# Frequency Modulation and Erosion Performance of a Self-Resonating Jet
## 4 Conclusions  
The better erosion performance of the resonating cavitation jet has long been acknowledged. In the present study, the LPHF nozzle, one of the resonating nozzles, was investigated from both experimental and numerical perspectives. Various inspiratory methods were adopted to achieve frequency modulation. Further erosion experiments showed that both entrained air and forced excitation are capable of achieving better erosion performance. Based on the present investigation, the main conclusions that can be drawn are:  
1. The Gas-Spring Theory was verified by both the experiment and the numerical simulation. The cavitation cluster dominated the oscillating frequency in the LPHF nozzle and the non-linear interaction between the cavitation cluster and acoustic modulation should also be considered. The global structure of the spectral distribution can be viewed as the result of non-linear interactions and modulation processes. 2. The mechanism of frequency modulation was different with/without air intake. When no air was entrained, the dominant frequency increased linearly with the increasing pressure declines due to the decreasing accumulated time for the cavity cluster. For the LPHF nozzle with suction holes, the frequency of each inspiratory method did not vary monotonically with the pressure decrease. 3. For the LPHF nozzle with suction holes, frequency modulation could be achieved in a wide range by simply changing the number and distribution of the open suction holes. The modulation range was dependent on the pressure decrease. 4. For the forced exciting condition, the oscillating frequency was totally determined by the forced frequency of entrained air. With the increasing forced frequency, the mean volume of entrained air increased due to the fierce entraining and momentum transportation. 5. The removal rate was improved with the entrained air. The erosion performance was affected by both the volume of entrained air and the distribution of the air entry-path. The best erosion performance was achieved at the frequency closest to the fundamental oscillation frequency. Thus, it is necessary to consider various combinations of the number and distributions of suction holes in order to achieve the expected goal. The modulation of the jet has the great advantage of achieving an appreciable increase of material removal. In this study, a feasible method to improve the erosion performance of the LPHF nozzle has been proposed. Compared with a high-frequency water jet, it is much easier for the LPHF nozzle to achieve the desired frequency, as the oscillating frequency is quite low. Moreover, as the density of air is low, the wear problem can be ignored when compared with the use of a moving  
Figure 22: The erosion performance under forced excitation: (a) normalized volume; (b) normalized area. disk to interrupt the continuous water jet. This preliminary study could provide some suggestions for practical applications, and more accurate modulation should be achieved in future studies by considering the non-linear interaction. This research is financially supported by the National Key Basic Research Program of China (No. 2014 CB239203), the National Natural Science Foundation of China (No. 51474158) and the Program for New Century Excellent Talents in University of the Ministry of Education (Grant No: NCET-12-0424). [PERSON] and [PERSON] conceived and designed the experiments; [PERSON] and [PERSON] performed the experiments; [PERSON] performed the simulation, analyzed the data and wrote the paper; [PERSON] supervised the projects and the students with contributions to guide the research program. [PERSON] and [PERSON] reviewed and read the final manuscript. The authors  
* _[PERSON] et al. (1982)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]. Cavitating and Structured Jets for Mechanical Bits to Increase Drilling Rate. _J. Energy Resour. Technol._**1982**, _106_, 289-294. [CrossRef]
* _[PERSON] et al.