# Experimental Investigation on Jet Vector Deflection Jumping Phenomenon of Coanda Effect Nozzle
## 3 Results and Discussion
### Active Flow Control Frequency Selection  
The transient PIV flow field under the jet detachment process condition is shown in Figure 12; when the frame number = 10 and 30, the main jet attaches to the wall. The vortex structure produced by the outer shear layer near the side of the separation bubble structure is significant. When the frame number = 50, the distance between the main jet and the wall increases. It is evident that the vorticity of the separation bubble structure begins to decrease. At this time, the separation bubble structure begins to move towards the trailing edge of the vectoring nozzle, and the tail of the main jet begins to leave the lower wall of the vectoring nozzle. Figure 11: Experimental results of oil flow and pressure measurement under the condition of the jet attachment. **(a)** Results of oil flow experiments on the surface of the Coanda wall at the side of the jet attachment; **(b)** results of mean pressure measurements on the surface of the Coanda wall at the side of the jet attachment. Figure 12: Transient PIV velocity nephogram flow field structure under the jet detachment condition (velocity streamline using RBG color). When the frame number = 70, the vortex structure in the separation bubble area on the wall side has disappeared, the entrainment vortex begins to appear on the upper wall side of the vectoring nozzle, and the reverse suction vortex appears at the trailing edge of the lower wall of the vectoring nozzle. When the frame number = 90 and 110, the vector jet is entirely neutral. It can be seen from the above description that when the separation bubble from before broke, the vector deflection angle of the jet is not apparent. When the separation bubble breaks, the jet begins to deflect rapidly. Therefore, maintaining the separation bubble structure can avoid the jumping phenomenon. The PIV results of jet transient detachment process condition are used to construct the snapshot set (snapshot = 250). To determine the excitation frequency required for active flow control, dynamic mode decomposition was used to decompose the PIV snapshot set of the overall flow field and the separated bubble region (Region A). As shown in Figure 13a, the energy distribution of each mode of DMD is demonstrated. In the DMD of the global watershed, the energy proportion of the first five modes is 67.11%, 5.38%, 2.66%, 2.41%, and 2.09%, respectively. In the DMD of the separation bubble basin, the energy of the first five modes accounts for 75.48%, 9.07%, 2.59%, 1.52%, and 1.09%. Considering that the energy proportion of subsequent modes is less than 1%, the first five modes are further analyzed. Figure 13b shows the analytical solution of the dynamic mode decomposition \(\mathbf{\mu}_{i}\) The distribution diagram is of the real part and imaginary part of the \(\mathbf{\mu}_{i}\). When the analytical solution of the DMD is distributed on the unit ring with radius one, it shows that the solved flow field is stable, and the flow field will not change with time, or has strong periodicity. When the analytical solution is outside of the unit ring, the solved flow field is divergent, and the flow in the flow field will become chaotic. When the analytical solution is in the unit ring, the solved flow field is concurrent, and the flow field will change into a more stable flow with time. The analytical solution of the transient off--wall condition of the jet is distributed in the unit ring, which shows that the off--wall process of the jet converges with time. In other words, when open, the passive secondary flow valve is on the wall side, and the injection of a passive secondary flow will not affect the flow stability of the transient jet deflection. DMD decomposes the flow in the separation bubble region to accurately capture the required active flow control frequency. The DMD modal coefficient curve in the separation  
Figure 13: DMD results of the PIV velocity nephogram under jet transient detachment process conditions.