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An explicit adaptive grid approach for the numerical solution of the population balance equation

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Title: An explicit adaptive grid approach for the numerical solution of the population balance equation
Authors: Sewerin, F
Rigopoulos, S
Item Type: Journal Article
Abstract: Many engineering applications, such as the formation of soot in hydrocarbon combustion or the precipitation of nanoparticles from aqueous solutions, encompass a polydispersed particulate phase that is immersed in a reacting carrier flow. From a Eulerian perspective, the evolution of the particulate phase both in physical and in particle property space can be described by the population balance equation (PBE). In this article, we present an explicit solution-adaptive numerical scheme for discretizing the spatially inhomogeneous and unsteady PBE along a one-dimensional particle property space. This scheme is based on a space and time dependent coordinate transformation which redistributes resolution in particle property space according to the shapes of recent solutions for the particle property distribution. In particular, the coordinate transformation is marched in time explicitly. In comparison to many existing moving or dynamic adaptive grid approaches, this has the advantage that the semi-discrete PBE does not need to be solved in conjunction with an additional system governing the movement of nodes in particle property space. By design, our adaptive grid technique is able to accurately capture sharp features such as peaks or near-discontinuities, while maintaining the semi-discrete system size and adhering to a uniform fixed grid discretization in transformed particle property space. This is particularly advantageous if the PBE is combined with a spatially and temporally fully resolved flow model and a standard Eulerian solution scheme is applied in physical space. In order to accommodate localized source terms and to control the grid stretching, we develop a robust scheme for modifying the coordinate transformation such that constraints on the resolution in physical particle property space are obeyed. As an example, we consider the precipitation of BaSO4 particles from an aqueous solution in a plug flow reactor. Our findings demonstrate that for a given accuracy of the numerical solution the explicit adaptive grid technique requires over an order of magnitude fewer grid points than a comparable fixed grid discretization scheme.
Issue Date: 31-Aug-2017
Date of Acceptance: 30-Jan-2017
URI: http://hdl.handle.net/10044/1/45377
DOI: 10.1016/j.ces.2017.01.054
ISSN: 0009-2509
Publisher: Elsevier
Start Page: 250
End Page: 270
Journal / Book Title: Chemical Engineering Science
Volume: 168
Issue: 1
Copyright Statement: © 2017 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: Science & Technology
Engineering, Chemical
Population balance
Adaptive grid
Reacting flow
Chemical Engineering
0904 Chemical Engineering
0913 Mechanical Engineering
0914 Resources Engineering and Extractive Metallurgy
Publication Status: Published
Online Publication Date: 2017-02-01
Appears in Collections:Mechanical Engineering
Faculty of Engineering