# Novel Fluidic Oscillator Evaluation Considering Dimensional Modifications
## 3 Mesh and Boundary Conditions  
### Three-Dimensional Baseline Model  
The frontal view of the FO studied is presented in Figure 1, where the main parts are introduced. An upper and a lower channel, called the feedback channels (FCs), are placed on both sides of the mixing chamber (MC). The fluid enters through the power nozzle (PN), located on the left side of the figure, and leaves through the FO outlet. The red line observed in the mixing chamber's upper converging wall represents a line probe employed to measure the maximum pressure in this location. The same probe was also implemented on the MC's lower converging wall (not labeled in the figure). The main dimensions of the different parts of the FO presented in Figure 1 are defined next. The fluidic oscillator inlet (power nozzle) and outlet widths are 0.02 m and 0.0266 m, respectively. The width of the MC entrance is 0.0255 m, with the MC output width being 0.08356 m. The external and internal radius of the MC have values of \(Rext=0.0949\) m and \(Rint=0.0627\) m, respectively. The values of the different angles presented in Figure 1 are the FO's power nozzle angle, \(\theta=8.343^{\circ}\); MC inlet angle, \(\alpha=14.997^{\circ}\); and FO outlet angle, \(\beta=58.235^{\circ}\). The FO's thickness, measured in the spanwise direction is 0.01 m. The entire computational domain, which comprises a large buffer zone at the FO outlet and an inlet channel connected to the FO's inlet, is presented in Figure 2a; the radius of the buffer zone is 1.562 m, with the width of the inlet channel being 0.0808 m.  
This configuration is called the baseline or standard (STD) case and zoomed views of the 3D mesh employed in the MC and upper FC are presented in Figure 2b and c, respectively. Figure 2d introduces a zoomed view of the mesh near the wall in the cross-stream and spanwise directions. The entire mesh was designed using GMSH, it is fully structured and consists of 7,722,120 cells distributed in 21 layers across the spanwise domain, each layer having 367,720 cells. In order to properly capture the boundary layer evolution, care was taken to increase the mesh density near all the walls. The Reynolds number \(Re=54\),595, based on the FO's power nozzle width as the characteristic length, was kept constant throughout the entire study. The values of the minimum, maximum, and average y+ values obtained after the simulations and for the different wall surfaces belonging to the FO are summarized in Table 1. It is important to highlight that for all walls, the maximum y+ value was always obtained inside the buffer zone, where the mesh was more relaxed. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Wall** & **Min y+** & **Average y+** & **Max y+** \\ \hline Front and back & \(1.717\times 10^{-3}\) & \(1.397\) & \(8.822\) \\ Internal walls & \(9.347\times 10^{-4}\) & \(6.512\times 10^{-1}\) & \(2.178\times 10^{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: y+ values from the 3D simulation at different walls belonging to the FO. \(Re=54\),595. Figure 1: Fluidic oscillator mixing chamber’s main parameters. MC and FC main configuration (**a**). Main internal dimensions (**b**)  
Figure 2: Main view of the 3D computational domain used in the present study. Computational domain overall view (**a**). Mesh in the central part of the fluidic oscillator (**b**). Zoom view of the mesh at the upper feedback channel (**c**). Zoomed views of the mesh in the cross-stream and spanwise directions (**d**). At the computational domain inlet, Dirichlet boundary conditions for velocity and Neumann boundary conditions for pressure were considered. Neumann boundary conditions for velocity and an absolute pressure of \(10^{5}\) Pa were defined at the computational domain outlet (buffer zone outlet). Dirichlet boundary conditions for velocity and Neumann boundary conditions for pressure were established at all walls. The URANS \(k-\omega\) SST turbulence model was employed across the entire study.