Population balance methods utilised in multiphase flow simulations mark a significant advancement in computational fluid dynamics. However, existing approaches exhibit shortcomings, such as being prone to inaccuracies or being computationally prohibitive. Addressing these challenges, a recent innovation in closure for the method of moments is the introduction of quadrature based moments methods (QBMM). Discretising a distribution by a number of discrete elements, QBMM facilitate efficient and accurate tracking of density distributions, particularly for particle size distributions (PSD). However, obtaining the full particle size distribution information using these methods requires reconstructing the distribution from a finite set of moments, which is not a trivial step.
This study introduces a novel integration of the maximum entropy reconstruction (MER) into QBMM, establishing a robust and rapid framework for the time evolution and reconstruction of PSDs. As proof of concept for this framework, we focus on the direct quadrature method of moments (DQMOM) with spatially homogeneous and monovariate distributions. We show that coupling of MER with DQMOM has numerous advantages. To verify the framework, special cases of constant growth, aggregation, and breakage are considered for which analytical solutions can be found.
Furthermore, we show the advantage of using DQMOM with volume-based over length-based distributions, and address numerical as well as theoretical issues. Validation of the framework is successfully conducted on the evolution of the PSD from a twin-screw wet granulation dataset, considering all primary physical mechanisms inherent in a wet granulation process, namely growth, aggregation, and breakage. This showcases the consistency of the proposed framework and underscores its applicability to real-world scenarios.
The software consists of a fully working MATLAB (Version R2023a) script for a non-dimensional and dimensional direct quadrature method of moments coupled to a maximum entropy reconstruction. Additional methods that are needed to run the quadrature method of moments (reading in data, adaptive Wheeler algorithm, kernels, etc.) and the maximum entropy reconstruction (Gaussian qudrature, Cholesky inversion, etc.) including input data consisting of different density distributions from a twin-screw wet granulation dataset are available. The input data was derived from the dataset by Plath et al. 2021 (https://doi.org/10.4121/14248433.v1).
" authors: - family-names: Plath given-names: Timo orcid: "https://orcid.org/0000-0003-2854-2592" - family-names: Luding given-names: Stefan orcid: "https://orcid.org/0000-0001-7598-0929" - family-names: Weinhart given-names: Thomas orcid: "https://orcid.org/0000-0002-2248-7644" title: "Data to reproduce the paper: "Population balance modelling and reconstruction by quadrature method of moments for wet granulation"" keywords: version: 1 identifiers: - type: doi value: 10.4121/f5cfe2b8-2896-433a-887e-45c397d64ade.v1 license: CC BY 4.0 date-released: 2024-06-27