Numerical simulation of mass transfer with and without first order chemical reaction in two-fluid flows

Abstract

This work investigates the mass transfer process with and without first order chemical reaction by direct numerical simulation of two-fluid flows within mini-channels. The large potential of two-fluid flows for mass and heat transfer processes, operated in mini- and micro-systems such as micro bubble columns and monolithic catalyst reactors, motivated the present research. The study is based on the implementation of the species conservation equation in computer code TURBIT-VoF. The implementation of the equation is validated against different solutions of simplified mass transfer problems. The demanding treatment of the interfacial concentration jump described by Henry's law is examined with great concern. The diffusive term is successfully compared against one- and two-dimensional theoretical solutions of diffusion problems in two-phase systems. The numerical simulation of mass transfer during the rise of a 4mm air bubble in aqueous glycerol is performed and compared against another numerical simulation in order to test the convective term. The implementation of the source term for homogeneous and heterogeneous chemical reaction is successfully validated against theoretical solutions of mass transfer with chemical reaction in single-phase flows. The numerical simulations are focused on bubble train-flows flowing co-currently in mini-channels. Taking advantage of the periodic flow conditions exhibited in axial direction, the analysis is restricted to a flow unit cell, which consists of one bubble and one liquid slug. As concerns the hydrodynamics of all simulations performed, good agreement is obtained for the non-dimensional bubble diameter, the ratio of bubble velocity to the total superficial velocity and for the relative velocity in comparison with experimental data. The influence of the unit cell length on mass transfer from the bubble into the liquid phase of an arbitrary species is investigated in square channels having the hydraulic diameter D* h = 2mm. Short unit cells are found more effective than long unit cells for mass transfer, in agreement with published investigations performed for circular channels. This is related to the length of the liquid film between bubble and wall which becomes rapidly saturated due to short diffusion lengths and long contact time and leads to a decrease of the local concentration gradient. The major contribution to mass transfer occurs through the cap and the bottom of the bubbles, as reported also in experimental investigations. For mass transfer with heterogeneous chemical reaction more mass is consumed at the wall for systems having long unit cells, as a consequence of the increased lateral surface and more vigorous recirculation in the liquid slug. For species having a large solubility in the continuous phase, diffusion dominates over reaction allowing short unit cells to be more effective for mass transfer with heterogeneous reaction. A formulation of the mass transfer coefficient based on averaged concentrations is proposed for mass transfer processes and successfully compared against another approach based on the mass balance at interface. In complete agreement with experimental and theoretical studies, the study reveals that long liquid slugs and short bubbles are more efficient than short liquid slugs and long bubbles, respectively.