# Analysis of a Novel Fluidic Oscillator under Several Dimensional Modifications
## 6 Results  
### Reynolds Number Modification  
One of the main characteristics of any fluidic oscillator is its linear relation between the inlet Reynolds number and the FO output mass flow frequency. Four Reynolds numbers, \(\mathrm{Re}=\) 27,483, 41,224, 54,595, and 68,707, based on the mixing chamber inlet width and velocity, were simulated to evaluate the actual FO linear performance. The result was a perfect linear behavior defined by the equation \(f(Hz)=0.0005364786\times Re-0.18617977\) with a correlation coefficient of \(R^{2}=0.999966\). It needs to be considered that this equation is valid in the range of Reynolds numbers presented here. The unsteady (time-dependent) mass flow at the FO outlet and at the lower FC channel outlet are introduced in Figure 7 for the different Reynolds numbers studied. As the Reynolds number increases, the FO outlet mass flow average value and peak-to-peak amplitude keeps increasing (Figure 7a) amplitude increases by 270% when the Reynolds number raises from 27,483 to 68,707. The peak-to-peak amplitude of the FC mass flow suffers a much smaller growth with the Reynolds number increase: only 159% when comparing the minimum and maximum Reynolds numbers studied, with an average value around zero. In fact, the mass flow across the FC is non-symmetric: the mass flow flowing towards the FC outlet at Reynolds number 68,707 is about 36% larger than the one flowing towards the FC inlet, and the percentage raises to almost 68% for the minimum Reynolds number studied (see Figure 7b). To unveil why the FO and FC mass flow amplitudes and frequencies change at different Reynolds numbers, we need to understand the origin of the self- sustained oscillations. In this regard, we will next focus on studding the stagnation pressure fluctuations inside the MC. Perhaps one of the most relevant parameters to consider is the stagnation pressure unsteadiness at the mixing chamber (MC) outlet's inclined walls. The stagnation pressure oscillations appear to be directly correlated with the momentum pressure and mass flow terms measured at the FC outlet. These three parameters are presented in Figure 8a,c,e, respectively. On the right-hand side of Figure 8, the time-averaged values of the MC lower inclined wall stagnation pressure, the net momentum time-averaged pressure term measured at the lower FC outlet, and the time-averaged mass flow momentum measured at the same location are presented (see Figure 8b,d,f, respectively). These figures also show the peak-to-peak amplitude of these variables as a function of the Reynolds number evaluated. The unsteady net momentum obtained when considering the pressure and mass flow terms measured simultaneously at both feedback channel outlets and for all Reynolds numbers evaluated is presented in Figure 8g, the corresponding time-averaged and peak-to-peak amplitude values are introduced in Figure 8h. Figure 7: Fluidic oscillator outlet unsteady mass flow (**a**) and feedback channel mass flow (**b**) as a function of the Reynolds number. From the unsteady graphs, it appears as if the frequencies associated with the stagnation pressure term measured at the MC inclined wall and for the different Reynolds numbers are also observed in the unsteady values representing the pressure momentum,  
Figure 8: Unsteady stagnation pressure measured at the mixing chamber lower inclined wall (**a**), time-averaged values and peak-to-peak amplitudes (**b**). Pressure momentum terms measured at the FC lower outlet (**c**) and their respective average values and peak-to-peak amplitudes (**d**). Dynamic mass flow momentum terms measured at the FC lower outlet (**e**), and their respective average values and peak-to-peak amplitudes (**f**). Instantaneous net momentum obtained when considering pressure and mass flow momentum terms at both FC outlets (**g**), average values, and the peak-to-peak amplitudes (**h**). All graphs consider the four Reynolds numbers studied.