# Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators
## 3 Computational Setup
Figure 5 represents the wall y+ field distribution on the VG and bottom walls. For the current study, the maximum value of y+ corresponds to 0.366 and its average is 0.044. In this work, the open source code OpenFOAM (Version 2.4.0, The OpenFOAM Foundation Ltd., London, UK) [30] has been used for simulating a rectangular VG on a flat plate with negligible pressure gradient. This CFD code is an object-oriented library written in C++ to solve computational continuum mechanics problems. The solver potential Foam, which solves potential flows, was used to generate starting fields (initialization of fields) in order to speed up the convergence process. This solver is suitable to generate initial conditions for more advanced solvers such as the one used in the present work named simpleFoam. The simpleFoam solver has been applied for steady-state, incompressible and turbulent flows using the RANS (Reynolds averaged Navier-Stokes) equations. Second order discretization schemes were employed in the CFD simulations. The k-omega SST (shear stress transport) turbulence model developed by [PERSON] [31] was used for all the computations. This turbulence model is a combination of two models: [PERSON]'s k-\(\upomega\) model for the near wall region and the k-\(\varepsilon\) model for the outer region and in free shear flows. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicator** & **Acceptable Values** & **Current Research Values** \\ \hline Cell aspect ratio & 1–10 & 5.92 \\ Equiangular skewness & \textless{}0.85 & 0.169 \\ Maximum included angle & \textless{}120\({}^{\circ}\) & 105.24\({}^{\circ}\) \\ Minimum included angle & \textgreater{}20\({}^{\circ}\) & 74.75\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quality meshing parameters. Figure 5: Wall y+ field distribution on the VG and bottom walls. Simulations were performed on a personal server-clustered parallel machine with Intel(r) Core i7-6700 CPU 3.40 GHz \(\times\) 8 cores and 32 GB RAM on 64-bit Linux. The domain was automatically divided into eight subdomains to solve in parallel and to reduce the simulation time. The computational cost was approximately 12 days per simulation. A mesh independency study has been done with the boundary layer velocity profile at the plane 10 H downstream of the VG and at z = 0 cross-wise position. Figure 6a shows a comparison between the CFD curves of three studied meshes: 2 million (coarse), 4 million (medium) and 8 million (fine) cells for the baseline case with a VG height of H = 5 mm. Figure 6b represents the BL velocity profiles of the fine mesh (blue) versus the experimental one (black) provided by [25]. Verification of sufficient mesh resolution was performed based on the Richardson extrapolation method and applied to the normalized peak vorticity \(\omega_{\mathrm{x}}/(U_{\infty}/\mathrm{H})\) at the plane position of 10H behind the vane. Table 3 shows the results of the mesh independency study. A monotonic convergence was achieved. The normalized streamwise velocity curve of the fine mesh and the experimental one presented in Figure 6b fit reasonably well. This higher resolution mesh has been used for the current computations and applied to the three low profile vanes H, H\({}_{1}\) and H\({}_{2}\).