CFD study on mixing enhancement in a channel at a low reynolds number by pitching a square cylinder

An active mixing mechanism, to mix two fluids containing different mass concentrations of a solute when they must flow at a very low Reynolds number (Re=1), is analysed in this paper by means of Computational Fluid Dynamics (CFD). The mixing mechanism is based on the pitching of a square cylinder located in the middle of a straight channel. To that end, several 2D numerical simulations have been conducted for different frequencies (f^p) and amplitudes (A) of the pitching motion but for a fixed cylinder-to-channel width ratio. The studied values of the parameters f^p and A have been chosen according to the Central Composite Design and Optimal Space Filling algorithms, which allow to study the desired range of variation of both parameters with just 18 design points optimally distributed on the f^p−A plane. After carrying out these simulations the response surface of the mixing efficiency is obtained, from which an optimal value of f^p and A can be found to get the maximum mixing efficiency (∼ 45%), being more than 15 times higher than when the mixing takes place with the cylinder steady. Despite of that, since in mixing, specially at micro scale, is also important the energy needs to run the microdevice, an average input power coefficient, which takes into account the power needs both to run the channel and to pitch the square cylinder, has been also calculated. In order to find the optimal working point of the mixing device, that is, the one giving the highest efficiency with the lowest input power requirements, a mixing energy cost (i.e. an input energy-efficiency ratio) has been also evaluated which shows that the highest efficiency configuration is not the one with the lowest cost, being, as we shall show, the former around 1.7 times more expensive than the latter.