## 1 Introduction
[PERSON] and [PERSON] [15] have investigated the three well-known low Reynolds number (LRN) turbulence models, Launder and Sharma (LS), Lam-Bremhorst (LB), and Biswas and Fukuyama (BF) models, and they have been concluded that none of them is able to predict the quantitative aspects of transition correctly by comparing them with the ERCOFTAC T3A test case. A new low Reynolds turbulence model has been proposed by them for the prediction of transition on gas turbine blades, and they have obtained important improvements [16]. [PERSON] et al. [17] have proposed a low Reynolds number nonlinear eddy viscosity model, and they have expressed that a substantial improvement in the representation of the transition process has been achieved. [PERSON] et al. [14] have introduced a correlation-based transition model using local variables and have applied this new model to various test cases ([PERSON] [18]). They have mentioned that the basic model framework (transport equations without the correlations) will be called the Gamma-Theta (\(\gamma\)-Re\({}_{\Theta}\)) model. The V2F turbulence model has been tested by comparing the results with the ERCOFTAC T3B case by [PERSON] and [PERSON] [19]. They have concluded that the V2F model predicts an earlier onset of transition compared to the data. Another new transition model that uses the RANS (Reynolds Averaged Navier-Stokes)-based intermittency transport equation, coupled with the Wilcox low Reynolds k-\(\omega\) model with no modification, has been proposed by [PERSON] et al. [20]. Some improvements have been obtained in the prediction accuracy for high-freestream turbulence cases that are commonly found in gas turbines. [PERSON] [18], in his doctoral study, modified the SST turbulence model for unstructured mesh structures and presented a correlation-based turbulence model using local variables that can solve the turbulence transition region more accurately. This model was soon included in the ANSYS CFX R13 commercial CFD code. [PERSON] conducted validation studies on flat plates, helicopter aerodynamics, aircraft wing aerodynamics, and turbine blade aerodynamics in his doctoral study and demonstrated that this model was more successful than [PERSON]'s SST model in the transition region. After this turbulence transition model was integrated into the ANSYS CFX code under the name Gamma-Theta, it was integrated into the other most well-known CFD codes in the market, ANSYS Fluent and Star CD, and became the most widely used turbulence model in the industry for solving the transition region. In the literature, the Gamma-Theta model has been used and validated in studies numerically examining the transition region [21; 22; 23]. [PERSON] et al. [21] stated that the turbulence model that best solves the conjugate heat transfer in the transition region from laminar flow to turbulence is Gamma-Theta and that it is possible to obtain successful results by modifying other two-equation models like Gamma-Theta. [PERSON] et al. [22] studied the Gamma-Theta transition turbulence model on a plane plate and N3-60_04 turbine airfoil. As a result of the study, they stated that the Gamma-Theta turbulence model is in good agreement with the experimental results and can solve the transition to bypass wake-induced turbulence very well. [PERSON] and [PERSON] [23] studied to determine the effects of inlet-turbulence intensity and pressure gradient on the transition region flow characteristics numerically using the Gamma-Theta model. They stated that the critical Re number changes only with the turbulence intensity, and that the pressure gradient does not affect the critical Re number much in zero pressure gradient and favorable pressure gradient flows, and the pressure gradient effect can be neglected. Another method used in transition predictions is the use of empirical correlations:  
[PERSON] and [PERSON] [24] proposed a correlation between the Reynolds number of the transition to turbulence and the inlet-turbulence intensity, depending on the boundary-layer momentum thickness.