# Analysis of a Novel Fluidic Oscillator under Several Dimensional Modifications
## 6 Results
### Reynolds Number Modification
mass flow momentum, and net momentum values shown in figures 8c,e,g, respectively, showing a correlation between all these parameters. In fact, the frequencies associated with the different parameters and different Reynolds numbers are presented in Table 5, where it is demonstrated that a correlation between all these parameters has to exist. Notice that the main frequency is almost identical for all the parameters evaluated. To further evaluate the link between the four parameters presented in Figure 8, the reader should now focus on Figure 8b,d,f. When comparing the peak-to-peak amplitude for the three parameters introduced in these figures and considering the minimum and maximum Reynolds numbers analyzed, it is observed that the maximum peak-to-peak amplitude is about 6.5 times larger than the minimum one, which corresponds to the minimum Reynolds number. In other words, the mixing chamber inclined wall stagnation pressure unsteadiness appears to be driving the momentum pressure term unsteadiness as well as the mass flow momentum term unsteadiness measured at the FC lower outlet. At this point and based on the information presented in Table 5 and Figure 8, we can conclude that the self-sustained oscillations appear to be controlled by the stagnation pressure unsteadiness at the MC inclined walls. To further reinforce this hypothesis, it is relevant to highlight that the momentum pressure term measured at a FC outlet width is nearly three orders of magnitude higher than the mass flow one Figure 8c,e. The net momentum is very small compared with the pressure momentum term measured on a FC single outlet, but it is about four times larger than the mass flow momentum of a single FC outlet, compare Figure 8g,e. This clarifies that small variations in the pressure momentum have a deep effect on the net one. To understand the relevance of the pressure net momentum terms versus the mass flow ones measured instantaneously at both FC outlets, Figures 9 and 10 were generated. The first of the two figures compares the two unsteady net momentum terms for the minimum and maximum Reynolds numbers studied, where it states that the value of the net  
Figure 9: Instantaneous net momentum pressure and mass flow terms measured at the feedback channels outlet sections and for the minimum and maximum Reynolds numbers studied. (**a**) Reynolds number 27,483. (**b**) Reynolds number 68,707. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reynolds Number** & **Re = 27,483** & **Re = 41,224** & **Re = 54,595** & **Re = 68,707** \\ \hline
**Parameter** & \multicolumn{4}{c}{**Main Frequency [Hz]**} \\ \hline MC wall pressure & 7.5 & 11 & 14.53 & 18.55 \\ FC Pressure & 7.52 & 10.86 & 14.62 & 18.57 \\ momentum & 7.52 & 10.88 & 14.53 & 18.26 \\ Net momentum & 7.25 & 10.85 & 14.6 & 18.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Main frequency as a function of the Reynolds number and the unsteady parameter evaluated. momentum pressure term at Re = 27,483 is 3.27 times larger than the net momentum mass flow term. In fact, the relation between the pressure and mass flow net momentum terms remains rather constant for all Reynolds numbers studied; this is clearly observed in Figure 10, where the peak-to-peak amplitude of both net momentum terms is presented for the four Reynolds number evaluated. All these graphs clarify that for the FO configuration presented in this study, the forces acting onto the jet as it enters the mixing chamber are mostly due to the pressure operating at the FC outlets, yet the forces due to the FC mass flow term are of the same order of magnitude as the pressure ones. At this point, it is important to recall the work performed by [25; 26; 27], where it was stated that the jet was pressure-driven and mass flow forces were playing a secondary role. The much more relevant role played by the FC mass flow forces in the present FO configuration is believed to be due to the particularly short and wide feedback channels employed in the present fluidic oscillator.