A FENE-P \(k-\epsilon\) turbulence model for low and intermediate regimes of polymer-induced drag reduction.

*(English)*Zbl 1282.76054Summary: A new low-Reynolds-number \(k-\epsilon\) turbulence model is developed for flows of viscoelastic fluids described by the finitely extensible nonlinear elastic rheological constitutive equation with Peterlin approximation (FENE-P model). The model is validated against direct numerical simulations in the low and intermediate drag reduction (DR) regimes (DR up to 50%). The results obtained represent an improvement over the low DR model of F. T. Pinho et al. [“A low Reynolds number turbulence closure for viscoelastic fluids”, ibid. 154, No. 2–3, 89–108 (2008; doi:10.1016/j.jnnfm.2008.02.008)]. In extending the range of application to higher values of drag reduction, three main improvements were incorporated: a modified eddy viscosity closure, the inclusion of direct viscoelastic contributions into the transport equations for turbulent kinetic energy (\(k\)) and its dissipation rate, and a new closure for the cross-correlations between the fluctuating components of the polymer conformation and rate of strain tensors \((NLT_{ij})\). The \(NLT_{ij}\) appears in the Reynolds-averaged evolution equation for the conformation tensor (RACE), which is required to calculate the average polymer stress, and in the viscoelastic stress work in the transport equation of \(k\). It is shown that the predictions of mean velocity, turbulent kinetic energy, its rate of dissipation by the Newtonian solvent, conformation tensor and polymer and Reynolds shear stresses are improved compared to those obtained from the earlier model.