## 3 DEMO HCPB Single Pin Simulation Setup
### OpenFOAM Model  
The OpenFOAM model was set up to calculate temperature, velocity, and tritium concentration fields consistently in a multiphysics simulation frame. On the other hand, existing results should be integrated as far as possible with regard to, e.g., validation questions. Therefore, the model uses the mesh as well as the temperature fields of the designers' 3D CFD simulations, see Figure 2. However, the below OpenFOAM simulation is 2D and uses only a 1\({}^{\circ}\) slice of this mesh. The mesh had to be modified as it did not contain a breeder purge gas return channel. Import of the coolant velocity flow field (via the CGNS file format) to OpenFOAM basically worked, too; however, density and other data turned out incomplete in such a way that advective transport in OpenFOAM did not come out properly. Therefore, both the purge flow and the coolant flow fields are calculated first with OpenFOAM with the original thermal field as constant background field until steady state flow is achieved. During the transient, the OpenFOAM flow fields and the original thermal field remain constant background fields, i.e., thermal and kinetic equations are switched off. Further simplifications are that (a) the neutron multiplier, and (b) the trapping are disregarded, and (c) no pulsed operation is taken into account (this allows interesting steady-state mass balances). The most interesting output quantities are tritium permeation to the coolant flow and tritium inventories in the structures. Figure 3 shows the 2D OpenFOAM mesh with about 8000 cells. This (half) cross-section of a single pin also indicates the purge and coolant flow characteristics. Note that the actual shape of the breeder part \"nose\" towards the first wall side has meanwhile changed compared to Figure 1.  
Figure 1: DEMO helium-cooled pebble bed (HCPB) fuel pin with purge gas loop. Figure 2: 3D temperature field in a 60\({}^{\circ}\) sector of a DEMO HCPB fuel pin [1]. Figure 4 indicates the 1D tritium generation rate as expected from MCNP (Monte Carlo N-Particle code) calculations [13]. This 1D behavior is mapped to the breeder zone region. The corresponding total tritium generation rate for a single pin is 4.38 \(\times\) 10\({}^{-8}\) g/s, which would extrapolate to about 340 g/day for the entire DEMO reactor (disregarding the neutron multiplier contribution). Table 1 summarizes the key numeric parameters used in the below simulations. The purge flow field is laminar flow through a porous media. The fvOptions mechanism of OpenFOAM is used to insert an explicit porosity source to the equations. An isotropic Darcy coefficient of 7 \(\times\) 10\({}^{6}\) m\({}^{-2}\) was selected to receive a homogenous flow field over the breeder cross section. An average purge flow speed of 1 cm/s is assumed as a typical value. The coolant flow field is simulated as turbulent flow using the RANS k-\(\omega-\)SST model, which was also used by the designers [1]. Due to the considerable diffusivity of T in the coolant (about 2 \(\times\) 10\({}^{-6}\) m\({}^{2}\)/s) the precise flow field is not that important. The coolant gas mass flow rate for a single pin is 2.4 \(\times\) 10\({}^{-2}\) kg/s, i.e., about a factor of about 1 \(\times\) 10\({}^{4}\) higher than the purge gas mass flow rate (which explains why the purge gas typically is neglected in designers' thermal analyses). With regard to a leak-tolerant design for DEMO HCPB it is under discussion to raise the purge gas pressure level to the coolant gas pressure level of 80 bar. Therefore, additional simulations with 80 bar purge gas pressure are performed for a first estimate of consequences to permeation and inventories. Geometry and temperature fields are kept the same for comparability; however, this is not intended to suggest that the current DEMO HCPB breeder pin design is operable at 80 bar purge gas pressure, too. Figure 4: 1D tritium generation rate from MCNP calculations [13]. Green: interpolated data for inboard pin; blue: extrapolated data for outboard pin.