*3.6. Data Analysis of the Self-Priming Pump Based on CFD*

In the self-priming process of a self-priming centrifugal pump, the gas in the section is exhausted to the outlet pipe through the operation of the pump. In Figure 14, the inlet surface of the inlet section is defined as "In"; the inlet surface of the gas-liquid mixing cavity is defined as "In2" and the outlet surface of the gas-liquid separation cavity is defined as "Out2". The outlet surface of the outlet pipe is defined as "Out". In order to illustrate the self-priming capability of the pump, the gas volume coefficient, gas flow coefficient, water flow coefficient, impeller void fraction, and diffuser void fraction are defined in Formulae (2) to (4), respectively.

$$\mathbf{C}\_{\mathbf{V}} = V\_{\mathfrak{G}} / V\_{\mathfrak{G}\mathbf{t}\_{\mathbf{V}}} \tag{2}$$

$$\mathbf{C} = \mathbf{Q}\_{\mathfrak{G}} / \mathbf{Q}\_{\mathbf{d}} \tag{3}$$

$$\mathbf{C}' = Q\_{\mathbf{w}} / Q\_{\mathbf{d}} \tag{4}$$

where *C*<sup>V</sup> is the gas volume coefficient in the pump; *V*<sup>g</sup> is the sum of the internal gas volume of the pump's components, except for the outlet pipe, in m3; *V*<sup>g</sup> is the gas volume in the pump in the initial state, which is equal to the gas volume in the inlet section, in m3; *C* is the gas flow coefficient in the pump; *C'* is the water flow coefficient in the pump; *Q*<sup>g</sup> is the gas flow in the self-priming process in m3/h; *Q*<sup>w</sup> is the water flow in the self-priming process in m3/h; *Q*<sup>d</sup> is the water flow at the rated condition after the pump operates normally in m3/h.

**Figure 14.** Definition of several typical surfaces of the self-priming pump.

Figure 15 shows the gas volume coefficient *C*<sup>V</sup> and the gas flow coefficient *C*out2 on the "Out2" surface during the self-priming process. A negative gas flow coefficient means that the gas flows out of the pump, whereas a positive one indicates that the gas flows into the pump. In accordance with the previous analysis, the self-priming process of the pump was divided into three stages as follows: initial (*t* ≤ 0.5 s), middle (0.5 s < *t* < 4 s), and final (4 s ≤ *t*). These self-priming stages are shown as I, II, and III in Figure 14. When 0 s < *t* ≤ 0.15 s, the amplitude of *C*out2 was close to 0, and the value of *C*<sup>V</sup> remained 1, indicating that the gas in the inlet section began to reach the "Out2" surface at *t* = 0.15 s. When *t* > 0.15 s, the distribution of *C*out2 showed a serious fluctuation, which shows the unsteady characteristics of the self-priming process of the pump. When 0.15 s < *t* ≤ 0.5 s, the amplitude of *C*out2 increased initially then decreased; afterward, it reached the maximum of 0.15. When 0.5 s < *t* ≤ 4 s, it decreased and reached the minimum of 0.02. When 4 s < *t* ≤ 5.8 s, it increases again, reaching the maximum of 0.56. When 5.8 s < *t* ≤ 8 s, it decreases again and finally approached 0, indicating that the gas in the pump was basically exhausted. In the entire self-priming process, the value of *C*<sup>V</sup> continuously decreased, and the decrement rate was affected by *C*out2.

**Figure 15.** Gas volume coefficient *C*<sup>V</sup> and gas flow coefficient *C*out2 on the "Out2" surface during the self-priming process.

The impeller and diffuser are the core components of the self-priming pump. Figure 16 displays the gas flow coefficient *C*ip\_in and *C*ip\_out of impeller inlet and outlet in the self-priming process. When 0 s < *t* ≤ 0.05 s, the value of *C*ip\_in increased from 0 to 0.8, while that of *C*ip\_out increased from 0 to 0.65, indicating that part of the gas remained in the impeller. When 0.08 s < *t* ≤ 0.5 s, the working capacity of the impeller was weakened due to the increase of the impeller void fraction in the initial self-priming stage, and the amplitudes of *C*ip\_in and *C*ip\_out decreased and approached 0, showing a certain positive correlation between them. When 0.5 s < *t* ≤ 4 s, the amplitudes of *C*ip\_in and *C*ip\_out fluctuated continuously but increased first and then decreased on the whole. The reason for the increment was that the amplitudes of *C*ip\_in and *C*ip\_out were close to 0 at *t* = 0.5 s, while the reason

for the decrement was that the lower the pressure at the impeller inlet, the slower the rising rate of the water column in the inlet section, and the slower the suction rate of the impeller. When *t* > 4 s, the water in the inlet section flowed into the impeller in the final self-priming stage, causing the drainage capacity of the impeller to increase sharply. The amplitudes of *C*ip\_in and *C*ip\_out continued to increase, and the maximum value was close to 0.2. Then, as the total amount of gas in the pump decreased, the amplitudes of *C*ip\_in and *C*ip\_out continued to decrease, and finally close to 0.

**Figure 16.** Gas flow coefficient *C*ip of impeller inlet and outlet in the self-priming process.

Figure 17 shows the gas flow coefficient *C*df\_in and *C*df\_out of the diffuser inlet and outlet in the self-priming process. It can be seen that the changing law of *C*df\_in and *C*df\_out was basically the same as that of *C*ip\_in and *C*ip\_out. In the initial, middle, and final self-priming stages, the value of *C*df\_in and *C*df\_out first increased and then decreased.

**Figure 17.** Gas flow coefficient *C*df of diffuser inlet and outlet in the self-priming process.

As a standard characteristic parameter of the pump, pressure is one of the important factors affecting the self-priming capability of the self-priming centrifugal pump. Figure 18 presents the pressure *P*in on the "In" surface and pressure *P*out2 on the "Out2" surface in the self-priming process. It can be seen that the value of *P*in was basically kept at 5 kPa, due to that the "In" surface was 0.5 m under water and the pressure value was only affected by atmospheric pressure. In addition, the value

of *P*out2 was rapidly increased from 0 kPa to 5 kPa in the initial self-priming stage, it remained stable in the middle self-priming stage, and rapidly increased to 10 kPa in the final self-priming stage.

**Figure 18.** Pressure on the "In" surface and "Out2" surface in the self-priming process.

Figure 19 illustrates the pressure *P*ip\_in and *P*ip\_out of the impeller inlet and outlet in the self-priming process. It can be seen that when 0 s < *t* ≤ 0.05 s, after the impeller filled with water started to rotate, the value of *P*ip\_in rapidly decreased from 0 kPa to −27 kPa and then increased to 7 kPa, while the value of *P*ip\_out increased to 45 kPa. When 0.05 s < *t* ≤ 0.5 s, with the rapid increase of the impeller void fraction, the working capability of the impeller was sharply weakened, the value of *P*ip\_in and *P*ip\_out decreased to −2.5 kPa and 3.5 kPa, respectively. When 0.5 s < *t* ≤ 4 s, since the gas in the inlet section was slowly exhausted out of the pump, the water column in the inlet section raised continuously, and the value of *P*ip\_in showed a downward trend, while the value of *P*ip\_out was basically stable. When 4 s < *t* ≤ 8 s, the value of *P*ip\_in dropped sharply and the value of *P*ip\_out raised significantly due to the sharp decrease of the impeller void fraction. Finally, when the impeller void fraction was close to 0, the value of *P*ip\_in and *P*ip\_out remained at −25 kPa and 42 kPa.

**Figure 19.** Pressure on the impeller inlet and outlet in the self-priming process.

Figures 20 and 21 present the pressure difference between the two ends of backflow channel *P*bc and water flow coefficient *C'*bc in the whole self-priming process and middle self-priming stage. It can be seen that in the initial self-priming stage, the value of *P*bc and *C'*bc reached the maximum rapidly, then decreases rapidly. In the middle self-priming stage, the value of *P*bc and *C'*bc constantly fluctuated. In the final self-priming stage, the values of *P*bc and *C'*bc increased sharply and remained essentially stable. Moreover, the value of *C'*bc had a positive correlation with *P*bc, which was especially evident in the middle self-priming stage, as shown in Figure 20. In the middle self-priming stage of *t* = 2.65 s, the maximum value of *P*bc reached 2.8 kPa, while the maximum value of *C'*bc was 0.095.

**Figure 20.** Pressure difference between the two ends of backflow channel *P*bc and water flow coefficient *C'*rc in the whole self-priming process.

**Figure 21.** Pressure difference between the two ends of backflow channel *P*bc and water flow coefficient *C'*bc in the middle self-priming stage.
