Transition to turbulence and mixing in a viscoelastic fluid flowing inside a channel with a periodic array of cylindrical obstacles
Muzio Grilli, Adolfo Vázquez-Quesada, and Marco Ellero
Accepted
Using Lagrangian simulations of a viscoelastic fluid modelled with an Oldroyd-B constitutive equation, we demonstrate that the flow through a closely-spaced linear array of cylinders confined in a channel undergoes a transition to a purely elastic turbulent regime above a critical Weissenberg number (We). The high-We regime is characterized by an unsteady motion and a sudden increase in the flow resistance in qualitative agreement with experimental observations. Furthermore, a power-law scaling behavior of the integral quantities as well as enhanced mixing of mass is observed. A stability analysis based on the Dynamic Mode Decomposition method (DMD) allows us to identify the most energetic modes responsible of the unsteady behavior which correspond to filamental structures of polymer over/under-extension advected by the main flow preserving their shape. These time-dependent flow features resemble strictly the elastic-waves reported in recent numerical simulations.