# 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
Near the upper and lower blades and the straight section wall of the nozzle at the Z = 20 mm plane, local TKE is higher. With increasing \(L_{pf}\), the TKE near the upper blade at this cross-section gradually decreases. The flow field parameters of cross-section c and d are shown in Figure 9:0 According to Figure 17, as \(L_{pf}\) increases, the mean velocity \(v_{c}\) of cross-section c decreases gradually from 20.41 m/s to 19.35 m/s, while the mean velocity \(v_{d}\) of cross-section d fluctuates slightly, with a change of only 0.07 m/s. According to Figure 17, despite the minor changes in mean flow velocity, the mean TKE of both cross-sections decreases significantly. Specifically, the mean TKE \(k_{c}\) of cross-section c decreases linearly from 4.99 m\({}^{2}\)/s\({}^{2}\) to 3.95 m\({}^{2}\)/s\({}^{2}\), a reduction of 21%, and the mean TKE \(k_{d}\) of cross-section d decreases from 3.40 m\({}^{2}\)/s\({}^{2}\) to 1.78 m\({}^{2}\)/s\({}^{2}\), a reduction of 48%. This indicates that increasing \(L_{pf}\) significantly improves the TKE within the flow channel, resulting in smoother flow, even though the change in flow velocity in the latter part of the nozzle is minimal. The TKE distributions for cross-section c, cross-section d, and the nozzle outlet are shown in Figure 9:1 Regardless of the \(L_{pf}\) value, the TKE distribution patterns for these sections remain consistent. The TKE is higher near the supporting blade of cross-section c and is less affected by changes in \(L_{pf}\). As \(L_{pf}\) increases, both the area of the high TKE region and the peak TKE of cross-sections c and d decrease, leading to smoother incoming flow and a significant reduction in the high TKE region and peak TKE at the upper part of the nozzle outlet. Figures 17 and 18 together demonstrate that increasing \(L_{pf}\) reduces the nozzle  
Figure 9:2 TKE contour map of cross-sections with different \(L_{pf}\). inlet TKE substantially, which in turn decreases the nozzle outlet TKE and enhances the performance of the TJFM jet. As shown in Figure 19, when \(L_{p\!f}\) is gradually increased from 25 mm to 75 mm, the \(\gamma_{o}\) initially increases and then decreases. Specifically, as \(L_{p\!f}\) increases from 25 mm to 35 mm, \(\gamma_{o}\) increases from 0.9756 to 0.9762. Between 35 mm and 55 mm, \(\gamma_{o}\) exhibits minor changes, indicating a more uniform flow velocity distribution. The optimal uniformity (\(\gamma_{o}\) = 0.9763) occurs at \(L_{p\!f}\) = 45 mm. Beyond this point, \(\gamma_{o}\) decreases, reaching 0.9756 at 75 mm. With increasing \(L_{p\!f}\), the \(k_{o}\) at the nozzle outlet decreases consistently from 2.41 m\({}^{2}\)/s\({}^{2}\) to 1.88 m\({}^{2}\)/s\({}^{2}\), representing a 22% reduction. The peak TKE within the nozzle and the local pressure loss both decrease. Although the axial size of the internal passage increases, causing higher along-travel resistance, this increase is outweighed by the reduction in local pressure loss. Consequently, the \(\Delta p_{o}\) across the inlet and outlet of the internal flow passage decreases from 866.06 kPa to 858.53 kPa, a reduction of 0.9%. In summary, the supporting blade can correct the direction of water flow to a certain extent, but it also affects the exchange of kinetic energy inside the water flow to a certain extent, so that the velocity is divided into regions. With the increase in \(L_{p\!f}\), the second half of the automatic rectification of the water flow is divided, and the water flow has reached the outlet before it has time to interact with the other part, resulting in a decline in the uniformity of the outlet velocity. Figure 9:3 Flow field parameters of section c and section d: (**a**) mean velocity; (**b**) mean TKE. Figure 9:4 TKE contour map of section c, section d and outlet. Furthermore, as \(L_{pf}\) increases from 25 mm to 75 mm, the radial and tangential velocity components at the upper support vane decrease. The vortex area remains stable but gradually shifts towards the gun head inlet, and the TKE decreases.