Kinematic Properties of a Twisted Double Planetary Chaotic Mixer: A Three-Dimensional Numerical Investigation

Abstract

In this study, a numerical investigation based on the CFD method is carried out to study the unsteady laminar flow of Newtonian fluid with a high viscosity in a three-dimensional simulation of a twisted double planetary mixer, which is composed of two agitating rods inside a moving tank. The considered stirring protocol is a “Continuous sine squared motion” by using the dynamic mesh model and user-defined functions (UDFs)to define the velocity profiles. The chaotic advection is obtained in our active mixers by the temporal modulation of rotational velocities of the moving walls in order to enhance the mixing of the fluid for a low Reynolds number and a high Peclet number. For this goal, we applied the Poincaré section and Lyapunov exponent as reliable mathematic tools for checking mixing quality by tracking a number of massless particles inside the fluid domain. Additionally, we investigated the development of fluid kinematics proprieties, such as vorticity, helicity, strain rate and elongation rate, at various time periods in order to view the impact of temporal modulation on the flow properties. The results of the mentioned simulation showed that it is possible to obtain a chaotic advection after a relatively short time, which can deeply enhance mixing fluid efficiency.

A novel stretching and folding characterization method based on geometrical and physiological traits of chaotic and intermittent tracking signals

“…For example, Ser-Giacomi et al [19] investigated fluid transport within various regions of the fluid area by Lyapunov exponents (LEs). In addition, LE was used to assess the strength of stirred mixing chaoticity [20] or to evaluate the mixing quality in a planetary mixer [21]. Christov et al [22] used SFs to evaluate the mixing deformation of fluids and showed that the first and second LE could explain the rates of SF.…”