# Investigation of Point-Contact Strategies for CFD Simulations of Pebble-Bed Reactor [PERSON]
## 2 Materials and Methods
### Mesh Sensitivity  
Tetrahedral, hexahedral, and polyhedral mesh generation approaches were tested for each contact strategy. The bridging and diametral increase strategies resulted in a singular, complex body of all the fuel-free spherical shell regions. The parallel load distribution step required more computational time to decompose this body across the compute nodes. The capping and diametral decrease strategies resulted in many simple bodies. These geometries were significantly faster for interfacial definition (imprinting) and parallel discretization. Fully conformal meshes were generated using polyhedral and prism layer meshing operations. The Surface Remesher performed surface vertex re-tessellation of the 3D CAD to optimize surface faces based on the target edge length and proximity refinements. In the Polyhedral Mesher process, a tetrahedral mesh is first generated for the input surface. Second, the polyhedral mesh is generated from the underlying tetrahedral mesh. The Prism Layer Mesher generated a subsurface to extrude a set of prismatic cells from the solid-fluid interfaces into the core mesh of the fluid region. The sensitivity of the discretization on fluid flow and heat transfer behavior was quantified by performing mesh sensitivity studies for Cases 1-2. The Case 1 study is discussed in detail for each contact strategy. The diametral increase and bridging strategies had similar grid requirements. The diametral decrease and capping strategies required additional grid refinement to improve the prediction of the local velocity gradient in the small fluid pathways near the contact point. This refinement was also needed to achieve mesh independence for the pressure drop across the bed. For brevity, only the results from the bridging strategy are presented here. Coarse, medium, and fine meshes were generated using base cell sizes of 10 mm, 2 mm, and 0.7 mm, respectively. The resulting numbers of cells for each mesh were \(2.4\times 10^{6}\), \(7.4\times 10^{6}\), and \(41.0\times 10^{6}\). Figure 2 presents cross-sections of the bed for each mesh resolution. To evaluate the numerical discretization error, estimate the rate of grid convergence, and determine an acceptable mesh density for this problem, the widely accepted Richardson extrapolation technique [25] was used. QOIs were selected to quantify the grid convergence:  
* Volume-averaged pebble fuel temperature, \(T_{avg,\_fuel}\);
* Maximum pebble fuel temperature, \(T_{max,\_fuel}\);
* Volume-averaged fluid temperature, \(T_{avg,\_fluid}\);
* Volume-averaged fluid velocity magnitude, \(v_{avg,\_fluid}\);
* Maximum fluid velocity magnitude, \(v_{max,\_fluid}\);
* Surface-averaged fluid temperature on plane Z2 (z = 0.1 m), \(T_{avg,\_fluid,\_trans}\);  
Figure 2: Cross-sectional views of (**left**) coarse, (**middle**) medium, and (**right**) fine meshes used in the mesh sensitivity study for Strategy 3 (bridging). * Surface-averaged fluid velocity magnitude on plane Z2 (z = 0.1 m), \(v_{avg,fluid,trans}\);
* The pressure drop across the entire bed, \(\Delta P_{bal}\). The convergence of each dispQOLQIQI, \(\phi_{i}\), is shown in Figure 3 as a function of a 3D unstructured grid representative cell size, \(h\), and normalized by the extrapolated QOI with an infinite grid density, \(\phi_{extrap}\). For the coarse, medium, and fine meshes, \(h_{i}\) was defined as 2.15, 1.50, and 0.84 mm, respectively, using the definition of  
\[h=\left[\frac{1}{N}\sum_{i=1}^{N}(\Delta V_{i})\right]^{1/3}. \tag{19}\]  
Macroscopic plQOI, such as the volume-averaged metrics, had similar behavior and rates of convergence across the various contact strategies. For the coarse mesh, all relevant plQOI were within 3% of an extrapolated solution with an infinite grid density, except for the velocity magnitude selected at an arbitrary point in the bed. This discretization error was reduced to nearly 1% for all plQOI for the fine mesh.