## 2 Methods
### Adopted Model
This operation was performed in order to provide the coupled code with the capability to simulate the thermal stratification phenomena observed in the experimental results inside the pool. In particular, considering the results of a parallel work performed at the University of Pisa focusing on the prediction of this phenomenon in a CFD stand-alone application [22], heat transfer was assumed occurring through the thermal structures of the FPS and of the Fitting volume providing interesting results, the same surfaces are thus again considered for the present coupled calculation. During nominal operation conditions, the pool is in fact heated through these surfaces by the hot fluid flowing inside the CIRCE-loop; during the simulated accident, instead, more complex phenomena occur and heat transfer in both directions may be obtained as clearly highlighted later in this paper. The thermal coupling is achieved adopting an imposed heat flux condition, whose value is calculated by the CFD code, for the RELAP5 domain; the STH code instead provides the CFD domain with the corresponding wall temperature distribution: at each iteration, a check on the supplied heat is performed, assuring the energy balance. The semi-implicit approach was instead adopted for the time-advancement scheme; the flow chart in Figure 4 reports the main steps of this procedure. In the reported picture UCFD and USTH represent the input vectors for the CFD domain and STH code, respectively; YCFD and YSTH are instead the output vectors; the \(\Phi\) operator resumes instead all the internal operations occurring during the processing phase of each code. Eventually, the n apex refers to the current time step, while the k one refers instead to the current internal iteration. Figure 4: Time-advancing scheme. Figure 3: Computational fluid dynamics (CFD) domain boundary conditions. Each time-step is solved iteratively: several internal iterations are performed in order to achieve a suitable matching between the predictions of the CFD and STH codes at the thermal and fluid-dynamic boundaries. In particular, CFD firstly performs its calculation providing RELAP5 with updated values for pressures, mass flow and heat fluxes (Y\({}_{\text{CFD}}\)). RELAP5 subsequently performs its calculation considering the updated boundary conditions (U\({}_{\text{STH}}\) = Y\({}_{\text{CFD}}\)) and returns to the CFD code the updated boundary conditions (Y\({}_{\text{STH}}\)) to be compared with the previous ones. If the resulting changes are sufficiently small (i.e., the obtained residual R is small), the calculation moves to the following time-step; if not, a new internal iteration starts and the calculation for the current time-step is repeated until the convergence criteria are met. An under-relaxation factor of 0.5 was introduced for all the transferred quantities in order to increase the stability of this coupled application. The coupled calculation was performed starting from initial steady-state conditions obtained as a result of stand-alone calculations of the CFD and STH domains and adopting an iterative procedure. After each calculation, the relevant exchanged properties were calculated and provided as boundary condition for the other code until a defined convergence criterium was achieved. Nevertheless, as suggested in [23], the initial conditions of the presently considered PLOFA experiment probably did not completely achieve steady-state yet. As a consequence, in order to better reproduce the temperature distribution in the pool at the beginning of the experiment, the outlet temperature of HERO-SGBT was slightly increased with respect to the measured values and maintained constant during the initial iterative process, without taking into account the STH prediction. This assumption allowed predicting suitable initial conditions for the temperature calculated at the FPS inlet and for the fluid allocated in the bottom part of the pool also providing a good initial estimation for the mass flow rates and the pressure fields at the STH/CFD interfaces.