Comparison of numerical solution strategies for population balance model of continuous cone mill

Abstract

Population balance models are routinely used for modeling particulate processes involving breakage, agglomeration, crystallisation, etc. In this study, a comparison between three different numerical solution strategies for breakage population balance models is presented. Results are obtained for the fixed pivot technique, moving pivot technique and the cell average technique. These techniques are first compared for models whose solutions are analytically available. The comparison shows that fixed pivot lacks the accuracy of both moving pivot and cell average at coarser grids. At finer grids, all the three solution strategies give similar errors. With increasing grid fineness, all the three methods converge to a grid independent solution. Moving pivot is computationally the most expensive methods, followed by the cell average and fixed pivot. These methods are then applied to a conical screen mill modelled by a continuous population balance equation. For all the discretizations considered, cell average computes a higher median particle size value than the fixed pivot and moving pivot.

An Analysis of Uncertainty Propagation Methods Applied to Breakage Population Balance

“…In this study, only the fixed pivot method with 100 grid points is considered. A comparison of various discretization schemes for the cone mill is provided in [25].…”

A Modified Trapezoidal Technique with Improved Accuracy of Nonlinear Algebraic and Transcendental Equations

“…Uilhoorn et al examined stiff and nonstiff solvers, specifically integrated explicit Runge-Kutta schemes, to discover a quick and reliable spatial integration solver to gather gas flow transients within the context of particle filtering [9]. Bhonsale et al looked at the outcomes of three distinct numerical solution methodologies for breaking population balance models the cell average method, the moving pivot method, and the fixed pivot method [10]. Additionally, using these methods, Concepcion Ausin, M. explored more sophisticated numerical integration techniques and compared several numerical integration providers [11].…”

Numerical Simulation of Particle Dynamics in a Spiral Jet Mill via Coupled CFD-DEM

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