# Computational Characterization of Turbulent Flow in a Microfluidic Actuator
## 5 Effect of Feedback Channels Geometry Modification on Output Frequency  
The operational parameters of the studied fluidic oscillator are governed by its geometric configuration, which means that its output frequency is fixed for a given incoming Reynolds number. Therefore, an opportunity to modify such frequency arises from the alteration of the internal geometry, which would allow a customization of the fluidic actuator for specific applications. Figure 9: Sensibility study regarding the employed turbulence model (**a**) and turbulence intensity level at the inlet of the fluidic actuator (**b**). A previous study evaluated the effect of the width of the inlet and outlet sections of the mixing chamber, as well as the angles of the inner walls of the exit nozzle on the frequency and amplitude of the mass flow signal through the upper outlet [16]. They found a certain dependence of frequency and amplitude over the investigated parameters, as mentioned in the introduction. Here, however, we focus on the influence of the geometry of the feedback loops on the output operational frequency of the fluidic actuator. For that, two extra configurations have been considered, which are shown in Figure 10.  
As can be appreciated from Figure 10, the feedback loops connecting the rear area of the mixing chamber and its front part are rounder than in the original configuration, i.e., the radius of curvature of the channel elbows is larger. Moreover, the corners of both blocks, upper and lower, in the new configurations are not sharp \(90^{\circ}\) angles but have a certain curvature radius to preserve the width of the channels, and even in the case of C2, two of the corners have disappeared in each feedback loop. Such geometrical changes are aimed at easing the fluid circulation along the feedback loops. The grids of the modified configurations are similar in size and quality to the intermediate mesh of the original fluidic oscillator. In the C1 case, it consists of about 328,000 cells, whereas in the C2 case, it is around 314,000 cells. The numerical set up employed for these new configurations was the same as in the original case described in Section 2, including the turbulence model. Figure 11 shows the normalized mass flow through outlet 1 versus time for the three geometrical configurations: original, C1 and C2 at \(Re\approx 16,000\). It can be seen that as the feedback channels get rounder, the frequency of the oscillation decreases (i.e., the period is larger) and the mass flow curve is flattened in some parts of the increasing and decreasing branches (see areas inside the ovals in Figure 11) containing the inflection points; even in the C2 case, a plateau seems to be formed. On the other hand, the minimum and maximum values of the normalized mass flow in the three curves are very similar. Figure 12 shows velocity contours in the three geometrical configurations at approximately the same moment in the oscillation cycle, when the jet is bended downwards and the fluid is mainly divided between the exit nozzle of the mixing chamber and the upper feedback channel. Very similar flow patterns for the three geometries are observed at the outlet branches, with a large vortex in the lower branch and with very similar intensity. However, differences can be noticed in the upper recirculation loop, where the original (Figure 12a) and C1 (Figure 12b) configurations clearly show separated flow at the inlet corner of the feedback channel, but the fluid in the C2 configuration (Figure 12c) attaches to the outer wall of the loop without presenting any separated vortices. Moreover, the velocity magnitude within such vortices is lower in the C1 geometry, its shape being more elongated than in the original case; in other words, the vortex is stretched to conform to the  
Figure 10: Illustration of the two configurations evaluated with modified feedback loops. (**a**) Configuration 1, C1; (**b**) Configuration 2, C2. Additionally, the computational grid is shown, which can be better seen if zoom is applied. rounded walls.