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Item type:Publication, Access status: without files , An efficient multiscale bi-directional PBM-DEM coupling framework to simulate one-dimensional aggregation mechanismsThe mesoscale population balance modelling (PBM) technique is widely used in predicting aggregation processes. The accuracy and efficiency of PBM depend on the formulation of its kernels. A model of the volume- A nd time-dependent onedimensional aggregation kernel is developed for predicting the temporal evolution of the considered particulate system. To make the developed model physically relevant, the PBM model needs three unknown parameters as input: Volume-dependency in collisions, collision frequency per particle and aggregation probability. For this, the microscale discrete element model (DEM) is used. The system's collision frequency is extracted periodically using a novel collision detection algorithm that detects and ignores duplicate collisions. Finally, a multiscale bi-directional PBM-DEM coupling framework is presented to simulate the aggregation mechanism. PBM and DEM simulations take place periodically to update the particle size distribution (PSD) and extract the collision-frequency, respectively. The coupling framework successfully explains the dependence between the PSD and the collision frequency. Additionally, computational cost of the algorithm is optimized while maintaining the accuracy of the results. Lastly, the accuracy and efficiency of the developed framework are verified using two different test cases. In one of the examples, a simple aggregation is simulated directly inside the DEM for the first time.Publicationtype: Journal Article37 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Application of transformation matrices to the solution of population balance equations(Multidisciplinary Digital Publishing Institute (MDPI), 2019-08-14); ; ; ; The development of algorithms and methods for modelling flowsheets in the field of granular materials has a number of challenges. The difficulties are mainly related to the inhomogeneity of solid materials, requiring a description of granular materials using distributed parameters. To overcome some of these problems, an approach with transformation matrices can be used. This allows one to quantitatively describe the material transitions between different classes in a multidimensional distributed set of parameters, making it possible to properly handle dependent distributions. This contribution proposes a new method for formulating transformation matrices using population balance equations (PBE) for agglomeration and milling processes. The finite volume method for spatial discretization and the second-order Runge–Kutta method were used to obtain the complete discretized form of the PBE and to calculate the transformation matrices. The proposed method was implemented in the flowsheet modelling framework Dyssol to demonstrate and prove its applicability. Hence, it was revealed that this new approach allows the modelling of complex processes involving materials described by several interconnected distributed parameters, correctly taking into consideration their interdependency.Publicationtype: Journal ArticleScopus© Citations 7 347 289 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , On the approximate solutions of fragmentation equations(2018); ; Consider the following mathematical model representing particle fragmentation in one dimension [23]; A numerical model based on the finite volume scheme is proposed to approximate the binary breakage problems. Initially, it is considered that the particle fragments are characterized by a single property, i.e. particle’s volume. We then investigate the extension of the proposed model for solving breakage problems considering two properties of particles. The efficiency to estimate the different moments with good accuracy and simple extension for multi-variable problems are the key features of the proposed method. Moreover, the mathematical convergence analysis is performed for one-dimensional problems. All mathematical findings and numerical results are validated over several test problems. For numerical validation, we propose the extension of Bourgade & Filbet (2008 Math. Comput. 77, 851–882. (doi:10.1090/S0025-5718-07-02054-6)) model for solving two-dimensional pure breakage problems. In this aspect, numerical treatment of the two-dimensional binary breakage models using finite volume methods can be treated to be the first instance in the literature.Publicationtype: Journal Article133