# Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators
## 2 Baseline Experimental Data  
The current study is based on Advanced Aerodynamic Tools of Large Rotors (AVATAR) European project, and the parameters used for the validation of the computational results are the following ones:  
* Streamwise velocity profiles at different locations (AVATAR Task 3.1 [25])
* Velocity fields at streamwise planes 10H, 25H and 50H (AVATAR Task 3.1 [25])
* Fields of the normalized vorticity at different streamwise planes (AVATAR Task 3.2, [26])
* Turbulence kinetic energy fields at streamwise planes (AVATAR Task 3.2 [26])  
Taking into account the previous configuration and in order to characterize the primary vortex generated by the three different VGs, the following parameters have been proposed:  
* Streamwise velocity profiles at different streamwise locations.
* Primary vortex vertical and lateral positions to define the vortex trajectory.
* Peak vorticity \(\omega_{\rm x,max}\) development.
* Wall shear stress (WSS).  
According to the experimental data available in the AVATAR project and to reproduce the experiments of the VG on a flat plate performed in that project, the numerical simulations have been carried out at a Reynolds number Re = 2600 based on local BL momentum thickness \(\theta\) = 2.4 mm and with a free stream velocity of \(U_{\infty}\) = 15 m/s. A negligible pressure gradient on the plate is assumed. The angle of incidence of the vane to the oncoming flow is 18\({}^{\circ}\). The calculation of the local BL momentum thickness \(\theta\) was made by the application of Equation (1):  
\[\theta=\int_{0}^{\infty}\frac{u_{x}}{U_{\infty}}\bigg{(}1-\frac{u_{x}}{U_{ \infty}}\bigg{)}dy \tag{1}\]  
where \(u_{x}\) is the streamwise velocity component, \(U_{\infty}\) the free stream velocity and \(y\) the vertical coordinate normal to the wall.  
In order to validate the numerical model of the VG, the results of the numerical simulations are compared to the experimental data of the AVATAR Project [25; 26]. The experiments were carried out  
Figure 1: Sketch of the vortex generator (VG) dimensions with respect to the local boundary layer (not to scale).  
in the Boundary Layer Wind Tunnel of the Delft University of Technology. The tunnel can attain a maximum speed of 38 m/s in the wide-walled test section of 1.5 \(\times\) 0.25 m\({}^{2}\). The large separation of the side walls (1.5 m) minimizes end effects on the flow region of interest along the centerline zone. An adjustable back wall allows adjustment of the pressure gradient, ensuring a truly null pressure gradient when desired. The turbulence level at maximum free stream velocity was determined as 0.5%. Vortex generator dimensions were designed according to the previous research made by m, where the rectangular vortex generators were designed according to the study of [PERSON] et al. [28] and are summarized in Table 1.  
The placement of the VGs is such that flow impinges on the vanes in a divergent manner, producing counter-rotating, common down-flow embedded vortices. For each test case, 25 pairs of rectangular VGs were mounted in an array configuration, side by side, as shown in Figure 2, covering a spanwise distance of 0.75 m and centered on the tunnel centerline. This was done in order to minimize end-effects from the finite array. The vortex generator height is H = 5 mm and considering a negligible pressure gradient.