High-fidelity simulation of pebble beds: Toward an improved understanding of the wall channeling effect

TL;DR

This paper improves porous media models for pebble bed reactors by investigating flow phenomena near walls, focusing on geometric and flow features like surface area and turbulence to better predict flow diversion effects.

Contribution

It explores the geometric and flow factors influencing the empirical correlation between form loss coefficient and local porosity, enhancing the pressure drop model for PBRs.

Findings

Correlation between form loss coefficient and local porosity established

Relationship between surface area to volume ratio and porosity identified

Inverse relationship between TKE production and porosity observed

Abstract

Wall channeling is a phenomena of interest for Pebble Bed Reactors (PBRs) where flow is diverted into high-porosity regions near the wall. This diversion of flow can have a significant impact on maximum fuel temperatures and core bypass flow. Porous media models that are currently used to model PBRs for design scoping and transient simulation are lacking in their capabilities to model the wall channel effect. Recent efforts at Penn State have produced an improved porous media pressure drop equation that is more capable of modeling the velocity variations caused by the wall channel effect in a porous media model. Several pebble beds were divided into concentric rings of $0.05D_{peb}$, and average flow quantities and porosities were extracted for the ring. A correlation between the form loss coefficient and the local ring porosity was found, allowing for the addition of a correction factor to the form loss term of the KTA equation. The developed correlation was purely empirical, and thus a more thorough understanding of the underlying flow phenomena is desired. This study investigates geometric and flow features that can explain the observed correlation between the form coefficient and the local porosity that was used to generate the improved pressure drop equation. The solid surface area to volume ratio $S_v$ along with the production of Turbulent Kinetic Energy (TKE) is analyzed. A relationship between $S_v$ and the local porosity and an inverse relationship between the negative TKE production and the local porosity were found, pointing to the idea that inertial effects caused by different pore geometry in each ring contribute to the variation of the form constant with the local porosity.