## 3 Results and Discussion
### Time-Averaged Results
#### 3.1.1 Velocity Distribution  
The non-dimensional time-averaged velocity field for the sweeping jet in the free external domain is shown in Figure 6. As the results show, by increasing the Reynolds number, the spreading angle of the oscillating jet was enlarged for Re= 2680 to Re = 6440 and reached a maximum deflection of 90 degrees at Re = 6440. This meant that the flow was fully attached to the nozzle exit's diverging wall. Thus, by increasing the Reynolds number from 6440 to 10,730, the maximum deflection angle was almost constant because, for this range, the deflection angle was identical to the nozzle exit angle. However, as Re increased, the inhomogeneous velocity distribution became clearer, and the weak flow within the maximum concentration of the flow disappeared. Additionally, as [PERSON] et al. [30], suggested, by increasing Re, the jet spent more time at its maximum deflection because of the Coanda effect, and the oscillating jet did not move with a constant oscillating speed. Due to the Coanda effect, a recirculation bubble formed within the mixing chamber, which was a charge of the oscillating pattern at both the internal and external regions. Moreover, by increasing the Reynolds number, the size of the recirculation bubbles grew. Therefore, the spreading angle and frequency of the oscillating jet increased and a different flow pattern was created in the external region. The velocity ratio was defined as the maximum value of the non-dimensional v-component to the maximum value of the non-dimensional u-component. The results of the sweeping jet in the free external domain in Figure 6 show that by increasing the Reynolds number, this ratio increased from 0.46 to 1 for Re = 2680 to Re = 10,730. Therefore, for low Reynolds numbers, there is a strong streamwise velocity and weak transverse velocity of the continuous jet, with a small spreading angle jet. For the highest Reynolds number, the velocity ratio was increased, and the spreading angle grew to the maximum value (90\({}^{\circ}\)). Thus, as the jet flow rate increased, the jet momentum changed from an even distribution at the centerline for Re = 2680 to being mainly distributed on the lateral sides, which caused a V-shaped time-averaged velocity field. Thus, for the fixed geometry in the current work, the Strouhal number, St = \(f\) D\({}_{\text{h}}\)/U\({}_{\text{j}}\), was constant, since the oscillation frequency changed linearly with the velocity. Figure 5: Frequency versus Reynolds number for free external domain (the uncertainty was estimated at around 2% [38]). To investigate the effect of confinement on the flow pattern and the performance of sweeping jet, the non-dimensional time-averaged velocity field for the fully confined external domain is depicted in Figure 7. Although a sweeping jet pattern was produced and controlled by the internal part (double-feedback fluidic oscillator), the jet did not oscillate at this range of Reynolds number as it did for the sweeping jet in the free external domain. This phenomenon was opposite to the results of the previous study, while the external domain had steps in the normal direction to the emitted flow [31], where notable differences between the effect of confinement and Re number could be concluded. First, in the fully confined domain, at the lowest Reynolds number 2680 where the jet could not oscillate similar to the sweeping jet in the free external domain, the jet emitted to the cavity and created two identical recirculation zones, and due to the shear stress at the boundary of the jet, two vortices with equal sizes were created. Thus, by incrementing the Reynolds number to 6440, the shear stress at the boundary of the jet increased. Due to the Coanda vortex and different pressure distribution across the jet, the jet was inclined to attach to one side.