## 2 Materials and Methods
### Turbulent Flow Sub-Model Sensitivity Study  
The issues solved within the analysis of smoke and heat spreading are often highly turbulent, and, consequently, the description of the velocity and pressure field has a complicated form. The mainstream turbulence models include Reynolds-Averaged Navier-Stokes (RANS) for an in multiple variants (RANS k-\(\varepsilon\), RANS k-\(\omega\), RSM and others), Large Eddy Simulation (LES) and hybrid models. RANS method solved for sequential time steps in order to capture transient phenomena is referred to as Unsteady RANS (URANS). An in-depth review of the RANS and LES turbulence models was recently published by [PERSON] [41]. Although the flows in fire environment are usually turbulent, it is not necessarily the case in compartments post-discharge of a FES-gaseous system. Dependant on the hydrostatic pressure, the flow into and out of protected compartment may be turbulent or laminar, and the phenomena inside of the protected compartment may be driven mainly by diffusion and buoyancy. Nevertheless, for practical use of the method in ventilated compartments, and in case of fire, the turbulence model will be among the most important sub-models. As a direct discrete solution to Navier-Stokes equations is not possible in a large scale (with a reasonable amount of resources), following four approaches to turbulence modelling were investigated: URANS standard k-\(\varepsilon\), URANS Realizable k-\(\varepsilon\), Reynolds Stress Model (RSM) and Large Eddy Simulation (LES). RANS method applies a time-averaged solution of N-S equations, with the additional decomposition of velocity, pressure and field function into the averaged component and the fluctuation. In order to close the model, the Boussinesq hypothesis is applied, which relates the viscous friction and turbulent Reynolds stress. The total turbulent energy consists of following elements, which eventually lead to the formation of the kinetic energy term (k, 8), and the dissipation rate of the kinetic turbulence energy (\(\varepsilon\), 9):  
\[k=\frac{1}{2}\sum_{i=1}^{3}(\overline{v_{i}^{2}}) \tag{8}\]  
\[\varepsilon=(2\mu_{t}/\rho)s_{ij}^{\prime}s_{ii}^{\prime} \tag{9}\]  
where: \(\
u\)--kinetic viscosity, \(\rho\)--density, \(s\)--Reynolds stress. The turbulent viscosity term \(\mu_{t}\) is determined using the following relation (2.10):  
\[\mu_{t}=C\rho vl=\rho\mathrm{C}_{\mu}\frac{k^{2}}{\varepsilon} \tag{10}\]  
The constants of \"standard\" RANS k-\(\varepsilon\) are: \(C_{\mu}=0.09\); \(\sigma_{k}=1.00\); \(\sigma_{z}=1.30\); \(C_{1z}=1.44\); \(C_{2z}=1.92\). In realizable k-\(\varepsilon\) the turbulent viscosity is described in an elaborate form and forms a new equation that describes the dissipation rate of the kinetic turbulence energy, \(\varepsilon\). The Reynolds stress is calculated as incompressible strained mean, by combining the Boussinesq relationship and the eddy viscosity definition [18]. In the Realizable k-e model the \(C_{\mu}\) is no longer a constant, but a function of the mean strain and rotation rates, the angular velocity of the system rotation and the turbulence fields. It can be computed from Equation (11), with use of additional model constants \(A_{0}\) and \(A_{s}\):  
\[C_{\mu}=\frac{1}{A_{0}+A_{s}\frac{kU^{*}}{\epsilon}} \tag{11}\]  
\(U^{*}\) is computed with the inclusion of not only strains but also rate of rotation tensor, in frame with the angular velocity. The complete explanation of calculation procedure may be found in [18]. The model constants are: \(C_{1\epsilon}=1.44\); \(C_{2}=1.9\); \(\sigma_{k}=1.00\); \(\sigma_{\epsilon}=1.20\). The third RANS approach used in this work--the Reynolds stress equation model (RSM)--is often referred as second moment closure [42; 43]. It can be considered as much more elaborative traditional model, than previously described k-\(\varepsilon\) approach. In RSM model the hypothesis of isotropic eddy-viscosity is abandoned, and the N-S equations are solved for the Reynolds stresses, together with an equation for the dissipation rate.