title: Transition to turbulence and mixing in a viscoelastic fluid flowing inside a channel with a periodic array of cylindrical obstacles.
abstract: Using Lagrangian simulations of a viscoelastic fluid modeled 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 allows us to identify the most energetic modes responsible for the unsteady behavior, which correspond to filamental structures of polymer over- or underextension advected by the main flow preserving their shape. These time-dependent flow features strictly resemble the elastic waves reported in recent numerical simulations.
authors.affiliation: Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, 85747 Garching, Germany.
authors.forename: Muzio
authors.initials: M
authors.lastname: Grilli
authors.forename: Adolfo
authors.initials: A
authors.lastname: Vázquez-Quesada
authors.forename: Marco
authors.initials: M
authors.lastname: Ellero