# Analysis of Flow Field Characteristics in the Three-Phase Jet Fire Monitor Head
## 2 Materials and Methods
### Analysis of Characteristics of the IFF of TPIFM Head  
As shown in Figure 4, numerical simulation data were extracted from multiple cross-sections perpendicular to the axis of the fire monitor head. In section a, the obstruction caused by the bend in the powder pipe leads to an uneven velocity distribution, with lower velocities near the bend and the wall. In section b, the fluid is affected by the blunt body flow around the powder pipe, resulting in vortices on both sides of the upper section negatively impacting the axial flow. Section c, being close to the powder-pipe bend, still experiences significant uneven velocity distribution and local energy loss due to the blunt body flow. Section d shows an improvement in velocity distribution uniformity compared to section c. Section e further improves in velocity distribution uniformity, although it exhibits lower velocities at the top and higher velocities at the bottom. The velocity distribution at the outlet is consistent with section f but higher than at section f.  
Figure 4: Schematic diagram of cross-sections and velocity contour map. a, b, c, d, e and f are the cross sections of the IFF. Figure 3: Grid independence verification. To further study the IFF characteristics of the TPJFM head, velocity vector diagrams and TKE of the IFF at planes Z = 0 mm, Z = 10 mm, Z = 20 mm, and Z = 30 mm are shown in Figure 5a. Before the water flows through the powder-pipe bend, the velocity distribution is uniform and flows along the axial direction of the head. As the water approaches the powder-pipe bend, its flow direction changes due to the obstruction. At the Z = 0 mm section, the water flow direction shifts from the axial direction to a downward flow along the outer wall of the powder pipe. When the water flows through the area between the powder pipe bend and the supporting blades, the flow becomes more turbulent. At the Z = 10 mm section, recirculation occurs, with local flow directions opposing the main flow. At the Z = 30 mm section, further from the powder-pipe bend, turbulence is less pronounced than at the Z = 10 mm and Z = 20 mm sections, but the upper flow speed near the nozzle outlet remains lower than the lower flow speed. As shown by the TKE distribution in Figure 5b, turbulence is minimal before the water flows through the powder-pipe bend. Due to the disturbance from the powder-pipe bend, high TKE regions appear from the upper supporting blade to the powder pipe near the nozzle outlet. As the water flows through the connection between the powder pipe and the supporting blade, the flow direction changes and collides with the axial flow, increasing TKE in this small area with minimal impact on subsequent flow. The contraction of the nozzle outer wall and the expansion of the powder pipe increase local resistance and TKE at the nozzle's straight section entrance. The peak TKE at sections Z = 0 mm, Z = 10 mm, and Z = 20 mm is located near the powder-pipe bend to the upper supporting blade area. The Z = 30 mm section, further from the powder-pipe bend, shows the peak TKE shifted towards the nozzle outlet, located at the middle of the upper supporting blade. The velocity distribution uniformity index \(\gamma_{a}\) is selected to measure the velocity distribution uniformity of the flow field section. \(\gamma_{a}\) is calculated by Equation (10) as follows. \[\gamma_{a}=\frac{\sum_{i=1}^{n}[(|v_{i}-\overline{v_{a}}|)A_{i}]}{2|\overline {v_{a}}|\sum_{i=1}^{n}A_{i}} \tag{10}\]  
where \(A_{i}\) is the area of the \(i\) th grid in the cross-section, \(v_{i}\) is the value of the parameter \(v\) in the \(i\) th grid, m/s, and \(\overline{v_{a}}\) is the average value of the parameter \(v\) in the cross-section. The uniformity index \(\gamma_{a}\) for each section is shown in Figure 6. The velocity distribution uniformity is highest at the inlet. Sections a and b show a sharp decrease in velocity distribution uniformity due to the powder-pipe bend, with section c having the worst uniformity (\(\gamma_{a}\) = 0.8912).