## 3 Fire Scenario
### Boundary Conditions  
Boundary conditions at the fire focus are applied on a square floor surface area \(A_{\text{in}}\) (\(z=0\)) of the premises where the fire focus is located. In most of the simulations presented in this work a total heat release rate \(\text{HRR}=2.5\) MW is assumed, which lays in the range of typical HRR values (270 to 1200 \(\text{kWm}^{-2}\)) for fires that may occur in shops [31]. When using both the simplified fire model and the EDC combustion model, we assumed that the indicated HRR value (or the mean value around which HRR oscillates in the combustion model) is reached almost instantaneously. Although we could have used a more realistic curve to describe the evolution of HRR, this simplification will facilitate the comparison between codes (while avoiding the introduction of additional parameters) and will not hinder the study of the oscillatory flow through the ceiling vents, a process that is usually settled long before the fire starts to decay, at least for fire scenarios similar to that explored in this paper. When the combustion model is used, we assume that the burning fuel is heptane, with a heat of combustion \(\dot{W}_{\text{hept}}=44.566\) MJ kg\({}^{-1}\)[32]. The default values for all other chemical and physical properties set by the FDS code are assumed. The heptane evaporation speed and fuel burning rate will not be a part of the solution; instead, the above mentioned HRR value is imposed. As mentioned before, the parameter RADIATIVE FRACTION is set equal to 0. In the case of the simplified fire model (Section 2.3), inflow boundary conditions are applied at the inlet section of the fire focus. A mixture of gases with the composition indicated in Section 2.3 enters the domain with a mass flow rate \(\dot{m}_{\text{in}}\), at temperature \(T_{\text{in}}\) and velocity \(v_{\text{in}}\), yielding a convective HRR of \(2.5\) MW. The emissivity of the inlet surface is set to 0 to avoid any additional contribution to the heat release rate due to thermal radiation. To keep the thermal boundary conditions as similar as possible for both the combustion and simplified fire models, zero emissivity and a very small liquid conductivity value at the heptane free surface are imposed. To select a suitable value for \(A_{\text{in}}\), the area to which the fire is expected to spread should be taken into account. A suitable value of the inlet velocity \(v_{\text{in}}\) must also be selected to ensure a realistic ratio between inertial and buoyancy effects [33]. However, such parameters are expected to be less important the further one moves away from the focus of the fire, although their values must be chosen so that the dimensionless HRR (source Froude number [33]) remains representative of buoyant fires:  
\[\text{HRR}^{*}=\text{HRR}/(\rho_{a}c_{p}T_{a}D_{f}^{2}\sqrt{gD_{f}}), \tag{3}\]  
where subscript \(a\) denotes ambient value, \(c_{p}\) is the specific heat of air, \(g\) is the gravity acceleration and \(D_{f}\) is an equivalent fire focus diameter. In all the simulations we will assume an area of the fire focus inlet section \(A_{\text{in}}=3\) m\({}^{2}\), for which the above data provide a value of around 0.42 for \(\text{HRR}^{*}\), which is within the range considered normal for buoyant fires [33]. Table 1 shows the details of the four different combinations (labeled as cases G-1 to G-4) of \(T_{\text{in}}\) and \(\dot{m}_{\text{in}}\), which yield a convective HRR of \(2.5\) MW. The temperature range considered is intended to include the typical average temperatures of the combustion products. The mass flow rate of carbon dioxide is \(\dot{m}_{\text{in,CO}_{2}}=Y_{\text{in,CO}_{2}}\dot{m}_{\text{in}}\).