## 3 Numerical Model and Modelling Methods  
Fire applications accompanied with buoyancy and low Mach number flows can be solved via FDS, which uses appropriate representations of the Navier-Stokes equations via a second order finite difference numerical scheme. In this paper, FDS version 6.7.1 is used to model all the experimental cases mentioned earlier, where the ventilation boundary conditions of these experiments are unique, and FDS has not yet been tested/validated for these conditions [14; 34]. FDS uses the Large Eddy Simulation (LES) modelling technique where the turbulence model represents the closure of the Sub Grid Scale (SGS) flux term. FDS uses a variation of [PERSON]'s turbulent viscosity model as the default for the SGS closure. FDS models turbulent combustion using a simple mixing method to close the mean chemical source term, and each computational cell is considered as a turbulent batch reactor where the rate of mixing is dominated by turbulence. Therefore, the combustion modelling relies on the turbulence modelling, where the turbulence modelling is highly affected by the LES filter width (cell size), which in turn affects the SGS model and eventually the mixing. The radiative heat transfer is implemented in FDS via the solution of the Radiation Transport Equation (RTE) for grey gas model where the option of using a wide band model is also available. The RTE is solved via a method similar to the Finite Volume Method (FVM) and has some limitations in that the radiation transport is discretized via approximately 100 solid angles, with the option to increase the number of the angles if needed, particularly if targets are located far away from the radiation source. The increase in the number of angles increases the computational time as the radiation model usually accounts for approximately 20% of the computational time. To model the experiments via FDS, the experimental set-up reported above was implemented in the model, where the Type-K thermocouples were modelled to measure the temperature with the same thickness used in the experiments (1.5 mm). The heat flux was calculated using the device named as radiative heat flux and positioned as that for the TSCs and heat flux gauges. The gas species analysers were also modelled via the gas concentration device for the O\({}_{2}\) and CO\({}_{2}\) and located at the same location for the two gas analysers with respect to the different experiments. The flow probes were modelled via flow speed measuring devices located at the horizontal and vertical openings with the direction placed similar to that in the experiments. The fire was represented on a surface with the same location and dimensions as the tray used in the experiments, and the edges of the tray were modelled with the same thickness and material (5 mm thickness, 10 mm lip, and carbon steel as a material); the fire was modelled using the simple pyrolysis model in the FDS. That means the fire was represented via a Heat Release Rate Per Unit Area (HRRPUA) curve corresponding to that measured during the experiments. The computational domain was set to X = 1.12 m, Y = 1.5 m, Z = 0.9 m (e.g., the domain was extended sufficiently from the compartment's walls); the cell size used in all the simulations (except if other cell size is mentioned) was \(\Delta\) = 50 mm and based on the cell size sensitivity analysis conducted by [PERSON] et al. [9]; however, in this study a smaller cell size of \(\Delta\) = 25 mm was used in cases Case C_0.0025 and Case S_0.04 to accommodate the smaller horizontal opening sizes. The fuel was specified via the properties of the PP with a heat of combustion of 43.3 MJ/kg, soot yield of 0.058, CO yield of 0.024, and a radiative fraction of 0.37 [35]. The ambient temperature in the model was adjusted to be 10 \({}^{\circ}\)C to resemble the ambient conditions in the lab during the experiments.