Simulation of coalescence, break up and mass transfer in bubble columns by using the Conditional Quadrature Method of Moments in OpenFOAM

The evaluation of the mass transfer rates and the fluid-dynamics aspects of bubble columns are strongly affected by the intrinsic poly-dispersity of the gas phase, namely the different dispersed bubbles are usually distributed over a certain range of size and chemical composition values. In our previous work, gas-liquid systems were investigated by coupling Computational Fluid Dynamics with mono-variate population balance models (PBM) solved by using the quadrature method of moments (QMOM). Since mass transfer rates depend not only on bubble size, but also on bubble composition, the problem was subsequently extended to the solution of multi-variate PBM (Buffo et al. 2013). In this work, the conditional quadrature method of moments (CQMOM) is implemented in the open-source code OpenFOAM for describing bubble coalescence, breakage and mass transfer of a realistic partially aerated rectangular bubble column, experimentally investigated by Diaz et al.(2008). Eventually, the obtained results are here compared with the experimental data availabl

ON THE IMPLEMENTATION OF MOMENT TRANSPORT EQUATIONS IN OPENFOAM TO PRESERVE CONSERVATION, BOUNDEDNESS AND REALIZABILITY

Different industrial scale multiphase systems can be successfully described by considering their polydispersity (e.g. particle/droplet/bubble size and velocity distributions) and phase coupling issues are properly overcome only by considering the evolution in space and time of such distributions, dictated by the so-called Generalized Population Balance Equation (GPBE). A computationally efficient approach for solving the GPBE is represented by the quadrature-based moment methods, where the evolution of the entire particle/droplet/bubble population is recovered by tracking some specific moments of the distribution and the quadrature approximation is used to solve the "closure problem" typical of moment-based methods. In this contribution some crucial computational and numerical details concerning the implementation of these methods into the opensource Computational Fluid Dynamics (CFD) code OpenFOAM are discussed. These aspects are in fact very often overlooked, resulting in implementations that do not satisfy the properties of conservation, realizability and boundedness. These constraints have to be satisfied in a consistent way, with respect to what done with the other conserved transported variables (e.g. volume fraction of the disperse phase) also when higher-order discretization schemes are used. These issues are illustrated on examples taken on our work on the simulation of fluid-fluid multiphase system

SIMULATION OF A REACTIVE GAS-LIQUID SYSTEM WITH QUADRATURE-BASED MOMENTS METHOD

The description of the interaction between fluid dynamics and fast chemical reactions in gas-liquid systems is complicated by the fact that the gas phase is poly-dispersed, namely it is constituted by bubbles characterized by a distribution of velocity, size and composition values. Phase coupling can be successfully described only if the modeling approach acknowledges the existence of this distribution, whose evolution in space and time is governed by the so-called Generalized Population Balance Equation (GPBE). A computationally efficient approach for solving the GPBE is represented by the Quadrature-Based Moment Methods (QBMM), where the evolution of the entire bubble population is recovered by tracking some specific moments of the distribution. In the present work, one of these methods, the Conditional Quadrature Method of Moments (CQMOM) has been implemented in the OpenFOAM two-fluid solver compressibleTwoPhaseEulerFoam , to simulate a chemically reacting gas-liquid system. To reduce the computational time and increase stability, a second-order operator-splitting technique for the solution of the chemically reacting species was also implemented, allowing to solve the different processes involved with their own time-scale. This modeling approach is here validated by comparing predictions with experiments, for the chemical absorption of CO 2 in NaOH solution, performed in a rectangular bubble column

On the realizability and boundedness of the moments in a bubbly gas-liquid pipe flow

The quadrature-based moment methods (QBMM) are widely used to solve the population balance equation (PBE), which provides a useful understanding of the evolution of disperse systems, e.g. bubbly gas-liquid flow. A key element of the methods is the moment-inversion algorithm that fails if the set of moments is not realizable. When the moment transport equations (derived from the PBE) include the convective term, employing standard high-order discretization schemes may cause the non-realizability problem. As a result, several realizable high-order schemes have been developed to address this issue. This work makes use of a bubbly developing pipe flow to investigate the performance of three schemes including 1st- and 2nd-order schemes, which can prevent the non-realizability problem. Eventually, the predictions will be discussed from the point of view of moment boundedness, a property that must be respected to obtain physical predictions

Simulation of Polydisperse Bubbly Flows with CFD and PBM: Importance of Interfacial Forces

Developing reliable Computational Fluid Dynamics Population Balance Model (CFD-PBM) is beneficial for studying the behavior of any industrial-scale polydisperse mixing system. Overall performance of this method relies on the closure relations employed in the averaged field equations. This work focuses on the relations proposed for the lift and wall lubrication forces used in the momentum balance equation. The selected relations are assessed using the experimental data of a polydisperse bubbly flow. Following this, the necessity of adjusting lift coefficient for improving the results is illustrated. Finally, the evolution of the bubble size distribution predicted by the CFD-PBM is evaluated against the experimental data

Computational Modeling of Magnesium Hydroxide Precipitation and Kinetics Parameters Identification

Magnesium is a critical raw material and its recovery as Mg(OH)2 from saltwork brines can be realized via precipitation. The effective design, optimization, and scale-up of such a process require the development of a computational model accounting for the effect of fluid dynamics, homogeneous and heterogeneous nucleation, molecular growth, and aggregation. The unknown kinetics parameters are inferred and validated in this work by using experimental data produced with a T2mm-mixer and a T3mm-mixer, guaranteeing fast and efficient mixing. The flow field in the T-mixers is fully characterized by using the k-ε turbulence model implemented in the computational fluid dynamics (CFD) code OpenFOAM. The model is based on a simplified plug flow reactor model, instructed by detailed CFD simulations. It incorporates Bromley's activity coefficient correction and a micro-mixing model for the calculation of the supersaturation ratio. The population balance equation is solved by exploiting the quadrature method of moments, and mass balances are used for updating the reactive ions concentrations, accounting for the precipitated solid. To avoid unphysical results, global constrained optimization is used for kinetics parameters identification, exploiting experimentally measured particle size distribution (PSD). The inferred kinetics set is validated by comparing PSDs at different operative conditions both in the T2mm-mixer and the T3mm-mixer. The developed computational model, including the kinetics parameters estimated for the first time in this work, will be used for the design of a prototype for the industrial precipitation of Mg(OH)2 from saltwork brines in an industrial environment