## 5 Post-Test Numerical Analysis
### Set-Up of the Best-Estimate Methodology  
The application of the best-estimate methodology passes through four steps. The first step is the selection of the parameters and the responses of interest. For the current scenarios about 100 parameters are considered and categorized as:  
* Concentrated pressure drops at geometrical discontinuities;
* Roughness of the pipes walls;
* Thickness of the FWMU face under heat load;
* Material's properties (thermal conductivity and specific heat capacity);
* Inlet pressure of channels 1 and 5 (both affected by the LOFA);
* Input parameters of the conduction enclosure model.  
In turn, the responses of interest are the outlet pressure and temperature from channels 2, 3, 4, 7, 8, and 9. However, the temperature sensor on channel 7 showed unreliable values, so it was not actively considered in the analysis.  
The second step is the definition of the uncertainty for each parameter. This aspect is one of the most complex ones, because most of the considered parameters are calculated through correlations. The evaluation of the uncertainty of such correlations is not a straight-forward process, and it requires a good knowledge of their applicability range and the conditions for which they were developed for. In this regard, the definition of the uncertainty might be a source of the user's effects, but the numerical framework of the methodology is capable of softening this aspect through the inclusion of the available experimental data.  
The adopted uncertainties are summarized in Table 6. These values were obtained from the data from the tests for determining the hydraulic characteristics of the channels performed on the FWMU [11], and from the data corresponding to the steady-state operation at 300 and 330 kW/m\({}^{2}\) acquired during the testing campaign.  
The third step is the set-up of a strategy to evaluate the influence of each parameter on each response (sensitivity). Several approaches can be followed, but without an analytical solution of the problem only the brute force approach can be applied. This approach is based on the execution of several code runs each characterized by the variation of a single parameter. Usually, each parameter is varied twice; in the first run it is increased by 3-5% and in the second one it is decreased by the same amount. The sensitivity for the specific parameter is then calculated as:  
\[S_{\pi\alpha}=\frac{\alpha^{+}-\alpha^{-}}{r^{+}-r^{-}} \tag{1}\]  
where \(\alpha\) and \(r\) are the parameter and the computed response of interest, respectively. The subscripts + and - denote values assumed (parameter) or calculated (response) in the two runs. The main drawback of this brute-force method is the computational time and the management of the code's runs (twice the number of the parameters selected).  
The fourth and last step is the application of the numerical framework described in [16]. The framework will provide a best-estimate value for each parameter and computed response, together with their best-estimate standard deviations. In due regard, if properly applied the methodology might provide an insight of the capabilities of the employed numerical code. If a remarkable difference still exists between the experimental and best-estimate response the cause could be an undue user's effect or an effective code's limitation. Then, through a detailed analysis of the code models and the user's assumptions it should be possible to identify the source of the discrepancy.