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Quadrature-based moment methods for the population balance equation: An algorithm review

Li, D. and Li, Z. and Gao, Z. (2019):
Quadrature-based moment methods for the population balance equation: An algorithm review.
In: Chinese Journal of Chemical Engineering, 27 (3), pp. 483 - 500. ISSN 1004-9541,
DOI: 10.1016/j.cjche.2018.11.028,
[Article]

Abstract

The dispersed phase in multiphase flows can be modeled by the population balance model (PBM). A typical population balance equation (PBE) contains terms for spatial transport, loss/growth and breakage/coalescence source terms. The equation is therefore quite complex and difficult to solve analytically or numerically. The quadrature-based moment methods (QBMMs) are a class of methods that solve the PBE by converting the transport equation of the number density function (NDF) into moment transport equations. The unknown source terms are closed by numerical quadrature. Over the years, many QBMMs have been developed for different problems, such as the quadrature method of moments (QMOM), direct quadrature method of moments (DQMOM), extended quadrature method of moments (EQMOM), conditional quadrature method of moments (CQMOM), extended conditional quadrature method of moments (ECQMOM) and hyperbolic quadrature method of moments (HyQMOM). In this paper, we present a comprehensive algorithm review of these QBMMs. The mathematical equations for spatially homogeneous systems with first-order point processes and second-order point processes are derived in detail. The algorithms are further extended to the inhomogeneous system for multiphase flows, in which the computational fluid dynamics (CFD) can be coupled with the PBE. The physical limitations and the challenging numerical problems of these QBMMs are discussed. Possible solutions are also summarized.

Item Type: Article
Erschienen: 2019
Creators: Li, D. and Li, Z. and Gao, Z.
Title: Quadrature-based moment methods for the population balance equation: An algorithm review
Language: English
Abstract:

The dispersed phase in multiphase flows can be modeled by the population balance model (PBM). A typical population balance equation (PBE) contains terms for spatial transport, loss/growth and breakage/coalescence source terms. The equation is therefore quite complex and difficult to solve analytically or numerically. The quadrature-based moment methods (QBMMs) are a class of methods that solve the PBE by converting the transport equation of the number density function (NDF) into moment transport equations. The unknown source terms are closed by numerical quadrature. Over the years, many QBMMs have been developed for different problems, such as the quadrature method of moments (QMOM), direct quadrature method of moments (DQMOM), extended quadrature method of moments (EQMOM), conditional quadrature method of moments (CQMOM), extended conditional quadrature method of moments (ECQMOM) and hyperbolic quadrature method of moments (HyQMOM). In this paper, we present a comprehensive algorithm review of these QBMMs. The mathematical equations for spatially homogeneous systems with first-order point processes and second-order point processes are derived in detail. The algorithms are further extended to the inhomogeneous system for multiphase flows, in which the computational fluid dynamics (CFD) can be coupled with the PBE. The physical limitations and the challenging numerical problems of these QBMMs are discussed. Possible solutions are also summarized.

Journal or Publication Title: Chinese Journal of Chemical Engineering
Journal volume: 27
Number: 3
Uncontrolled Keywords: Population balance equation, Quadrature-based moment method, Multiphase flow, Computational fluid dynamics
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Simulation of reactive Thermo-Fluid Systems (STFS)
Date Deposited: 18 Nov 2019 08:40
DOI: 10.1016/j.cjche.2018.11.028
Official URL: http://www.sciencedirect.com/science/article/pii/S1004954118...
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