# Effects of Nozzle Exit Angle on the Pressure Characteristics of SRWJs Used for Deep-Hole Drilling
## 1 Introduction  
When water is pressurized and flows through a tiny orifice, a high-speed waterjet possessing strong impact power is generated. It is claimed that a high-speed waterjet is able to disintegrate most existing materials by transmitting high energy to an extremely small area and is extremely suitable for cutting hard rocks [1]. Currently, waterjet technology is being widely used in the energy field as an efficiency operation assisting drilling [2]. For example, [PERSON] et al. [3] studied the damage models of rock breaking assisted with a high-speed waterjet, in order to improve the life and working efficiency of conical cutters used in excavation. As waterjet technology has been efficiently used for slotting in coal mining of low permeability, [PERSON] et al. [4] investigated the mechanism of pressure relief and permeability enhancement under the waterjet slotting process. As the demand for energy is dramatically increasing year by year, improving the efficiency of energy exploitation is always a focus of researchers. In order to improve the working performance of waterjets used for rock breaking, several types of waterjet have been proposed. These are the cavitating waterjet, pulsed waterjet, self-resonating waterjet (SRWJ)), and the abrasive waterjet. Each of these has much stronger impact power and higher working efficiency than the conventional plain waterjet under the same operating conditions [5; 6; 7]. The SRWJ has the advantages of both a cavitating waterjet and a pulsed waterjet, and thus has attracted the attention of a number of researchers [8; 9]. To be more specific, the SRWJ was first proposed by [PERSON] et al. [10] in the early 1980s, based on the fact that the large-scale orderly patterns that existed in the noise producing region of a jet could be enhanced and controlled by a slight periodic surging imposed at the jet exit [11]. Generally, a SRWJ is generated by taking advantage of the passive acoustic resonance tuned to the preferred Strouhal number of the submerged jet to cause large-scale turbulent motions of the jet. Subsequently, [PERSON] and [PERSON] designed several nozzles that can generate a SRWJ, including the \"pulser\", \"laid-back pulser\", \"pulser-fed\", and \"organ-pipe\" [12]. Then, by comparing the performance of these nozzles using experimental and numerical methods, it was demonstrated that the organ-pipe nozzle was the most promising due to its compact and simple structure. Moreover, by making use of the power generated by the collapse of the cavitation bubbles and the water hammer stress wave generated by the pulsations, the SRWJ showed significantly increased performance in its erosion capability and is used in a wide range of applications. For example, [PERSON] et al. [13] employed a SRWJ in petroleum engineering in China and found the penetration rate of deep-hole drilling could be improved by as much as 31.5%. They also demonstrated that the amplitudes of the pressure oscillation and the maximum impact pressure of the SRWJ could show improvements of 24% and 37%, respectively, compared with waterjets injected from a conventional cone-shaped nozzle [14]. Additionally, [PERSON] et al. [15] used a SRWJ to impact aluminum alloy as a new peening method for improving its properties. They found that the hardness and residual stress after the waterjet peening process could be increased by 61.6% and 148%, respectively. With the rapid development of SRWJs, not only is their application widening, but the demand for higher performance is also greatly increasing. Therefore, some researchers are focusing on clarifying the characteristics and properties of SRWJs rather than on applications. In more specific terms, [PERSON] et al. [16] established a new mathematical model to describe the size variations of the cavitation bubbles, aiming at clarifying the process of bubble collapse. [PERSON] et al. [17] analyzed the oscillation mechanism of a SRWJ, by both numerical and experimental methods, and found that the cavitation clouds dominate the oscillating frequency.