Understanding the Dynamics of Viscoelastic Turbulent Flows and Polymer Drag Reduction in Minimal Flow Units

Adding a small amount of flexible polymers into a turbulent flow can cause substantial reduction in its friction drag by influencing the fundamental dynamics of the self-sustaining turbulent structures. In this study, we isolate the essential components of the self-sustaining process by conducting direct numerical simulations (DNS) in minimal flow units (MFU) of viscoelastic turbulent flows. These MFU solutions obtained at various polymer parameters recover all key transitions in viscoelastic turbulent flows reported previously in experiments at much higher Re, including the onset of drag reduction, low degree of drag reduction (LDR), high degree of drag reduction (HDR) and maximum drag reduction (MDR). At the MDR regime, the mean velocity profile is insensitive to changing polymer parameters. The LDR-HDR transition is characterized by a sudden increase in the minimal box size of sustaining turbulence, which may correspond to a qualitative change in the self-sustaining mechanism. With these solutions, we study the effects of polymer on turbulent coherent structures and the dynamics of the self-sustaining process, based on which the mechanism behind the multistage transition scheme in viscoelastic turbulent flows can be better understood.