
A Neural Network based Framework to Model Particle Rebound and Fracture
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In dilute, particle-laden flows, the most important contact forces to which the particles are exposed are caused by interactions with solid walls. For the simulation of such flows, especially when several hundred of thousands of particles are considered, Euler--Lagrange methods are a common choice due to their efficiency and accuracy. In Euler--Lagrange methods, the particles are assumed to point particles such that interactions with solid walls cannot be spatially resolved, but have to be modeled, e.g., using rebound models. Rebound models are designed to predict a new particle trajectory based on the surface’s material and the properties of the impinging particle. In general, these models are empirically derived, sometimes physically motivated and often equipped with tuning parameters to match the corresponding measured particle rebound, while the actual stochastic nature of the rebound and particle breakage are typically neglected. However, this affects the resulting particle trajectories and is particularly critical at high impact velocities. Further improvements have therefore been proposed to consider higher statistical moments, or energy losses due to particle breakage. In this talk, a data-driven rebound model based on artificial neural networks is presented. This enables to include specific physical effects such as particle breakage or rough walls, while easily allowing to consider further physical constraints. To this end, state of the art methods from function approximation, more precisely, deep dense neural networks are employed. The networks are trained through a supervised learning approach, where the neural network maps the impacting particles’ characteristics to its new particle trajectory after rebound. The particle breakage is based on a fracture probability distribution to determine if a particle breaks. We will illustrate the predictive performance of the final model by the use of experimental measurements of the statistical, high-velocity rebound of sand particles. Finally, the advantages and constraints of such a data-driven approach are discussed.