# Effects of Nozzle Exit Angle on the Pressure Characteristics of SRWJs Used for Deep-Hole Drilling
## 5 Conclusions  
Aiming at improving the efficiency of deep-hole drilling, the pressure oscillations of SRWJs were experimentally studied with organ-pipe nozzles of various exit angles. The \(P_{max}\) and \(P_{a}\) under the different exit angles were analyzed. It should be noted that we have not made sufficient progress to present a complete discussion on the influence mechanism of the exit angle on SRWJs, and further theoretical and mathematical investigations should be carried out. However, the present study still makes a contribution to an improved understanding of how the pressure characteristics are influenced by the exit angle. The main results are shown below:  
1. The exit angle of the organ-pipe nozzle greatly affects the axial pressure oscillations of SRWJs, with different angles causing obviously different values of \(P_{max}\) and \(P_{a}\) at standoff distances of \(S\)\(>10\) mm.
2. The exit angle of \(0^{\circ}\) always leads to the largest values of \(P_{max}\) and \(P_{a}\) under the two inlet pressures, and makes the jet possess the typical pressure feature of a SRWJ; while for the other exit angles, both \(P_{max}\) and \(P_{a}\) decrease rapidly with the increasing standoff distance.
3. At an inlet pressure of 10 MPa, the exit angle of \(90^{\circ}\) always results in the minimum values of \(P_{max}\) and \(P_{a}\) at almost all the testing standoff distances, while at an inlet pressure of 20 MPa, the exit angle of \(60^{\circ}\) takes the place of \(90^{\circ}\).
4. When the exit angle is \(0^{\circ}\), both \(P_{max}\) and \(P_{a}\) have a convex quadratic relationship with the standoff distance, while they have a concave quadratic relationship with the standoff distance when the exit angle is \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), and \(90^{\circ}\).  
Conceptualization, X.W.; investigation, Z.W., M.Y., and Q.F.; writing--review and editing, D.L.  
**Funding:** This research was financially supported by the National Natural Science Foundation of China (No. 51805188), the China Postdoctoral Science Foundation Founded Project (No. 2017M620313), and the National Key Research and Development Program of China (No. 2018 YFC0808401).  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
\(D_{j}\) & jet diameter (m)  
\(D_{i}\) & inlet diameter of organ-pipe nozzle (m)  
\(D_{c}\) & chamber diameter of organ-pipe nozzle (m)]  
\(D_{e}\) & exit diameter of organ-pipe nozzle (m)  
M_a_ & Mach number, \(U_{j}/c\)  
\(K_{n}\) & mode number  
\(L_{c}\) & chamber length of organ-pipe nozzle (m)  
\(L_{e1}\) & length of the straight part of the nozzle exit (m)  
\(L_{e2}\) & length of the divergent part of the nozzle exit (m)  
A\({}_{1}\) & upstream cross-section area at the contraction (m\({}^{2}\))  
\(A_{2}\) & downstream cross-section area at the contraction (m\({}^{2}\))  
\(S_{d}\) & Strouhal number  
\(U_{j}\) & jet velocity (m/s)  
\(P_{a}\) & pressure oscillation amplitude (MPa)  
\(P_{max}\) & pressure oscillation peak (MPa)  
\(P_{min}\) & minimum pressure oscillation (MPa)  
\(P_{i}\) & inlet pressure (MPa)  
\(P_{0}\) & environment pressure (MPa)  
\(S\) & standoff distance (m)  
\(f_{0}\) & frequency of the pressure wave (Hz)  
\(f_{v}\) & structuring frequency of the jet (Hz)  
\(\lambda\) & length of the standing wave (m)  
\(c\) & local sound speed (m/s)  
\(n\) & natural number  
\(\rho\) & water density (kg/m\({}^{3}\))  
\(g\) & gravity acceleration (m/s\({}^{2}\))  
\(h_{f}\) & frictional head loss (m)  
\(h_{j}\) & local head loss (m)  
\(\eta\) & coefficient of the frictional head loss  
\(k\) & coefficient of the local head loss  
\(l\) & length of the flow channel (m)  
\(u\) & flow velocity in the nozzle (m/s)  
\(\theta\) & exit angle of organ-pipe nozzle (\({}^{\circ}\))  
\(\gamma\) & experimental error of \(P_{a}\)