# Novel Fluidic Oscillator Evaluation Considering Dimensional Modifications
## 6 Results
### Mixing Chamber Angular Modifications (2D-CFD)
In reality, the main effect on the MC angular modification is observed when evaluating the FO outlet jet oscillation frequency, then it keeps increasing with decreases in the MC inlet angle (MC entrance width increase); see Figure 12b. For entrance 1, \(\delta_{1}=\delta_{STD}+15\), the FO's frequency is 27.27 Hz and increases to 34.82 Hz when entrance 4, \(\delta_{1}=\delta_{STD}-15\), is considered. It must also be highlighted that as the internal angle decreases, the FC reverse flow also decreases Figure 12c; therefore, the FO outlet frequency increase can also be associated with the FC reverse flow decrease. And, this also applies when comparing the 3D and 2D simulations in Figure 8, where for the same internal dimensions the 3D case generated higher frequencies than the 2D one, with the 3D FC reverse flow being much smaller than in the two-dimensional case. Figure 11: Feedback channel and fluidic oscillator outlet instantaneous velocity profiles at eighth equi-distant time steps taken along a full oscillation cycle. Feedback channel lower outlet velocity profiles, case \(\delta_{1}=\delta_{STD}+15\) (**a**), and case \(\delta_{4}=\delta_{STD}-15\) (**c**). Fluidic oscillator outlet velocity profiles, case \(\delta_{1}=\delta_{STD}+15\) (**b**), and case \(\delta_{4}=\delta_{STD}-15\) (**d**). One of the key points when trying to understand the performance of any FO is the study of the origin of the self-sustained oscillations. In order to start understanding the time-dependent forces acting on the jet as it enters the MC, Figure 13 introduces, for the four MC inlet angles studied, the unsteady net mass flow and pressure forces acting on the jet and considering both FC outlets. This corresponds to the instantaneous application of the first and second terms of Equation (16) on both FC outlets. The first thing to notice is that the maximum mass flow force's magnitude is about 35% of the pressure force's magnitude. The peak-to-peak amplitude of the net mass flow forces increases with the MC inlet angle decrease. The same happens for the net pressure forces, although it appears that for the STD case the peak-to-peak amplitude is slightly larger than for the rest of the cases. Note also that for the entrance 3 and entrance 4 cases, the unsteady pressure amplitude remains the same. The increase in the net mass flow force's magnitude is directly linked to the increase in the FC mass flow measured at the FC outlet, while the pressure force  
Figure 12: For the four MC internal angles considered, this figure introduces the fluidic oscillator outlet dynamic mass flow (**a**), its associated frequency (**b**), and the FC lower outlet mass flow (**c**). Figure 13: Feedback channel outlet net mass flow forces (**a**) and net pressure forces (**b**) as a function of the different mixing chamber angles studied. is mostly connected to the dynamic stagnation pressure increase measured at the MC outlet's converging walls, which in turn depends on the jet inside the MC impinging on such converging walls. Therefore, a higher peak-to-peak amplitude indicates that the jet is impinging more perpendicularly to the MC's converging walls, raising the pressure along the corresponding FC. When comparing the pressure and mass flow forces from Figure 13a,b, a phase lag is observed between both parameters. It seems the mass flow forces actuate about 0.02 s after the pressure forces. This delay is likely to be the time needed for the mass flow to travel from the FC inlet to the FC outlet. The left-hand-side column of Figure 14 represents the four different MC angular positions evaluated, the stagnation pressure unsteady value measured at the MC's lower converging wall, the time-dependent pressure and mass flow forces measured at the lower FC outlet, and the instantaneous net force evaluated at both FC outlets. The graphs introduced in the right-hand-side column characterize the time-averaged and peak-to-peak amplitudes of the respective time-dependent values introduced in the left-hand-side column.