# Computational Fluid Dynamics of Compartent Fires: A Review of Methods and Applications
## 3 CFD Simulation in Compartment Fires
### Computational Mesh  
CFD models divide the room volume into thousands of small cubicles or control volumes. Differential equations are solved for each control volume in space and time, resulting in point-to-point fluctuation in the characterizing variables [27; 28]. Therefore, numerical simulation of compartment fires requires discretizing the computational domain into a grid or mesh, where governing equations of fluid dynamics, heat transfer, and combustion are solved numerically. FDS adopts rectilinear volumes (cubic meshes) and uniform meshing [12], while OpenFOAM and ISIS can utilize cubic and unstructured grids such as tetrahedral, polyhedral, and hybrid meshes [29].  
[PERSON] et al. [30] studied the effects of extending computational domain on numerical simulation. It was found that the extended domains created more similar results to the real fire scenario. Therefore, in compartments with an opening in the boundary walls, the computation domain should be extended beyond the physical or geometric boundary.  
[PERSON] et al. [31] investigated the effects of extending computational domain and grid size on the numerical simulation of propane fires in an enclosed compartment. Their results indicated that the simulation being limited only to the compartment boundaries influenced the ventilation effect and as a result, affected the predicted HRR. They recommended that the numerical domain should be extended more than half the hydraulic diameter of the door for a fuel-controlled fire, and the full hydraulic diameter for a ventilation-controlled fire.  
In a compartment with a vertical opening, the domain should be extended in the perpendicular direction of the opening and in relation to the heat release rate of the fire  
Figure 4: Required steps for CFD simulation of compartment fire.  
and the hydraulic diameter of the opening, according to [PERSON] et al. [32]. In other words, the greater the heat release rate of the fire, the more extended the domain should be.  
While [31] and [32] proposed Equation (1) for the domain extension, [PERSON] et al. [33] modified it to cover the HRR dependency on the transition phase between over-ventilated and under-ventilated fire. The optimized value of the domain extension was recommended as Equation (2):  
\[Domain\ Extension=\begin{cases}0.5\times D_{H},&\quad Fuel\ Controlled\\ D_{H},&\quad Ventilation\ Controlled\end{cases} \tag{1}\]  
\[Domain\ Extension=\begin{cases}\begin{array}{c}0.6\times D_{H},&0<\alpha \leq 0.5\\ D_{H},&\alpha>0.5\end{array}\end{cases} \tag{2}\]  
where \(D_{H}\) is the hydraulic diameter of the door and \(\alpha\) is the room aspect ratio.  
The mesh grid independency check is one of the essential tasks which should be performed in the numerical modeling in order to optimize the simulation time [17]. [PERSON] [34] was among the first to use explicit concept of the characteristic fire diameter in compartment fire modeling and described it as Equation (3):  
\[D^{*}=\left(\frac{\dot{Q}}{\rho_{\infty}c_{p}T_{\infty}\sqrt{\dot{g}}}\right) ^{\frac{2}{5}} \tag{3}\]  
where \(\dot{Q}\) is the maximum heat release rate, \(g\) is gravity, and \(\rho_{\infty}\), \(c_{p}\), and \(T_{\infty}\) are the density, specific heat, and temperature of the ambient air, respectively. The ratio of characteristic fire diameter to the grid size should be more than 10 for reliable results [35].  
According to [PERSON] et al. [36], quoted by [PERSON] and [PERSON] [37], in a numerical simulation of a pool fire, a minimum number of 20 cells are required in the pool diameter to obtain a good prediction of the experimental measurement. However, [PERSON] and [PERSON] [38] later recommended having at least 10 cells across the burner as a 'rule of thumb'.  
[PERSON] et al. [39] studied the numerical simulation of pool fires in a compartment and found out that finer mesh grids adjacent to the fire source can improve the temperature predictability of the model.