## 4 Conclusions  
In the current study, the effect of the external domain of an oscillating jet emitted from a double-feedback fluidic oscillator in a quiescent flow was studied via 2D-TR-PIV. Two different geometries were carried out, fully confined, and free external domain. In addition, the Re number was increased to investigate the effect of the flow rate on the flow pattern. For the free external domain, the frequency of the jet was changed linearly by the Reynolds number, and the jet spreading angle was also increased till it reached its saturated value. However, for the fully confined geometry, the velocity distribution pattern was completely different. In order to get unsteady flow characteristics, the POD method and phase-averaged analysis were conducted, and coherent structures were obtained. Some of the significant results were as follows:  
* Confinement of the external domain led to create two identical vortices at the lowest Re number and caused the jet to have a smaller spreading angle than the free external domain.
* For Re = 6440, a V-shaped pattern was created in the free external domain, but for the fully confined geometry, the presence of a vortex at the exit region of the fluidic oscillator prevented the formation of a periodic flow, and the jet bent toward it.
* For the fully confined geometry at Re = 10,730, the potential of the main jet tended to cope with the strength of the created vortices, and it was expected that by increasing the Re number, an oscillating pattern would be observed.
* A linear relation between the Reynolds number and the non-dimensional circulation ratio \((\mathrm{DU}_{j}/\Gamma)\) exists for the fully confined case. In contrast, this ratio for the free external domain is almost constant and independent from the Re number.
* For the fixed internal geometry, a linear relation between the Reynolds number and oscillation frequency leads to the Strouhal number, \(\mathrm{St}=f\,\mathrm{D}_{\mathrm{h}}/\mathrm{U}_{j}\), being constant.
* POD analysis reveals the fact that for the fully confined case, the third mode was still energetic at Re = 6440, and the first three modes stood for the large coherent flow structures. However, for the free external domain, the first two modes were energetic and showed the periodic behavior of the oscillating flow.
* Phase-averaged analysis showed that for the fully confined case, although the jet was attached to the sidewalls, there was an oscillating pattern at its small oscillation area, with high frequency.  
Figure 19: Phase identification for the free external domain at Re = 6440.  
Figure 20: Phase identification for the fully confined external domain at Re = 6440.  
**Supplementary Materials:** The following are available online at [[http://www.mdpi.com/2076-3417/10/23/8668/s1](http://www.mdpi.com/2076-3417/10/23/8668/s1)]([http://www.mdpi.com/2076-3417/10/23/8668/s1](http://www.mdpi.com/2076-3417/10/23/8668/s1)). Video S1: A movie of instantaneous velocity contour measured by the time-resolved PIV at Re = 6440 with fully confined external domain. This phenomenon is a non-ergodic process due to Coanda effect.  
**Author Contributions:** H.S.-K.: Visualization, Conceptualization, Methodology, Software, Investigation, Writing--review & editing. S.M.: Formal analysis, Investigation. K.C.K.: Supervision, Funding acquisition, Writing--review & editing. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was funded by the [National Research Foundation of Korea (NRF)] grant number [No. 2020R1A5A8018822, No. 2018R1A2B2007117], which is funded by the [Korean government (MSIT)].  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could influence the work reported in this paper.