## 3 Methodology for the Numerical Simulation and Results Analysis
### Geometry and Structure  
Dimensions of the model are based on the characteristics mentioned in Section 2 and shown in Figure 1. Although real devices often contain some small asymmetrical parts, they have been neglected here so that the structure of the model is purely axisymmetrical, except at the transition sections, where the through holes are symmetrical with respect to a longitudinal plane. Neglected asymmetrical parts are located on the outer surface of the structure. Therefore, they do not influence the behavior of the inner fluid. Thus, in order to reduce computation cost, and assuming that the studied phenomena are symmetrical,only a half portion of the real system was modeled (from 0\({}^{\circ}\) to 180\({}^{\circ}\)). Therefore, while the real system has a cylindrical shape, the model has a semi-cylindrical shape. Symmetry conditions are applied on the cutting plane (\(x\)-\(y\) plane, with \(x\) being the longitudinal axis and \(y\) being a transversal axis), by imposing the displacements normal to the plane to be zero.  
In real devices, the different parts of the outer structure are welded. In the model, welded joints are modeled as simple planar interfaces with rigid connections. Connections between the rod and its extensions at both ends are rigid. Mechanical connections between the rod extension and the outer structure in the model are representative of real ones. The lower rod extension (on the right of Figure 1) is rigidly connected to the outer structure at the inlet transition, and the upper rod extension (on the left) is pinned to the outer structure at the outlet transition.  
The fuel model is simplified in a homogeneous solid volume instead of several stacked pellets. The cladding is modeled with shell elements (four nodes shell elements based on [18] and referred to as \"\(Q4 GS\)\" in EPX, see [19]); the fuel cylinder and all the other structural parts are modeled with cubic elements (\"\(CUBE\)\" elements in EPX). The average axial, radial, and circumferential dimensions of an element of the outer structure around the main section are respectively about 2.3 mm, 1.5 mm, and 2 mm. Around geometrical singularities, the mesh is finer (axial, radial, and circumferential dimensions of the finest elements located in the inlet transition are about 2 mm, 0.5 mm, and 1 mm). This size is a compromise between (1) the aim of accurately simulating fast variations of pressure and velocity around geometrical singularities and (2) computation cost. The calculation time step and, hence, computation cost depends directly on the mesh size in the structure. Then, for the sake of accuracy, the fluid mesh is adjusted to match the structural mesh. Moreover, as the fluid is inviscid, it is not necessary to refine fluid mesh in the radial direction near the boundary. Figure 3 shows views of the mesh around the inlet and the outlet transitions, where there are the most significant geometrical singularities.  
Every structural part is modeled with its respective material (zircaloy, stainless steel, fuel material). Small pieces such as wires, screws, or sensors are neglected.