## 3 Modelling, Parameter Adjustment, and Results
### Burner Modeling  
For the modeling of the burner, three aspects have to be considered:  
* Geometrical aspects: burner dimensions and its location inside the analyzed domain;
* the total amount of heat introduced into the booth by burning the fuel;
* the heat release rate per unit area, HRRPUA (kW/m\({}^{2}\)) evolution over time [30,32,33]. Burner dimensions and location was set in the experiments with the dimensions 0.25 \(\times\) 0.60 m\({}^{2}\), and were located at 0.3 m from the floor and 0.3 m from the outside wall on the longitudinal plane. The FDS software allows for two ways of modelling the heat source: either by introducing the mass of fuel consumed over time, \(Mi\) (kg), or introducing the heat emitted by the heat source over time by the burner, \(S_{q}\) (MJ). In order to avoid the error that might be introduce the type of LPG used in the model, we preferred to use the heat source, instead of the fuel mass. The total amount of heat introduced into the analyzed domain is equal to the real experiment heat release of the burner, \(S_{q}\) (MJ), and was determined as a function of the mass of fuel consumed during the experiment, \(M_{i}\) (kg), multiplied by the lower calorific value of the LPG gas, \(Q_{i}\) (MJ/kg), (Equation (3)) [30]. Thus, the average value of the HRRPUA was evaluated using Equation (3), depending on the measured mass of the gas. \[\rm HRRPUA=\frac{S_{q}(MJ)}{S_{burner}(m^{2})\cdot T(s)}=\frac{Mi(kg)\cdot Qi \left(\frac{MJ}{kg}\right)}{S_{burner}(m^{2})\cdot T(s)}=\frac{0.315(kg)\cdot 3 8\left(\frac{MWs}{kg}\right)}{0.15(m^{2})\cdot 760(s)}=105\left(\frac{kW}{m^{2}}\right) \tag{3}\]  
The profile of the temperature evolution over time is largely influenced by HRRPUA variation over time. In order to establish the correct method of introducing HRRPUA in the FDS, we want to match the profile variation of the temperature over time, obtained from the numerical model to the experimentally obtained profile. Several cases of HRRPUA variation were analyzed in FDS (for each case the total amount of energy released is the same, \(S_{q}\) = 0.315 kg \(\cdot\) 38 MJ/kg = 11.97 MJ = 3.325 kWh): (1) one case with constant HRRPUA value, (2) one case with linear increase of HRRPUA, and (3) three cases with linear decrease of HRRPUA (different slopes of variation). Figure 5: Calibration of the container thermal conductivity; (a) temperature error variation Err \({}^{\circ}\)C and (b) standard deviation of the model error \(\sigma_{\rm Err}\)\({}^{\circ}\)C.  
It can be noticed that, for the increasing HRRPUA, we obtained a temperature profile with values at the beginning of the time monitoring interval that was smaller than the experimentally measured ones and higher towards the end of the monitoring interval (Figure 6). On the contrary, for the decreasing HRRPUA, we obtained a temperature profile with values at the beginning of the time monitoring interval that were higher than the experimentally measured ones and smaller towards the end of the monitoring interval. Our numerical findings are in good accord with the phenomenological aspects. It can be observed (Figure 6) that the closest temperature variation, obtained from the model, to the experimentally measured one is obtained for the HRRPUA introduction with a decreasing linear function, with HRRPUA = 105 (kW/m\({}^{2}\)) and the FDS HRRPUA variation factors F\({}_{\text{t = 0 = 8}}\) = 1.15 (-) (corresponding to HRRPUA = 1.15\(\cdot\)105 = 120.8 kW/m\({}^{2}\)) and F\({}_{\text{t = 760 = 8}}\) = 0.85 (-) (corresponding to HRRPUA = 0.85\(\cdot\)105 = 89.3 kW/m\({}^{2}\)). This observation is correct, from a phenomenological viewpoint; as fuel is consumed, the pressure in the LPG tank decreases and, despite the existence of the pressure regulator, the amount of fuel introduced to the burner slightly decreases over time. All these characteristics were established for the CALIB1 ventilation operation type and further tested for CALIB2 and CALIB3.