Flow past a cylinder in diluted polymer solutions

Abstract

Putting a small amount of polymer into the water is one of the most important ways to control turbulent flow passively. We here investigate the flow past a cylinder at a broad range of both Reynolds numbers and Weissenberg numbers by direct numerical simulation in two dimensions. The models used for Newtonian fluid or dilute polymer in solution are respectively Navier-Stokes and Oldroyd-B models. The obstacles are taken into account using the volume penalization method. The robust finite difference code keeps numerical stability well at high Weissenberg numbers. The cylinder drag may enhance or reduce in the two dimensional Reynolds number-Weissenberg number space. The flow features have a strong link to the drag behavior. Furthermore the elastic instability occurs and is captured when Weissenberg number is high; and the energy balance of the system is checked.