## 5 Results and Discussion  
Model comparison of flow and chemical kinetic mechanisms for methane-air combustion has been presented for Sandia Flame D [34] with Ansys Fluent, and the grid and boundaries are also used in this work. The Reynolds Stress Model (RSM) [35; 36; 37] was used for all the simulations. The chemical kinetic mechanism of GRI 3.0 [26] was used due to the incurred errors being at a low level. An EDC model with the primary constants \(C_{\rm D1}=0.135\) and \(C_{\rm D2}=0.50\) was used to model the turbulence-chemistry interaction for Sandia Flame D. Reasonable predictions [34] were obtained, with the peak of the maximum temperature over-predicted more than 100 K along the axis in comparison to the experiments [24], whereas the peak of the maximum temperature in the reaction shear layer was over-predicted by 500 K for Sandia Flame D with the original EDC model [38], even though the radial extent of the temperature distributions is well captured. This indicates that the mean reaction rate is over-predicted and should be modified according to Equation (33). Based on the above discussions of EDC model constants, numerical predictions for Sandia Flame D, which has strong turbulence with \(Re=22\),400, are presented using the selected model constants as shown in Table 1.  
Cases 1-4 are chosen since the primary model constants are generally used in the EDC model [2; 5; 20]. Cases 5-7 are chosen since those constants have been used for the predictions of turbulence-chemistry interactions under hot diluted combustion of CH\({}_{4}\)/H\({}_{2}\)[19]. Cases 8-16 correspond to the limits of C\({}_{\rm D2}\) at 0.11 and 0.91 [21] with \(C_{\rm D1}=0.1357\). Cases 17-20 are chosen since they have been used for the prediction of MILD combustion [18]. The secondary EDC constant, \(C_{\alpha}\), with a range from 6 to 50 [21; 27] is shown in Table 1 for all 20 combinations of the primary EDC constants \(C_{\rm D1}\) and \(C_{\rm D2}\). The \(C_{\alpha}\) value for case 7 is found largely outside the range when the primary constants \(C_{\rm D1}=0.134\) and \(C_{\rm D2}=27\) are used. \(\gamma_{\lambda}\) at \(Re_{\rm T}=250\) in Table 1 is determined by Equation (21). Limited \(Re_{\rm T}\), i.e., \(Re_{\rm T}=C_{\gamma}^{4}\), as shown in Table 1, is obtained by requiring the \(\gamma_{\lambda}\) value to be less than unity, which makes the denominators of Equations (32) and (33) positive. \(\frac{L^{*}}{\eta}=\frac{2}{3}\left(\frac{3C_{\rm D1}^{\alpha}}{C_{\rm D1}^{ \alpha}}\right)^{1/4}\) is the ratio of the fine structure length scale to the Kolmogorov scale from Equation (17). \(Re^{*}\) is the fine-structure Reynolds number from Equation (19). Values of \(Re_{\rm T}\) at \(\varepsilon_{2}/\varepsilon=0.10\), \(\varepsilon_{2}/\varepsilon\) at \(Re_{\rm T}=50\), and \(Re_{\rm T}=1\), following the criteria proposed by [PERSON] [21], are obtained from Equation (22) and values of \(Re_{\rm T}\) at \(\gamma_{\lambda}=1\) are obtained from Equation (21). The lower-than-unity length scale, \(\frac{L^{*}}{\eta}\), shown in Table 1, means reactions have been assumed to occur in structures smaller than the Kolmogorov scales. Thus, the EDC model with the primary constants \(C_{\rm D1}\) and \(C_{\rm D2}\) for these cases assumes the reactions occur in very small spotty areas entitled as fine structures in the flow field while each fine reactor is contained in the Kolmogorov eddy, which may make the reaction zone kinetically control distribution in the reaction zone [19]. The results using the recommended models in our previous work [34] and the primary constants \(C_{\rm D1}\) and \(C_{\rm D2}\) in Table 1 are given in Figures 3-14, including the mean axial velocity, the mean temperature, the Reynolds normal stress, and the major and minor species. All simulations were carried out using the commercially available software ANSYS Fluent 2021R1 [28]. Some of the results are found to be comparable with those of the Large-Eddy simulation [39; 40; 41].