# Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators
## 5 Conclusions  
Vortices generated by a passive rectangular vane-type VG on a flat plate have been studied. Numerical simulations at a Reynolds number Re = 2600 based on the local BL momentum thickness \(\theta\) = 2.4 mm and free stream velocity \(U_{\infty}\) = 15 ms\({}^{-1}\) have been carried out using the RANS method.  
Computational fluid dynamics simulations are able to reproduce the physics of the primary vortex generated by a rectangular passive VG with reasonably good reliability. As numerical methods are the most frequently-used ones applied in optimizing VGs on wind turbine blades, the extensive information presented in the current study can be used as guidance for successful design and implementation of VGs on wind turbine blades and to carry out parametric dependencies of the VGs on different flow conditions. Because of the large range of parameters inherent in the problem (incident angle, interspacing between vanes, device orientation, vane height and length, etc.), an in-depth understanding of the fluid flow is needed to be correctly applied.  
Furthermore, a qualitative comparison of the spanwise velocity, normalized vorticity and turbulence kinetic energy fields at different plane positions downstream of the VG has been introduced to see how the vortex is developed. It is verified that when using an appropriate mesh, fields such as axial velocity, vorticity and TKE are determined with reasonable accuracy.  
A correlation study and comparison of the vortex parameters such as vortex trajectory, peak vorticity and streamwise BL velocity profiles with three different VG heights has also been carried out. It should be noted that, in the development of the center vortex trajectory, the points overlap each other in the lateral path for the three different VG heights, but not in the vertical path.  
It has been demonstrated for the three analyzed geometries that, for the same level of vorticity, the vertical path of the primary vortex and the wall shear stress downstream of the vane are higher as the actuator height increases. The wall shear stress has a direct influence on the quantity of energy transfer. Then, if a delayed stall is desired, the best geometry will be the one with the best wall shear stress increment. Thus, it could be concluded that the highest VG H\({}_{1}\) = 6.25 mm is more suitable for separation control applications.  
The funding from the Government of the Basque Country and the University of the Basque Country UPV/EHU through the SAIOTEK (S-PE11 UN112) and EHU12/26 research programs, respectively, is gratefully acknowledged.  
Figure 15: Wall shear stress comparison in the streamwise direction from the VG trailing-edge to 50H (spanwise distance z = 0) of the three different VG heights and without any vane on the wall.  
**Author Contributions:** [PERSON], [PERSON] and [PERSON] prepared and ran the numerical part. They also wrote the manuscript. The post-processing was done by [PERSON]. [PERSON] and [PERSON] provided constructive instructions in the process of preparing the paper.  
**Conflicts of Interest:** The authors declare no conflict of interest.