Influence of rheological parameters on polymer induced turbulent drag reduction

Direct numerical simulations (DNS) of polymer induced drag reduction in turbulent channel flows up to the maximum drag reduction (MDR) limit have been performed using a fully spectral method in conjunction with kinetic theory based elastic dumbbell models for the description of polymer chain dynamics. It is shown that to obtain significant levels of drag reduction large polymer chain extensibility and high Weissenberg numbers are required. In addition, it is demonstrated that to capture flow dynamics in the high drag reduction (HDR) and MDR regimes, very long computational domain lengths of the order of 10⁴ wall units are required. The simulation results in turn have been used to develop a scaling that describes the interplay between rheological parameters (i.e., maximum chain extension and relaxation time) and the extent of drag reduction as a function of Reynolds number. In addition, turbulence statistics are analyzed and correlations between the polymer body force and velocity fluctuations have been developed with particular emphasis on the HDR and MDR regimes. These observations have been used to decipher the effect of polymer additives on the dynamics of the flow and drag reduction.