## 3 Results and Discussion  
Laminar and turbulent numerical solutions for the ERCOFTAC T3A experimental test case on a flat plate are provided and discussed in Figure 5 below. \begin{table}
\begin{tabular}{l l} \hline Density & 1.116 kg/m\({}^{3}\) \\ \hline Viscosity & 1.725 Pa.s \\ \hline Conductivity & 0.02428 W/mK \\ \hline Specific heat & 1003.8 J/kgK \\ \hline \end{tabular}
\end{table} 
Table 1: Thermophysical properties of air. Figure 4: (**a**) Full computational domain mesh structure (135,610 nodes), (**b**) magnification of inlet-section mesh structure of the flat plate, and (**c**) magnification of the leading-edge mesh structure of the flat plate. Figure 3: Mesh independence study. When defining the Reynolds number in the flow on a flat plate, the characteristic length is used as the length in the flow direction. In Figure 5, from the experimental results, we see that the transition to turbulence begins at a local Re number of approximately 140,000 in the flow, and that the flow becomes fully turbulent at a local Re number of approximately 270,000. In Figure 5, it is seen that the laminar numerical solution provides results that are inconsistent with the experimental data, as expected, in the turbulent transition and turbulent flow regions. It is seen that the results obtained using the Std. k-\(\varepsilon\), Std. k-\(\omega\), SST k- \(\omega\), and RNG k-\(\varepsilon\)turbulence models are also inconsistent in the laminar and turbulent transition regions, as expected. As shown in Figure 5, the Gamma-Theta-SST turbulent transition model also agrees with the experimental results in the turbulent transition region, besides good agreement in both the laminar and the turbulent regions. The above results show that the Gamma-Theta model is a suitable model for solving laminar, turbulent transition, and turbulent regions in flat-plate flow. However, although the compatibility with the experimental results in the turbulent transition region is not as good as in the laminar and turbulent regions, it can be said that it is at a quite acceptable level when the complexity of the flow in the transition region and the fact that other turbulence models cannot capture this region at all are taken into account. In the transition region, the Gamma-Theta model starts the transition earlier than the experimental data and completes the transition a little earlier. The friction coefficient is estimated to be, at most, 40% higher than the experimental results in this region. These results are for the ERCOFTAC T3A inlet-turbulence intensity \(\mathrm{Tu}=3.3\%\) experimental case, and the turbulence-length scale is not specified in this experimental case; the length scale is taken as LS = 0.026 m in the calculations in this study. A certain part of the approximately 40% deviation from the experimental results in this region can be attributed to this. When we inspect Figure 5, if the flow was completely turbulent (\(\mathrm{Re}_{\mathrm{x}}>270\),000), it is seen that the Gamma-Theta model is the most suitable turbulence model, and the model with the same suitability as this model is the Std. k-\(\omega\) model. The other most suitable models are the SST- k-\(\omega\), Std. k-\(\varepsilon\), and RNG k-\(\varepsilon\)models, respectively. However, although the Gamma-Theta and Std. k-\(\omega\) models are almost in agreement with the experimental data, the other models predict the friction coefficient below the experimental data at Reynolds numbers smaller than \(\mathrm{Re}_{\mathrm{x}}=440\),000, and it can be said that all of them show almost the same performance. Again, if the flow was completely laminar, it is seen from Figure 5 that the numerical solution is in very good agreement with the experimental data in the laminar region (0 \(<\) Re \(<\) 170,000). The Gamma-Theta turbulence model, which is the most suitable model to investigate the effect of inlet-turbulence intensity, was selected, and the effect of inlet-turbulence  
Figure 5: Comparison of Gamma–Theta (GT), Std. k-\(\varepsilon\), RNG k-\(\varepsilon\), Std.