Comparison of three-dimensional flow mixing via pulsation and dynamical stirring: application to the mixing of parallel streams at different temperatures
Authors: Sastre Francisco , Martin Elena B. , Velazquez Angel , Baïri Abderrahmane 
Published: September 2021

Purpose
This paper aims to compare the performance of flow pulsation versus flow stirring in the context of mixing of a passive scalar at moderate Reynolds numbers in confined flows. This comparison has been undertaken in two limits: diffusion can be neglected as compared to convection (very large Peclet) and diffusion and convection effects are comparable. The comparison was performed both in terms of global parameters: pumping power and mixing efficiency and local flow topology.

Design/methodology/approach
The study has been addressed by setting up a common conceptual three-dimensional problem that consisted of the mixing of two parallel streams in a square section channel past a square section prism. Stirring and pulsation frequencies and amplitudes were changed and combined at an inlet Reynolds number of 200. The numerical model was solved using a finite volume formulation by adapting a series of open-source OpenFOAM computational fluid dynamic (CFD) libraries. For cases with flow pulsation, the icoFoam solver for laminar incompressible transient flows was used. For cases with stirring, the icoDyMFoam solver, which uses the arbitrary Lagrangian–Eulerian method for the description of the moving dynamical mesh, was used to model the prism motion. At the local flow topology level, a new method was proposed to analyze mixing. Time evolution of folding and wrinkling of sheets made up of virtual particles that travel along streak lines was quantified by generating lower rank projections of the sheets onto the spaces spanned by the main eigenvectors of an appropriate space-temporal data decomposition.

Findings
In the limit when convection is dominant, the results showed the superior performance of stirring versus flow pulsation both in terms of mixing and required pumping power. In the cases with finite Peclet, the mixing parameters by stirring and flow pulsation were comparable, but pulsation required larger pumping power than stirring. For some precise synchronization of stirring and pulsation, the mixing parameter reached its maximum, although at the expense of higher pumping power. At the local flow topology level, the new method proposed to quantify mixing has been found to correlate well with the global mixing parameter.

Originality/value
A new systematic comparative study of two methods, stirring and pulsation, to achieve mixing of passive scalars in the mini scale for confined flows has been presented. The main value, apart from the conclusions, is that both methods have been tested against the same flow configuration, which allows for a self-consistent comparison. Of particular interest is the fact that it has been found that accurate synchronization of both methods yields mixing parameters higher than those associated to both methods taken separately. This suggests that it is possible to synchronize mixing methods of a different nature to achieve optimum designs. The new theoretical method that has been proposed to understand the mixing performance at the local level has shown promising results, and it is the intention of the authors to test its validity in a broader range of flow parameters. All these findings could be taken as potential guidelines for the design of mixing processes in the mini scale in the process industry.