# CFD Assessment of Car Park Ventilation System in Case of Fire Event
## 2 Materials and Methods
### Simulation Setup in OpenFOAM
#### 2.3.3 Integration of Beams as Porous Medium and Jet Fans as Momentum Sources  
A simplified approach is utilized to assess the effect of multiple beams distributed throughout the parking area. In this approach, the beams are treated as porous mediums with an infinite pressure gradient, effectively functioning as solid walls without air penetration. The modeling technique employed for this purpose is the Darcy-Forchheimer porous medium model. According to this model, the flow rate (\(Q\)) of any fluid into the porous medium bed is directly proportional to the filter area (\(A\)) and the difference in fluid head  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Static Pressure [Pa]** & **0** & **50** & **100** & **150** & **200** & **250** & **300** & **400** & **500** & **600** \\ \hline
**Flux [m\({}^{3}\)/s]** & 22.3 & 21.9 & 21.39 & 20.86 & 20.31 & 19.75 & 19.17 & 17.9 & 16.45 & 14.6 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Flux and static pressure values for inlet/outlet axial fans obtained from manufacturer-provided data.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Boundary** & \(p\)**[Pa]** & **\(U\) [m/s]** & **\(K\) [m\({}^{2}\)s\({}^{-2}\)]** & \(\varepsilon\) [m\({}^{2}\)s\({}^{-3}\)]** \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Inlet/outlet \\ (supply/exhaust) \\ shafts) \\ \end{tabular} } & Type: fanPressure—patchType: & pressure—file: & & & & \\  & total Pressure—file: & letOutletVeloicity— & fixedValue—value: & fixedValue—value: & \\  & fanCurve—direction: in & value: uniform & \$internalField: uniform & SinternalField: uniform & SinternalField: uniform \\  & (supply) or out (exhaust)—\(p0\): & & (0,0,0) & 0.375 & 14.855 \\  & uniform 0 & & & & \\  & fixedValue—value: uniform 0 & & zeroGradient:\(\frac{\partial U}{\partial n}=0\) & zeroGradient:\(\frac{\partial k}{\partial n}=0\) & zeroGradient:\(\frac{\partial k}{\partial n}=0\) \\ \multirow{2}{*}{
\begin{tabular}{c} Walls \\ \end{tabular} } & zeroGradient:\(\frac{\partial p}{\partial n}=0\) & fixedValue—value: & kqRWallFunction— & epsilonWallFunction— & value: SinternalField: & value: SinternalField: \\  & uniform (0,0,0) & uniform 0.375 & uniform 14.855 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Definition of boundary conditions in OpenFOAM.  
between the inlet and outlet of the medium (\(\Delta h\)), while being inversely proportional to the thickness of the bed (\(L\)), as follows [32]:  
\[Q=\frac{C\times A\times\Delta h}{L} \tag{6}\]  
The Darcy-Forchheimer model [33] works as a sink in the momentum equation. To implement the beams as porous media, the elements confined by the beams (or beam coordinates) must be defined in the topoSet dictionary and adjusted in the porousityProperties dictionary in OpenFOAM.  
In contrast, the induction fans in this study are defined as momentum sources. These momentum sources introduce a source term in the momentum equations that acts in the opposite direction to the porous media. To incorporate the induction fans into the simulation, the corresponding cellZones must be defined in the topoSet dictionary. Subsequently, all necessary adjustments will be made in the fvOptions dictionary. The velocity of the momentum sources is assumed to be 22.3/11.2 m/s, based on the specifications provided for the jet fans (see Section 2.1.3).