# Investigation of Point-Contact Strategies for CFD Simulations of Pebble-Bed Reactor [PERSON]
## 1 Introduction  
The primary objective of this study was to identify the optimal strategy to address the point-contact singularity commonly encountered when explicitly modeling pebble-bed reactor cores for CFD simulations. Pebbles modeled as perfect spheres within structured or unstructured beds are in point-contact configurations with the adjacent pebbles (particle-particle) as well as internal reactor vessel and neutron reflector surfaces (particle-wall). This effort investigated structured beds. While unstructured bed flow fields are different, the contact strategy options are the same regardless of if the beds are structured or unstructured. The most desirable contact strategies are those that prioritize minimizing the porosity error as much as possible while providing a thermal connection to enable specifying an effective point-contact thermal resistance. Therefore, the recommended contact strategies and sizing selection are expectedto hold for unstructured beds. Also, a study investigating externally heated unstructured beds reached similar conclusions as this effort with internally heated pebbles regarding the opportunity cost of each strategy and the sizing recommendations [1]. However, the overall conclusions are expected to hold for unstructured beds. Such point singularities must be avoided to discretize the computational domain into finite-volume elements. The commonly used techniques to avoid these point contacts can be placed into two groups, which either decrease or increase the pebble volume. The methods that decrease the volume include decreasing the pebble diameter or charfering the pebble near the point contact. Decreasing the pebble diameter is the most straightforward approach for model building, the least difficult to mesh, and often the preferred starting point. The first 3D explicitly modeled pebble bed with simultaneous heat transfer and fluid flow was investigated in 2004 via a pebble diametral reduction [2]. At that time, and today, the experimental techniques lack the ability to provide detailed local heat transfer measurements for contact strategy validation. The quasi-DNS results of a single FCC unit cell were generated for model development and validation [3]. These quasi-DNS results used the diametral reduction strategy to avoid the point-contact singularity. The authors mentioned that their objective was to keep the inter-pebble gap reasonably small while adhering to the DNS mesh constraints. A 4.2% diametral reduction was chosen, a significantly greater decrease than the values studied in this paper (0.1-1%). The diametral reduction strategy is still used today in modern LES approaches with thousands of explicitly modeled pebbles [4] and DNS simulations with up to 150 pebbles [5]. Such a global geometric change was recognized to significantly alter the bed porosity and pressure drop [1]. Therefore, local geometric modifications are also of interest. The capping method involves chamfering the contacting pebbles and filling the chamfered volume with fluid [6]. There are also global and local increase volume methods that include increasing the pebble diameter or charfering the contacting pebbles near the point contact and filling the nearby volume with a bridge of solid pebble material. Eleven explicitly modeled pebble beds were studied using global diametral increases [7; 8]. However, a range of values did not consider estimating the sensitivity of the diametral increase and making suggestions about the desired amount of overlap. Two disadvantages of the diametral increase strategy include (1) having the potential to introduce new contacts with nearby adjacent pebbles, and (2) the fluid domain meshing is still complex in the small interstices near the original point-contact singularity [1]. Each method has a unique impact on the thermal hydraulic behavior of the bed.