Numerical simulations for flows in a blade free planetary mixer: dynamical systems and flow quantification

Abstract

Flows in a blade free planetary mixer with a free surface were investigated numerically with the moving coordinate system, considering both Coriolis and centrifugal forces, to incorporate the revolutionary and rotational motions together. The level-set method was employed to describe the free surface, and surface tension was incorporated through the continuous surface stress model. Both Newtonian and non-Newtonian fluids (power-law and Herschel-Bulkley models) were employed to investigate the mixing mechanism and performance with free-surface evolution, shear rate distribution, power consumption, and dynamical systems structures. The results show that the free surface shape is primarily affected by gravity and two centrifugal (rotation and revolution) accelerations. The free surface shape appears independent of revolution speed at speeds exceeding 1000 RPM, where the effect of gravity can be neglected. Using the Poincar & eacute; map, the dynamical systems structures were analyzed within the mixer and it was observed that the size of coherent structures reduces with increasing revolution speed, indicating enhancement of mixing performance. High shear rate regions appear locally near the vessel walls, and the dimensionless maximum shear rate was expressed as a function of the Reynolds number and the vessel size. Power draw depends strongly on revolution speed, particularly on rheological behaviors at a low revolution speed; but it becomes independent of rheological properties at a high revolution speed due to formation of inertia-dominated flow. A flow quantification framework is proposed, achieving power number predictions in terms of the Reynolds number for a given fixed ratio between rotation and revolution at high speed.