## 2 Materials and Methods
### MELCOR Models
#### 2.6.2 Complete Model  
The single-channel mode was used as basis to develop the model to simulate the selected LOFA scenarios. The entire FWMU installation and most of the pipes present in the test section of the HELOKA-HP facility were reproduced paying particular attention to the real geometry and dimensions of the system, still trying to minimize the nodalization influence on the results.  
The MELCOR model for the entire FWMU installation was the result of the merging of ten single-channel calibrated models. Compared to these single-channel models, only a slight modification in the number of CVs modeling horizontal and vertical nozzles was introduced to have a more accurate representation of their real length. The CVs were initially set in non-equilibrium state, and they were filled with pure Helium as a working fluid. Heat structures were employed to model the steel nozzles as well as the FWMU plate. In particular, HSs for the upper and lower part of the plate (henceforth, Top and Bottom plates, respectively) were arranged in order to have a direct correspondence between upper and lower structures. In addition, more HSs were created to reproduce the walls between the tubes. An adiabatic condition was imposed on the outer side of all the structures, except the ones under direct heat load, whereas convective heat transfer coefficients were evaluated by the code itself on the inner side, employing the Dittus-Boelter correlation. The heat load was considered constant for the duration of each test and homogeneous on the whole heated area.  
To compensate for the lack of a conduction model in MELCOR and considering the importance of the heat exchange among neighboring HSs during a LOFA event [4], a  
Figure 3: Single-channel model (out of scale).  
conduction model was introduced through control functions to reproduce the temperature distribution of the top plate of FWMU, especially when under heat load. The model was based on the principle that each rectangular heat structure constituting the top plate exchanges heat with four neighbor HSs, one for each side. The exchanged heat was imposed as an internal power source for each structure through a control function, the value of which was defined as the sum of the contribution from the surrounding HSs, as shown in Figure 4.  
The piping system was reproduced by means of control volumes and flow paths. Given the presence of temperature, pressure, and flow sensors, it was possible to reduce the portion of the facility to be modeled from the position of the inlet temperature sensors up to the flowmeter at the outlet (Figure 2). These pipes are:  
* The inlet pipes spanning from the inlet temperature/pressure sensors up to the Swagelok connecting them with the FWMU nozzles;
* The outlet pipes from the FWMU nozzles up to the two outlet headers (one for Channels 1-5, and the other for Channels 6-10;
* The outlet headers up to the position of the flow meters.  
The piping arrangement adopted in the facility makes the outlet headers the sole flow connections between the channels of each branch (the two branches are independent). For all inlet/outlet pipes and for both headers, a \"doubling\" procedure similar to the one presented for the single-channel model was applied, still considering a maximum influence on the results equivalent to 1/1000 of the lowest pressure in the system.  
Inlet conditions of each tube were set through 10 time-dependent volumes, whilst two time-dependent flow paths were modeled in order to impose the mass flow rate for the two circuits cooling the FWMU. Attention was also paid to the correct reproduction of the pressure losses across the pipes: proper form losses coefficients were employed in the bends or in the segments with flow area variations.