## 2 Thermal Analysis and Design Improvement of the WCLL COB Segment TC Region
### The TC Region Reference Design Configuration
#### 2.1.1 The TC Region FEM Model  
In order to assess the thermal behavior of the TC region reference geometric configuration, a realistic 3D FEM model is set up. In particular, it reproduces the WCLL COB upper slice, housing the TC, plus two adjacent parallel slices (Figure 2). Hence, the model includes the TC together with the proper portions of the 2 mm thick tungsten layer, the SB, the horizontal and vertical stiffening plates (SPsh and SPsv), the BSS and, finally, the foreseen DWTs conceived according to the v06a layout. As to the latter, 22 DWTs per slice are included in the adjacent parallel slices, whereas 16 tubes are included in the slice housing the TC. Moreover, the PbLi breeder is modeled too, as shown in Figure 2. Lastly, the cooling water flow domain is not directly modeled, in order to speed up calculations and allow to investigate a wide range of configurations. Nevertheless, its effect is properly taken into account by means of a specific boundary condition aimed at the simulation of its convective heat power removal.  
Figure 1: The top cap region reference geometric configuration.  
A spatial discretization grid composed by \(\sim\)5.9 M nodes connected in \(\sim\)4.6 M tetrahedral and hexahedral linear elements is set up for the thermal analysis. Details of the mesh are shown in Figure 2. The mesh features adopted for this study (element type and average size, meshing methods, element growth rates) are inherited from previous studies developed in this field, and they are able to ensure a very good compromise between accuracy of the results and computational burden saving.  
Figure 2: The 3D FEM model of the TC region plus adjacent slices—details of the mesh.  
Then, the following loads and boundary conditions are applied to assess the thermal performance of the TC region under the WCLL BB normal operation steady-state scenario, according to the provisions of the WCLL BB load specifications [11]:  
* Non-uniform heat flux on the tungsten armor plasma-facing surface, characterized by a maximum value \(\Phi_{\text{FW}}\) equal to 0.24 MW/m\({}^{2}\)[12] on the straight FW decreasing to 0 by a cosine law on the bend tungsten surfaces according to the formula \[\Phi(\theta)=\Phi_{\text{FW}}\cdot\cos{(\theta)}\] where the \(\theta\) angle is defined so as to be equal to 0\({}^{\circ}\) at the FW straight-bend interface and 90 \({}^{\circ}\) at the end of the FW bend (Figure 2).
* Non-uniform nuclear 3D power density, given by the heat power deposited within the structural and breeder materials by neutrons and gammas, drawn from [13].
* Non-uniform decay 3D heat power density, given by the heat power deposited by the gamma decay of activated nuclei, drawn from [14].
* Convective heat transfer between water and cooling channels/DMTs, simulated by a simplified approach foreseeing a unique bulk temperature for each channel (Tbulk) and convective heat transfer coefficients (HTCs) initially calculated using the Dittus-Boelter correlation and determined by means of a proper iterative procedure [15]. As an example, the imposed Tbulk and the HTCs calculated at the end of the iterative procedure for the thermal analysis of the reference TC region are 311.5 \({}^{\circ}\)C and 31407 W/(m\({}^{2}\)\({}^{\circ}\)C) for TC and FW-SWs channels, 307 \({}^{\circ}\)C and 17420 W/(m\({}^{2}\)\({}^{\circ}\)C) for the 1 st round of DWTs, and 323.5 \({}^{\circ}\)C and 27257 W/(m\({}^{2}\)\({}^{\circ}\)C) for the 2 nd round (i.e., the recirculation groups) of DTWs.
* Imposed temperature to the water manifolds regions, equal to 311.5 \({}^{\circ}\)C, corresponding to the average temperature between the water inlet and outlet.  
The temperature-dependent material properties available in [16; 17; 18] are implemented in the FEM model for the considered materials, namely Eurofer, PbLi and tungsten, respectively.