## 3 Experimental and Simulation Set-Up Details
### Oxy-Fuel Jet Flame (Flame B3)  
The oxy-fuel jet flame B3 is one of the flame series that were experimentally studied in [43]. It exhibits a Reynolds number Re = 18,000, making it interesting for LES investigations. The reacting turbulent burner is composed mainly of two jets; a central jet with an inner diameter d\({}_{\text{B3-fuel}}\) = 5 mm (the wall thickness is 0.5 mm) for the fuel stream with a mixture of 55% H\({}_{2}\) and 45% CH\({}_{4}\), and a coaxially arranged jet with diameter d\({}_{\text{B3-oxy}}\) = 96.5 mm for the premixed oxidizer composition of 68% CO\({}_{2}\) and 32% O\({}_{2}\). In fact, it has been reported in [63; 64], that air flame stability is established once the O\({}_{2}\)% content is around 30% which explains the specie percentages used for the oxidizer stream in this study. Further, the existence of H\({}_{2}\) in the fuel jet helps the flame to remain attached to the nozzle as indicated in [43]. Figure 3 presents the 3D configuration of flame B3 featuring the computational domain in a conical shape assuming that the base and the sides are inlets for the oxidizer, which helps the numerical convergence of the calculations. The block-structured hexahedral grid applied consists of 89 blocks and 2,800,770 cells in an O-ring arrangement. 8450 cells are used for the fuel pipe jet, with minimum cell size equal to 5.31 \(\times\)\(10^{-12}\) m\({}^{3}\) and maximum cell size located in the outlet region with 1.09 \(\times\)\(10^{-10}\) m\({}^{3}\). To assess the LES quality, various criteria are available, as reported in [46; 47; 48; 49; 50; 51; 52; 53; 54; 55]. In the present paper we adopt the approach proposed by [PERSON] et al. in [66] and [PERSON] in [7]. Thus, based on the ratio of the LES local mesh size \(\Delta\) to the Kolmogorov length scale \(\eta\), it turns out that \(\Delta/\eta\leq\) 12 in almost the entire computational domain, which reflects that more than 80% of the turbulent kinetic energy are resolved, along with the Taylor scales. Thereby, the Kolmogorov length scale, that has to be estimated by RANS solution following the procedure in [67], has been evaluated by RANS calculations from [4]. The outlet plane is at x = 80 d\({}_{\text{B3-fuel}}\), with waveTransmissive condition and fixed pressure P = 1 atm. Similar to the previous case, zero gradient boundary conditions are imposed for other variables and the temperature is initially uniformly distributed. More details for the operating conditions are summarized in Table 2. To evaluate the convergence of the number of stochastic fields, SFi, calculations for different cases (using 4,8,16 SFi) were also run in this case, however on 160 processors for 0.16 s of physical time with time step \(\Delta\)t = 2.5 \(\times\)\(10^{-7}\). For the inlet turbulent flow field velocity of both studied cases, an in house turbulence inflow generator according to [68] was used.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Flame Jet** & \(f\) & **PV** & **T (k)** & **U\({}_{\text{b}}\) (m/s)** & **\(\
u\) (m\({}^{2}\)/s)** \\ \hline Central jet & 0.156 & 0 & 294 & 49.6 & 1.513 \(\times\)\(10^{-5}\) \\ Pilot jet & 0.043 & 7 & 1880 & 11.4 & 1.513 \(\times\)\(10^{-5}\) \\ Coflow & 0 & 0 & 291 & 0.9 & 1.513 \(\times\)\(10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Conditions for the piloted jet Flame-Sandia-D.  
Figure 2: Sandia Flame-D burner, (**a**) Description of the experimental configuration, (**b**) The numerical configuration generated (**c**) 3D structured grid used with a zoom of the inlet nozzle region where smoother grid is applied.