## 5 Post-Test Numerical Analysis
### The RELAP5-3D Model  
As compared to the work presented in [15], given the different aim of these post-test and validation analyses, the model includes only the mock-up and the connected pipes extending upstream to the position where the inlet temperature sensors downstream to the flow meters instead of the whole HELOKA loop (Figure 20). Since the helium flow boundary conditions were taken from the experiment, this choice allowed a substantial reduction in the computational time while still preserving the relevant information concerning the experiment. The modeled ancillary pipes are:  
* The inlet pipes from the position of the inlet coolant temperature sensors up to the FWMU nozzle (volumes in light green in Figure 20). These inlet pipes are not reproduced for channels 6-10, as the sensor placed on a straight pipe has a length of less than 10 cm;
* The outlet pipes (volumes in gray in Figure 20);
* The outlet headers up to the position of the flow meters (volumes in dark gray in Figure 20).  
The adopted model mainly consists of pipe components connected together by means of single junctions. The number of nodes of each pipe was chosen after a sensitivity analysis aimed at reducing the influence of the spatial discretization on the results. The inlet conditions of the ten FWMU channels (red and blue volumes in Figure 20) were imposed with ten time-dependent volume, while the total mass flow rate through each branch of the FWMU was imposed by means of two time-dependent junctions reproducing the flow meters on the outlet headers. Because of the few sensors installed at the inlet of the FWMU, the same inlet coolant temperature was adopted for channels 1-5 and 6-10 based on the reading of the sensors installed on channels 3 and 8. The inlet pressure in channels 1 and 5 was assumed as a mean value of the readings from the sensors installed in channel 2, 3, and 4. A similar approach was also adopted for channels 6 and 10, but the values from the sensors installed on channels 7, 8, and 9 were used instead.  
Three physical models of the RELAP5-3D code were required to reproduce the experimental tests [17]:  
* The hydro-dynamic model to reproduce the pressure drop through each channel. In the 0% valve opening scenario backflows in some FWMU channels occurred because of the low mass flow rate. The magnitude of these backflows depend on the equilibrium between the pressures drops in forward and reverse directions in a single channel as well as the equilibrium between the pressure drops among the five channels belonging to the same inlet and outlet branch.
* The heat transfer between the coolant and the heated surface in steady and transient conditions. Several correlations were available to reproduce this phenomenon, but the Gnielinski correlation [18] was deemed the most appropriate one, as mentioned in [19].
* The conduction of the heat through the thickness of the heated surface (axial heat transfer). As a matter of fact, the heat coming from the electron beam gun was partially removed by the coolant and partially transferred to the non-heated channels because of the conduction occurring through the thickness of the top plate. This phenomenon plays a major role in the LOFA scenarios and can be considered in RELAP5-3D through the activation of the conduction enclosure model.