## 3 WCLB BB Performance
### Magneto-Hydrodynamic (MHD) Performance  
Concerning the WCLL BB magneto-hydrodynamic (MHD) performance, a series of local and global studies has been carried out. In particular, local MHD analyses were performed through direct numerical simulation with both ANSYS CFX and FLUENT. The system-level assessment of MHD pressure loss in the PbLi loop was carried out with a semi-analytical model that integrated theoretical relations and numerical results. The simulations of the BZ considered two different regions of the design: the radial channels and the frontal PbLi region close to the FW. Geometrically, both regions were found to have very different degrees of complexity, mainly due to the density and shape of the water tubes (Figure 3). In order to simplify the analyses, these two regions were treated separately. The radial channels were first analysed using a fully developed model. This kind of models assumes that far enough from the 3D elements, the induced currents are cross-sectional (2D). The simulations enabled the computing of the influence of the conductor tubes on the steady-state PbLi velocity profile (Figure 16). The presence of water tubes disturbed the induced current distribution, thus producing zones of different velocities in their vicinity. Heat transfer computations in the radial channels were carried out afterwards using the 2D MHD velocity profile as an input. It was found that heat transfer by advection could be significant in these regions. Unfortunately, fully developed models do not allow one to compute buoyancy effects in radial channels. The maximum temperature at the PbLi/EUROFER interface was found to be 580 \({}^{\circ}\)C (Figure 17), slightly above the temperature limit. Figure 15: Mass flow rate computed in each elementary cell equivalent pipe. The second group of analyses were dedicated to the frontal region of the BZ, close to the FW [31]. These needed to include buoyancy interactions since it is expected that they play a major role in this region. Therefore, 3D magneto-convection simulations were carried out. The system of study only included the FW region of one of the six parallel circuits of the BZ (the second or the fifth circuit). Additionally, in order to use a structured mesh (increasing the stability of the solution), the geometry as simplified. The tubes were assumed to be oriented along the toroidal direction, neglecting the 3D effect caused by the tube curvature. This simplification could have a significant impact in the region next to the radial channels, but it is not expected to significantly affect the regions closer to the FW, which were the main object of interest of the analyses (see tube layout in Figure 6). Figure 18 depicts the velocity stream lines and temperature contours in the central radial-poloidal plane obtained in the transient simulations after 200 s. The presented results correspond to a situation with a moderate Hartmann number (Ha = 1000). The gravity field was adjusted to maintain the actual ratio between buoyancy and Lorentz's forces. This was done because it was found that, with the employed mesh, it was hard to preserve stability and charge conservation for Ha values higher than 3000. Figure 16: Velocity profile of an inlet radial channel with three tubes embedded in the flow. Figure 17: Temperature field at the PbLi/EUROFER interface in one central radial channel. According the obtained results, medium-size convective vortexes oriented with the magnetic field were formed next to each tube and next to the FW. The simulation confirmed that the PbLi almost exclusively moved via natural magneto-convection in most of the FW region. Indeed, no appreciable effects caused by the inlet velocity or temperature of the radial channels in most of the domain were found. The temperature distribution was very similar to the one obtained using a pure conductive model, and no hotspot above the EUROFER temperature limit was found.