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

Application of dissipative particle dynamics to interfacial systems: Parameterization and scaling

Dissipative Particle Dynamics (DPD) is a stochastic particle model that is able to simulate larger systems over longer time scales than atomistic modeling approaches by including the concept of coarse-graining. Whether standard DPD can cover the whole mesoscale by changing the level of coarse-graining is still an open issue. A scaling scheme originally developed by Füchslin et al. (2009) was here applied to interfacial systems as one of the most successful uses of the classical DPD method. In particular, equilibrium properties such as the interfacial tension were analyzed at different levels of coarse-graining for planar oil–water interfaces with and without surfactant. A scaling factor for the interfacial tension was found due to the combined effect of the scaling scheme and the coarse-graining parameterization. Although the level of molecular description was largely decreased, promising results showed that it is possible to conserve the interfacial tension trend at increasing surfactant concentrations, remarkably reducing modeling complexity. The same approach was also employed to simulate a droplet configuration. Both planar and droplet conformations were maintained, showing that typical domain formations of multi-component systems can be performed in DPD by means of the scaling procedure. Therefore, we explored the possibility of describing oil–water and oil–water–surfactant systems in standard DPD using a scaling scheme with the aim of highlighting its advantages and limitations

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

The PP&S100 Project: Process Control as an Information System Instance

The Project PP&S100, Problem Posing & Solving, is part of a set of initiatives promoted by the General Directorate of the Italian Ministry of Education, Research and University, for supporting the many innovations that have recently affected curricula at the upper secondary level. Main goals of the project include strengthening computer science culture and enhancing its role as a scientific discipline; founding education processes on logics, mathematics and computer science weaved together to pursue an interdisciplinary scenario, building a culture of "problem posing and solving" by investing across a broad disciplinary group of subjects, ensuring growth of computer science based training of trainers and practicing activities within specific social networks and virtual learning environment to share learning materials, teaching supplies, mentoring and self-evaluation. This work presents a hierarchical conceptual model for "Computational Thinking" assumed by PP&S100, formalized according to the outcomes shown by information systems courses held at the Politecnico di Torino and validated using Process Control as an information system instanc

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

Effect of different good solvents in flash nano-precipitation via multi-scale population balance modeling-CFD coupling approach

A computational and modeling approach is used to highlight the key factors that affect polymer nanoparticles (NP) formation in flash nano-precipitation (FNP), when the good solvent, e.g., acetone, is replaced by acetonitrile, tetrahydrofuran and tert-butanol. A population balance model is coupled with computational fluid dynamics to study the kinetics effects on FNP. The mean NP size is predicted in terms of mean radius of gyration via the Flory law of real polymers. The effect of different good solvents is modeled in terms of solute–solvent interactions, using the Flory–Huggins theory and Hansen solubility parameters. Promising results show how the proposed methodology is able to investigate the role played by different good solvents, analyzing single factors at the time. A deep insight into both the dynamics of mixing and the dynamics of aggregation is therefore reached and the main mechanisms involved are pointed out, showing a good agreement with experimental data