Integral Formulation of the Smoluchowski Coagulation Equation using the Cumulative Quadrature Method of Moments (CQMOM)

2012 ◽  
pp. 1130-1134 ◽  
Author(s):  
Menwer Attarakih ◽  
Hans-Jörg Bart
Keyword(s):  
Method Of Moments ◽  
Integral Formulation ◽  
Quadrature Method ◽  
Smoluchowski Coagulation Equation ◽  
Quadrature Method Of Moments ◽  
Coagulation Equation

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.

Quadrature Method of Moments for the PDF Modeling of Droplet Coalescence in Turbulent Two-Phase Flows

2009 ◽  
Author(s):  
Roel Belt ◽  
Olivier Simonin
Keyword(s):  
Method Of Moments ◽  
Transport Equations ◽  
Fluid Particle ◽  
Joint Fluid ◽  
Collision Term ◽  
Quadrature Method ◽  
Balance Equations ◽  
Two Phase ◽  
Quadrature Method Of Moments ◽  
Made In

In this work, Eulerian transport equations are derived for a polydispersed cloud of droplets in a turbulent carrier flow, which take into account the effects of polydispersion and coalescence. The approach is an extension of the Direct Quadrature Method Of Moments (DQMOM) formalism initially proposed by Marchisio and Fox (2005, J. Aerosol Sci., 36, pp. 43–95). In the initial DQMOM approach of Marchisio and Fox, the effects of polydispersion and coalescence can only be accounted for in the mass balance equations. By combining the DQMOM approach and the joint fluid-particle pdf approach of Simonin (1996, Von Karman Lecture Notes), Eulerian transport equations can be written in the frame of the DQMOM formalism for the velocity, agitation and fluid-particle covariance, which quantities are required to predict the behavior of a cloud of droplets in a turbulent flow. It is formally shown that the Eulerian transport equations in the DQMOM framework are the same equations as those in the multi-class Eulerian approach, except that now there is a collision term in the equations. The collision term due to coalescence can be easily expressed due to the assumptions made in the DQMOM framework, and it is shown that it couples the transport equations of the different classes and dispersed phase statistics, according to the change of number, mass and momentum during coalescence.

scholarly journals Modeling soot oxidation with the Extended Quadrature Method of Moments

2017 ◽  
Vol 36 (1) ◽  
pp. 789-797 ◽  
Author(s):  
Achim Wick ◽  
Tan-Trung Nguyen ◽  
Frédérique Laurent ◽  
Rodney O. Fox ◽  
Heinz Pitsch
Keyword(s):  
Method Of Moments ◽  
Soot Oxidation ◽  
Quadrature Method ◽  
Quadrature Method Of Moments

Simulation of pure sedimentation of raindrops using quadrature method of moments

2012 ◽  
Vol 106 ◽  
pp. 61-70 ◽  
Author(s):  
Achintya Mukhopadhyay ◽  
Gary Jasor ◽  
Wolfgang Polifke
Keyword(s):  
Method Of Moments ◽  
Quadrature Method ◽  
Quadrature Method Of Moments
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