Particle Collisions for Arbitrary Smooth Shaped Objects

The 350-year-old basic work of Newton on mechanics allows us to calculate the position of a planet exactly. However, if we throw a stone into a river and try to predict its position in a week, these predictions are impossible or there are large errors. To date, the understanding of the physical processes in sediment transport in rivers is limited and largely empirical. With this project we want to take a small step towards answering the question of where a stone thrown into the river is after a week. This is important because sediment surplus in rivers can lead to flooding while a sediment deficit can lead to deepening of the river bed. In our research project, we specifically investigate how stone collisions on the river bed affect sediment transport. Sediment transport is determined by the interaction of stones with the flowing water and the interaction of stones with each other. Spherical or ellipsoidal stones have been used to investigate these interactions in a simplified manner. However, these collisions are fundamentally different from the interactions of stones that the river has shaped. Therefore, mathematical and numerical models have to be developed for the investigation of collisions with stones of arbitrary shape. Laboratory tests are being carried out with river stones. These are based on already known pendulum experiments with spherical particles. In addition to tracking the particle movement before, during and after the collision, the surrounding flow field is measured using state-of-the-art measurement methods (4D-PTV with shake-the-box). A mathematical collision model is developed from this. The mathematical collision model is implemented within the software application "VFS - Geophysics". This software is used for the numerical simulation of flows and their interaction with solids (e.g. stones). It is expanded to include the collision model module. Finally, the numerical model is tested simulating a sediment transport experiment under real flow conditions of a river.

The 350-year-old basic work of Newton on mechanics allows us to calculate the position of a planet exactly. However, if we throw a stone into a river and try to predict its position in a week, these predictions are impossible or there are big mistakes. To this day, our understanding of how sediments are transported in rivers is limited and largely empirical. It is very important to be able to predict sediment transport in rivers, not least for flood safety issues. In our research project, we specifically investigated how stones on the river bed that collide with each other affect sediment transport. Sediment transport is determined by the interaction of stones with the flowing water and the interaction of stones with each other. In order to investigate these interactions, spherical or ellipsoidal stones have been used in earlier studies. Our hypothesis was that stones formed by the river move in a different manner than spheres and ellipsoids. A mathematical and numerical model was therefore developed to investigate collisions with stones of arbitrary convex shape. To this end, laboratory tests were carried out with river stones. First, the movement of the river stones was tracked before, during and after the collision. In addition, the generated flow field was measured using modern measurement methods (3D-tr-PTV with shake-the-box). We were able to develop an experimental method that can measure and visualize the vortex structures generated in the flow around the stones. This method can be used in general, for example to investigate the interaction of riparian vegetation with the flow. A mathematical collision model was developed from the laboratory tests. This was implemented as part of the "VFS-Geophysics" software application. This software is used for the numerical simulation of flows and their interaction with solid bodies (e.g. stones, embankments, trees, ships, etc.). VFS-Geophysics was extended by the collision model module. Using the developed collision model, we were able to show that river stones behave fundamentally differently in their movement at the river bed than spheres or ellipsoids, which is why it is important to correctly model the actual shape of the stones in the computer simulations. With this project, we have taken a small step towards answering the question of where a stone thrown into the river will be after a week.