## 3 Predictions with Different Turbulence Models
The temperature peak locations predicted with SKE (\(\sim\)2040 K@\(x/d\)-35), RKE (\(\sim\)2026 K@\(x/d\)-38), and RSM (\(\sim\)2055 K@\(x/d\)-38) were shifted towards the burner (Figure 4a), and the peak with SKE-R (\(\sim\)2090 K@\(x/d\)-53) was shifted downwards from the burner a little (Figure 4a) compared to the experiments (\(\sim\)1945 K@\(x/d\)-45). These deviations and others, shown in Figures 4 and 4 and Table 3, have also been found by other predictions [34; 37]. The temperature peak location predicted with RSM (\(\sim\)2083 K@\(x/d\)-45) agreed well with the experiment location, with an over-prediction of approximately 138 K. Compared with the results by RSM and SKE-R, the tuning of the SKE model constant yielded a worse peak location, a better prediction of the temperature sloped up to its peak, and large deviations between the predictions and the experiments appeared downwards of the peak. However, an increase of the production term in the \(\varepsilon\)-equation by tuning the standard model constant from 1.44 (SKE) to 1.6 (SKE-R) led to a considerable decrease of the turbulent kinetic energy, shown in Figure 4b, and thus to a very poor agreement between the predicted and the experimental results in this work. Therefore, predictions by SKE-R could be ignored. Compared to the experiments of the turbulent kinetic energy, the best results were reached by the RSM predictions. It should also be noted that the choice of turbulence model affected the prediction of the peak values and the peak locations of the scalars, as shown in Table 3. For the predictions of major species, the largest deviation was found for the peak values of the O\({}_{2}\) mass fraction. Checking the minimum O\({}_{2}\) mass fraction profiles shown in Figure 4c demonstrates that they are acceptable, especially that by RSM. The differences between simulations by RSM and measured data were not significant for the temperature and the main species such as O\({}_{2}\), H\({}_{2}\)O, and CO\({}_{2}\). The behavior of these species had the same trend as that for the temperature. The profiles of the values for composition along the axis replicated the behavior of the temperature. The peak of the mean mass fraction of CO\({}_{2}\) (Figure 4f) was largely over-predicted by SKE-R compared to those by the other four models. The mean mass fraction of CH\({}_{4}\) along the axis, predicted by SKE-R shown in Figure 4e, occasionally agreed quite well with the experiments. However, those predicted by the others shown in Figure 4e were under-predicted, especially close to the temperature peak, implying that CH\({}_{4}\) along the axis was burnt out earlier than in the experiments due to the strong mixing and spreading. If the results from SKE-R were ignored, the CH\({}_{4}\) predictions by RSM agreed best with the experiments among the predictions. The mean mass fraction of N\({}_{2}\) along the axis, predicted by SKE-R shown in Figure 4g, was under-predicted compared to those predicted by the other four turbulence models. The best predictions were done with RSM, while about half of the predicted N\({}_{2}\) results by SKE-R were again very close to the experiments. With the exceptions of SKE-R and SKE, differences between the simulations and the measured data were not significant for the mean axial velocities, as shown in Figure 4. Very small differences were found from the predicted results by the turbulence models of RKE, SST, and RSM--identified as EDC-53/RKE, EDC-53/SST, and EDC-53/RSM, respectively, in Figure 5--with the EDC-based detailed chemical kinetic mechanism. All the predictions by RKE and SST agreed very well with each other. The predicted scalar data by RSM and the experiments, shown in Figures 4 and 4, were very close. Therefore, the RSM model was selected for the turbulence simulation of the Sandia Flame D in all further calculations for its relatively better predictions.