Modelling the effective thermal conductivity in the near–wall region of a packed pebble bed

Abstract

Inherent safety is claimed for gas-cooled pebble bed reactors, such as the South African Pebble Bed Modular Reactor (PBMR), as a result of its design characteristics, materials used, fuel type and physics involved. Therefore, a proper understanding of the mechanisms of heat transfer, fluid flow and pressure drop through a packed bed of spheres is of utmost importance in the design of a high temperature Pebble Bed Reactor (PBR). In this study, correlations describing the effective thermal conductivity through packed pebble beds are examined. The effective thermal conductivity is a term defined as representative of the overall radial heat transfer through such a packed bed of spheres, and is a summation of various components of the overall heat transfer. This phenomenon is of importance because it forms an intricate part of the self-acting decay heat removal chain, which is directly related to the PBR safety case. In this study standard correlations generally employed by the thermal fluid design community for PBRs are investigated, giving particular attention to the applicability of the correlations when simulating the effective thermal conductivity in the near-wall region. Seven distinct components of heat transfer are examined namely: conduction through the solid, conduction through the contact area between spheres, conduction through the gas phase, radiation between solid surfaces, conduction between pebble and wall, conduction through the gas phase in the wall region, and radiation between the pebble and wall surface. The effective thermal conductivity models are typically a function of porosity in order to account for the pebble bed packing structure. However, it is demonstrated in this study that porosity alone is insufficient to quantify the porous structure in a randomly packed bed. A new Multi-sphere Unit Cell Model is therefore developed, which accounts more accurately for the porous structure, especially in the near-wall region. Conclusions on the applicability of the model are derived by comparing the simulation results with measurements obtained from various experimental test facilities. This includes the PBMRs High Temperature Test Unit (HTTU) situated on the campus of the North-West University in Potchefstroom in South Africa. The Multi-sphere Unit Cell Model proves to encapsulate the impact of the packing structure in a more fundamental way and can therefore serve as the basis for further refinement of models to simulate the effective thermal conductivity.