*5.3. Single Fluidic Oscillator without External Flow*

The effect of a bent outlet on the oscillator performance was first examined for the single fluidic oscillator shown in Figure 1. Figure 9 shows the variations of jet frequency with the mass flow rate at different bending angles for the single fluidic oscillator without external flow (Figure 1). The range of mass flow rate is . *m* = 0.19 − 0.72 g/s. The frequency generally increases as the mass flow rate increases. It also increases with the bending angle (β) for the mass flow rates larger than 0.41 g/s. However, β = 20◦ and 25◦ show almost the same values of frequency throughout the whole mass flow range.

All the tested bending angles show larger frequencies than the reference model with β = 0 (Figure 1a), regardless of the mass flow rate. In the low mass flow range of 0.2–0.4, the frequency shows similar variations at β = 5–15◦ and β = 30–35◦. However, beyond the

mass flow rate of 0.4, the frequency varies differently according to the bending angle. At <sup>β</sup> = 40◦, the frequency largely increases for low mass flow rates ( . *m* = 0.19 and 0.30 g/s), but for the mass flow rates larger than 0.3 g/s, the oscillation of the jet disappears, and the jet becomes steady.

**Figure 9.** Frequency variations with mass flow rate for various bending angles (β).

Figures 10 and 11 show the variations of peak velocity ratio at the outlet (*FVR*) and the friction coefficient (*Ff*) with the mass flow rate at different bending angles, respectively. As shown in Figure 10, the peak velocity ratio generally increases with the mass flow rate for positive bending angles. However, in the case of the reference model (β = 0), *FVR* has a maximum value of about 0.9 at around . *m* = 0.4 g/s and shows the lowest values among the tested bending angles for the mass flow rates larger than 0.4 g/s. At . *m* > 0.5 g/s, *FVR* increases with β in a range of β = 0–15◦, but it decreases with β at β = 15–25◦, and β = 15◦ shows the highest peak velocity ratios among the tested bending angles. In the other range, the variation of *FVR* with the bending angle (β) is quite complicated.

**Figure 10.** Variations of peak velocity ratio with mass flow rate for various bending angles. (**a**) in the case of the reference model (β = 0) and (**b**) in the case of β = 20◦, 25◦, 30◦ and 35◦.

However, in the case of the friction coefficient, the variations with the bending angle and mass flow rate are relatively simple, as shown in Figure 1. Except for the case of the reference model (β = 0), *Ff* shows maxima for all the tested bending angles and it increases almost uniformly with the bending angle for β > 0◦ throughout the whole mass flow range. The maximum *Ff* occurs around . *<sup>m</sup>* = 0.4 g/s for <sup>β</sup> <sup>≤</sup> <sup>25</sup>◦, but it shifts to around . *m* = 0.5 g/s for β = 30◦ and 35◦. The reference model with β = 0 shows values of *Ff* between those of <sup>β</sup> = 5◦ and 10◦ for mass flow rate less than . *m* = 0.5 g/s, but it shows values similar to or less than those of <sup>β</sup> = 10◦ for . *m* > 0.5 g/s.

**Figure 11.** Variations of dimensionless pressure drop with mass flow rate for various bending angles.

Figure <sup>12</sup> shows the velocity fields in the fluidic oscillator at . *m* = 0.299 g/s and 0.622 g/s for four bending angles (β = 0◦, 15◦, 35◦ and 40◦). Two different phases (Φ = 90◦ and 270◦) of the oscillation are shown for each case. It is observed that the angle of jet oscillation at the outlet is reduced slightly as the mass flow rate increases, especially at β = 35◦. As the bending angle (β) increases in a range of β less than 40◦, the angle of jet oscillation and the jet width increase at both mass flow rates. This is related to the phenomena where the main flow shifts to the wall of the bent outlet opposite to the direction of bending, as shown in Figure 12. This flow shift causes an increase in the peak velocity inside the outlet nozzle and a shift in its location, which seem related to the increase in the jet frequency with bending angle shown in Figure 9. Additionally, the increase in the peak velocity causes a decrease in the pressure, which becomes the reason for the decrease in the pressure drop with bending angle shown in Figure 11. It is also found that the size of the main vortex in the mixing chamber is reduced as β increases. However, the vortex in the feedback channel near the inlet increases with β until β = 35◦, especially at the higher mass flow rate. However, at β = 40◦, the oscillation disappears as discussed above, even though a slight oscillation remains inside the chamber at the higher mass flow rate.
