Numerical modeling of the mixing flow of second-order fluids with helical ribbon impellers

Abstract

Rheology is known to have a strong impact on the flow behavior and the power consumption of mechanically agitated tanks. In the case of viscoelastic fluids, the role of elasticity on power draw has yet to be elucidated, though recent studies with helical ribbon impellers indicate that elasticity increases torque. The objective of this paper is to show that, in the case of second-order fluids, the use of a simple constitutive equation derived from a second-order retarded-motion expansion succeeds in predicting a rise in power draw owing to elasticity. The equations of change governing fluid flow are solved using a finite element method combined with an augmented Lagrangian method for the treatment of the non-linear constitutive equation. We show, in particular, how the underlying non-linear tensor equations can be solved directly using a spectral decomposition of the related matrix operator. First, the numerical methodology is explained. Next, simulation results are presented in the case of a tank provided with a helical ribbon. These results are then compared with experimental data. A rise of power draw, similar in shape but smaller than that measured experimentally, may be noted when elasticity is increased.