# Frequency Modulation and Erosion Performance of a Self-Resonating Jet
## 1 Introduction
Another model was a multiphase cavitation mixture model based on the transport equation for the phase change. An additional equation for the vapor (or liquid) volume fraction, including source terms for evaporation and condensation (i.e., bubble growth and collapse), was introduced by [PERSON] et al. [16]. Similar techniques with different source terms were adopted by [PERSON] et al. [17],  
Figure 1: Schematic diagram of the 120\({}^{\circ}\) -impinging edge Helmholtz nozzle. [PERSON] [18] and [PERSON] et al. [19]. There have been various comparative studies of the various cavitation models [20; 21; 22; 23]. In 2014, the four-equation cavitation model was proposed by [PERSON] [24], which is very attractive for studying thermodynamic effects and cryogenic cavitation. As the vapor phase plays an important role in the oscillating process in the LPHF nozzle, due to its compressibility, air could be also introduced for frequency modulation. Besides, the air-water jet is capable of enhancing the material removal efficiency and can be controlled for specific machining operations. [PERSON] [25] concluded that the material removal rate became sensitive to the amount of air supplied and became a maximum value corresponding to an optimum air flow-rate. The air-water jet technology was also applied in oil drilling, proposed by [PERSON] [26], to help increase the rate of penetration (ROP). [PERSON] [27] conducted experiments on specimens impinged by the pulsed air-water jet. It turned out that the air entrained into the cavity significantly affects the material removal rate. For the LPHF nozzle, there are fierce entraining and momentum transports around the bulk flow due to sudden expansion. As a result, a negative pressure zone occurs in the oscillating chamber. The air intake can be achieved simply by drilling suction holes around the circumference of the chamber. In addition, [PERSON] and [PERSON] [11] conducted preliminary experiments in which the suction hole was intermittently blocked by fingers, and significant changes in the oscillating pressure were observed. They also claimed that oscillations will be enhanced if the suction hole is closed when the air cluster contracts, but kept open when the air cluster expands. It transpired that the air-water jet from a LPHF nozzle could not only improve the material removal rates but could also be used for frequency modulation. While limited research has focused on the frequency modulation of the LPHF nozzle via intake air, especially with the forced air excitation, it is reasonable to speculate that the frequency characteristics and the erosion efficiency of the LPHF nozzle is interrupted by the air intake. In this paper, both the experimental method and the simulation are introduced in Section 2. In the discussion, the Gas-Spring Theory is verified from both the numerical simulation and experimental perspectives. The paper then looks at how the effects of air intake on the oscillating frequency was investigated, as well as the range of frequency modulation. Finally, it looks at how the erosion experiments were conducted to evaluate the efficiency of the air-water jet with forced air excitation at various frequencies.