A low Reynolds number turbulence closure for viscoelastic fluids

A Reynolds-averaged Navier-Stokes equation framework is developed for modeling polymer-induced turbulent drag reduction by utilizing the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive relationship to describe fluid rheology. A self-consistent system of model equations is derived. The dominant correlations among the flow and polymer conformation variables are identified by analyzing results from recent direct numerical simulations (DNS) for dilute polymer solutions. Closures are developed for turbulent correlations that arise from viscoelasticity and incorporated into a single-point k − ɛ model. Comparison of model predictions with DNS data obtained for an identical set of rheological and geometric parameters in the low drag reduction regime allows for a critical evaluation of the model and closure approximations. Overall, the model predictions are encouraging. This approach can be extended to higher order turbulence models and cases with higher levels of drag reduction.