# Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators
## 4 Results
The velocity in the middle of the vortex increases as it goes away, and the vortex increases, as can be seen by the reduction of the yellow. The normalized vorticity \(\omega_{x}/(U_{\infty}/\mathrm{H})\) fields at different streamwise planes are illustrated in Figure 9. The vorticity is a pseudovector field, which describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow. As shown in Figure 9, the experimental data and the CFD case of H = 5 mm are very similar, endorsing the accuracy of the current computations. As expected, the vorticity in the core of the vortex decreases as the distance increases, and that decrease is more significant at the planes 25H and 50H. The higher the vane, the larger is the vorticity in the vortex core. Figure 8: Comparison of the out-of-plane streamwise velocity fields \(u_{x}\) between experimental and numerical simulations of the three cases H, H\({}_{1}\) and H\({}_{2}\). Streamwise plane positions from top to bottom: 5H, 10H, 25H, 50H. The comparison of the turbulence kinetic energy fields is represented in Figure 10. The turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow and is a measure of the intensity of the turbulence. It is defined as follows:  
\[K=\frac{1}{2}\Big{(}\overline{u_{x}^{2}}+\overline{u_{y}^{2}}+\overline{u_{z}^{ 2}}\Big{)} \tag{2}\]  
where \(u_{x}\), \(u_{y}\) and \(u_{z}\) are the velocity field components. As shown in Figure 10, the TKE field comparison between the experimental case and the simulations is very similar at the planes 25H and 50H, whereas at the plane 10H, the experimental case does not have a quick development as the simulation has. On the one hand, for the case of the largest vane height H\({}_{1}\), the intensity of turbulence results in a higher y coordinate than the baseline H and then the shortest VG H\({}_{2}\). That means that as a consequence of the height of the VG, the turbulent flow moves through at a higher elevation. On the other hand, as the flow moves away from the trailing edge of the actuator, the energy is dissipated to a greater extent in the smallest vane H\({}_{2}\). Furthermore, it is clearly visible that for the case of H\({}_{1}\) = 6.25 mm at the plane 5H behind the VG, the energy created as a consequence of the vortex is the maximum one in comparison with the other cases H and H\({}_{2}\). Figure 11 shows the normalized streamwise velocity (\(u_{x}/U_{\infty}\)) profiles for the three different VG heights H\({}_{1}\) = 4.16 mm, H = 5 mm and H\({}_{2}\) = 6.25 mm at the 10H, 25H and 50H downstream positions. As shown in Figure 11, at the downstream position 25H and spanwise position z = D/2 and at 50H and spanwise positions z = D/2 and z = D/3, the differences of the curves are notable. In order to analyze the vortex evolution, up to three parameters were previously identified in past studies made by [PERSON] et al. (2016) and [PERSON] et al. (2016) on the streamwise longitudinal vortex embedded in turbulent boundary layers. Therefore, the proposed parameters to characterize the primary vortex generated by a passive rectangular VG are the streamwise peak vorticity \(\omega_{\mathrm{x,max}}\), the vortex path and the wall shear stress (WSS). The peak vorticity is used to locate the center of the streamwise vortex in each plane position downstream of the VG and, subsequently, to determine  
Figure 9: Comparison of the normalized streamwise vorticity \(\omega_{\mathrm{x}}/(U_{\infty}/\mathrm{H})\) between experimental and numerical simulations. Streamwise plane positions from top to bottom: 5H, 10H, 25H and 50H. the vortex trajectory. In addition, the WSS is a parameter associated with the vortex induced rate of mixing of the outer flow with the boundary layer. The trajectory of the primary vortex generated by a vane-type VG plays a determining role in the mixing performance.