CFD study on laminar mixing at a very low Reynolds number by pitching and heaving a square cylinder

In this work, CFD is used to show how the combined motion of heaving and pitching a 2D square cylinder located in the middle of the channel can be used to enhance mixing of two fluids flowing at a very low Reynolds number along a rectangular channel. Both type of motions are applied and enforced with a phase difference at the same time, but at difference frequencies and amplitudes, in order to see if mixing efficiency can be enhance. The characteristics of five governing input parameters and output results are examined. The input parameters consist of two frequencies, one for heaving and one for pitching, and two amplitudes, one for heaving and one for pitching. The output results are mixing efficiency, input power coefficient and mixing energy cost. The Optimal Space Filling algorithm is used to generate 60 different combinations of the input parameters which are used in the numerical studies. Different response surfaces of the output parameters are obtained. It is noted that certain combinations of the input parameters produce the highest mixing efficiency (around 55%), the lowest input power coefficient (around 260 units) or the lowest mixing energy cost (around 13 units) are found. On the other hand a multi-objective optimisation is also carried out in order to find the input parameters that give rise to the highest possible mixing efficiency with lowest possible input power coefficient. A set of optimal solutions leading to Pareto Front is obtained which shows the trade-off between the objectives. Three potential optimal candidates are proposed in this paper.