## 3 Predictions with Different Turbulence Models
The turbulence models, i.e., SKE, SKE-R, RKE, SST, and RSM, were validated with the EDC-based detailed chemical kinetic mechanism, identified in the results as EDC-53/SKE, EDC-53/SKE-R, EDC-53/RKE, EDC-53/SST, and EDC-53/RSM, respectively. Following standard best practice, radiation heat transfer was approximately solved using discrete ordinate (DO) radiation equation with 100 (4 \(\times\) 5 \(\times\) 5 \(\times\) 1) directions along with the weighted sum of gray gas model (WSGGM) [64] for absorption coefficient. For a more accurate solution of a radiation equation, an efficient exponential wide band (E-EWB) model [65; 66; 67] with a user-defined function (UDF) or full-spectrum \(k\)-distribution (FSK) look-up table and its improvement [68; 69; 70; 71; 72; 73] can be used. The emphasis of this work is on the choices of the turbulence models and the chemical kinetic mechanisms for engineering modeling purposes. The main settings of the turbulence models are shown in Table 2. The comparisons were done with the only difference of the turbulence models used for the five cases. The EDC was used to model the turbulence-chemistry interaction with the default EDC constants. A comparison of the predicted flame temperatures is displayed in Figure 3. The predicted flame construction by the turbulence models of SKE, RKE, and SST were found to be quite similar. The flame shape predicted by SKE-R (shown in Figure 3b) was the longest and apparently different from the other four, and the results might not have been correctly predicted by the SKE-R model. This implied that the chemical reactions are strongly affected by the turbulent flows. The flame shape predicted by RSM, shown in Figure 3e, was shorter than that by SKE-R but longer that those by others. Scalar data are presented in Figures 4 and 5. Mean temperature, turbulent kinetic energy, and main mean composition profiles along the axis are shown in Figure 4 for the Sandia Flame D with the turbulence models of SKE, SKE-R, RKE, SST, and RSM. Mean axial velocity profiles are shown in Figure 5 for the Sandia Flame D with the turbulence models. \begin{table}
\begin{tabular}{p{108.4 pt} p{108.4 pt} p{108.4 pt} p{108.4 pt} p{108.4 pt}} \hline \hline
**Case** & **Turbulence Models** & **Options** & **Near-Wall Treatment** & **Model Constants** \\ \hline EDC-53/SKE & Standard \(k\)-\(\varepsilon\) model & Viscous heating; production limiter & & \\ EDC-53/SKE-R & Standard \(k\)-\(\varepsilon\) model with changed constant \(C_{1\varepsilon}\) & Viscous heating; production limiter & & \\ EDC-53/RKE & Realizable \(k\)-\(\varepsilon\) model & Viscous heating; production limiter & & \\ EDC-53/SST & Shear-stress transport (sst) \(k\)-\(\omega\) model & Low-Re correction; viscous heating; production limiter & & \\ EDC-53/RSM & Reynolds stress model & Quadratic pressure-strain; Wall BC from \(k\) equation & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main settings of turbulence models. Figure 4: Comparison of the turbulence models of SKE, SKE-R, RKE, SST, and RSM for the Sandia Flame D: mean temperature, turbulent kinetic energy, and main mean composition profiles along the axis with the detailed chemical kinetic mechanism of GRI-Mech 3.0. Figure 3: Iso-contours of mean temperature with turbulence models of SKE, SKE-R, RKE, SST, and RSM for the Sandia Flame D with the detailed chemical kinetic mechanism of GRI-Mech 3.0. Since the used chemistry and the turbulence-chemistry interaction model were the same, the differences shown in Figures 3-5 must have mainly resulted from the turbulent flow models. It is well-known that round-jet results for RANS, in particular for two-equation models but also for multi-equation models, depend on the choice of model constants. The present results indicated that the challenges were very related to turbulent flow modelling.