Numerical simulation of the swirling flow of a finitely extensible non-linear elastic Peterlin fluid

Abstract

Viscoelastic fluids have been shown to undergo instabilities even at very low Reynolds numbers, and these instabilities can give rise to a phenomenon called elastic turbulence. This phenomenon, observed experimentally in viscoelastic polymer solutions, is driven by the strong coupling between the fluid velocity and the elasticity of the flow. To explore the emergence of these instabilities in a viscoelastic flow, we have chosen to explore, by means of direct numerical simulations, a particular case called von Kármán swirling flow. The simulations employ the finitely extensible nonlinear Peterlin model to represent the dynamics of a dilute polymer solution. Notably, a log-conformation technique is used to solve the governing equations. This method is useful in overcoming the high Weissenberg number problem. The results obtained from the simulations were generally in good agreement with experiments. The torque on the top plate was decomposed into Newtonian and polymeric components, and it was found that the polymeric component was dominant. In addition, flow visualizations revealed that a toroidal vortex was strongly correlated with the distribution of the stresses on the rotating plate.