## 3 Modelling, Parameter Adjustment, and Results  
### Introduction  
The purpose of this paragraph is to present the numerical model useful for the fire simulation propagated in indoor environment, in order to understand the temperature evolution in time. The purpose of our study is to understand the relationship between two active systems for fire protection, the ventilation and sprinkler systems, and how the operation of the ventilation system could influence the efficiency of the sprinkler system. These two systems influence one another, by means of the air temperature around the sprinkler position. This is the why we chose temperature as the calibration parameter at a point located close to the sprinkler position (point S24). Besides this main parameter, other criteria are also used for the modelling of this phenomenon. The model is determined on the measured data CALIB1 and tested on the experimental data from CALIB2 and CALIB3.  
The Fire Dynamics Simulator (FDS) solver was used for modelling of fire dynamics and the temperature evolution indoors. FDS is a practical software, commonly used in fire modeling [28; 29]. This software used an approximate form of Navier-Stokes equations, appropriate for low Mach. The large eddy simulation (LES) technique was adopted, in order to handle the sub-grid scale convective motion. FDS requires the geometry of the room, calculation time, choice of the grid density, characteristics of the material for the walls, amount of heat introduced over time, and combustion characteristics, such as the amount of smoke produced, extracted air flow, and so on.  
During the experiment, the locations of the thermocouples (Section 2.5 and Figure 2) are represented by means of the two planes inside the experimental booth. During the numerical simulation, we determined the temperature field all over the simulated domain. The calibration of the numerical model was carried out according to the temperature value of point S24 (Figure 2). This point represents the position of the 24 th experimental thermocouple, and it is located at the intersection of the two planes (horizontal and longitudinal). Moreover, this temperature sensor presents the advantage of being in an approximately median area of the container, in the immediate vicinity of a sprinkler. Sensors in the flame area, hot air outlet, cold air inlet, and immediate vicinity of the envelope have been avoided.  
Figure 2: Graphical representation of the model.  
The real-time modeling solution was adopted, which, as small-scale fire modeling, was not sufficiently studied [30]. The calibration of the numerical model is the process by which the input parameters of the numerical model are determined, so that the numerical model results would be close to those obtained experimentally. The calibration of the model was performed knowing the temperature distribution during the CALIB1 experiment. The order of the model development phases were as follows: the (1) geometry was defined in FDS, (2) boundary conditions and the initial conditions were setup, (3) grid cell dimension of the modelling domain was analyzed, (4) ventilation exhaust setup was introduced in the model, (5) thermal conductivity of the experimental test chamber was calibrated, and, finally, (6) HRRPUA in the model was calibrated, in order to suit the real HRR variation that occurred due to the pressure dropping in the LPG tank. The HRRPUA parameter was left at the end of the calibration process; in order to avoid that, this correction would cover the significant correction of the thermal conductivity of the experimental test chamber.