Direct numerical simulation of the turbulent channel flow of a polymer solution

In this work, we present from first principles a direct numerical simulation (DNS) of a fully turbulent channel flow of a dilute polymer solution. The polymer chains are modeled as finitely extensible and elastic dumbbells. The simulation algorithm is based on a semi-implicit, time-splitting technique which uses spectral approximations in the spatial coordinates. The computations are carried out on a CRAY T3D parallel computer. The simulations are carried out under fully turbulent conditions albeit, due to computational constraints, not at as high Reynolds number as that usually encountered in polymer-induced drag reduction experiments. In order to compensate for the lower Reynolds number, we simulate more elastic fluids than the ones encountered in drag reduction experiments resulting in Weissenberg numbers (a dimensionless number characterizing the flow elasticity) of similar magnitude. The simulations show that the polymer induces several changes in the turbulent flow characteristics, all of them consistent with available experimental results. In particular, we have observed, associated with drag reduction, a decrease in the streamwise vorticity fluctuations and an increase in the average spacing between the streamwise streaks of low speed fluid within the buffer layer. These findings suggest a partial inhibition of turbulence generating events within the buffer layer by the macromolecules after the onset of drag reduction. This inhibition is further shown to be associated with an enhanced effective viscosity attributed to the extensional thickening properties of polymer solutions, as proposed in the past by Metzner, Lumley and other investigators. Using the simulation results obtained for different sets of parameter values which modify the relaxational and extensional properties of the model, we propose a set of criteria for the onset of drag reduction.