Simulation of polydisperse multiphase systems using population balances and example application to bubbly flows

Simulation of a reacting gas–liquid bubbly flow with CFD and PBM: Validation with experiments

“…12. The comparison between these two cases clearly pointed out the need of reliable boundary conditions for similar simulations [35], which is an aspect often overlooked when similar test cases are considered both on the experimental and modeling point of 29 A C C E P T E D M A N U S C R I P T view. However, even without any knowledge of the mean bubble size formed by the gas sparger, the results obtained by means of the use of standard correlations are in general satisfactory, also in the reactive case considered in this work.…”

“…1. Following our previous work on this topic, our QMOM and CQMOM implementation in the OpenFOAM (v. 2.2.x) solver compressibleTwoPhaseEulerFoam [35] is used here to simulate a reacting gas-liquid system, for which experimental data are available in the literature [40]. It is important to stress here that the CFD model is fully predictive: all the model constants have been derived from theory and no fitting constants are adjusted here to match experiments.…”

“…All of them have been implemented in different CFD codes for the simulation of gas-liquid systems. In particular QMOM has been used in Ansys Fluent for the simulation of stirred tanks [19] and in OpenFOAM for the simulation of bubble columns [35], DQMOM in TransAT for the simulation of gas-liquid pipe flows [36] and in Ansys Fluent for the simulation of stirred tanks [20], whereas CQMOM has 4 A C C E P T E D M A N U S C R I P T been used in Ansys Fluent and OpenFOAM for the simulation of simultaneous bubble coalescence, breakage and mass transfer [37,38] as well as in an in-house code [39]. The performance of some of these methods has been compared [21] and recently reviewed [22].…”

“…This correlation predicts a mean bubble diameter of 6.2 mm, which is higher than the value used by Darmana and coworkers in their simulation[40] (i.e., 5.5 mm) and likely coming from experimental evidences. The reader may refer to our previous work[35] for further details on the bubble inlet condition.To investigate what is the influence of the different parts of the model, different simulations are carried out. Firstly, the case without chemical reaction, for which experimental data of global gas hold-up and a time-averaged gas velocity profile at one height of the column are avaible, is simulated.…”

Modeling and simulation of mixing in water-in-oil emulsion flow through a valve-like element using a population balance model

“…In this perspective, the use of computational fluid dynamics (CFD) to solve an Eulerian multi-fluid model coupled with a population balance model (PBM) has shown to be an efficient tool to simulate polydisperse multiphase flow (Chen et al, 2005;Zucca et al, 2006;Silva et al, 2008;Petitti et al, 2010Petitti et al, , 2013Passalacqua et al, 2010;Silva and Lage, 2011;Yan et al, 2011;Buffo et al, 2012Buffo et al, , 2013a. Recently, Marchisio and Fox (2013) showed that this formulation can be deduced directly from the so-called generalized population balance equation (GPBE) that is basically the conservation equation for the particle number density including its dependence on all particle and fluid variables that may affect the particulate system behavior.…”