Maximum drag enhancement asymptote in turbulent Taylor–Couette flow of dilute polymeric solutions

Abstract

Direct numerical simulations in a wide-gap turbulent viscoelastic Taylor–Couette flow in the Reynolds number (Re) range of 1500 to 8000 reveals the existence of a maximum drag enhancement (MDE) asymptote. The statistical properties associated with the turbulent and polymer dynamics demonstrate that the turbulent drag enhances with the increase of the Weissenberg number (Wi) and eventually saturates above a critical Wi, namely, the flow reaches the MDE state. The mean velocity profile in MDE state closely follows a logarithmic-like law with an identical slope (κK=2.32) and a Re-dependent intercept. A detailed analysis of flow structures reveals that the MDE asymptote results from the creation and eventual saturation of small-scale elastic and inertio-elastic Görtler vortices in the inner- and outer-wall regions, respectively. These vortical structures arise due to competing effects of polymer-induced stresses that either suppress or promote turbulent vortices. A close examination of competing forces in the azimuthal direction shows that the ratio of polymeric to turbulent stresses reaches a large plateau, underscoring the elastic nature of the MDE state. Moreover, the energy production mechanism in the MDE state further supports: (1) the universal interplay between polymers and turbulent vortices in a broad range of curvilinear and planar turbulent flows, and (2) the fact that the elastically induced asymptotic saturation of drag modification is an inherent property of elasticity-driven and/or elasto-inertial turbulence flow states. Overall, this study provides concrete evidence for our earlier postulate that asymptotic flow states in unidirectional turbulent viscoelastic flows are of elastic nature.