Solution of the population balance equation using the sectional quadrature method of moments (SQMOM)

Attarakih, Menwer; Drumm, Christian; Bart, Hans‐Jörg

doi:10.1016/j.ces.2008.05.006

Cited by 126 publications

(97 citation statements)

References 21 publications

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“…Eine Kopplung mit der CFD erfolgt über den charakteristischen SauterDurchmesser. Kombinierte Modelle, wie die Sequentiell Quadrature Method of Moment (SQMOM), berücksichtigt die Vorteile der Klassenmethode sowie der Momentenmethode [49]. Hierbei ist eine Unterteilung der Distribution in zwei oder mehrerer Tropfengrößen möglich, wobei die einzelnen Klassen wieder über einen Momentenansatz dargestellt werden, wodurch weite Distributionen mit einer relativ kurzen Rechenzeit adäquat dargestellt werden kön-nen.…”

Section: Partikelclusteranalyseunclassified

Droplet Cluster – Analysis, Simulation and Visualization

Bart

Hlawitschka

Mickler

et al. 2011

Chemie Ingenieur Technik

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Droplet Cluster -Analysis, Simulation and VisualizationOptical measurements are performed with an inline measurement technique in laboratory and pilot plant columns to obtain information about the droplet swarm at specific locations as a function of process parameters, e.g., time, energy input, and throughput. The column simulation tool LLECMOD was extended to packed and pulsed columns with the possibility of a free choice of the dispersed phase and mass transfer direction. The CFD simulation provides the basis for 3D simulation of hydrodynamics in stirred extraction columns. A one-group population balance model allows a determination of the changing droplet size with little additional CPU time. An enhanced visualization of the column data in 3D space allows fast and targeted analysis of the apparatus behavior.

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Section: Partikelclusteranalyseunclassified

Droplet Cluster – Analysis, Simulation and Visualization

Bart

Hlawitschka

Mickler

et al. 2011

Chemie Ingenieur Technik

Self Cite

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“…Therefore, various numerical algorithms have been developed for solving PB equations such as method of moment [114][115][116][117], method of characteristics [108,[118][119][120][121], Monte Carlo techniques [122,123], and discretization methods including finite element technique [119,124,125], cell average methods [107], hierarchical solution strategy based on multilevel discretization [126], method of classes [82,95], fixed and moving pivot method [127,128], and finite difference/volume methods [90,119,[129][130][131]. Table 1 summarises these numerical solution methods with the further reviews below.…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

2016

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Crystal morphology is known to be of great importance to the end-use properties of the crystal product and affect the down-stream processing such as in filtration and drying, but was previously regarded as too challenging to achieve automatic closed-loop control. As a consequence, previous work has focused on control the crystal size distribution (CSD) where the size of a crystal is often defined as the diameter of a sphere that has the same volume of the crystal. This paper reviews very promising new advances made in recent years in morphological population balance models for modelling and simulation of crystal shape distribution (CShD), measurement and estimation of crystal facet growth kinetics, as well as in 2D and 3D imaging for on-line characterisation of crystal morphology and CShD. A framework is presented integrating various components in order to achieve the ultimate objective of model-based closed-loop control of CShD. The knowledge gaps and challenges that require further research are also identified.

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“…It was introduced firstly in studying the growing mechanism of sulfuric acid droplet (McGraw, 1997), then QMOM has been used to study the law of particle breaking, sedimentation and growing etc. (Attarakih et al 2009). While in particle agglomeration, some researchers have put it in the study of orthokinetic interaction (Zhang, 2010), further studies are still needed.…”

Section: Introductionmentioning

confidence: 99%

The Use of Quadrature Method of Moments (QMOM) in Studying the Mechanisms of Aerosol Agglomeration and its Practical Use

Liao¹,

Wu²,

Yao

et al. 2015

AJHMT

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The efficiency of dust collector is relatively low when dealing with PM2.5. Agglomerating the aerosols under acoustic field is a preliminary method to make the efficiency improve. Acoustic agglomeration of aerosol mainly includes four mechanisms: orthokinetic interaction, hydrodynamic interaction, acoustic wake effect and Brown agglomeration. All mechanisms have their own characteristics with the change of acoustic field. Among witch orthokinetic interaction plays the leading role, while Brown agglomeration is the weakest. Besides, Brown agglomeration is only related to the change of temperature and other air characteristics, thus it changes little under the effect of acoustic field. Compared with experimental methods, simulating the agglomerate process on computer is much faster and more economical. To overcome the flaws of traditional ways in simulation of long-time, hard to make exact hypotheses and difficult to make the formulas close, quadrature method of moments (QMOM) is employed when doing simulations, and taking it into practical use. The results of QMOM show a good match with group method, while it takes less time and does not need to make unnecessary hypotheses. Besides studying the characteristics of acoustic agglomeration, QMOM will also be easy to be used in other fields of studies with similar dynamic equations.

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Solution of the population balance equation using the sectional quadrature method of moments (SQMOM)

Cited by 126 publications

References 21 publications

Droplet Cluster – Analysis, Simulation and Visualization

Droplet Cluster – Analysis, Simulation and Visualization

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

The Use of Quadrature Method of Moments (QMOM) in Studying the Mechanisms of Aerosol Agglomeration and its Practical Use

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