## 4 Results
### Application to Oxy-Fuel Jet Flame B3  
The LES hybrid ESF/FPV was now appraised on the oxy-flame B3 in terms of comparison with available measurements, and then applied to analyze the effect of CO2 dilution on the oxy-flame behavior. First, Figure 8 shows qualitatively both experimental and numerical instantaneous temperature field for oxy-flame B3. Thereby, the region close to the nozzle of the burner is particularly zoomed in order to clearly display the measurement planes. The predicted flame length observed in Figure 8c agrees reasonably well with the experimental data, which reached approximately Lflame = 100 dB3-fuel (see in Figure 8a). Figure 8b shows the instantaneous temperature contour on radial planes at different axial positions; it can be seen that the temperature field spreads radially and toward the outlet of the burner. The flame is also shown attached to the burner nozzle as it is observed experimentally under consideration of the important amount of diluted H2 in the fuel mixture. In the zoomed region above  
Figure 8: Instantaneous temperature field for the oxy-flame B3: (**a**) Measurements, (**b**) 2D contours on radial planes at different axial locations, (**c**) Left: 3D snapshot obtained with LES hybrid ESF/FPV. Right: A zoom of the region above the fuel nozzle. Figure 7: Probability density function of temperature within a mixture fraction range = 0.1 at different axial positions; z/d = 15 and 30. Comparison between experiment and simulation results; Solid lines: LES hybrid ESF/FPV results with different SFi numbers, Dashed line: Measurements. the fuel nozzle (Figure 8c right), the temperature field reaches the maximum predicted value, which corresponds to 2250 K found in experiments. The quantitative validation was achieved by comparisons with experimental data in Figures 9-12 of the evolution of main species and temperature, as well as of the scatter plots and probability density function of scalars at different axial positions. To ensure the convergence of the number of stochastic fields (SFi) various simulations are performed by applying different numbers of Stochastic Fields (4, 8 and 16). Figure 9 shows the evolution of the mean values of CO and H\({}_{2}\)O species mass fractions at different axial positions. The amounts of CO and H\({}_{2}\)O mass fractions were much higher than values obtained with air diluted flame cases. Especially, close to the nozzle, the CO and H2O mass fractions were equal to 0.11 and 0.18, respectively. However, these values increased to almost 0.2 for both species at higher axial positions. In this way, the present LES results confirm the RANS-based findings of [PERSON] et al. in [4], which agree with [PERSON] et al. in [71], who reported that the CO\({}_{2}\) 68% diluted with pure oxygen in the oxidizer inlet is not inert. This plays an important role in increasing CO and H\({}_{2}\)O gases formation since the additional CO\({}_{2}\) reacts with H to form CO. Figure 10 presents the mean quantities of O\({}_{2}\) and H\({}_{2}\) species mass fractions. In both figures, the results with 16 SFi achieved better agreements at radial profiles once compared to results with 4 SFi. This is not surprising, since four stochastic fields are not sufficient to reproduce the exact evolution of measured quantities (see also previous case: Sandia flame-D results using 4 SFi). Figure 9: Comparison between experimental data for oxy-flame flame B3 and LES hybrid ESF/FPV numerical results for different numbers of SFi at different axial positions; z/d = 3; 5 and 10. Radial profiles of mean mass (**a**) CO species, (**b**) H\({}_{2}\)O species. Figure 11: Instantaneous scatter plots of temperature versus mixture fraction at the axial position z/d = 3. Comparison between experiment and simulation results; **(a)** Experimental data, **(b)** LES hybrid ESF/FPV with 16 SFi. Figure 12: Probability density function of temperature within a mixture fraction range = 0.04, at different axial positions (**a**) z/d = 3, **(b)** z/d = 5 and (c) z/d = 30.