3D active mixing of confined power law aqueous polymer solutions: a comparative numerical study
Authors: Martin Elena B. , Sastre Francisco , Velazquez Angel , Baïri Abderrahmane 
Published: November 2022

Purpose
This paper aims to study the influence that the second invariant of the rate-of-strain tensor of a power law polymeric fluid (aqueous solution of hydroxyethyl cellulose [HEC]) has on convective mixing performance downstream of a 3D confined oscillating prism. Newtonian and non-Newtonian Reynolds numbers, the mass concentration of HEC and prism oscillation frequency were varied.

Design/methodology/approach
A conceptual problem was designed. Its objective was to analyze the convective mixing of two adjacent flow streams when they pass around a moving confined prism. The rectangular prism had a square section, and its sinusoidal motion was prescribed inside a channel with a square section too. OpenFOAM libraries were used to simulate the flow field. Regarding prism motion, the icoDyMFoam solver was used. The problem was analyzed both at the global level (mixing parameter) and local level (detailed flow topology).

Findings
For constant Reynolds number, increasing mass concentrations of HEC (in the range from 0.2% to 0.5%) led to better mixing parameters. The improvement was linked to the effect that the second invariant of the rate-of-strain tensor had on flow topology. It was found that mixing is maximum when the prism motion and its wake (the frequency of the first instability) are synchronized. In practical terms, this means that the optimum stirring frequency does not need to be very high; it suffices that it ensures that synchronization occurs. The dominant vorticity shedding pattern found was the so-called 2P mode. However, a significant difference was found when compared to the free-stream situation. While in the former, the two vorticity regions that make up the 2P pair come from the prism, in the present confined case, one came from the prism, and the other came from the wall. Another difference was that in the present case, the 2P pairs were much more elongated than in the free stream case, and this had a significant influence on the stretching and bending of streak lines and, therefore, on mixing.

Practical implications
The study that has been presented has a practical industrial implication for the processes industry because it provides guidelines to design active mixers that deal with aqueous power law polymeric solutions. In parallel, it opens up some new research lines in the direction of studying whether the mixing concept might be modified so as to develop a fully passive system that could be far simpler and, possibly, more attractive to industry.

Originality/value
The originality and value of the study are associated to the systematic approach that has been followed. It has allowed to establish a clear pattern regarding the active mixing behavior of HEC solutions in confined flows. To the best of authors’ knowledge, this could be the first study of this type in the literature. Also, the study has contributed to understand the vorticity shedding patterns that appear in these types of problems and how they shape wake topology and, consequently, mixing performance. The finding that optimum mixing requires synchronization of stirring motion frequency and wake first natural frequency of instability may help to improve the design and operation of industrial mixers dealing with polymeric aqueous solutions.