Turbulent drag reduction in plane Couette flow with polymer additives: a direct numerical simulation study

Abstract

Drag reduction (DR) in plane Couette flow (PCF) induced by the addition of flexible polymers has been studied via direct numerical simulation (DNS). The similarities and differences in the drag reduction features of PCF and plane Poiseuille flow (PPF) have been examined in detail, particularly in regard to the polymer-induced modification of large-scale structures (LSSs) in the near-wall turbulence. Specifically, it has been demonstrated that in the near-wall region, drag-reduced PCF has features similar to those of drag-reduced PPF; however, in the core region, intriguing differences are found between these two drag-reduced shear flows. Chief among these differences is the significant polymer stretch that arises from the enhanced exchanges between elastic potential energy and turbulent kinetic energy and the commensurate observation of peak values of the conformation tensor components $\unicode[STIX]{x1D60A}_{yy}$ and $\unicode[STIX]{x1D60A}_{zz}$ in this region. This finding is in stark contrast to that of drag-reduced PPF where the polymer stretch and the exchanges between elastic potential energy and turbulent kinetic energy in the core region are insignificant; to this end, in drag-reduced PPF, peak values of the conformation tensor components appear in the near-wall region. Therefore, this study paves the way for understanding the underlying flow physics in drag-reduced PCF, particularly in the context of elastic theory. Moreover, the longitudinal large-scale streaks at the channel centre of drag-reduced PCF are greatly strengthened due to the increased production/dissipation ratio; the LSS imprint effects on the near-wall flow of drag-reduced PCF monotonically increase as the Weissenberg number is enhanced.