# Analysis of Flow Field Characteristics in the Three-Phase Jet Fire Monitor Head
## 3 Results and Discussion  
### Analysis of the Influence of the Powder-Pipe Bending Angle on the TPJFM IFF  
We conducted numerical simulations on the IFF of the TPJFM head for six groups within the \(A_{p}\) range of 90\({}^{\circ}\) to 120\({}^{\circ}\), keeping other parameters unchanged. The water flow rate through the monitor head was 70 L/s. Cross-sectional data at Z = 0 mm, Z = 10 mm, Z = 20 mm, and Z = 30 mm were extracted to analyze the impact of \(A_{p}\) on the IFF of the monitor head. As shown in the velocity and streamlines contour maps in Figure 7, with the increase in \(A_{p}\), the cross-section of the powder pipe along the XZ plane changes from a circular shape to an ellipse with the major axis along the flow direction of the monitor head. This accelerates the flow velocity near the inlet side of the powder-pipe bend. The increase in \(A_{p}\) also reduces the width of the wake region behind the powder-pipe bend, decreasing the disturbance effect on the IFF. After the water flows through the powder-pipe bend, the curvature of the streamlines decreases, and the flow loss along the bend side of the monitor head is reduced. As \(A_{p}\) increases, the velocity difference between the upper and lower sides of the monitor nozzle decreases, improving the velocity distribution uniformity in the IFF of the monitor head. The TKE contour maps in Figure 8 show that at \(A_{p}\) = 90\({}^{\circ}\), the sections at Z = 0 mm, Z = 10 mm, and Z = 20 mm have higher TKE near the inlet  
Figure 6: Line graph of uniformity of velocity distribution of cross-sections. Figure 7: Velocity and streamlines contour map of cross-sections with different \(A_{p}\). bend to the supporting blades, extending to the nozzle outlet, resulting in an average TKE of 2.99 m\({}^{2}\)/s\({}^{2}\) at the nozzle outlet. As \(A_{p}\) increases, the flow space between the powder-pipe bend and the supporting blades changes, resulting in significant differences in the flow state and TKE distribution. Apart from this area, the TKE distribution in other sections remains similar to that of the \(A_{p}\) = 90\({}^{\circ}\) model. With the increase in \(A_{p}\), the peak TKE in the IFF of the monitor head gradually decreases, and the area of high TKE significantly reduces. At the \(Z\) = 30 mm section, the high TKE near the upper supporting blade is significantly lower for the \(A_{p}\) = 120\({}^{\circ}\) model compared to the \(A_{p}\) = 90\({}^{\circ}\) model. The results indicate that increasing \(A_{p}\) from 90\({}^{\circ}\) to 120\({}^{\circ}\) significantly reduces the peak TKE in the IFF and at the nozzle outlet. The parameters at the nozzle outlet and the PD across the IFF of the monitor head directly impact the jet performance of the fire monitor. More uniform velocity distribution, lower TKE, and lower PD across the IFF enhance the fire monitor's jet coherence and stability, improving its range. The outlet flow parameters for different \(A_{p}\) are shown in Figure 9. As the powder-pipe bend angle \(A_{p}\) increases from 90\({}^{\circ}\) to 120\({}^{\circ}\), the velocity uniformity index \(\gamma_{o}\) at the nozzle outlet increases from 0.973 to 0.976, the \(k_{o}\) at the nozzle outlet decreases from 2.99 m\({}^{2}\)/s\({}^{2}\) to 2.39 m\({}^{2}\)/s\({}^{2}\), and the \(\Delta p_{o}\) across the IFF decreases from 876.65 kPa to 861.53 kPa. At \(A_{p}\) = 120\({}^{\circ}\), the velocity distribution at the nozzle outlet is the most uniform, and the TKE is the lowest. Additionally, the increase in \(A_{p}\) reduces local resistance within the monitor head. As \(A_{p}\) increases, the flow velocity difference between the upper and lower parts is reduced and uniformity is increased. The PD is reduced because the water flow is subjected to less resistance when passing through the inclined powder tube. The degree of turbulence in a vertical pipeline is larger than that in an inclined pipeline, and the TKE is also larger.