# Simulation and Experimental Research on the Energy Loss of Confluence Pipelines
## 2 Numerical Simulation of the Flow Field of a Confluence Pipeline
### Simulation Setup and Result Analysis
Since the inlet and outlet of the confluence pipeline examined in this study are at the same height, \(z_{1}\) = \(z_{2}\), Equation (16) holds:  
\[h_{w}=\frac{p_{1}-p_{2}}{\rho}-\frac{v_{1}^{2}-v_{2}^{2}}{2g} \tag{16}\]  
The energy loss coefficient can be calculated based on Equation (17):  
\[\xi=\frac{2 gh_{w}}{v^{2}} \tag{17}\]  
where \(\xi\) is the calculated energy loss coefficient of the confluence pipeline with different structures. As shown in Figure 4, the velocity distribution of fluid particles at the junction of the T-shaped confluence pipeline is irregular, and the velocity and direction of fluid particles are disordered. A local vortex is formed at the horizontal junction of the T-shaped confluence pipeline, and the flow velocity increases rapidly after confluence. Since the two fluid particles collide with each other in the opposite direction of velocity after confluence, the velocity distribution of fluid particles is disordered after confluence, and they extend toward the wall of the confluence pipe. Figure 3: Confluence pipelines with different structures. (**a**) T shape; (**b**) Y shape; (**c**) bifurcated; and (**d**) arc shape. Therefore, the energy loss of the T-shaped confluence pipeline is severe. The velocity distribution of fluid particles at the junction of the Y-shaped confluence pipeline is more regular than that of the T-shaped confluence pipeline; however, the velocity distribution at the corner of the Y-shaped confluence pipeline is still disordered. In addition, the velocity direction and size of fluid particles in this area are disordered. At the corner of a Y-shaped confluence pipeline in particular, the velocity distribution between fluid particles is complex, resulting in mutual collision and friction between fluid particles, leading to partial energy loss. The particle velocity distribution of the fluid in the convergence area of the bifurcated confluence pipeline is relatively regular compared with that of the Y-shaped confluence pipeline. When the fluid in the branch pipe of the bifurcated confluence pipeline flows into the main pipeline area, the fluid in the branch pipe collides with the fluid in the main pipeline; therefore, the velocity distribution between particle points is relatively disordered, resulting in partial energy loss. However, since the particle velocity distribution of the fluid at the intersection of the bifurcated confluence pipeline is relatively uniform, the energy loss of this pipeline is smaller. Compared with the T-shaped confluence pipeline, Y-shaped confluence pipeline, and bifurcated confluence pipeline, the velocity distribution of fluid particles in the arc confluence pipeline at the intersection is relatively regular. The fluid particle velocity of the arc confluence pipeline changes relatively gently due to the elbow transition at the intersection. It can be seen from the velocity vector diagram of fluid particles that the fluid particles in the arc confluence pipeline do not undergo the same severe particle collision and mixing as those in the T-shaped, Y-shaped, and bifurcated confluence pipelines; however, there are also changes in the velocity of fluid particles at the confluence due to the mutual collision of fluid particles, and the fluid moves toward the outer wall of the pipeline at the confluence. We conducted CFD simulation analysis on different pipelines under Reynolds numbers of 4000, 4800, 6400, 7520, 9600, 11,200, 12,800, 14,400, 16,000, 20,800, 25,600, 30,400, 35,200, 40,000, 44,800, 48,000, and 56,000. Figure 5 shows the energy loss coefficient of the confluence pipelines with different structures. The energy loss coefficient of the confluence pipeline with different structures gradually decreases with the increase in Reynolds number and ultimately tends to be stable.