Gennari, Gabriele
(2023)
A CFD methodology for mass transfer of soluble species in incompressible two-phase flows: modelling and applications.
PhD thesis, University of Nottingham.
Abstract
Continuous flow chemistry is an interesting technology that allows to overcome many of the limitations in terms of scalability of classical batch reactor designs. This approach is particularly relevant for both photochemistry and electrochemistry as new optimal solutions can be designed to limit, for example, the issues related to light penetration, reactor fouling, excessive distance between electrodes and management of hazardous compounds, whilst keeping the productivity high. Such devices operate often in a two-phase regime, where the appearance of a gas in the form of a disperse bubbly flow can be either a desirable feature (e.g. when the gas is needed for the reaction) or the result of a spontaneous reaction (e.g. electrochemistry). Such systems are very complicated flows where many bubbles populate the reactor at the same time and deform under the effect of several forces, such as surface tension, buoyancy and pressure and viscosity terms. Due to the solubility of gas in the liquid solvent, the disperse phase exchanges mass with the liquid (where the reactions generally occur) and the volume of the bubbles changes accordingly. Such physics is mainly a convection-dominated process that occurs at very small length scales (within the concentration boundary layer, which is generally thinner than the hydrodynamic one) and numerical tools for routine design are based on simplifying assumptions (reduced order methods) for the modelling of this region. However, such approaches often lead to errors in the prediction of the mass transfer rate and a fully-resolved method is generally needed to capture the physics at the interface. This last approach comes with a high computational cost (which makes it non suitable for common design processes) but can be employed in simplified scenarios to explore fundamental physics and derive correlation formulae to be used in reduced order models.
For the above reasons, this work aims at developing a high-fidelity numerical simulation framework for the study of mass transfer of soluble species in two-phase systems. The numerical modelling of these processes has several challenges, such as the small characteristic spatial scales and the discontinuities in both concentration and velocity profiles at the interface. All these points need to be properly taken into account to obtain an accurate solution at the gas-liquid interface. In this thesis, a new methodology, based on a two scalar approach for the transport of species, is combined with a geometric Volume of Fluid method in the open source software Basilisk (http://basilisk.fr/). A new algorithm is proposed for the treatment of the interfacial velocity jump, which consists of the redistribution of the mass transfer term from the interfacial cells to the neighbouring pure gas ones, in order to ensure the conservation of mass during the advection of the interface. This step is a crucial point of the methodology, since it allows to accurately describe the velocity field near the interface and, consequently, to capture the distribution of species within the concentration boundary layer.
The solver is extensively validated against analytical, experimental and numerical benchmarks, which include suspended bubbles in both super- and under-saturated solutions, the Stefan problem for a planar interface, dissolving rising bubbles and competing mass transfer of mixtures in mixed super- and under-saturated liquids.
Finally, the methodology is used for the study of real applications, namely the growth of electrochemically generated bubbles on a planar electrode and the mass transfer of a single bubble in a Taylor-Couette device. The effects of the main parameters that characterise the systems (e.g. contact angle, current density and rotor speed) on the growth/dissolution rate of bubbles are investigated. Although these systems need to be necessarily simplified to allow for direct numerical simulations, these examples show that the insight gained into the fundamental physics is valuable information that can be used to develop reduced order models.
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