# Frequency Modulation and Erosion Performance of a Self-Resonating Jet
## 3 Results and Discussion
### Erosion Performance  
The erosion patterns of concrete specimens are presented in Figure 18. The erosion region caused without air intake was in the shape of a cone, but the erosion region under the action of the air-water jet had an irregular shape due to the air within the jet forcing radial motion.  
Using the jet without entrained air for reference, the relative erosion performance of four inspiratory series is compared in Figure 19. The red bars show the influence of the air entrainment on the normalized erosion volume and the blue bars show the normalized erosion area. The erosion performance was improved with the air entrainment to some degree. Assuming that a high number of open suction holes corresponds to a high air-flow rate, it transpired that both air-flow rates and air entry-path affected the erosion performance. Although the cavitation in the chamber was suppressed by the air intake, a moving air coat was created to reduce the friction between the water jet surface and the surrounding air. As the water hammer pressure is attributed to both velocity and the mixture  
Figure 17: Dominant frequency in the frequency modulation.  
Figure 18: The erosion pattern of specimens.  
density, there seems to have been a \"trade-off\" between the jet velocity increase and the mixture density decrease when air was entrained into the chamber. Besides, according to the research by [PERSON] [43], cavitation bubbles move away from the nozzle without expanding much while the gas expands rapidly upon exit after discharging, so the erosion areas with entrained air increase as a result.  
As for the forced air excitation, it transpired that the oscillating frequency of the chamber pressure was completely determined by the forced frequency of air excitation (Figure 20). In the practical applications, the frequency could be modulated at the desired value according to the specified situation by the method of forced air excitation. With increasing forced frequency, the mean volume of entrained air increased due to the fierce entraining and momentum transportation.  
Figure 19: The erosion performance under various suction series.  
Figure 20: Time-resolved signals under forced excitation: (**a**) chamber pressure and (**b**) volume of entrained air.  
The erosion pattern of forced air excitation is presented in the Figure 21. As only one suction hole was open, the asymmetric flow was intensified with the forced air excitation. Jet deflection in the air-entry direction occurred, while little effect was observed in the other direction. As a result, \"flat slot\" shapes were observed on the specimens. With increasing forced frequency, stronger alternating shearing stress in the specimen occurred, and hence led to crack growth and crack branching of the specimen more easily.  
A significantly more effective erosion performance is observed in Figure 22 for the forced excitation frequency at 0.25 Hz, which was the closest to the oscillating frequency without air intake. It was necessary to select the forced frequency near to the fundamental frequency rather than the high frequency in order to achieve better performance. Besides, the volume of entrained air and the distribution of the air entry-path should also be considered. For the erosion volume, the series 3.0 achieved the maximum value, while series 2.0 achieved the maximum erosion area. Various combinations of the number and distributions of suction holes needed to be determined to achieve the expected goal (best erosion volume or largest erosion areas).  
Figure 21: The erosion pattern of specimens under forced excitation (Series 1.0).