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. 2022 Sep 17;13(9):1545.
doi: 10.3390/mi13091545.

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

Telha Mostefa  1 , Aissaoui Djamel Eddine  1 , Naas Toufik Tayeb  2 , Shakhawat Hossain  3 , Arifur Rahman  4 , Bachiri Mohamed  5 , Kwang-Yong Kim  6
Affiliations

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

Telha Mostefa et al. Micromachines (Basel). .

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.

Keywords: Poincaré section; active mixer; chaotic mixing; high viscous fluid; kinematic properties; twisted double planetary; unsteady flow.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
The geometrical shape of the considered double planetary mixer.
Figure 2
Figure 2
Velocity magnitude profiles versus X, Y, and Z coordinates for various mesh densities at t = 3 s.
Figure 3
Figure 3
Velocity vectors in the (a) XY, (b) YZ, and (c) XZ planes at 18 s (6τ).
Figure 4
Figure 4
Profiles of the secondary flows at different periods.
Figure 5
Figure 5
Initial selected positions of the Poincaré map.
Figure 6
Figure 6
Poincaré map for the twisted double planetary mixer at different periods (3 s, 6 s, 12 s, and 18 s).
Figure 6
Figure 6
Poincaré map for the twisted double planetary mixer at different periods (3 s, 6 s, 12 s, and 18 s).
Figure 7
Figure 7
Initial chosen groups for the Lyapunov exponent method.
Figure 8
Figure 8
Evolution of the Lyapunov exponent for the twisted double planetary mixer after 18 s.
Figure 8
Figure 8
Evolution of the Lyapunov exponent for the twisted double planetary mixer after 18 s.
Figure 9
Figure 9
Strain rate profiles at every time period.
Figure 10
Figure 10
Vorticity profiles at every time period.
Figure 11
Figure 11
Helicity profiles at every time period.
Figure 12
Figure 12
Instantaneous kinematic properties: (a) strain rate, (b) vorticity, and (c) absolute elongation.
See this image and copyright information in PMC

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