# Novel Fluidic Oscillator Evaluation Considering Dimensional Modifications
## 6 Results
### Mixing Chamber Angular Modifications (2D-CFD)
Four videos characterizing the velocity and pressure fields for the maximum and minimum MC internal angles studied are presented in the Supplementary Materials. The instantaneous velocity distributions measured at the FO outlet and at the FC lower outlet are presented in Figure 11, where the results from the maximum (\(\delta_{1}=\delta_{STD}+15^{\circ}\); entrance 1) and minimum (\(\delta_{4}=\delta_{STD}-15^{\circ}\); entrance 4) mixing chamber inclination angles are compared. The respective oscillation cycles are divided into eight equidistant time steps, the first one, T0, corresponding to the initial time presented in Figures 9 and 10. When looking at the FO outlet velocity distributions (Figure 11b,d) and comparing them with those obtained from the baseline case 3D simulations presented in Figure 6a, it can be concluded that the three graphs show very similar results: the maximum and average velocities are almost identical, around 60 m/s and 40 m/s, respectively. The maximum velocity peaks appear alternately at both sides of the FO outlet, and despite the fact the pressure field graphs are not presented in Figure 11, it can be stated that the relation between the pressure and velocity fields shows the same trend described when introducing Figure 6, which obeys the energy equation. A comparison of the 2D instantaneous velocity distributions at the FC lower outlet for \(\delta_{1}=\delta_{STD}+15^{\circ}\) (Figure 11a), \(\delta_{4}=\delta_{STD}-15^{\circ}\) (Figure 11c), and the baseline 3D results (Figure 6c) clearly shows the existence of FC reverse flow in all three cases. As previously observed, the FC reverse flow decreases with the MC inlet angle decrease; in fact, for the smallest inlet angle evaluated, the maximum reverse flow velocity magnitude is about 35 m/s and appears for a very small fraction of time, about one-eighth of the oscillation cycle; note that the velocity magnitude is about 50 m/s for the maximum MC angle considered and reverse flow exists for half an oscillation cycle. A comparison of the reverse flow from the baseline case 3D results with the 2D results gathered from the maximum and minimum MC angles evaluated shows that the 2D-CFD results overestimate the maximum reverse flow velocity, but the time period at which reverse flow exists is quite properly determined. Note that for the 3D baseline case the existence of reverse flow lasts for about three-eighths of the oscillation period, which is between the time for the maximum MC angle, 50% of the cycle, and the minimum FC angle, one-eighth of the oscillation period. As already observed in the 3D baseline case simulations, for the 2D simulations presented in Figure 11a,c, the velocity distribution associated with the fluid coming from the FC outlets and entering the MC is much more uniform than the reverse flow velocity distribution, with the maximum associated velocities also being smaller. Figure 9: Instantaneous velocity and pressure fields along a full oscillation period divided in four equidistant time steps. \(\delta_{1}=\delta_{STD}+15^{\circ}\). Entrance 1. Figure 10: Instantaneous velocity and pressure fields along a full oscillation period divided into four equidistant time steps. \(\delta_{4}=\delta_{STD}-15^{\circ}\). Entrance 4. Until this point, the main generic effects of the flow inside the MC at the FO outlet and the FC outlet for the entrance 1 and entrance 4 configurations have been studied. From now on, an analysis of the four MC angular configurations is presented and discussed. For the four MC angles studied, the FO outlet mass flow dynamics and corresponding frequency is presented in Figure 12. As expected, the average mass flow remains constant for all the four MC angles considered, the peak-to-peak amplitude tends to decrease with MC internal angle decreases, and a maximum variation of about 18% is observed between the maximum and minimum amplitudes evaluated (Figure 12a).