(328g) Observation of Maximum Drag Enhancement Asymptote in Turbulent Taylor-Couette Flow of Dilute Polymeric Solutions

The existence of a maximum drag enhancement (MDE) asymptote in a wide gap (radius ratio of 0.5) turbulent viscoelastic Taylor--Couette flow in the Reynolds number (Re), range of 1500 to 8000 is demonstrated via direct numerical simulations. Specifically, it is shown that the turbulent drag is gradually enhanced as the Weissenberg number (Wi) is increased and eventually saturates above a critical Wi. The mean velocity profile in this MDE state closely follows a logarithmic-like law with an identical slope and a Re-dependent intercept. A detailed analysis of the dominant flow structures reveals that the MDE asymptote results from the creation and eventual saturation of streamwise-oriented small-scale elastic and inertio-elastic Goertler 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 in the near-wall regions. The statistical properties associated with the turbulent and polymer dynamics demonstrate that the flow reaches an asymptotic state. i.e., MDE and a commensurate saturation of turbulent drag occurs. A close examination of competing forces in the azimuthal direction shows that the ratio of polymeric to turbulent stresses reaches an exceptionally 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 turbulent vortices and polymer chain dynamics 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 (EDT) and/or inertio-elastic turbulence (EIT) flow states. Overall, this study provides concrete evidence that our earlier assertion that asymptotic flow states in unidirectional turbulent flows of dilute polymeric solutions, namely, MDR and MDE are elastically dominated is valid.