## 3 Results
### Vortex Size  
The vorticity on a perpendicular plane to the streamwise direction is a function of three variables, the distance from the vortex center, the peak vorticity of that plane, and the radius size. The calculation of the vortex radius is a difficult task for experimental and CFD data. [PERSON] et al. [32] and [PERSON] et al. [25] showed that the vorticity profile generated by a vortex generator in a plane normal to the streamwise direction and in a line passing horizontally through the vortex center has a Gaussian distribution-type shape and that the vortex center defined by the peak vorticity is located in the center of this Gaussian distribution. The vorticity profile fits the Gaussian distribution better in the peak values than in the tails. A way to overcome this fitting problem in the tails comes by a innovative definition of the vortex size by means of the concept of the half-life radius (\(R_{05}\)). The \(R_{05}\) is defined as the radial distance from the vortex center to the point where the half-value of the peak vorticity is located, as proposed by [PERSON] [34]. In Figure 6, the vorticity distribution in a spanwise plane normal to the free stream velocity at x distance from the VG trailing edge can be observed. In order to obtain the vorticity profile associated to the vortex center, the vorticity values of a horizontal line (shown in white color) passing through the vortex center are extracted. For each VG case, the vorticity profile that crosses the vortex center of 12 spanwise planes normal to the streamwise direction was extracted. These planes are placed from \(3\delta\) to \(25\delta\) distances from the trailing edge of the VG. Equations (2) and (3) represent the Gaussian distribution of the vorticity in a plane normal to the streamwise velocity, where \(r\) represents the radial coordinate, \(\omega\) is the vorticity expressed in s\({}^{-1}\), \(R_{0.5}\) the half-life radius in m and the dimensionless constant \(k\) with value of 1. According to [PERSON] et al. [32], the \(R_{0.5}\) can be determined by calculating the half-value of the peak vorticity \(\omega_{peak}\). \[\omega(r)\ =\ \omega_{peak}e^{k(\frac{r}{R_{0.5}})^{2}} \tag{2}\]  
\[\text{if}\quad r=R_{0.5}\quad\text{and}\quad\omega(r)\ =\ 0.5\quad\left\{ \begin{array}{l}k=\ln(\frac{\omega(R_{0.5})}{\omega_{r}})\ =\ \ln(\frac{1}{2})\\ \omega(r)\ =\ \omega_{peak}e^{\ln(\frac{1}{2})(\frac{r}{R_{0.5}})^{2}}\end{array} \right. \tag{3}\]  
Figure 6: Vorticity distribution in a spanwise plane normal to the free stream velocity at x distance from the VG trailing edge. Primary and secondary vortexes with a vorticity field are shown in a normal plane to the free stream velocity. The white horizontal is parallel to the z-axis and passes through the vortex center. Figure 7 shows the CFD results for the \(R_{0.5}\) considering the four different incident angles, \(\beta=10^{\circ}\), \(15^{\circ}\), \(18^{\circ}\), and \(20^{\circ}\), and some of the experimental (EXP) measurements obtained by [PERSON] [34]. Represented values are normalized with respect to the local boundary layer thickness (\(\delta\)) in the VG leading edge. The vortex size considering the criteria of the \(R_{0.5}\) shows an increasing trend along the planes placed normal to the streamwise direction. This increasing trend obtained in the CFD simulations is as well observed in the measurements of [PERSON] [34] for the incident angles. As it gets farther from the vortex generator TE, the half-life radius gets higher values. Although the slope representing the evolution of the vortex size increases as the incident angle does, it is more dependent on the distance from the trailing edge of the VG. Considering the VG height, bigger values of half-life radius are obtained for higher VG vanes. Even if the highest vane follows a similar trend, with each incident angle, it takes bigger values in small distances from the TE for the \(10^{\circ}\) incident angle.