Investigation of elastic turbulence in cellular flow through a finite volume solver

This thesis investigates the fundamental differences between Newtonian and non-Newtonian fluids, focusing on the behavior of polymer solutions under various flow conditions. Non-Newtonian fluids exhibit complex rheological properties, such as shear-thinning, shear-thickening, and viscoelasticity, which are absent in Newtonian fluids. We explore these characteristics through detailed simulations of polymer solutions to study elastic turbulence in a two-dimensional periodic domain V = [0, 2π] subjected to a cellular force. Elastic turbulence, characterized by chaotic flow patterns driven by elastic stresses rather than inertial forces, occurs in polymer solutions at low Reynolds numbers. Our study involves two sets of simulations at different Weissenberg numbers (Wi), specifically Wi = 10 and Wi = 20. Each set comprises two simulations with and without stabilization method to ensure numerical accuracy and stability. The simulations reveal that the introduction of polymers into a Newtonian solvent significantly alters the flow structure and stability. At Wi = 10, the presence of elastic turbulence is clearly observable, primarily triggered by instabilities in the elastic properties of the fluid. At Wi = 20, the simulations show a more pronounced and chaotic elastic turbulence with complex vortex formation and flow patterns. The comparison of different stabilization methods demonstrates their impact on capturing the intricate dynamics of elastic turbulence accurately.