# Analysis of a Novel Fluidic Oscillator under Several Dimensional Modifications
## 7 Discussion of the Results, Origin of the Self-Sustained Oscillations  
Until this point, the main unsteady characteristics of the FO have been analyzed at different Reynolds numbers, outlet widths, and MC inclined angles. For all cases studied, a large reverse flow at the FC has been observed (see Figures 7b, 12b and 16b). In fact, this large reverse flow was not previously observed in the FO configurations studied by [14; 25; 26; 27] or even by [28], where the same FO configuration was studied but at a very low Reynolds number. In the present subsection, an oscillation cycle is carefully analyzed, linking the velocity and pressure fields at different instants with the forces acting over the jet; the concept here is to unveil the forces acting on the jet as it enters the mixing chamber and understand why the jet keeps oscillating, even when this large reverse flow exists. Figure 20 introduces the mass flow and pressure forces pushing the jet on each feedback channel outlet for an oscillation cycle in separate graphs, and the overall forces acting over the jet are also presented. Four different time instants, shown as vertical lines in these graphs, will serve to analyze the unsteady forces on the jet as well as the velocity and pressure fields associated, these fields are introduced in Figure 21. The oscillation period starts at time 1.375 s, the jet inside the MC is around its upmost position, the lower FC is still pressurized (Figure 21a,b) and the forces acting on the jet as it enters the MC are still pushing the jet upwards (Figure 20). In this figure, for convenience both FC pressure forces are represented as positive. However, this situation is about to change since the upper FC reverse mass flow (which is almost at its maximum value) is about to interact with the jet inside the MC. Such interaction generates the pressure fluctuations observed in the pressure momentum graph shown in Figure 20 and are due to the temporal modification of the location and intensity of  
Figure 19: Fluidic oscillator internal velocity magnitude field (**a**,**c**) and pressure field (**b**,**d**). Minimum MC inclined angle (Angle 1) (**a**,**b**), Maximum MC inclined angle (Angle 3) (**c**,**d**). the stagnation pressure point at the MC converging wall. Notice as well that at this instant the lower FC mass flow is around its maximum (Figures 12b and 16b). It is also relevant to note the large vortical structure appearing at the center of the MC, which appears to be pulling down the right-hand side of the jet inside the MC. The next time period presented, corresponds to time 1.390 s and 1/4 of the oscillation period. At this instant, the upper FC is pressurizing, the forces on the jet change from positive to negative as it enters the MC, the jet inside the MC is moving downwards, and the jet leaving the FO is around its lower angular position (Figure 21c,d). The FO outlet mass flow is at the maximum (Figure 12a), and the FC mass flow on both FCs is about zero (Figures 12b and 16b). On the next quarter of a period \(T=1/2\), time 1.41 s, the jet inside the MC is about to reach its lower position, the upper FC is pressurized (but this situation is about to change), then the reverse mass flow at the lower FC is going to interact with the main jet at the MC, as it happened at \(T=0\). Such jet interaction will generate pressure fluctuations which will finally change the direction of the forces acting on the jet entering the MC (see Figures 20 and 21e,f). The outcome of these effects is observed in Figure 21g,h (time 1.425 s, \(T=3/4\)), in which it is observed that the lower FC is pressurizing. Both FCs' mass flows are about zero, the jet inside the MC is moving upwards, the jet at the FO outlet is about to reach its upper angular position, and the FO outlet mass flow is around its maximum value (Figure 12a). Figure 20: Unsteady mass flow and pressure forces measured at both feedback channel outlets and the overall forces acting on the jet; about half of a cycle is presented here. Baseline case configuration (STD) at \(Re=54\),595.