An algebraic closure for the DNS of fiber-induced turbulent drag reduction in a channel flow

An algebraic closure for the non-Newtonian Navier–Stokes equations is presented which accounts for the effect of a dilute fiber suspension. The model is intended to be used in simulations of turbulent drag reduction by fiber additives, and can be considered as a computationally efficient alternative to the existing rheological models for fiber suspensions in turbulent wall-bounded flows. It is based on the assumption that the suspended elongated particles are aligned with the local velocity fluctuation vector. The model is proved to be Galilean invariant. One-way coupled simulations and comparison with a direct solution of the underlying Fokker–Planck equation show a considerable improvement over an existing and comparable model. Finally, two-way coupled simulations demonstrate that the model predicts flow statistics that are in very good agreement with those obtained by the moment approximation approach. Interestingly, the model is realistic in terms of the polymer concentration. Using the proposed model, the cost of simulating a drag-reduced flow in terms of CPU-time is slightly more than that of a Newtonian flow.

► An algebraic closure for the non-Newtonian Navier-Stokes equations.
► Applicable to simulations of turbulent drag reduction by fiber additives.
► The proposed model is proved to be Galilean invariant.
► Prediction of flow statistics in very good agreement with the results of the moment approximation approach.
► The proposed model is realistic in terms of the fiber concentration.