# Computational Fluid Dynamics of Compartent Fires: A Review of Methods and Applications
## 3 CFD Simulation in Compartment Fires
### Physical Models
#### 3.3.5 Extinction  
When either the local concentration of the fuel or oxygen, or the local temperature is too low to sustain the combustion process (reducing the heat feedback to the fuel source), thermal quenching happens which is known as extinction [113]. Modeling the extinction in fire and flame is always challenging [114]. Especially as it is not totally clear in compartment fires as it is caused by various factors including the concentration of the existing oxygen, critical flame temperature, radiative heat feedback to the fuel, etc. [115; 116; 117; 118; 119].  
According to [PERSON] et al. [120], CFD tools used for simulations of compartment fire consider one of the following elements:  
* A critical flame temperature (CFT) (a constant value in the range of 1450-1780 K) which does not consider the effects of turbulence [121];
* A critical Damkohler number to model flame extinction, which is defined as Equation (6). \[Da=\frac{\tau_{mixing}}{\tau_{chemical}}\] (6) where \(\tau_{mixing}\) is the characteristic time of the mixing between fuel and air and \(\tau_{chemical}\) is the characteristic chemical time. Extinction is expected to happen for low \(Da\) values [114].  
FDS provides two different extinction models, both considering the CFT concept. In the first model, flames cannot sustain combustion if insufficient thermal energy is available to maintain the chemical reactions. In other words, the flame is assumed to extinguish if the gas temperature drops below CFT; if the temperature is more than 600 \({}^{\circ}\)C, the flame does not extinguish as long as the oxygen concentration is not zero. On the other hand, the second model does not only rely on CFT, but also considers the availability of fuel and oxygen to ensure that the temperature will be higher than CFT [62]. Figure 7 illustrates the range of extinction or flammability for different modeling approaches in FDS.  
ISIS also utilizes the second extinction model like FDS (right hand side in Figure 7) [41]. In OpenFOAM, extinction is typically handled within combustion solvers through sub-models for turbulence-chemistry interaction, combustion, and heat transfer. These sub-models evaluate the conditions under which fires disappear, focusing on parameters such as temperature and oxygen concentration.  
Using a Damkohler number as a flame extinction criterion (instead of the approach that compare the LES-filtered temperature with a critical ignition temperature to determine whether the fire is extinguished or re-ignites [114; 122]) in compartment fire was the main objective of [PERSON] et al.'s [114] study. They used the global combustion equation (GR1) for the combustion modeling, while defining two more reactions in which fuel being  
Figure 7: Schematic diagram of extinction criteria in FDS based on CFT and oxygen concentration. Extinction Model 1 (**left**) and Extinction Model 2 (**right**). Adopted from FDS User Guide [62].  
converted to non-burning fuel and re-ignition of the non-burning fuel occurs. Flammability or the extinction of the fuel (flame) is specified based on whether the Damkohler number is greater or smaller than the critical value, respectively. A critical Damkohler number close to one is the criteria for the extinction regardless of other thermal or aerodynamics effects, according to [PERSON] et al. [114].  
It should be noted that considering extinction within the capability of combustion models mentioned in Section 3.3.2, and according to [113, 123, 124], quoted by [PERSON] et al. [88], IFC and EDM are not able to model the extinction while FGM is, making FGM as a good choice for compartment fire modeling.