# Experimental Investigation on Jet Vector Deflection Jumping Phenomenon of Coanda Effect Nozzle
## 3 Results and Discussion
### Active Flow Control Frequency Selection
(**a**) The modal energy distribution of DMD under the conditions of the jet detachment process; (**b**) the distribution of the real and imaginary parts of the eigenvalues on the unit circle under the conditions of the jet detachment process. bubble area, and the modal coefficient curve, remain convergent. As such, the DMD in the separation bubble region captures the flow mode in the separation bubble rupture process. As shown in Figure 14, the nephogram of the DMD velocity vector of the first\(-\)order mode is shown, and the PSD of the first\(-\)order mode is 6.2 Hz. The first\(-\)order mode is the time\(-\)average result of the separation bubble region during the transient wall separation of the jet. In Figure 15a the nephogram of the DMD velocity vector of third\(-\)order mode is shown, and the PSD of third\(-\)order mode is 78.16 Hz. The high\(-\)value watershed of the third\(-\)order mode is similar to the separation shedding vortex structure. In Figure 15b, the attenuation degree of the modal coefficient curve of the third\(-\)order mode is significantly higher than that of other modes, indicating that the flow region represented by the third\(-\)order mode tends to be stable at the earliest. Therefore, the third\(-\)order mode is characterized as a separation shedding vortex structure. In Figure 16a, the nephogram of the DMD velocity vector of the fourth\(-\)order mode is shown, and the PSD of fourth mode is 89.45 Hz. The high\(-\)magnitude area of the fourth\(-\)order mode is the velocity region at the trailing edge of the lower wall of the nozzle. In Figure 16b, the modal coefficient curve of the fourth mode has a specific periodic frequency, indicating that the flow represented by the fourth\(-\)order mode still exists after the separation bubble breaks. Combined with the high magnitude location, the fourth\(-\)order mode characterizes the backward suction vortex at the trailing edge of the lower wall of the nozzle. The magnitude of the velocity of the inverted vortex is shallow, which does not affect the overall flow. Figure 14: First\(-\)order mode PSD = 6.2 Hz. (**a**) Decomposition results of the PIV velocity nephogram modal DMD in the Region A; (**b**) the DMD modal coefficient curve in the Region A.  
Figure 15: Third\(-\)order mode PSD = 78.16 Hz. (**a**) Decomposition results of the PIV velocity nephogram modal DMD in the Region A; (**b**) the DMD modal coefficient curve in the Region A. As shown in Figure 17a, the nephogram of the DMD velocity vector of the fifth\(-\)order mode is shown, and the PSD of the fifth\(-\)order order mode is 97.83 Hz. The high\(-\)magnitude area of the fifth\(-\)order mode is the vortex region outside of the jet shear layer and inside the separation bubble. In Figure 17b, the attenuation degree of the modal coefficient curve of the fifth mode is linear. This linear attenuation trend is not consistent with the flow in the process of jet transient wall separation. Combined with the high magnitude location, the fifth\(-\)order mode characterizes the momentum transferred from the outer shear layer of the jet to the separation bubble. When the jet is attached to the wall in a steady state, the energy of the separation bubble structure is transferred from the momentum of the shear layer outside of the jet to the inside of the separation bubble structure. When the jet transiently leaves the wall, the momentum of the shear layer outside of the jet has no transmission medium, resulting in the gradual attenuation of the original momentum inside the separation bubble. Therefore, it can be judged that the fifth\(-\)order mode is characterized by the momentum of the shear layer outside of the jet. Combined with the above analysis, the control frequencies of the pulsed jet as 6.2 Hz and 78.16 Hz are selected. The two frequencies represent the global flow frequency and the separation bubble structure frequency in the jet separation process, respectively.