# Review of Convective Heat Transfer Modelling in CFD Simulations of Fire-Driven Flows
## 5 Applications
### Pool Fires  
The target test case includes the medium-scale (i.e., 30 cm) methanol pool fire (i.e., 19 kW) experiments reported by [PERSON] et al. [60] while the presented numerical results are reproduced from [67]. A cylindrical domain having dimensions 1.5 m \(\times\) 1.8 m was used to model the case. The base mesh consisted of 2 cm cells on the centreline which were then stretched towards the side and top boundaries of the domain (i.e., ratio of initial to final grid size was 1.5). A local grid refinement strategy was then employed in order to have a grid resolution of 0.5 cm in the near-field region of the pool fires (i.e., see Figure 3). Turbulence was modelled with the dynamic Smagorinsky model employing a variable Prandtl number approach. Chemistry was considered to be infinitely fast and turbulence-chemistry interactions were modelled with the Eddy Dissipation Model (EDM) considering a turbulent mixing time scale (i.e., \(C_{EDM}=2\)). Radiation was modelled with the finite volume discrete ordinates model (fvDOM) and the absorption/emission term was modelled through the weighted sum of gray gases model (WSGGM). In total, 72 solid angles were used for angular discretization in the solution of the radiative transfer equation (i.e., with radiation solved every 20 th time step). The characteristic lengths, \(L_{c}\), for the natural and forced convection modelling approaches presented below are chosen as \(L_{c,\ natural}=A_{s}/p=0.075\) m and \(L_{c,\ forced}=D=0.3\) m, respectively (see Section 3.1.3).  
The predicted convective heat fluxes at the methanol pool surface with different approaches for modelling the convection are presented in Figure 4. Overall, a strong grid dependency is observed in the predictions with the approaches based on the effective thermal diffusivity, forced and natural convection (i.e., for all methods directly relying on the first grid cell values when determining the convective heat fluxes). With the use of coarse grid sizes (i.e., few cells across the pool diameter), fuel and oxidiser mix rapidly and produce high reaction rates above the pool surface. As the grid size is refined (i.e., more cells across the pool diameter), a fuel-rich region starts to develop, which then produces lower reaction rates above the pool surface. The result of this is that higher temperature differences (i.e., calculated based on the first grid cell and the surface temperature) are obtained when coarser cells are used as opposed to finer cells. This resulting decrease in the temperature difference, \(\Delta T\), when the grid becomes smaller affects the calculated convective heat fluxes directly (i.e., through [PERSON]'s law) as well as the calculated Grashof numbers for natural convection scenarios indirectly. The forced convection approach is not significantly affected by this aspect as it does not directly depend on temperature, rather on the velocity in the first grid cell which remains fairly constant around the centreline. Nevertheless, a noticeable grid dependency is observed at radial locations which are off-centre. The approach based on the stagnant film theory (i.e., Equation (40)), for which the convective heat fluxes do not directly depend on the local gas phase temperature (i.e., rather temperature is only used for the calculation of the convective heat transfer coefficient \(h\)), shows minimal effects of grid dependency. The reader is referred to [24; 25], where additional analysis is included as well as the predicted temperature and velocity fields above the surface of the methanol pool fires are presented.  
Figure 3: Overview of the computational domain, local grid refinement (i.e., 2 cm, 1 cm, 0.5 cm) employed in the numerical simulation of the 30 cm methanol pool fire [67].