Effect of Temporal Modulation on the Local Kinematic Process of Two-Dimensional Chaotic Flow: A Numerical Analysis

Abstract

In this work, a numerical analysis based on CFD method is carried out to examine an unsteady laminar flow of Newtonian fluids in a two-dimensional simulation of a mixer, which is composed of two rods inside a moving cylindrical tank. Three stirring protocols are considered: Non-modulated “NM”, Continuously modulated “CM” and non-continuously modulated “ALT” by using the dynamic mesh technique and user defined functions “UDF’s” for the velocity profiles. The chaotic advection is obtained by temporal modulation of the rotational velocity of the cylinder and the rods to enhance the mixing of the fluid for very low Reynolds number. For this purpose, we applied the Poincaré map as a reliable mathematic tool to check mixing quality by tracking particles inside the fluid domain. Additionally, we investigated the evolution of local flow proprieties such as rotation rate, deformation rate and elongation rate at different time periods in order to see the effect of temporal modulation on the fluid kinematics. Among the considered protocols, the results of the mentioned simulation showed that it is possible to obtain a chaotic advection only for non-continuously modulated protocol which enhance mixing fluid efficiency.