# Computational Fluid Dynamics of Compartent Fires: A Review of Methods and Applications
## 3 CFD Simulation in Compartment Fires
### Physical Models
#### 3.3.4 Heat Transfer: Radiation Transport
P (\(\Omega\), \(\Omega^{\prime}\)) is the phase function, which describes how radiation from direction \(\Omega^{\prime}\) is scattered into the direction \(\Omega\). The integral over all solid angle \(4\pi\) accounts for scattering contributions from all directions in the direction of interest. Radiation heat transfer is challenging in numerical modeling as this type of energy moves at light velocity, compared to gas or sound velocity [43]. Moreover, this type of heat transfer is computationally expensive and between 50 and 70% of simulation time in LES modeling of combustion is assigned to that [101]. However, there is an option in CFD tools to neglect solving RTE (e.g., \"No Radiation Transport\" in FDS and \"noRadiation\" in OpenFOAM) which may result in almost 20% less CPU time [102; 102]. Different methods in CFD have been developed and are used based on the modeler choice and conditions, being responsible for solving the RTE:  
* PL[103; 104]: This is the simplest method which simplifies the RTE by assuming that radiation is isotropic and diffusive in nature, making it computationally efficient and easy to implement. It approximates RTE based on the spherical harmonics method. It assumes isotropic radiation and works well for optically thick media (such as smoke and flames in fires). P1 is less accurate in optically thin media (to overpredict radiative fluxes from localized heat sources or sinks in optically thin media [104]) but is suitable for optically thick cases, such as fires with heavy smoke. Optically thin media and walls exposed to uncertain boundary conditions may result in the inaccuracy of the P1 method [94]. P1 considers scattering without any additional computational cost [104]. * Discrete Ordinates Method (DOM) [105]: This is is a finite volume method which solves the RTE by dividing the angular space into several discrete directions and solving for each direction. DOM can model anisotropic radiation and complex geometries, although it requires higher computational resources compared to P1, especially when fine angular resolution is needed. Furthermore, in optically thin regions, errors arise because DOM does not inherently treat scattering accurately and can produce ray effects where artificial patterns of radiation appear. * Discrete Transfer Ray-Tracing Method (DTRM) [99]: This method traces rays from heat sources to surfaces, calculating radiation directly along these paths. DTRM assumes negligible scattering and is less accurate in optically thick media or for environments with strong scattering effects such as soot. In flows where fire is dominant (such as compartment fire), soot is the determining factor rather than product gases in thermal radiation [7]. Therefore, DTRM is not a good choice in a CFD simulation of a compartment fire. * S2S Model (opaque Solid): This is a technique to simulate radiative heat transfer between surfaces in systems where the media between the surfaces is non-participating (i.e., it does not absorb, emit, or scatter radiation). This model simplifies radiative heat transfer by only considering radiation exchange between solid surfaces. The S2S model cannot account for the effects of soot, smoke, or combustion gases on radiation, which limits its application. But, in case of compartment fire, it can be used for the radiation model of solid surfaces such as walls, ceilings, floors, furnishing, and objects inside the compartment. Choosing the RTE model can significantly impact the accuracy and computational efficiency of the CFD simulation. In a compartment fire, radiation from the flames, smoke, and hot gases significantly affect heat transfer and make participating media (soot, product gases, etc.) important factors in modeling. As mentioned, P1 can be considered as an appropriate method for optically thick conditions like smoke-filled compartments, but it may struggle with flame radiation and near-wall effects (optically thin conditions).