A collective dynamics-based method for initial pebble packing in pebble flow simulations

In the simulation of pebble flow in Pebble-Bed High Temperature Reactors (PB-HTRʹs), high-fidelity methods, such as discrete element method (DEM), are usually employed to simulate the dynamic process of the pebble circulation. Such simulation normally takes extraordinarily long time to reach the dynamic equilibrium state, in which the pebble distribution is statistically steady. However, if an initial dense packing of pebbles can be provided, which is close to the realistic packing at the equilibrium state and can be easily implemented without much computational effort, then the high-fidelity pebble flow simulation can take much less time to reach the dynamic equilibrium state. In this paper, a collective dynamics-based method is developed to generate an initial pebble packing for the subsequent high-fidelity pebble flow simulations. In the new method, pebbles are packed by two processes: a sequential generation process allowing overlaps and an overlap elimination process based on a simplified normal contact force model. The latter provides an adaptive and efficient mechanism to eliminate the overlaps accounting for different overlap size and pebble size, thus can pack tens of thousands of pebbles within several minutes. Applications of the new method to packing pebbles in both cylindrical and annular core geometries are studied for two types of PB-HTR designs: HTR-10 and PBMR-400. The resulting packings show similar radial and axial packing fraction distributions compared to the dynamic equilibrium packing state produced by the DEM pebble flow simulation. Comparisons with other existing random packing methods, such as the gravitational deposition method, have shown that the developed method not only exhibits excellent computation efficiency, but also presents desirable potential in other applications as a general packing algorithm for packing mono-sized or poly-sized spheres in a large container.