###### Abstract  
A viscoelastic turbulence model in a fully-developed drag reducing channel flow is improved, with turbulent eddies modelled under a \(k-\varepsilon\) 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 \(NLT_{ij}\) 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, \(E_{\tau_{p}}\), 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. drag reduction; FENE-P fluid; viscoelastic RANS model; OpenFoam CFD +
Footnote †: journal: Applied Physics Letters  
0000-0001-5000-5000]M.M. in this area come from [PERSON] [3; 4], [PERSON] [5] and [PERSON] [6]. [PERSON] 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. More recent studies have been proposed for the theory of the mechanisms of drag-reducing polymer additives [7; 8]. Several Direct Numerical Simulation (DNS) studies were conducted to understand further the energy exchanges between the polymer chains and turbulence structures [9; 10; 11; 12; 13; 14]. It is now known to at least low to moderate levels of DR, that the mechanism is the suppression of the near-wall streamwise vortices by polymers that stretch in the extensional flow, and then relax as they are rolled into other vortices, generating forces that tend to weaken these vortices. Quantitatively, this can be expressed as a polymer body force [9], which is positive in the streamwise direction, with an opposite sign (anti-correlation) in the wall direction. DNS is a great resource to explore the underlying mechanics of drag-reducing viscoelastic turbulent flows. However, for the majority of engineering motivations, DNS is not practical because of the high number of variables which requires a substantial expense of memory and CPU-time. This cost is more prevalent in high DR (HDR) schemes in which the near-wall velocity streaks become more elongated, requiring an increased demand on computational resources. An alternative approach in capturing flow features at much less computational demands is the application of Reynolds-averaged Navier-Stokes (RANS) models, whose interest has increased in recent years. One of the original implementations of elastic effects within turbulence models was achieved by [PERSON] [15] and [PERSON] et al. [16]. Their work focused on low-Reynolds number \(k-\varepsilon\) turbulence models, applying a Generalised Newtonian Fluid (GNF) constitutive equation involving dependency of the fluid strain hardening on the third invariant of the rate of deformation tensor. Following these studies, an anisotropic version was also developed which included an increased Reynolds stress anisotropy [17], along with a Reynolds stress turbulence model [18], both able to satisfactorily predict drag-reducing behavior. Nevertheless, the models are constrained because of the inelastic formulation of the GNF constitutive equations.