# Analysis of a Novel Fluidic Oscillator under Several Dimensional Modifications
## 3 Mesh Assessment  
Figure 1 introduces the central part of the (FO) investigated in the present study. The mixing chamber (MC) is the core of the FO; above and below it, the feedback channels (FC) can be observed. Flow enters through the power nozzle (PN) and leaves through the main outlet. The red line shown in the mixing chamber upper converging wall is simply a line probe to allow the measurement of the maximum stagnation pressure in this location. Although not shown in the figure, the same line probe was also placed at the lower converging wall. The different dimensions of Figure 1 are as follows: FO power nozzle width 0.02 m, FO power nozzle angle \(\theta=8.343\) degrees, MC entrance 0.0255 m, MC output 0.08356 m, MC inlet angle \(\alpha=14.997\) degrees, FO outlet width 0.0266 m, FO outlet angle \(\beta=58.235\) degrees, external radius \(Rext=0.0949\) m, and internal radius \(Rint=0.0627\) m. The computational domain inlet width, which can be seen in Figure 2a, is 0.0808 m and the radius of the buffer zone, also seen in the same figure, is 1.562 m. This configuration is flat, having a spanwise length of 0.01 m; it is called the baseline case, and in the present manuscript, the main effect on the FO performance when modifying the FO outlet width and the MC inlet angle is analyzed. Figure 1 also shows the positive and negative directions taken for each of the two geometry modifications. A fully structured two-dimensional (2D) mesh (extruded in the spanwise direction and using a single cell) with 367,720 cells was used to evaluate the flow at a Reynolds number \(\text{Re}=54\),595, the characteristic length being the fluidic oscillator power nozzle. In fact, in order to obtain simulated results independent of the mesh resolution, four different mesh densities were initially evaluated, their respective number of cells were, 62,143; 180,065; 367,720; and 718,920. Table 1 summarizes the minimum, maximum, and average \(y+\) as well as the outlet mass flow frequency associated, obtained for the different mesh resolutions. The last column indicates the frequency error versus the frequency obtained using the denser mesh; notice that the error gathered using a mesh of 367,720 cells  
Figure 1: Fluidic oscillator mixing chamber main parameters. Figure 2: Main view of the computational domain used in the present study. (**a**) Computational domain overall view. (**b**) Mesh in the central part of the fluidic oscillator, upper view. (**c**) Upper feedback channel inlet, zoomed view of the mesh. is negligible. Figure 2a presents the entire computational domain with the mesh associated, and Figure 2b,c introduces a zoomed view of the upper feedback channel mesh. The boundary conditions employed in all simulations were as follows: Dirichlet boundary conditions for velocity and Neumann boundary conditions for pressure at the inlet. An absolute pressure of \(10^{5}\) Pa and Neumann boundary conditions for velocity were considered at the buffer zone outlet. Neumann boundary conditions for pressure and Dirichlet boundary conditions for velocity were set to all walls. This considers a turbulent intensity of \(I=0.1\%\), a fluid velocity of \(U=10\) m/s, and a computational domain inlet width of \(L=0.0808\) m (see Figure 2a). The following equations were used for the different turbulence properties: \(k=(3/2)U^{2}I^{2}\); \(\epsilon=C_{\mu}(k^{3/2}/L)\), where \(C_{\mu}=0.09\); \(\omega=\epsilon/\left(C_{\mu}k\right)\); and \(v_{t}=k/\omega\). Using those equations, values for the turbulent kinetic energy \(k\), the turbulent dissipation rate \(\epsilon\), the specific dissipation range \(\omega\), and the turbulent kinematic viscosity \(v_{t}\) at the computational domain inlet were, respectively, \(k=1.5\times 10^{-4}\) (m\({}^{2}\)/s\({}^{2}\)), \(\epsilon=2.046\times 10^{-6}\) (m\({}^{2}\)/s\({}^{3}\)), \(\omega=0.152\) (s\({}^{-1}\)), and \(v_{t}=9.9\times 10^{-4}\) (m\({}^{2}\)/s). Table 2 summarizes the boundary conditions employed for the CFD simulations.