## 4 Results and Discussion  
### Model Validation  
Figure 3 illustrates the OH-PLIF images obtained from the experiment and the mean OH concentration from the numerical results of four CH\({}_{4}\)/H\({}_{2}\)/air flames. The OH-PLIF images shown in Figure 3a represent the signal intensity of OH fluorescence corresponding to the instantaneous OH concentration during combustion. Figure 3b demonstrates the OH radical concentration obtained using LES. The flame macrostructure is exhibited by the mean OH concentration. It can be seen that LES shows excellent consistency with the OH-PLIF images in terms of the flame macrostructure for all cases. Specifically, the LES captured the \"M\" shape flame very well for the 90H2 flame.  
A comparison of the \(\alpha\) angles between the flame edge and burner axis (shown in Figure 3) from the experiment and simulation procedures is shown in Figure 4, where an overall agreement between the two sets of results can be observed. With an increase in the hydrogen ratio, \(\alpha\) increased for both the experiment and simulation cases. A large \(\alpha\) means an increased turbulent burning velocity, which mainly results from the larger reactivity of hydrogen [29]. It can be seen that the LES in this study has a good prediction capability if the boundary conditions are specified properly.  
The experimental and numerical mean axial velocities of the non-reacting flow normalized by the inlet velocity are compared in Figure 5. As shown in Figure 5a, the experimental results showed that there was an inner recirculation zone (IRZ) just behind the bluff body,  
Figure 4: The angle between the flame edge and centerline for both the experiment and simulation results.  
Figure 3: Flame structure. (**a**) The time-averaged OH signal obtained using the OH\(-\)PLIF technique; (**b**) time\(-\)averaged OH mass concentration from the LES. (**a**) Experiment; (**b**) LES.  
and an outer recirculation zone (ORZ) formed near the wall because of the influence of condensed space on the flow field. The layer between the fresh mixture and IRZ is defined as the inner shear layer (ISL). The mixing layer between the fresh mixture and near the negative-velocity ORZ is defined as the outer shear layer (OSL). These flow features were well-predicted in the simulation. Figure 5b shows a comparison of the mean axial velocities between the numerical and experimental results, indicating that good agreement was achieved between the two sets of results. The mean relative errors of axial velocity were approximately 16%, computed according to the data points calculated from the experiment and simulation results. Figure 5c shows the mean azimuthal velocity. Discrepancies could be observed near the ISL, and these discrepancies may be attributed to the uncertainties of the experimental data. On the other hand, a discrepancy near the inner shear layer could also be observed in the results presented by [PERSON] et al. (2018), and this discrepancy may have been caused by the SGS model.  
Figure 5: (**a**) The mean axial velocity field of non-reacting flow; (**b**) the mean axial velocity profiles \(U/U_{\rm m}\), and (**c**) the mean azimuthal velocity profiles \(V/V_{\rm m}\) of non-reacting flow.  
Comparisons of the mean axial and azimuthal velocity profiles of the four flames at various heights are also presented in Appendix C. The discrepancy near the ISL is likely caused by both the SGS and the constant sub-grid wrinkling factor models. Because of the reactions occurring near the ISL and the complexity of combustion, especially with respect to the challenge of predicting flames with different hydrogen ratios, the differences between the experimental and simulation results are acceptable. The simulation reproduced the general trend of the flow field and flame.