Numerical investigation of flow instabilities in T-shaped micro-mixers: benchmark between finite volume and spectral element methods

Micro-reactors are a new attractive technology for process development and intensification in the pharmaceutical and fine chemistry industries that currently mostly rely on batch/semi-batch processes, often operated with high dilution to avoid reaction runaway. Instead, micro-reactors, made of channels < 1 mm, work continuously with high heat transfer capacity due to the high surface to volume ratio, allowing low dilution and hence high yield, low energy consumption and environmental impact. Moreover, scale-up procedures from lab to industrial scale are not needed, as the required production rate is simply met by a numbering-up of the reactors. The flow is laminar so special techniques should be adopted to promote mixing; in particular, passive micro-reactors are able to mix efficiently reactants without any external force and just through a special design, able to break the flow symmetries. In the simplest passive micro-reactor the inlets join the main channel with T-shaped branches. So far, its efficiency for liquid mixing has been studied using water, thus identifying different flow regimes depending on the Reynolds number. Surprisingly, unsteady time-periodic motions, able to improve mixing, were observed in the laminar regime. Experiments in micro-reactors are difficult to be carried out because of the small dimensions; moreover the analysis of flow instabilities requires high acquisition rates, thus adding further complexity; hence computational Fluid Dynamics (CFD) appears well suited to address the problem. The present work employs Direct Numerical Simulations (DNS) to investigate the unsteady flow regime in T-mixers using both water and non-ideal mixtures as inlet fluids. Indeed, there is a lack of information for the latters, even though the practical use of micro-reactors involves fluids different than water and often of organic nature. DNS were performed with two different CFD codes: the commercial finite volume solver Fluent by ANSYS Inc. and the open source spectral-element code NEK5000. Although the different numerical setup, the comparison between the two approaches was very satisfactory. The flow instabilities were found to be present for different mixture rheology and in all cases were able to improve mixing even by more than 50%.