## 2 Materials and Methods
### Numerical Model--Assumptions  
Numerical tests of gas flow were carried out in a closed array, based on the experiment described in Section 2.2 and [11]. A numerical representation of the test rig was developed, following the dimensions shown in Figure 2. The leakages were introduced as physical holes in the skin (modelled explicitly, as they were in the experiment). Numerical tests were conducted following assumptions analogical to the relevant experimental data presented in the paper [11]. The numerical model took into consideration the diversified conditions of the environment outside and inside the measurement chamber, which greatly determined the density of air and fire-extinguishing gases taken for the calculations. The fire-extinguishing gas discharge from the cylinders was not modelled explicitly, nor was the fire within the protected premises, and the impact of the simplifications are discussed in Sections 3 and 4. The calculations were initiated assuming a uniform concentration of the fire-extinguishing gas in the whole chamber volume. In most cases, the assumed fire-extinguishing gas concentration amounted to 45%, which corresponds to 11.5% oxygen concentration (v/v) in the chamber (Table 1). One should note here that the retention time is defined as the time from starting the analysis to reaching oxygen concentration of 13% at any measurement point. The modelling took into account the presence of temperature gradient outside the measurement for better representation of the reference experiment. A constant value of temperature after discharge and mixing of gases in the chamber was assumed, according to the experimental data (Figure 3; Figure 4). Time discretisation was performed with a fixed discrete time step of 0.5 s, and the convergence criteria were analysed: \(10^{-3}\) for continuity, mass transport, the kinetic energy of turbulence (k) and the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline No. & Ar [5w/v] & N215w/v & \(\mathbf{A\rho=d_{0}}\) & Gas Molar & Volume Fraction & Volume & Temp. (total) [K] & Temp. (ins.) [K] & p [ InP] \\  & & & \(\mathbf{d_{0}}\) [kg/m\({}^{2}\)] & Mass M & Oxygen & Fraction Gas & Temp. (total) [K] & Temp. (ins.) [K] & p [ InP] \\ \hline \(1\) & 50 & 50 & 0.192 & 33.557 & 0.115 & 0.45 & 289.75 & 288.45 & 1003 \\ \(2\) & 0 & 100 & \(-\)0.039 & 28.013 & 0.115 & 0.45 & 288.75 & 289.25 & 1003 \\ \(3\) & 10 & 90 & 0.007 & 29.122 & 0.105 & 0.50 & 293.15 & 29415 & 1010 \\ \(4\) & 6.9 & 93.1 & \(-\)0.007 & 28.778 & 0.115 & 0.45 & 290.25 & 291.55 & 1002 \\ \(5\) & 7.8 & 92.2 & \(-\)0.003 & 28.878 & 0.113 & 0.46 & 292.65 & 292.05 & 1008 \\ \(6\) & 7.5 & 92.5 & \(-\)0.004 & 28.845 & 0.115 & 0.45 & 292.85 & 294.35 & 995 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of initial conditions taken for modelling. Figure 4: Initial conditions for numerical calculations—comparison of the air temperature (289–294 K) outside the chamber with the temperature of the mixture of fire-extinguishing gas and air inside the chamber; the scenario numbers refer to Table 1.  
Figure 3: Initial conditions for numerical calculations—comparison of the density (1.185–1.225 g/m\({}^{3}\)) of air outside the chamber with the density of fire-extinguishing gas and air mixture inside the chamber; the scenario numbers refer to Table 1.  
dissipation of the kinetic energy of turbulence (\(\varepsilon\)), and \(10^{-6}\) for the conservation of energy. For the Large Eddy Simulation (LES) solver, the time step was shortened to obtain the convergence. The SIMPLE numerical scheme was chosen for pressure-velocity coupling. Spatial discretisation was performed with second-order upwind schemes, except the momentum equation for the LES model, in the case of which the bounded-central differencing method was used. The gradient was calculated using Green-Gauss theorem, based on node values. The exterior domain was closed with third-type wall boundary conditions (external domain was sealed). However, the volume of the domain was 103 times larger than the internal chamber.