**6. Conclusions**

The effects of bending outlet nozzles on the characteristics of a fluidic oscillator were investigated using URANS analysis with and without external flow in a range of bending angles (β) of 0–40◦. In the case without external flow, the frequency increased with the mass flow rate and also with the bending angle in a range of mass flow rates larger than 0.41 g/s. The reference model (β = 0◦) showed the lowest frequencies for all tested mass flow rates. The largest frequencies were shown at β = 40◦ for low mass flow rates, but the jet stopped oscillating for the mass flow rates larger than 0.30 g/s.

The peak velocity ratio (*FVR*) also increased with the mass flow rate except for the reference model, which showed the lowest *FVR* values for the mass flow rates larger than 0.4 g/s. For mass flow rates larger than 0.5 g/s, *FVR* increased with β in a range of β = 0–15◦, but it decreased thereafter until β = 25◦. The pressure drop through the oscillator (*Ff*) increased almost uniformly with β throughout the mass flow range for β > 0◦. *Ff* showed maxima around . *<sup>m</sup>* = 0.4 g/s for <sup>β</sup> <sup>≤</sup> <sup>25</sup>◦, which shifted to . *m* = 0.5 g/s for β = 30◦ and 35◦. The reference model showed an *Ff* level similar to that of β = 10◦.

The external flow was found to reduce the jet frequency, except at β = 40◦. The average relative difference in the frequency between the cases with and without external flow increased as β increased. For bending angles less than 40◦, the largest relative difference was 7.62% at <sup>β</sup> = 35◦ and . *m* = 0.30 g/s. As in the case without external flow, the jet oscillation disappeared at <sup>β</sup> = 40◦ for . *m* > 0.30 g/s. At this bending angle, the

external flow increased the frequency by 14.4% for . *m* = 0.30 g/s. With the external flow, the jet also became steady at <sup>β</sup> = 35◦ for the highest mass flow rate . *m* = 0.62 g/s, unlike the case without external flow. Therefore, it seems that the external flow generally suppresses the oscillation.

Except at β = 40◦, the external flow increased the peak velocity ratio for all mass flow rates. At <sup>β</sup> = 40◦, however, the external flow largely reduced *FVR*, especially for . *m* = 0.30 g/s, where the jet oscillation still existed. The effect of external flow on *FVR* was dominant in the cases where the jet oscillation disappeared, and the effect of β on the relative difference in *FVR* was not remarkable in the other cases, where the range of the relative difference was 2.33−8.50%. The external flow increased *Ff* by 3–14% in the tested β range, regardless of mass flow rate. The lowest relative differences in *Ff* were found at β = 20◦. The existence of the jet oscillation did not affect *Ff*.

As for the lift coefficient of the airfoil, β = 40◦ did not show the lowest values, but the values were similar to those at β = 20◦. This reflects both the positive effect of the increase in the pitch angle and the negative effect of the disappearance of the jet oscillation on the lift coefficient. The drag coefficient generally decreased as the bending angle increased, except at β = 40◦, where the drag coefficients were much larger than those at β = 35◦, except for Cμ = 1.02, where the jet still oscillated. The results obtained in this study provide information how the characteristics of a fluidic oscillator change with the bending angle of the outlet nozzle, which may be necessary in some practical applications. Improvement in the aerodynamic performance of airfoils using fluidic oscillators would contribute to energy savings in the operation of aircraft. Further research is required to find the difference in the aerodynamic performance of an airfoil between the cases using straight and bending fluidic oscillators.

**Author Contributions:** N.-H.K. performed numerical analysis and provided original draft manuscript. K.-Y.K. revised and finalized the manuscript. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2019R1A2C1007657).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
