## 1 Introduction  
The aim of this work is to provide a contribution to the emerging research area related to the development of CFD techniques for the prediction of flows' laminar-to-turbulent transition. This issue is particularly relevant in the study of the flow field developing around wind turbine airfoils. In this regard, the prediction of the flow's laminar-to-turbulent transition is extremely important, especially when Laminar Separation Bubbles (LSBs) occur near the leading edge of the airfoil [1]. Reynolds-Averaged Navier-Stokes (RANS) approaches can be considered very appealing for the aerodynamic design of modern wind turbines due to their limited computational resource requirements. However, these methods are often not reliable since they are developed under the hypothesis of a fully turbulent regime. In order to overcome this drawback, some locally formulated transition models have been included in the RANS equations [2; 3; 4]. This paper focuses on Local Correlation based Transition Models (LCTM), which have demonstrated acceptable accuracy in a wide range of applications. LCTM methods integrate CFD, compatible transport equations, and empirical correlations for transition modeling purposes. In this context, it is essential to underline that transition models compatible with the RANS approach have become popular methods to deal with flows at moderate Reynolds numbers. Indeed, under these specific flow conditions, the transition from a laminar to a turbulent regime can have a significant impact, not only on the design of wind turbine blades, but also in several aerodynamic applications [5; 6]. Standard LCTM approaches use two additional transport equations, one for the turbulence intermittency factor and the other for the transition onset correlation. The transition model, called \(\gamma-\widetilde{\text{Re}_{\theta,t}}\), provides correlations for the sake of initiating the transition process in the equations. More recently, [PERSON] et al. [7] proposed a new version of the \(\gamma-\widetilde{\text{Re}_{\theta,t}}\) model, named the \(\gamma\) model, which avoids the \(\widetilde{\text{Re}_{\theta,t}}\) transport equation by employing an algebraic scheme. It is important to put into evidence that the LCTM methods were initially coupled with the Shear-Stresses Transport (SST) \(k-\omega\) turbulence model by developers. However, several papers concerning the the adoption of the Spalart-Allmaras (SA) turbulence model in the \(\gamma-\widetilde{\text{Re}_{\theta,t}}\) context have appeared in recent years [8; 9; 10; 11; 12; 13; 14]. The main reason behind this choice is due to the fact that the SA equation has produced very good results in the computation of external flows. Furthermore, the model has also shown a lower computational cost than the SST \(k-\omega\) model. Despite this evident attention to the LCTM-SA approach, only one paper focused on the \(\gamma\) model coupling with the SA equation was published by [PERSON] et al. [13]. They proposed an implementation for compressible flows developed within the open-source SU2 library. In this paper, we present recent advances in the development of laminar-to-turbulent transition modeling based on the SA equation. In particular, starting from our implementation, introduced in [11; 12; 15], we discuss the impact of a low Reynolds number correction for the turbulent variable. Furthermore, we also introduce and assess a new implementation of the \(\gamma-\)SA model derived from the contribution of [PERSON] et al. [13]. Specifically, we discuss the impact of a positivity preserving implementation for the intermittency transport equation, confirming the key role of the numerical solution procedure adopted for LCTM techniques [16]. The reliability and effectiveness of the proposed approaches are also discussed in the paper. Several benchmark cases, spanning a wide range of Reynolds numbers, are faced. This paper is organized as follows. Section 2 presents the governing equations considered here. Section 3 briefly describes the discretization technique.