# Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators
## 4 Results  
Numerical simulations of the vortex generating vane on a flat plate were performed. Three dimensions of a single low-profile vane H = 5 mm, H\({}_{1}\) = 6.25 mm and H\({}_{2}\) = 4.16 mm at an incident angle to the oncoming flow of \(\beta\) = 18\({}^{\circ}\) were computed and compared with experimental results. The extraction of the data from the computations was conducted in a similar way to the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Mesh Resolution**} & \multicolumn{3}{c}{**Richardson Extrapolation**} \\ \hline  & **Coarse** & **Medium** & **Fine** & **P** & **R** & **RE** \\ \hline \(\omega_{\mathrm{x}}/(U_{\infty}/\mathrm{H})\) & 0.35 & 0.62 & 0.66 & 2.75 & 0.15 & 0.66 \\ \hline \hline \end{tabular}  
* RE represents the extrapolated solution, R the ratio of errors and p the order of accuracy.  
\end{table} 
Table 3: Results of the mesh independency study 1. Figure 6: Comparison of the normalized streamwise velocity profile at the 10H downstream plane position and spanwise position of z = 0 corresponding to the baseline case of H = 5 mm. (**a**) CFD curves for three different meshes: coarse (green), medium (red) and fine (blue); (**b**) Boundary layer (BL) velocity profiles of the fine mesh (blue) versus the experimental one (black). procedure described in [14], in planes normal to the wall downstream of the VG to capture the development of the vortex. Table 4 shows the height H of the baseline VG and the heights in the other simulated cases H\({}_{1}\) and H\({}_{2}\). The VG H\({}_{1}\) has been designed with an aspect ratio AR = 2, which is the highest one, and the VG H\({}_{2}\) with an aspect ratio AR = 3. First of all, a comparison between experimental and CFD streamwise velocity profiles has been carried out for the baseline case H at the planes 10H, 25H and 50H downstream of the vane; see Figure 7. Additionally, four different cross-wise locations are analyzed, which are at z = 0, z = TE (VG trailing edge), z = D/3 and z = D/2, where D = 30 mm. At the crosswise location of z = 0, the numerical results fit quite well to the experimental ones. As the flow moves away from the center z = 0 to the spanwise direction, some differences can be found between the experimental and the numerical streamwise velocity profiles. \begin{table}
\begin{tabular}{c c c c} \hline
**VG** & **h/s** & **Height (mm)** & **AR** \\ \hline H1 & 0.31 & 6.25 & 2.0 \\ H & 0.25 & 5.00 & 2.5 \\ H2 & 0.21 & 4.16 & 3.0 \\ \hline \end{tabular}
\end{table} 
Table 4: Vortex generator dimensions and aspect ratios (AR). Figure 7: Normalized streamwise velocity profiles 0 at different streamwise locations 10H (top), 25H (middle) and 50H (bottom) behind the VG. Solid black lines (-) correspond to the experimental data and the blue ones (-) to numerical profiles. According to the information available in the AVATAR project, three variables have been chosen for qualitative comparison between the numerical and the experimental results: the streamwise velocity, the normalized streamwise vorticity and the turbulence kinetic energy. The experimental fields were only available at the downstream plane positions from 10H-50H. Figure 8 shows the out-of-plane streamwise velocity fields on spanwise planes at three different locations 5H, 10H, 25H and 50H downstream of the vortex generator. The comparison includes the results of the simulations corresponding to the three different VG heights and the experimental data. The height of the vortex generated by the vane increases as the vortex is moving away from the flat plate in the streamwise direction. At the farthest plane position studied 50H, the two vortexes that are visible in the near wake plane positions seem to be unique. The roll-up process largely occurs before the 10H location. The wake evolution is typical of the induced flow field where the velocity deficit is clearly observed in the places nearer the core of the vortex. The vortex size and the velocity at its center increase as it moves away from the flat plate.