## 5 Results and Discussion
### Minor Species Profiles  
The mean mass fraction profiles for minor species, i.e., CO, H\({}_{2}\), NO, and OH, using 20 combinations of the primary EDC constants \(C_{\rm D1}\) and \(C_{\rm D2}\) are shown in Figures 11-14. Compared to the experiments, large differences in the predicted mean mass fractions of minor species among the cases and the experiments occur at the peak temperature zone where the mixtures burn most intensely. The radial peaks in minor species profiles were not accurately reproduced. [PERSON] et al. [43] claimed that the productions of minor species, such as CO and OH, were strongly sensitive to temperature fluctuations, especially upstream of the flame. In Figure 11a, the mean CO mass fractions along the axis of cases 17 and 18 are found to agree well with the experiments at locations upstream of the peak temperature, but are slightly under-predicted downstream of the peak temperature. Among the cases using the primary constant \(C_{\rm D2}\) in the limits, i.e., from 0.11 to 0.91, the remarkably improved predictions of case 8 agree better with the experiments than those of the other cases. Results of case 7 deviate the most from the experiments, thus this case is not recommended. In addition, the proposed constants in case 7, as shown in Table 1, violate the criteria presented by [PERSON] [21]. Results of other cases stay between those of cases 8-16. The results for the radial mean CO mass fraction are over-predicted at the zones upstream of the peak temperature, as shown in Figure 11. Large differences in the deviations from the experiments occur in the zones where the mixtures burn intensely, as shown in Figure 11, which may also be due to the over-predicted mean reaction rates. The mean H\({}_{2}\) mass fractions, which are quite similar to the profiles of the mean CO mass fraction shown in Figure 11, are shown in Figure 12. Among the cases with the primary constant \(C_{\rm D2}\) in the limits, the predicted results of case 8 agree better with the experiments than those of the other cases. In Figure 13, the mean NO mass fractions along the axis and the radii of cases 8, 17, and 18 are found to agree well with the experiments. However, the EDC constants of cases 17 and 18 violate the criteria for the proposed EDC constants [21]. The results of the other cases are significantly over-predicted, especially at locations around the peak temperature where the mixtures burn intensely, and large deviations among the cases are found for the mean NO mass fraction profiles. The results [38] of Sandia Flame D with the original EDC constants, which is case 4 in this work, also show that the results of the mean NO mass fractions are significantly over-predicted. Therefore, the EDC constant combinations of case 8 are suggested for the modeling of Sandia flame D.  
The prediction of OH is particularly challenging due to the strong nonlinearity of the species' evolution [44]. Compared to the respected measured data, the level of agreement for OH was subpar, with largely over-predicted peaks using all of the EDC constants. All results were found to significantly over-predict around the peak value locations where the mixtures burn intensely, as shown in Figure 14. However, the results of the peak value locations and the varied tendency are correctly predicted. The calculated maximum mass fractions are significantly over-predicted in comparison to the measured data. Large deviations among the cases are found for the mean OH mass fractions. Among the cases with the primary constant \(C_{\rm{D2}}\) in the limits, the result of case 16 is the upper profile limit, and case 8 is the lower profile limit. Results of other cases are within the limits of cases 8 and 16 except for cases 7 and 17-20. The predictions of cases 17-20 are found to be reasonable for some quantities, such as the mean temperature and the mean major and minor mass fractions, in comparison to the experiments.