Direct numerical simulation and linear stability analysis of the flow in a pebble bed

The flow in a tightly packed array of spheres is important to various engineering fields. In nuclear engineering applications, for instance, researchers have proposed core geometries of the pebble bed reactor (PBR) type cooled by gas or molten salt. Proper core cooling, both at operation and during accident conditions, is a key issue that must be addressed in any reactor design; and the limited amount of data available for the complicated geometry of PBR cores makes this task even more complex. A detailed understanding of coolant flow patterns and properties must be developed in order to meet safety requirements and ensure core longevity. We address this issue by using the spectral-element computational fluid dynamics code Nek5000, developed at Argonne National Laboratory, to conduct both large eddy simulation (LES) and direct numerical simulation (DNS) of fluid flow through a single face-centered cubic sphere lattice with periodic boundary conditions. Moreover, a statistical analysis of the flow field and a global linear stability analysis of the laminar flow were performed in order to investigate the mechanism of laminar-turbulent transition in this geometry. One of the main objectives of the present study is, in fact, to determine how the Reynolds number affects the development of asymmetries within the flow patterns.