.3390/app10228140

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.

Highlights

Since the pioneering experiment by Toms [1], it is known that the additions of small amounts of long-chain flexible polymers to a turbulent flow can drastically reduce the transport energy by decreasing the turbulent drag
A new finite volume C++ computational solver was developed in the OpenFOAM software by modifying the k − ε sub-class files and introducing the finitely extensible nonlinear elastic-Peterlin (FENE-P) viscoelastic quantities such as: the polymer stress to the momentum equation; conformation tensor transport equation; and modified damping function to include elastic effects
Following the numerical procedure proposed in the previous section, the model performance is assessed against a range of different flow and rheological parameters presented in the Direct Numerical Simulation (DNS) data within Table 1

Summary

Introduction

Since the pioneering experiment by Toms [1], it is known that the additions of small (parts per million) amounts of long-chain flexible polymers to a turbulent flow can drastically reduce the transport energy by decreasing the turbulent drag. The effects are most evident in turbulent shear flow, in which dissolving the polymers in solution can reduce friction losses by as much as 80%. After the discovery of the drag reduction (DR) phenomena, several comprehensive studies were carried out to understand the physical mechanisms of the interactions between the turbulent structures and polymer chains. Sci. 2020, 10, 8140 in this area come from Lumley [3,4], Hoyt [5] and Virk [6]. Lumley suggests that the DR phenomenon is the result of an increase in effective viscosity in an area outside the viscous sub-layer and in the buffer layer, caused by polymer chains stretching in a turbulent flow

Methods

Results

Conclusion