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A numerical method for the simulation of an aggregation‐driven population balance system
Author(s) -
Hackbusch Wolfgang,
John Volker,
Khachatryan Aram,
Suciu Carina
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2656
Subject(s) - population balance equation , kernel (algebra) , finite element method , population , mathematics , domain (mathematical analysis) , numerical analysis , computer simulation , computer science , convolution (computer science) , flow (mathematics) , mathematical optimization , finite difference , mathematical analysis , simulation , geometry , engineering , artificial intelligence , demography , structural engineering , combinatorics , sociology , artificial neural network
SUMMARY A population balance system that models the synthesis of urea is studied in this paper. The equations for the flow field, the mass and the energy balances are given in a three‐dimensional domain, while the equation for the particle size distribution is given in a four‐dimensional domain. This problem is convection‐dominated and aggregation‐driven. Both features require the application of appropriate numerical methods. This paper presents a numerical approach for simulating the population balance system, which is based on finite element schemes, a finite difference method and a modern method to evaluate convolutIon integrals that appear in the aggregation term. Two experiments are considered and the numerical results are compared with experimental data. Unknown parameters in the aggregation kernel have to be calibrated. For appropriately chosen parameters, good agreements are achieved of the experimental data and the numerical results computed with the proposed method. A detailed study of the computational results reveals the influence of different parts of the aggregation kernel. Copyright © 2011 John Wiley & Sons, Ltd.