# Structural Optimization of Slotting Nozzle Used to Improve Coal-Seam Permeability
## 2 Structural Optimization of Slotting Nozzle Design
### Numerical Experiments to Optimize Slotting Nozzle Index  
Numerical simulation of the performances of the slotting nozzles was carried out using CFD modeling. Each slotting nozzle was installed vertically on the slotting device, within which there was high-speed turbulent flow. The control equation therefore comprised equations of continuity, the Navier-Stokes equation, and realizable \(k\)-\(\varepsilon\) equations. The geometric model was relatively small; therefore, quadrilateral mesh generation was used to generate the meshes of the inner and outer flow fields. The grid spacing was 0.5 mm. The geometric model of the slotting nozzle flow field is shown in Figure 2.  
The finite-volume method was used to disperse the control equation; simple algorithms were used to couple the pressure and velocity. The fluid was assumed to be ideal, that is, the flow was steady, and gravity and cavitation were not be taken into consideration. The boundary conditions are shown in Table 2.  
In the process of optimizing the slotting nozzle structural parameters, a submerged water jet was used to simulate the inner and outer flow fields. Since the submerged water jet had the characteristics of fast attenuation, using a smaller model to simulate the slotting nozzle outflow could clearly distinguish the advantages and disadvantages of the structure and save calculation time. The numerical simulation results of Experiment 1 are shown in Figure 3.  
Figure 3 shows that the high-pressure water underwent acceleration inside the slotting nozzle, and the dynamic pressure gradually increased in this section; however, the dynamic pressure on the section did not change uniformly. In particular, in the area between the bend of the flow channel and the convergent section, the distribution of the slotting dynamic pressure was greatly influenced by the structure of the flow channel. At the turning point of the main channel of the slotting device into \begin{table}
\begin{tabular}{l c} \hline \hline
**Inlet Pressure** & **28 MPa** \\ \hline Inlet turbulence intensity & 10\% \\ Inlet flow diameter & 23 mm \\ Outlet pressure & 1 atm \\ Outlet turbulence intensity & 10\% \\ Outlet flow diameter & 3 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical experiment boundary conditions. Figure 2: Geometric model of slotting nozzle flow field: 1 is the pressure inlet; 2 and 3 are boundary walls; 4 is the pressure outlet. the slotting nozzle, the dynamic pressure distribution was larger in the upper part of the nozzle axis, but smaller in the lower part. When high-pressure water entered the stable section of the slotting nozzle, the distribution of dynamic pressure was high in the middle and low on both sides of the same cross-section. An obvious low-pressure zone formed near the inner wall of the slotting nozzle. The non-uniform distribution of the dynamic pressure inside the slotting nozzle created conditions for the generation of vortices and flow recirculation. The formation of a large number of vortices and recirculation greatly reduce the quality of the water jet. Based on simulated data of internal and external flow fields of sixteen different slotting nozzles, the axial and longitudinal dynamic pressure curves of the water jet at a distance of 150 mm from the slotting nozzle outlet were plotted, as shown in Figure 4.  
The curves of Figure 4a show that with an increase of the abscissa, the dynamic pressure gradually decreased and its rate of change gradually decreased. Slotting nozzles with different structural parameters had different outlet dynamic pressures for the same pressure source. The type 0-30-9 slotting nozzle (stable segment length \(L=0\) mm, convergent angle \(\theta=30^{o}\), and straight segment length \(l=9\) mm) had the best performance. Not only was the outlet dynamic pressure larger than those of other slotting nozzles, but the attenuation of the axial pressure was slower. Slotting nozzle type 9-10-12 had the worst performance.