## 3 Results and Discussion
### Time-Averaged Results
#### 3.1.1 Velocity Distribution
However, the internal side was oscillating due to the effect of the Coanda vortex and the feedback loop (or recirculation zone) within the mixing chamber, but the jet could not oscillate at the cavity because the momentum or the strength of the jet was not enough to cope with the power of the vortex, shear stress, and vortex's suction toward the boundary of the jet. Indeed, Section 3.2. describes this phenomenon in more detail, which states that the frequency of the oscillating jet at the external domain was around 0.001 [Hz], while for the internal domain it was calculated to be around 0.4 [Hz]. Furthermore, when the recirculation zone at one side of the cavity was created, due to the small diameter and high velocity, it led to a high-pressure shortage in this recirculation area. This caused the jet to be pulled toward the one side wall, which led to supply the large-pressure shortage and more deflection of the jet. Moreover, when the jet reached the sidewall, further shrinking of the recirculation area could not be achieved. Thus, when the increment of the shortage of pressure in this recirculation area diminished then the pressure increased. Subsequently, the other recirculation area at the cavity started to be stronger than before, which caused the jet after a while to attach to the opposite side of the wall, which showed the non-ergodicity pattern in the cavity. The compelling point was that the frequency of this oscillation at the cavity that illustrated the shifting from the left to the right side walls of the external domain, in Re = 6440, equaled to 0.001046 [Hz],  
Figure 6: Time average of (**a**) streamwise velocity, (**b**) transverse velocity, (**c**) velocity magnitude, and (**d**) streamline for free external domain at Re= 2680, 6440, and 10,730 and z/D\({}_{\rm h}\) = 0.  
which was smaller than the internal part and the sweeping jet in the free external domain, both of which were almost 0.4 [Hz]. Thus, it could be postulated that the jet's oscillation was independent of the time at the external region or cavity. For Re = 10,730, the jet was generated by the fluidic oscillator and changed the direction from right to left, so the final time-averaged pattern was inclined toward the centerline with the highest velocities. However, the jet was not symmetrically distributed, but almost a steady and continuous jet was obtained in the time-averaged results (Figure 7). Additionally, the fully confined geometry had a higher maximum value of the non-dimensional velocity distribution at a constant flow rate or Re number for both the u-component and the v-component (Figure 7). This occurred because the volume of the surrounding fluid was higher for the free external domain case, and the jet core was weaker due to the entrainment flow towards the jet core. For the free external domain, the flow was entrained from the direction normal to the oscillation pattern, and this entrainment increased, while the contact area between the jet and ambient fluid increased by increasing the flow rate. In contrast, for the fully confined geometry, the entrainment was prevented, and some strong vortices were created, which affected the flow pattern, as illustrated in Figure 7.  
For Re = 2680, two vortices were created on both sides of the jet, which led to a smaller spreading angle in comparison to the free external domain, as shown in Figure 7. By increasing Re to 6440, the jet could not oscillate freely and attached to the left side wall of the cavity because the vortex became strong and pulled the jet toward it (because of the shear layer, some small vortices were created and accumulated together, which led to a large vortex). In fact, there was no entrainment flow toward the external domain from the normal direction. Subsequently, to satisfy the continuity equation, the vortex was inclined to circulate continuously. This led to the control of the flow in the external region and did not allow the flow to oscillate. The strength of the oscillating jet was not enough, and the V-shaped pattern could not be produced.