# Computational Characterization of Turbulent Flow in a Microfluidic Actuator
## 4 Flow Visualization and Analysis
Looking at the right column of Figure 7, it is noticed that pressure grows in the mixing chamber when the jet impinges on the exit nozzle walls; it is maximum when the jet impacts the exit nozzle wall with the steepest angle (e.g., Figure 7b,i) and minimum when the flow directly reaches the exit nozzle. The high pressure values at the impinging points are clearly noticed in Figure h,i,k,l, and the large vortex formed in the outlet branches in Figure 7h,l presents the minimum pressure values. In this way, an oscillation pattern of the pressure field is developed, which is connected with the mass flow cycle (in fact, they have opposite phases), a fact that has been referred to as \"axial pumping\" [14] in the fluid actuator. Interestingly, previous studies usually report only the behavior of the velocity field, so that the present work is one of the first studies to show explicitly the pressure field cycle inside this kind of device. Figure 8 displays the turbulent kinetic energy \(k\) contour field along one oscillation cycle at the corresponding times of Figure 7. It can be noticed that the highest values of \(k\) are attained in the mixing layers generated by the jet in the mixing chamber and in the outlet branches, as well as in the recirculation zones that flank the jet between the upper and lower blocks. It is precisely in such areas where large velocity gradients are generated, leading to substantial turbulent kinetic energy production. However, in the surroundings where the jet impinges the exit nozzle walls, \(k\) adopts moderate values because in such zones, turbulent dissipation is high. The large vortical structures developing in the mixing chamber and in the outlet branches are zones of high values of turbulent kinetic energy (see Figure 8a,c,d,f,g), as already observed in the study [PERSON] et al. [3], which also exhibits low pressure values. In Figure 8b,e, the maximum values of \(k\) are located within the outlet branches where the jet emerging from the mixing chamber exit nozzle reaches the upper wall (Figure 8b) or lower wall (Figure 8e) of such branches. Next, the sensibility of the results regarding the turbulence model is presented for the base case. Apart from the mentioned SST k-\(\omega\) turbulence model, the standard k-\(\varepsilon\), Transition SST and Reynolds Stress Model (RSM) formulations have been tested at \(Re~{}\approx~{}16,000\). The standard k-\(\varepsilon\) model [19] is by far the most used two-equation turbulence model due to its numerical robustness and stability; however, it has well-known limitations regarding the description of rotating and adverse pressure gradient flows with boundary layer separation. The RSM [20] is a seven-equation turbulence model which solves differential equations for the Reynolds Stress tensor components, avoiding the second moment closure by means of  
Figure 8: Contour plots of the turbulent kinetic energy \(k\) inside the fluidic oscillator along one cycle. See details of subfigures within the main text. the Boussinesq approximation; it is claimed to be superior to classical two-equation models for describing anisotropic flows and flows with strong curvature and/or swirl effects and adverse pressure gradients. Finally, the transition version of the SST k-\(\omega\) model [21] has been evaluated. This model includes a formulation for taking into account the effects of the transition from laminar to the turbulent boundary layer. It solves two extra equations, one for the transition momentum thickness Reynolds number and another for the intermittency; therefore, it is really a four-equation turbulence model that has shown its potential in a wide range of engineering applications providing good agreement with experiments (e.g., [22; 23; 24; 25]). Figure 9 shows the normalized mass flow profiles at outlet 1 in the base case at \(Re\approx 16,000\). As can be seen in Figure 9, there are some differences between the additional tested turbulence models, but all of them provide a shorter period than the SST k-\(\omega\) model.