# Vortex Breakdown Control by the Plasma Swirl Injector
## 3 Results and Discussion
The upstream stagnation point and the center of the breakdown bubble migrated upstream with increasing actuation strength, whereas the downstream stagnation point maintained a constant position. Bubble-type breakdown was stable under these conditions. The overall shape of the bubble did not change significantly with the strength of actuation increased from 18 kV to 21 kV. The interior structures of the bubble were nearly the same, containing one major cell or vortex ring. The gross exterior appearance of the bubble was axisymmetric, while the internal structure was asymmetric to some extent. The length-to-diameter ratio of the bubble was approximately 1.61 and 1.48, with the maximum diameter occurring at approximately \(Z=20\) mm and \(Z=18\) mm for 18 kV and 20 kV, respectively. With the increase of the excitation voltage, the asymmetry between the two different sides of the vortex ring increased, but the number of vortex rings did not increase. Figure 3: _Cont._  
Figure 3: \(Cont\). Figure 4 summarizes the axial velocity profiles along the centerline (X = 0 mm) for the five cases with voltages ranging from 0 kV to 21 kV. The figure shows that the gradual increase of voltage resulted in a gradual deceleration of the axial velocity along the centerline and a gradual appearance and upstream movement of the vortex breakdown. Without plasma actuation, the axial velocity at the injector outlet was 1.2 m/s. Moving downstream, the axial velocity linearly decreased to \(Z=22\) mm, achieving a lower value of 0.23 m/s. Then a velocity plateau appeared, which means the velocity remained essentially unchanged. Applying the 12 kV excitation, the axial velocity distribution in the \(Z=0\)-20 mm zone moved down slightly, and the injector outlet velocity dropped to 0.99 m/s, but the overall change was not obvious, and the velocity plateau positions coincided. When the excitation was increased to 15 kV, the injector outlet velocity decreased to 0.62 m/s, and the axial velocity, in the range of \(Z=0\)-20 mm, decreased appreciably. However, because the vortex breakdown zone was very small and did not pass through the jet centerline, the stagnation point and recirculation zone cannot be captured in the axial velocity distribution along the centerline. When the excitation was increased to 18 kV, the injector outlet velocity decreased to \(-0.1\) m/s, and an obvious backflow zone appeared in the region of \(Z=0\)-40 mm. When the excitation was further increased to 21 kV, the overall velocity distribution changed slightly. Although the magnitude of the reverse velocity increased slightly, the length of the vortex zone and the position of the stagnation point remained basically unchanged. The velocity increased linearly after it reached the minimum value at \(Z=22\) mm, and no velocity plateau could be observed. Figure 5 shows the axial velocity magnitude contours and streamlines with a bulk velocity of 5.7 m/s. The plasma actuation-induced bubble-type vortex breakdown was still obvious, while the interior structures of the bubble contained one major cell as well. However, the size of the bubble decreased, which indicates that the effect of plasma actuation decreases with the increase of flow rate. More work is needed to establish the correlations between the effectiveness of plasma actuation, the jet inlet velocity, and other parameters, in order to gain a full understanding. Further research is needed to enhance the plasma flow control authority to put this method into engineering applications, including full-scale applications. Figure 3: Contours of mean axial velocity magnitude, streamlines, and vectors (left: magnitude contours and streamlines; and right: vectors) in the XZ plane with bulk velocity of 3 m/s.