A viscoelastic k-ε-v2¯-f turbulent flow model valid up to the maximum drag reduction limit

• Direct numerical simulations of turbulent channel flow of FENE-P fluids.
• Turbulence closures developed for all time averaged nonlinear terms.
• Model for the whole range of drag reduction includes influence of rheological parameters.
• Predictions of velocity, stresses and turbulent characteristics agree with DNS data.

A tensorially consistent near-wall four equation model is developed to model turbulent flow of dilute polymer solutions. The model is validated up to the maximum drag reduction limit, by utilizing the data obtained from direct numerical simulations using the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model. Eight sets of direct numerical simulation (DNS) data are used to analyze budgets of relevant physical quantities, such as the nonlinear terms in the FENE-P constitutive equation, the turbulent kinetic energy, the wall normal Reynolds stress and dissipation transport. Closures were developed in the framework of the k-ε-v2¯-f model for the viscoelastic stress work, the viscoelastic destruction of the rate of dissipation, the viscoelastic turbulent viscosity, and the interactions between the fluctuating components of the conformation tensor and of the velocity gradient tensor terms. Predicted polymer stress, velocity profiles and turbulent flow characteristics are all in good agreement with the literature, from which six independent DNS data sets were used covering a wide range of rheological and flow parameters, including high Reynolds number flows, and showing significant improvements over the corresponding predictions of other existing models.