scholarly journals Modelling of Bubbly Flow Using CFD-PBM Solver in OpenFOAM: Study of Local Population Balance Models and Extended Quadrature Method of Moments Applications

2018 ◽  
Vol 2 (1) ◽  
pp. 8 ◽  
Author(s):  
Ehsan Askari ◽  
Pierre Proulx ◽  
Alberto Passalacqua
Keyword(s):  
Method Of Moments ◽  
Bubbly Flow ◽  
Local Population ◽  
Population Balance ◽  
Quadrature Method ◽  
Quadrature Method Of Moments

scholarly journals CFD-PBM Coupled Simulation of Liquid-Liquid Dispersions in Spray Fluidized Bed Extractor: Comparison of Three Numerical Methods

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Dan Zheng ◽  
Wei Zou ◽  
Chuanfeng Peng ◽  
Yuhang Fu ◽  
Jie Yan ◽  
...  
Keyword(s):  
Fluidized Bed ◽  
Method Of Moments ◽  
Chemical Engineering ◽  
High Reliability ◽  
Scale Up ◽  
Population Balance ◽  
Numerical Code ◽  
Balance Model ◽  
Quadrature Method ◽  
Quadrature Method Of Moments

A coupled numerical code of the Euler-Euler model and the population balance model (PBM) of the liquid-liquid dispersions in a spray fluidized bed extractor (SFBE) has been performed to investigate the hydrodynamic behavior. A classes method (CM) and two representatively numerical moment-based methods, namely, a quadrature method of moments (QMOM) and a direct quadrature method of moments (DQMOM), are used to solve the PBE for evaluating the effect of the numerical method. The purpose of this article is to compare the results achieved by three methods for solving population balance during liquid-liquid two-phase mixing in a SFBE. The predicted results reveal that the CM has the advantage of computing the droplet size distribution (DSD) directly, but it is computationally expensive if a large number of intervals are needed. The MOMs (QMOM and DQMOM) are preferable to coupling the PBE solution with CFD codes for liquid-liquid dispersions simulations due to their easy application, reasonable accuracy, and high reliability. Comparative results demonstrated the suitability of the DQMOM for modeling the spray fluidized bed extractor with simultaneous droplet breakage and aggregation. This work increases the understanding of the chemical engineering characteristics of multiphase systems and provides a theoretical basis for the quantitative design, scale-up, and optimization of multiphase devices.

CFD Modelling of Bubbly Flow in Adiabatic Upward Pipe Using a Solver Based on OpenFOAM® With the Quadrature Method of Moments

2014 ◽  
Author(s):  
Carlos Peña-Monferrer ◽  
Alberto Passalacqua ◽  
Sergio Chiva ◽  
José L. Muñoz-Cobo
Keyword(s):  
Method Of Moments ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Phase Flow ◽  
Computational Results ◽  
Quadrature Method ◽  
Cfd Modelling ◽  
Two Phase ◽  
Quadrature Method Of Moments

An Eulerian-Eulerian approach was used to model adiabatic bubbly flow with CFD techniques. The OpenFOAM® solver twoPhaseEulerFoam was modified to predict upward bubbly flow in vertical pipes. Interfacial force and bubble induced turbulence models are studied and implemented. The population balance equation included in the two-fluid model is solved to simulate a polydisperse flow with the quadrature method of moments approximation. Two-phase flow experiments with different superficial velocities of gas and water at different temperatures are used to validate the solver. Radial distributions of void fraction, air and water velocities, Sauter mean diameter and turbulence intensity are compared with the computational results. The computational results agree well with the experiments showing the capability of the solver to predict two-phase flow characteristics.

scholarly journals New developments of the Extended Quadrature Method of Moments to solve Population Balance Equations

2018 ◽  
Vol 365 ◽  
pp. 243-268 ◽  
Author(s):  
Maxime Pigou ◽  
Jérôme Morchain ◽  
Pascal Fede ◽  
Marie-Isabelle Penet ◽  
Geoffrey Laronze
Keyword(s):  
Method Of Moments ◽  
Population Balance ◽  
Quadrature Method ◽  
Balance Equations ◽  
New Developments ◽  
Population Balance Equations ◽  
Quadrature Method Of Moments

Numerical Methods for the Solution of Population Balance Equations Coupled with Computational Fluid Dynamics

2020 ◽  
Vol 11 (1) ◽  
pp. 339-366 ◽  
Author(s):  
Mohsen Shiea ◽  
Antonio Buffo ◽  
Marco Vanni ◽  
Daniele Marchisio
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Method Of Moments ◽  
Fluid Model ◽  
Population Balance ◽  
Quadrature Method ◽  
Balance Equations ◽  
Flow Models ◽  
Population Balance Equations ◽  
Quadrature Method Of Moments

This review article discusses the solution of population balance equations, for the simulation of disperse multiphase systems, tightly coupled with computational fluid dynamics. Although several methods are discussed, the focus is on quadrature-based moment methods (QBMMs) with particular attention to the quadrature method of moments, the conditional quadrature method of moments, and the direct quadrature method of moments. The relationship between the population balance equation, in its generalized form, and the Euler-Euler multiphase flow models, notably the two-fluid model, is thoroughly discussed. Then the closure problem and the use of Gaussian quadratures to overcome it are analyzed. The review concludes with the presentation of numerical issues and guidelines for users of these modeling approaches.

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