Multiscale granular-fluid dynamics in pebble bed reactor cores

Abstract

In addition to the study of three different practical designs, generic investigations on the scaling effect and pebble wear are also conducted. The coupled modeling approach developed in this thesis can provide better predictions of pebble flow packing density distribution, pebble flow velocity profile, and a more realistic pebble wear, by considering the effect from the coolant fluid on the pebble flow motion and contact force/stress. These pebble flow dynamic properties are the key parameters for the reliable analysis and design of pebble bed reactors.

In pebble bed reactors (PBRs), densely-packed, slowly-moving fuel pebbles are circulating within the core, while exchanging momentum and energy with coolant that passes through the packed bed. Two flows exist in PBRs: pebble flow and coolant flow. Each flow presents different physical properties that are of interest to the PBR analysts. Pebble and coolant flows are highly correlated with each other by the pebble-fluid interactions. Physical properties of each flow can be affected by this interplay. Previous research has shown that the heat transfer and neutronic performance of the PBR core depend on the packing density and velocity distributions of the pebble flow, which are two important dynamic properties of the pebble flow. The pebble wear due to rubbing of contacting pebbles, which can generate radioactive, combustible graphite dust and change the sphericity of the pebble fuel, is also an important flow property that is related to the PBR operation safety. Hence the fluid effect on the pebble flow packing density distribution, velocity profile and pebble wear needs careful quantifications in the analyses of different PBR designs. For example, the Pebble Bed-Fluoride salt-cooled High-temperature Reactor (PB-FHR) design, where the buoyancy from the molten fluoride salt coolant is the driving force behind pebble circulation and the fluid-pebble force accounts for a significant portion of the buoyancy. Another example is the large-scale 400 MWt Pebble Bed Modular Reactor (PBMR-400), where the helium coolant with a high mass flow rate exerts large drag force on a pebble that is higher than the pebble gravity. Most existing analyses on PBRs, however, assume that the pebble flow properties are not significantly affected by the coolant flow.

The goal of this thesis is to investigate the fundamental principles of the pebble-coolant flows that determine the pebble flow packing density and velocity profile, and to identify the degree of the fluid-pebble interaction effect on the pebble flow properties as well as the pebble wear. The Discrete Element Method (DEM) is adopted to model the pebble flow accounting for all the inter-pebble, pebble-wall contact physics. For the coolant flow modeling, due to the large scale of PBR cores, it is computationally prohibited to use rigorous microscopic approach such as Direct Numerical Simulation (DNS) for a full core analysis. Volume averaged Computational Fluid Dynamics (CFD) approach is employed to analyze the coolant motion, with an empirical drag model and an effective viscosity model introduced for closure. The pebble flow packing density distribution, velocity distribution and contact force/stress distribution are calculated. The computational results for HTR-10 (which is a small scale gas-cooled PBR) and PB-FHR cases are compared to analyze the effect from the coolant fluid on the pebble flow dynamics.

In order to theoretically understand how the pebble packing density and velocity profile are affected by coolant fluid, the mesoscale granular strain and stress are introduced to illustrate the cell volume-averaged pebble flow behavior. In order to theoretically analyze the easiness for a pebble assembly to be affected by external shear stress, the empirical law between packing fraction and inertial number, and the relation between granular friction coefficient and inertial number are used.

For the HTR-10 design, the fluid-induced shear stress is very low compared with local granular pressure and therefore barely changes the granular friction coefficient. This means that the local pebble flow shear rate and packing density will not be greatly affected by the fluid. For the large scale annular core PBMR-400 design, despite of much larger fluid force, the fluid effect is similar to HTR-10 where no appreciable bulk packing fraction difference or axial pebble flow velocity distribution change are observed, although the much larger contact force brings in pebble wear concern. For the PB-FHR design, the fluid effect on pebble flow packing density is prominent at the near wall region of the lower core. Other pebble flow quantities in PB-FHR, such as pebble rotation rate and radial gradient of axial pebble flow velocity will also be affected by the molten salt coolant significantly in the bulk region that close to the outlet.