## 2 Numerical Models
### Simplified Fire Model  
As an alternative to the EDC combustion model, we have modeled the fire by directly introducing the gases generated from combustion, at temperature \(T_{\text{in}}\), through an inlet section of area \(A_{\text{in}}\), with a mass flow rate \(\dot{m}_{\text{in}}\).  
The combustion products constitute a mixture that is assumed to behave as a conserved scalar, whose properties (viscosity, thermal conductivity, mass diffusivity and molecular weight) are the average of those of its constituent species. The distributions of mass fractions of species are determined from the conserved scalar concentration and mass fractions \(Y_{\text{in,CO}_{2}}=0.1912\), \(Y_{\text{in,H}_{2}\text{O}}=0.0894\), and \(Y_{\text{in,N}_{2}}=0.7194\) at the fire focus. For a different composition of the combustion gases, the transport of CO and other species could be carried out in a similar way. Thus, the problem would be reduced to knowing the amount of CO and other species produced at the fire focus, which, in turn, would depend on the type of material burned and the ventilation conditions. As indicated above, in order to be realistic, the complex analysis of the influence of different types of burning materials on the evolution of the fire has been left outside the scope of this work.  
In the simulations involving both FDS and FLUENT the temperature dependency of the specific heats of carbon dioxide, water vapor and nitrogen, \(c_{p}^{i}\), was expressed by a 4 th order polynomial function \((c_{p}^{i}(T)=\sum_{j=0}^{4}k_{j}^{i}T^{j})\) and, in the case of air, by a 7 th order polynomial function \((c_{p}^{\text{air}}(T)=\sum_{j=0}^{7}k_{j}^{\text{air}}T^{j})\). This is the default option in FDS. The data in the FLUENT and FDS databases are very similar, although the default option in the former is to set the specific heat of any species as constant. The molecular weight, \(M_{\text{in}}=28.57\) g mol\({}^{-1}\), and specific heat, \(c_{p}^{\text{in}}=\sum_{j=0}^{4}k_{j}^{\text{in}}T^{j}\), of the mixture are calculated as  
\[M_{\text{in}}=\sum_{i=1}^{N}X_{\text{in},i}M_{i};\ c_{p}^{\text{in}}(T)=\sum_{ i=1}^{N}Y_{\text{in},i}c_{p}^{i}(T), \tag{1}\]  
where \(N=3\) is the number of species and \(X_{\text{in},i}\) the molar fraction of species \(i\).  
The rate of heat convected through the inlet section is calculated as  
\[\text{HRR}=\dot{m}_{\text{in}}\int_{T_{\text{ref}}}^{T_{\text{in}}}c_{p}^{ \text{in}}(T)\,\text{d}T, \tag{2}\]  
where the ambient temperature, \(T_{a}=300\) K, is set equal to the reference temperature \(T_{\text{ref}}\), and \(\dot{m}_{\text{in}}=\dot{m}_{\text{in}}v_{\text{in}}A_{\text{in}}\). Here, \(\dot{m}_{\text{in}}=p_{a}M_{\text{in}}/(R_{u}T_{\text{in}})\) is the density and \(v_{\text{in}}\) the velocity of the mixture of gases at the inlet section (\(p_{a}\) is the ambient pressure). It is assumed that the temperature, density, velocity and composition of the gas entering the domain are time-independent and uniform across the inlet section. Note that, once heat release rate (HRR) and \(A_{\text{in}}\) are fixed, the choice of \(T_{\text{in}}\) determines \(v_{\text{in}}\) and, thus, the mass flow rate, \(\dot{m}_{\text{in}}\). One of the goals of this paper is to determine whether the effects of turbulent mixing and flame radiation on fire evolution, in regions near or far from the fire focus, are well reproduced for different combinations of \(T_{\text{in}}\) and \(\dot{m}_{\text{in}}\) values.