## 2 Object Description  
The Flame D from the Sandia/TNF workshop, as shown schematically in Figure 1, is a piloted methane-air diffusion flame [40; 41; 42]. The central main jet consists of a methane-air mixture (with 25% by volume of CH\({}_{4}\)) corresponding to an equivalence ratio of 3.174. This is above the upper flammability limit of methane so combustion is still controlled by mixing. It was surrounded by a pilot flame and a slow co-flow of air outside. Flame D exhibits local extinction to a limited degree [37; 40]. Here, the pilot flame was burning a mixture of C\({}_{2}\)H\({}_{2}\), H\({}_{2}\), air, CO\({}_{2}\), and N\({}_{2}\) with an enthalpy and equilibrium composition that was equivalent to a mixture of methane and air at an equivalence ratio of \(\varphi=0.77\). The experimental data were documented in detail by [PERSON] et al. [42]. This flame was predicted by means of 2D steady RANS. The settings of the solver in all the simulations included a SIMPLE scheme for the pressure-velocity coupling, Green-Gauss based for the gradient, Presto! for the pressure, and second order upwind for the others. The thermodynamic models used in this work for EDCs were from GRI Mech, and the model for PDF was from the Fluent package. The computational domain extended from 5\(d\) behind the nozzle exit plane to 100\(d\) in the axial direction and 50\(d\) in the radial direction, where \(d\) stands for the main jet diameter. The 2D RANS simulations were carried out on a structured grid with an increased resolution close to the nozzle and the symmetry axis. The jet velocity at the nozzle exit was approximated by including the nozzle with length of 5\(d\) in the computational domain and axial velocity setting at the inflow boundary using the velocity profiles measured at the nozzle exit plane. The CFD simulations of Flame D were conducted on an axisymmetric numerical mesh. Though not shown in Figure 1,the following four meshes were used for comparison: A: 49 \(\times\) 50; B: 157 \(\times\) 71; C: 202 \(\times\) 88; and D: 252 \(\times\) 118. All the meshes gave very close results, and either could be used to produce a grid-independent solution. However, the finer mesh (mesh C, 202 \(\times\) 88 shown in Figure 1) with finer grids in the areas of the jet and the pilot was selected and used in all the simulations even though other grids could be used for this 2D steady work. Considering the model selections were for the engineering methane-air combustion, a much finer mesh was unnecessary. The burner geometry data and boundary conditions used for the simulations are shown in Table 1. It should be noted that the jet velocity, co-flow velocity, pilot velocity, and temperature in the experiment were in a range [42]. For example, the jet bulk velocity, the pilot bulk velocity, and the air co-flow velocity in the experiment were 49.6 \(\pm\) 2, 11.4 \(\pm\) 0.5, and 0.6 \(\pm\) 0.05 m/s, respectively, and these data for the velocity inputs were averaged as 49.7, 12.3, and 0.8 m/s, respectively, from the profiles. The pilot temperature in the experiment was 1880 \(\pm\) 50 K, while the setting was 1880 K. The profiles for the jet, pilot, and co-flow with the average values, shown in Table 1, were used in the simulation, and these settings, of course, induced different predictions with the experiments. The profiles for the boundary conditions of the average velocity and its fluctuations [42; 43], as well as the turbulent kinetic energy [43], are shown in Figure 2. The turbulent dissipation rate \(\varepsilon\) and the specific dissipation rate \(\omega\) used for the turbulence models could be estimated from the average and the fluctuations. Figure 1: Schematic configuration of the Sandia Flame D and the grids.