## 3 Predictions with Different Turbulence Models  
The validation procedure concerned the modelling of turbulence, for engineering purposes, with a detailed chemical kinetic mechanism. In order to support the choice of the associated turbulence models, simulations of the laboratory non-premixed turbulent flame, the Sandia Flame D [40; 41; 42], were performed. For the turbulence modelling, the Reynolds averaged Navier-Stokes approach (RANS) was applied to the simulations of the Sandia Flame D to estimate the influence of the accuracy of the turbulence modelling on the results. SKE, RKE, SST, and RSM turbulence models were compared in the first step because they can be used in engineering applications with acceptable expenses. For turbulence-chemistry interaction modeling, the EDC with the detailed chemical kinetic mechanism of GRI-Mech 3.0 was applied to the RANS simulations. The general requirements set on the CFD model predetermined the selection of the EDC to a certain degree. The investigations carried out served for the evaluations of the EDC and the RANS models considering the simulations of gas phase combustion. All simulations were carried out with the commercially available software ANSYS Fluent 19 [57]. To speed-up the CPU-intensive treatment of the detailed reaction kinetics, the EDC was applied in conjunction with the in-situ adaptive tabulation (ISAT) algorithm [58]. The method is based on a run-time tabulation of the local (realized) region of the chemical state space (species concentrations, temperature, and pressure) accessed during the CFD  
Figure 2: Inlet boundaries for the Sandia Flame D.  
simulation. ISAT combines both direct integration for new entries and linear interpolation between already directly integrated values within a specified interpolation error tolerance. The interpolation error tolerance determines the size of the ISAT table and the time needed for its generation. In addition, it strongly influences the accuracy of simulation results. It is important to choose adequate error tolerances for an ISAT table and for integrating the ordinary differential equations (ODEs) of chemical rates. The experiences of [PERSON] et al. [59] suggested that the ISAT and the ODE error tolerances should be not greater than \(6.25\times 10^{-6}\) and \(1\times 10^{-8}\), respectively. Final error tolerances of \(6.25\times 10^{-6}\) and \(1\times 10^{-12}\) were therefore used in all the calculations reported below. The default settings were used for the EDC constants. Turbulence modeling is known to have considerable effects on combustion results. Sensitivity to turbulence models was investigated by applying SKE, RKE, or RSM with an EDC-based detailed chemical kinetic mechanism and comparing it with experimental data [40; 41; 42] to determine the candidate turbulence model to be used in the simulations of industry-scale natural gas combustion furnaces. The standard constant values of SKE, \(C_{1\epsilon}\) and \(C_{2\epsilon}\), result in an over-prediction of spreading and turbulence diffusion of round jet flows [60]. This tends to increase downstream from a nozzle. The over-predicted mixing also exaggerates fuel conversion and hence affects the location of heat release and the development of density and the velocity fields. To reduce spreading/diffusion, various modifications have been suggested. The main approach is to change \(C_{1\epsilon}\) or \(C_{2\epsilon}\)[59; 60; 59; 61; 58; 62; 31]. Hence, for combustion-model investigations, although not in general, it was appropriate to make \"ad hoc\" modifications of the turbulence models to give the best representation of the turbulent flow field. Here for the SKE model, the constant \(C_{1\epsilon}\) of the \(\epsilon\)-equation was changed from 1.44 (the standard value) to 1.6, and this model is referred as SKE-R hereafter. This change is a standard correction proposed for this model to improve prediction of the jet spreading rate [59; 34].