# Analysis of Flow Field Characteristics in the Three-Phase Jet Fire Monitor Head
## 3 Results and Discussion
### Analysis of the Influence of Supporting Blade Length on the Flow Field inside the TPfFM Head  
Numerical simulations on the IFF of the TPJFM head were conducted for six groups with \(L_{f}\) as the design variable, keeping other parameters at their initial values. The range of \(L_{f}\) is from 50 mm to 75 mm. The impact of \(L_{f}\) on the IFF characteristics of the monitor head was analyzed. Figure 10: Velocity contour map of nozzle outlet with different \(A_{p}\). Figure 9: Line chart of changes in boundary parameters of IFF with different \(A_{p}\). The streamlines on the side of the monitor head with the powder-pipe bend are shown in Figure 11. The results indicate that the supporting blades are aligned with the main flow direction and have rounded edges, minimizing flow obstruction. Increasing the supporting blade length from 50 mm to 75 mm has a minimal impact on the axial flow within the monitor head. Cross-section d is located near the nozzle outlet edge by the supporting blades, where changes in \(L_{f}\) directly affect the velocity distribution and average TKE. This section serves as the entry to the annular water jet nozzle, with transverse velocity (perpendicular to the monitor head axis) directly affecting the flow smoothness into the nozzle. Therefore, the transverse velocity distribution contour map at cross-section d is shown in Figure 12. As \(L_{f}\) increases from 50 mm to 75 mm, both the X and Y direction velocity components near the upper supporting blade at cross-section d decrease significantly. The increased distance from cross-section d to the powder-pipe bend allows further flow rectification, converting more radial and tangential velocities into axial velocity. As the flow direction along the non-powder-pipe bend side is along the monitor head axis, the transverse velocity components before reaching the supporting blade near the nozzle outlet are minimal. The peak transverse velocity near the supporting blades at the without powder-pipe zone side is due to the water reconverging after passing the supporting blades. Hence, with increasing \(L_{f}\), the transverse velocity components near the supporting blades in the without powder-pipe zone remain unchanged. Figure 11: Streamlines with different \(L_{f}\). Figure 12: Transversal velocity contour map of cross-section d.  
The line charts of average TKE and average axial velocity at cross-section d for different \(L_{f}\) are shown in Figure 13. At cross-section d, the main flow direction is along the monitor head axis, and high transverse velocity regions are small. The transverse velocity is much lower than the axial velocity. Thus, although the transverse velocity decreases with increasing \(L_{f}\), the impact on the average axial velocity in this section is minimal. The average axial velocity at cross-section d fluctuates slightly, being lowest at 19.79 m/s for \(L_{f}\) = 50 mm and highest at 19.81 m/s for \(L_{f}\) = 65 mm. However, the reduction in local transverse velocity at cross-section d with increasing \(L_{f}\) leads to a significant decrease in average TKE, from 3.817 m\({}^{2}\)/s\({}^{2}\) at \(L_{f}\) = 50 mm to 2.964 m\({}^{2}\)/s\({}^{2}\) at \(L_{f}\) = 75 mm. As shown in Figure 14, with \(L_{f}\) increasing from 50 mm to 75 mm, the velocity uniformity index \(\gamma_{o}\) at the nozzle outlet fluctuates slightly. The maximum \(\gamma_{o}\) = 0.97626 occurs at \(L_{f}\) = 60 mm, and the minimum \(\gamma_{o}\) = 0.97617 occurs at \(L_{f}\) = 75 mm, with negligible variation. Changing the supporting blade length does not significantly improve the velocity distribution uniformity at the nozzle outlet. With increasing \(L_{f}\), the \(k_{o}\) at the nozzle outlet decreases from 2.51 m\({}^{2}\)/s\({}^{2}\) to 2.28 m\({}^{2}\)/s\({}^{2}\). The increased supporting blade length reduces the local turbulence caused by the powder-pipe bend, lowering the transverse velocity components before the nozzle inlet, providing the smoothest inflow at \(L_{f}\) = 75 mm, and minimizing TKE at the nozzle outlet.