Chiney, Abhinandan and Kumar, Sanjeev (2012) On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain. In: CHEMICAL ENGINEERING SCIENCE, 76 . pp. 14-25.
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The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.
|Item Type:||Journal Article|
|Additional Information:||Copyright for this article belongs to Elesevier|
|Keywords:||Population balance; Particulate processes; Mixing; Agglomeration; Mathematical modelling; Discretization methods|
|Department/Centre:||Division of Mechanical Sciences > Chemical Engineering|
|Date Deposited:||10 Jul 2012 07:32|
|Last Modified:||10 Jul 2012 07:32|
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