These slides were presented at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

Tracing particles and analyzing their settling and finally sedimentation has a variety of applications from geology to chemistry. Numerical analysis of particle tracing involves complex calculations of heterogenous flow dynamics. Although literature is rich with empirical or numerical solutions, the nature of the problem dictates customized models. In this study, a Reduced Order Model (ROM) is used to simulate the global behavior of the particles, as a function of time, during the settling and sedimentation phases, in response to different geometries and properties of the particles. The aim in doing that is also to unify several models in a given application into a more general model. By focusing on average metrics, such as the surface defined by the accumulating particles, it is possible to reduce the impact of the intrinsically non-linear behavior of the particles. This allows a compact model which can reproduce the critical aspects of the simulation, without the need for particle-to-particle tracking. As proof of concept, we focus on a collection of spherical particles relocating from a higher container to a lower one through an opening whose location and width are parametrized. A ROM is trained to mimic the simulations for accumulated particles free falling into a lower container. The requirements from such a ROM are to predict: i. the sedimentation of the particles still in the upper container, ii. the particle settling in the lower container, iii. the number of particles still in flow, iv. the altitude of particles still in flow, and v. velocity of the flowing particles. To handle the problem independent of individual particle trajectories, the data is pre-processed to extract the initial and instantaneous distributions of the particles. Such a pre-processing will allow to combine simulations with varying number of particles, impurities of particle shapes, and materials to be homogenized in one ROM. In this stage of the study, the initial sedimentation distribution of the particles in the upper container due to different shapes of the container and the opening location and size are the independent variables. The particles are processed into three distinct groups: still in the upper container, flowing, settled in the lower container. For those in the containers, the boundaries and geometry of the volume of space they occupy are identified, parametrized, and modelled. The resolution in the pre-processing of the particle distributions can be fine-tuned according to the accuracy requirements from the application. The model has been tested using designs not included in the training dataset. The predictions showed less than 10% of errors for the distribution of particles still in the upper container. The reliability of the particle settling predictions in the lower container is initially affected by the quasi-random distribution of the first particles and improves as the particles'™ accumulation becomes the dominating factor in the sedimentation distribution. That said, in transient cases the prediction quality increases. The overall numbers of particles that are still flowing at various stages are predicted successfully. Flowing particles can also be divided height-wise into subgroups. The approach has been proven to satisfy the initial requirements, by predicting the instantaneous sedimentation in seconds. Future work would include training the model with simulations including particles of different shapes, weight, and dimensionality, to assess both the model scalability to higher number of design parameters and its invariability to the number of particles. Such an extended model will open the doors to unify the custom numerical solutions in a given application dealing with particle flows.