# Investigation of Point-Contact Strategies for CFD Simulations of Pebble-Bed Reactor [PERSON]
## 2 Materials and Methods  
### Numerical Domain and Material Properties  
Figure 1 presents the computational domain used in this study. A total of 100 pebbles were explicitly modeled using a \(4\times 5\times 5\) structured array. Each pebble consisted of a fuel sphere surrounded by a fuel-free spherical shell. The fuel region represented a homogenization of TRISO particles within a graphite matrix. This region was defined as the power-producing volume with spatially constant volumetric heat sources (Figure 1b). Before making geometric modifications, the fuel region diameter, \(d_{fuel}\), was 0.04 m, and the fuel-free region outer diameter, \(d_{p}\), was 0.05 m. The heat transfer fluid inlet was located at the top of the domain, and the fluid outlet was located at the bottom. Three vertical planar slices were created to the domain to establish surfaces for symmetric boundary conditions. The resulting bed contained 45 whole pebbles and 55 sliced pebbles. The fourth vertical surface of the domain represented a radial reflector wall that was in contact with the pebbles. This surface was specified with a no-slip hydraulic boundary, a convective heat transfer coefficient of 10 W/(m\(\cdot\)K), and a 250 \({}^{\circ}\)C ambient temperature to approximate the thermal pathway through a radial reflector and reactor vessel to a prototypical gas-cooled reactor cavity. All boundary and interfacial conditions are specified in Table 2 for each region. The inlet turbulence parameters of turbulent kinetic energy, turbulent dissipation rate, turbulent viscosity, and turbulent thermal diffusivity were derived from the inlet specifications of 0.01 and 10 for turbulence intensity and turbulent viscosity ratio, respectively. The material properties, except the fluid density, were specified at 6 MPa and 250 \({}^{\circ}\)C. These are independent of temperature and position within the computational domain and are presented in Table 3. The fluid density was determined using a compressible flow solver and the ideal gas approximation. Also, the thermal contact resistance between pebbles was ignored, and the pebble chamfer bridges were treated as if they were made of the same material as the pebble fuel-free region. It is apparent and expected that pebble temperatures \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Region** & **Boundary** & **Condition** & **Value** \\ \hline Pebble fuel region & symmetry & symmetry plane & N/A \\  & fuel to fuel-free & contact interface & conformal conduction \\ \hline Pebble fuel-free region & symmetry & symmetry plane & N/A \\  & fuel-free to fuel & contact interface & conformal conduction \\  & fuel-free to fluid & contact interface & conformal convection \\  & fuel-free to reflector & temperature & 250 \({}^{\circ}\)C \\ \hline Heat transport fluid & symmetry & symmetry plane & N/A \\  & inlet & inlet velocity [1] & \(-3\) m s\({}^{-1}\) \\  & inlet & inlet temperature & 250 \({}^{\circ}\)C \\  & turbulence intensity & 0.01 \\  & turbulent viscosity ratio & 10 \\  & outlet & outlet pressure & 6 \(\times 10^{6}\) Pa \\  & fluid to reflector & temperature & 250 \({}^{\circ}\)C \\  & fluid to fuel-free & contact interface & conformal convection \\ \hline \hline \end{tabular}  
Adjusted for Case 2a (0 m s\({}^{-1}\)), Case 2b (0 m s\({}^{-1}\)), and Case 2c (\(-0.21\) m s\({}^{-1}\)).  
\end{table} 
Table 2: Boundary and interfacial conditions. are sensitive to how the near-wall region of the fluid domain is treated. Conjugate heat transfer problems require both the velocity and thermal boundary layers to be appropriately resolved. The ratio of these boundary layer thicknesses can be estimated by the molecular Prandtl number, \(Pr_{m}\) represented as  
\[Pr_{m}=\frac{c_{p,f}h}{k_{f}}=\frac{\text{viscous diffusion rate}}{\text{ thermal diffusion rate}} \tag{5}\]  
where \(c_{p,f}\) is the fluid-specific heat capacity, \(\mu\) is the fluid-dynamic viscosity, and \(k_{f}\) is the fluid thermal conductivity and yields a \(Pr_{m}\) of 0.664.