# Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators
## 3 Computational Setup  
The present study consists of a rectangular VG positioned on a flat plate with an incident angle to the oncoming flow. The height of the VG located at the flat plate in the simulations is going to be different, and the AR will consequently change, whereas the angle of attack will remain constant. The ARs of the three cases are AR\({}_{\text{H2}}\) = 2, AR\({}_{\text{H}}\) = 2.5 and AR\({}_{\text{H1}}\) = 3, and the heights are going to be H\({}_{\text{2}}\) = 4.16, H = 5 and H\({}_{\text{1}}\) = 6.25 mm, respectively. The computational domain dimensions are represented in Figure 3 normalized by the baseline VG case height H.  
Wake symmetry behind the VGs is assumed in the current simulations. Thus, the computational domain includes only one VG inclined to the oncoming flow instead of a pair. In that way, meshing and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vortex Generator (VG) Property** & **Symbol** & **Value (mm)** & **Size in h Units** \\ \hline VG height & H & 5.0 & 1 \\ Vane length & L & 12.5 & 2.5 \\ Distance between VG pairs & D & 30 & 6 \\ Trailing edge separation & d & 12.5 & 2.5 \\ Incident angle & \(\beta\) & 18\({}^{\circ}\) & - \\ Local boundary layer thickness & \(\delta\) & 20 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vortex generator geometry in the Advanced Aerodynamic Tools of Large Rotors (AVATAR) project. Figure 2: Vortex generator array layout. computational time can be considerably reduced. Figure 2 illustrates in green color the spanwise locations of the domain consisting of only one vane. The symmetry assumption used in the present computations can be justified by the previous studies of [PERSON] et al. [PERSON] et al. (2016) and [PERSON] et al. [PERSON] et al. (2016). The computational domain is divided into 28 blocks. The mesh has been refined near the VG and in the corners of the vane where the velocity gradients are large. In regions far away from the VG and the wake, the mesh density is lower. Five blocks are located around the VG and six blocks downstream of the vane to capture the generated primary vortex. The same block-based meshing strategy as in the study of [PERSON] et al. [PERSON] et al. (2016) has been followed. The total amount of cells is eight million, with a height of the first cell of \(\Delta y/\mathrm{H}=3.23\times 10^{-6}\), normalized according the baseline VG height. Around the vane, the mesh has 1.7 million cells, while the mesh downstream the VG for capturing the wake has approximately 2.4 million cells; see Figure 4. In order to resolve the boundary layer, cell clustering has been used close to the wall, and the wall dimensionless distance of the first layer of cells is less than \(y+<1\). Figure 4: View of the meshing around the rectangular VG. Figure 3: Sketch of the computational domain. Dimensions are scaled by the baseline VG height H (not to scale). Each surface of the domain has been assigned to a type of boundary condition. The vane's four different patches and the bottom of the domain were defined as a wall with a non-slip condition. The roof of the domain and the two lateral surfaces were defined as slip surfaces (symmetrical hypothesis). The velocity inlet was chosen for the entry of the fluid and pressure outlet for the exit of the fluid downstream the VG. The quality of the mesh was evaluated by five main indicators to analyze whether it can be classified as a high quality mesh; see Table 2. This set of parameters is a mix of industry standards, solver manuals and academia standards and should consequently not be regarded as the only choice of parameter selection. Equiangular skewness is an indicator of how optimal the cell shape is related to the corner angles. For hexahedral cells, skewness should not exceed 0.85 to obtain a fairly accurate solution. The cell aspect ratio of a cell is typically the ratio between the width and height. For critical flow areas, except those close to the wall, the cell aspect ratio should not exceed an average of 10.