Abstract
In order to save energy by broadening its application range, the influence of impeller trim on the performance of a two-stage self-priming centrifugal pump was numerically studied. The hydraulic performance experiments and self-priming experiments were carried out. And the unsteady performance of pressure fluctuation and radial force in the pump was analyzed. The results show that with the increase in impeller trim quantity, the best efficiency point of the pump would move to the small flow rate condition. Under the design flow rate, when both the two stages of the impeller were trimmed by 6%, head of the pump was reduced by 13%, efficiency of the pump was as well decreased by 1.69 percentage points, and self-priming time was increased by 1.7%. Thus, impeller trim can be used to meet the operating requirements in the head range of 94–107 m. With the increase in impellers trim quantity, the pressure fluctuation in the positive channel of the radial guide vane and the volute was smaller, while the radial force on the wall of radial guide vane and volute was also smaller.
Keywords
Introduction
Self-priming pump has the advantages of compact structure, convenient operation, long life, and strong self-priming capacity. It has been widely used in agriculture, fire control, municipal, electric power, mining and chemical industry, and other fields.1–4 It is especially suitable for occasions in which equipment needs to be started frequently, the work is mobile, the irrigation is difficult, or the drainage is flowing.
In actual operation, however, the performance of the pump under operating flow rate is not always consistent with the maximum efficiency point. Therefore, the method of trimming the impeller outlet diameter has been widely used to adjust the performance of pump, according to the similarity criterion.5–9 Impeller trim can not only expand the application range of the pump, which is helpful for the standardization and serialization of the pump production, but also stimulate a reasonable match for the maximum efficiency point and the required operating flow rate. Moreover, it can improve the operating efficiency of pumping system and reduce operating costs.10,11
Over the years, scholars have conducted a lot of research on the influence of impeller trim on the performance of the centrifugal pump. Khalifa 12 experimentally investigated the effect of trimming the impeller diameter on the pump performance and vibration levels and compared the changes of the pressure fluctuations inside the pump volute and around the impeller blade exits. Yang et al. 13 studied the effect and influence impeller trimming had on the performance of a single-stage centrifugal pump as turbine using experiment and numerical methods. By numerical simulation method, Wang and Liu 14 obtained the pressure distribution as well as velocity distribution of the internal flow field of the pump with different impeller outlet diameters and found that the impeller trim would lead to a decline of the pump performance.
However, the research into influence of impeller trim on the performance of multi-stage self-priming pump is relatively few. Therefore, the main motive of this article is to study the effects of impeller trim on the performance of a two-stage self-priming centrifugal pump with computational fluid dynamics (CFD) and experiment methods and then analyze the time-domain and frequency-domain characteristics of pressure pulsation and time-domain characteristics of the radial force under different impeller trims.
Determination of impeller trim
Two-stage self-priming centrifugal pump
The test pump is designed to be a two-stage self-priming centrifugal pump with a gear case. The design parameters of the self-priming centrifugal pump are as follows: Flow rate Qd is 60 m3/h, head of the pump H is 105 m, rotation speed of the pump n is 3540 r/min, and efficiency of the pump η is 60%. When the self-priming height of the pump is 4 m, the self-priming time of the pump Ts is <180 s. The self-priming centrifugal pump is required to be installed in the sprinkler. In this article, head of the first-stage pump H1 is 50 m, and head of the second-stage pump H2 is 55 m. The structure of the pump is shown in Figure 1. The main geometrical parameters of the original impeller, radial guide vane, and volute are shown in Table 1.
Structure of the two-stage self-priming centrifugal pump.
Main parameters of the original impeller, radial guide vane, and volute.
Figure 2 shows the calculation area of the whole flow field, including inlet extension part, first-stage impeller, radial guide vane, first-stage pump chamber, second-stage impeller, volute, second-stage pump chamber, gas–liquid separation chamber, and outlet extension part.
Calculation areas.
Determination of impeller trim
With the increasing impeller outlet diameter trim, the difference between actual performance of the pump and the expected performance will be enlarged. According to the literature, 15 the limit value of the impeller outlet diameter trim is related to specific speed of the pump ns, as shown in Table 2.
Relation between specific rotation speed and maximum allowable trim.
The specific speeds of the two-stage self-priming centrifugal pump designed in this article are 88.7 and 82.5. Therefore, the maximum allowable trims of the first-stage impeller and second-stage impeller are 26 and 27 mm, respectively. As the pump is self-priming, three schemes of impeller trim, as shown in Table 3, are established in order to preserve its performance.
Trim schemes of impeller outlet diameter.
Steady characteristic analysis
Numerical calculation method
In this article, mesh generation of calculation area in the whole flow field of the pump was made with the ICEM code. Due to the complexity of the pump structure, the tetrahedral grid with strong adaptability is used during mesh generation. In order to ensure the accuracy of the calculation, the grid independence check is performed. CFX code is used to simulate the original pump model numerically, and simulation results are shown in Table 4.
Grid independence analysis of the original model.
As displayed in Table 4, although the difference of total grid numbers is large, head deviation of the pump is within 0.5%. Thus, the simulation results are stable. Considering the accuracy and time of the numerical simulation, total grid number of 6,862,158 is selected to do the next numerical research.
The inlet boundary condition was set as a standard atmospheric pressure (1 atm), which assumed that the flow velocity in the inlet section is uniformly distributed. The outlet boundary condition is set as mass flow rate. All physical surfaces were set as no-slip wall and the near-wall regions were disposed with standard wall functions method. Equivalently, the components of time mean velocity and the pulse velocity in all directions were zero.
For two-stage centrifugal pump, shear-stress transport (SST) k–ω model, which is suitable for the numerical simulation of multi-stage centrifugal pump, is selected to predict hydraulic characteristics and analyze the unsteady performance.
Performance analysis
The centrifugal pumps in the four schemes are calculated with CFX code, and heads and efficiencies under five flow rates (0.6Qd, 0.8Qd, 1.0Qd, 1.2Qd, and 1.4Qd) are shown in Figure 3.
Numerical simulation curves of energy performance in the pump: (a) head and (b) efficiency.
As presented in Figure 3, with the constant trim of the two-stage self-priming centrifugal pump impeller, the head under the same flow rate is gradually reduced. This is because fluid energy generated by the impeller in the two-stage self-priming centrifugal pump was reduced with the decrease in the impeller outlet diameter. When the pressure at the outlet of the pump decreased, head of the pump constantly reduced. Under the design flow rate, the calculation head was reduced from 107.7 m in the original model to the 94.8 m in scheme 3.
As can be also seen from Figure 3, the calculation efficiencies of the two-stage self-priming centrifugal pump in the four schemes first increased and then decreased with the increase in flow rate. Under the small flow rate, the difference between efficiencies in the four schemes is small. Under the 0.6Qd, the calculation efficiency in the original scheme is 50.9% and the calculation efficiency in scheme 3 is 49.7%, which decrease by 1.2 percentage points. With the increase in the flow rate, the difference between efficiencies in the four schemes becomes larger. Under the 1.4Qd, the calculation efficiency in the original scheme is 60.1%, and the calculation efficiency in scheme 3 is 57.2%, which is decreased by 2.9 percentage points. With the increase in the impeller trim quantity, the calculation value of the efficiency decreases gradually.
Experiment verification
Hydraulic characteristic experiment
Hydraulic characteristic experiment bench of the two-stage self-trimming centrifugal pump is shown in Figure 4.
Sketch of energy characteristic test bench.
Hydraulic characteristic experiments were performed on the four schemes, and experiment curves are shown in Figure 5.
Experiment curves of energy performance in the pump: (a) head and (b) efficiency.
As shown in Figure 5, head in the three trim schemes and original scheme gradually decreases with the increase in flow rate. The head change trends are the same, and the four head curves are basically parallel. Under the same flow rate, the larger impeller trim is, the more head decreases. Under the design flow rate, head in scheme 3 is reduced from 108.22 m in the original model to 94.07 m, which decreases by about 13%.
According to Figure 5, the difference in experiment efficiency in the four schemes under the small flow rate is small. The difference in efficiency is reduced with the increase in flow rate. With the decrease in the impeller outlet diameter, the experiment efficiencies under the same flow rate also decrease, which is consistent with the results of numerical simulation. Under the design flow rate, the experiment efficiency of scheme 3 decreases from 60.58% in the original scheme to 58.89%, which decreases by 1.69 percentage points. And the high-efficiency areas in the four schemes are all relatively wide. In the flow rate range of 51.6–83.4 m3/h, the experiment efficiencies in the four schemes are all >56%. In short, the impeller trim has very little effect on the efficiency of the pump.
Figures 3 and 5 show that the numerical simulation can accurately predict the hydraulic performance of the pump, which provides a basis for the next analysis of pressure fluctuation and radial force.
Self-priming experiment
Self-priming experiment bench of the two-stage self-trimming centrifugal pump is shown in Figure 6.
Sketch of self-priming test bench.
In order to measure self-priming time of the two-stage self-priming centrifugal pump, the two-stage self-priming centrifugal pump is placed at a platform whose height is 4 m from the grand. A pipe upward bending is connected at the inlet of the pump, and the pipe is about 300 m higher than the pump shaft. With power supply, the motor drives the impeller to rotate at a high speed. Since the power is turned on to when the centrifugal pump completes the self-priming process, the time period is recorded. The water in centrifugal pump outlet also starts to flow out normally.
To reduce the experimental deviation, every experiment was repeated for three times, and the self-priming time Tp was measured when the self-priming height is 4 m, which is shown in Table 5. As seen in Table 5, with the increase in impeller trim quantity, the gap between the impeller and the diffuser chamber gradually increases, which affects the self-priming performance of the pump. After the first-stage and second-stage impeller outlet diameters are all trimmed by 6%, the self-priming time of the pump at the same self-priming height increases by 27 s, which is an increase of roughly 17%.
Self-priming experiment results.
In summary, when the first-stage and second-stage impeller outlet diameters are all trimmed by 6%, the efficiency of the pump under the design flow rate decreases by 1.69 percentage points, and the high-efficiency area is still wide. Even though the self-priming time increases, the pump can still pump water. Therefore, in the head range of 94–107 m, the two-stage self-priming centrifugal pump in this article can meet the operating requirements by trimming impeller.
Unsteady characteristic analysis
In order to further analyze pressure pulsation and radial force of the two-stage self-priming centrifugal pump, the unsteady numerical simulation on internal flow in the pump was carried out. According to the rotation speed of the impeller, the time step is set to 4.7081 × 10−5 s. That is, 1° which the impeller rotated was chosen as a time step. In order to ensure the accuracy of analysis, the impeller was set to rotate six cycles, with the sixth period of the calculation results selected to be analyzed.
Arrangement of monitoring points
In order to study the pressure fluctuation in the positive flow channel of radial guide vane under different flow rates, the monitoring points P1, P2, P3, and P4 were set up, as shown in Figure 7(a). The monitoring points P5, P6, P7, P8, and P9 are arranged in the flow channel of the volute, as shown in Figure 7(b).
Distribution of monitoring points in (a) radial guide vane and (b) volute.
Pressure fluctuation analysis
In order to quantitatively analyze the pressure fluctuation in the positive guide-vane flow channel of radial guide vane, the pressure fluctuation coefficient is defined as follows
where Δp is the difference between the instantaneous pressure and mean value, ρ is the fluid density, and u2 is the circumferential velocity of impeller outlet.
Under the design flow rate, time-domain diagrams of the pressure fluctuation in monitoring points P1, P2, and P3 are shown in Figure 8. Frequency-domain diagrams of the pressure fluctuation coefficient in monitoring points P1, P2, and P3 are shown in Figure 9.
Time-domain diagrams of pressure fluctuation at monitoring points: (a) P1, (b) P2, and (c) P3.
Frequency-domain diagrams of pressure fluctuation at monitoring points: (a) P1, (b) P2, and (c) P3.
From Figure 8, we can see that with the rotation of the first-stage impeller, pressure fluctuation of the three trim schemes and original scheme in the positive guide-vane flow channel of radial guide vane presents obvious periodicity. With the decrease in the first-stage impeller outlet diameter, pressures under the design flow rate in the positive guide-vane flow channel of radial guide vane gradually decrease. As to the monitoring point P1, the average pressure in scheme 1 is 470 kPa, the average pressure in scheme 2 is 450 kPa, and the average pressure in scheme 3 is 420 kPa. Compared with the original scheme, the average pressure in scheme 1 is reduced by 4.0%. Compared with scheme 1, the average pressure in scheme 2 is reduced by 4.3%. Compared with scheme 2, the average pressure in scheme 3 is reduced by 6.7%.
As seen from Figure 9, in the three trim schemes, the frequencies that corresponded to maximum pressure pulsation coefficient of monitoring points P1, P2, and P3 were all about 354 Hz, which is consistent with the blade frequency of the first-stage impeller. This is also consistent with the conclusions in the original model. So, it is obvious that the frequencies corresponding to the maximum pressure fluctuation coefficient are independent of the impeller outlet diameter which is only related to the rotation speed of the impeller (i.e. blade frequency of impeller). And with the constantly trimming of impeller outlet diameter, the maximum value of pressure fluctuation coefficient in low-frequency area gradually becomes smaller. Under the design flow rate, the maximum value of the pressure fluctuation coefficient in the monitoring point P1 of the original model is 0.044. Along with the decrease in the first-stage impeller outlet diameter, the maximum pressure fluctuation coefficient in scheme 3 is reduced to 0.040, which decreases by 9.1%. The maximum value of the pressure fluctuation coefficient of the monitoring point P3 in the original model is 0.017. Along with the increase in the first-stage impeller trim, the maximum pressure fluctuation coefficient in scheme 3 decreases to 0.012, which decreases by 29% and is significantly higher than 9.1% of monitoring point P1. Therefore, in the positive guide-vane flow channel of radial guide vane, along with the monitoring points moving away from the outlet of the first-stage impeller, the effect on the pressure fluctuation coefficient becomes larger with the decrease in the first-stage impeller outlet diameter.
In short, with the increase in impeller trim quantity, the pressure in the positive guide-vane flow channel of radial guide vane is gradually reduced, and the pressure fluctuation is gradually decreased. Due to the increase in the impeller trim quantity, the influence of the points far away from impeller outlet in the positive guide-vane flow channel of radial guide vane is larger with the decrease in impeller outlet diameter. Under the design flow rate, time-domain diagram of the pressure fluctuation in the monitoring point P4 in the negative guide-vane flow channel of radial guide vane is shown in Figure 10.
Time-domain diagram of pressure fluctuation at the monitoring point P4.
As exhibited in Figure 10, with the trimming of the impeller outlet diameter, the average value of the pressure on the outlet of the guide vane is gradually reduced. This is consistent with the change in pressure in the positive guide-vane flow channel. Besides, it is found that when impeller outlet diameter is trimmed, the pressure fluctuation of the guide vane decreases, and the periodicity becomes not obvious.
Under the design flow rate, time-domain diagrams of the pressure fluctuation in the monitoring points P5, P6, P7, P8, and P9 of volute are shown in Figure 11. Frequency-domain diagrams of pressure fluctuation coefficient in the monitoring points of volute are shown in Figure 12.
Time-domain diagrams of pressure fluctuation at different monitoring points in volute: (a) P5, (b) P6, (c) P7, (d) P8, and (e) P9.
Frequency-domain diagrams of pressure fluctuation at different monitoring points in volute: (a) P5, (b) P6, (c) P7, (d) P8, and (e) P9.
As can be seen from Figure 11, the pressure fluctuation in the flow passage of the volute presents obvious periodicity. This is caused by the rotor–stator interaction which is formed by rotating the second-stage impeller and the static volute. With the increase in the trim quantity of the second-stage impeller, the pressure of the same monitoring point in the volute is reduced. The average pressure value of the monitoring point P5 in scheme 3 is about 830 kPa. It decreases by 8.4%, compared with the original model of 900 kPa. The pressure in the volute is obviously higher than the pressure in the flow channel of the radial guide vane, which is almost two times larger than the pressure in the flow channel of guide vane.
As displayed in Figure 12, the pressure pulsation in the volute is basically consistent with that in the positive guide-vane flow channel of radial guide vane. The pressure fluctuation coefficients decrease with the increase in the impeller trim. The pressure fluctuation coefficient of the monitoring point P5 in scheme 3 is 0.029. The coefficient is reduced by about 25%, compared with the original model of 0.039. From this perspective of different monitoring positions in the spiral line, the pressure fluctuation coefficient decreases with the monitoring position moving away from the volute tongue. The pressure fluctuation coefficient at P5, which is close to the volute tongue, is about 0.03. The pressure fluctuation coefficient at P8 located in the eighth section is only about 0.01, which reduces by 66%. But the pressure fluctuation coefficient of the monitoring points in the diffuser section is much larger than that in the eighth section of volute. This is because the fluid moves into the diffuser section and then the pressure transiently increases.
Radial force analysis
Under the design flow rate, time-domain diagrams of the radial force on the wall of radial guide vane in the four schemes are shown in Figure 13.
Time-domain diagrams of the radial force on the wall of radial guide vane: (a) original, (b) scheme 1, (c) scheme 2, and (d) scheme 3.
As can be seen from Figure 13, the radial forces on the wall of radial guide vane are small. It is due to radial guide vane being a central symmetric hydraulic component. Under the design flow rate, the radial forces on the wall of the radial guide vane present obvious periodicity. With the increase in the trim quantity of the first-stage impeller, the periodicity is gradually weakened, and the radial forces are also reduced. Compared with the original model, the radial forces in scheme 3 decrease by 70%. This is caused by rotor–stator interaction of fluid in the channel of the radial guide vane being weakened with the increase in the impeller trim.
Under the design flow rate, time-domain diagrams of the radial force on the wall of volute are shown in Figure 14. From Figure 14, we can see that the radial force on wall of volute has obvious periodicity and presents six peaks and six troughs, which is the same as blade number of the second-stage impeller. This is caused by the rotor–stator interaction between the second-stage impeller blade and the volute tongue. Under the design flow rate, the radial forces on the wall of volute obviously decrease with the increase in the impeller trim. Under the design flow rate, the average value of the radial forces on the wall of volute in scheme 1 is 1980 N. The average value of the radial forces on the wall of volute in scheme 2 is reduced to 1930 N, which decreases by 2.5% compared with scheme 1. The average value of the radial forces on the wall of volute in scheme 3 is reduced to 1830 N, which decreases by 5.2% compared with scheme 2. At the same time, the pulsation of the radial force on the wall of volute is also weakened. Compared with the three trim schemes, the radial force on the volute wall is obviously reduced with the decrease in the diameter of the impeller outlet, although the trim is the same. And the pulsation of the radial forces is also obviously weakened. Under the design flow rate, the average value of the radial forces on the wall of volute in the original model is 2100 N. The average value of the radial forces in scheme 3 is reduced by 12.8%, compared with the original model.
Time-domain diagrams of the radial force on the wall of volute.
Conclusion
The influence of impeller trim on the performance of a two-stage self-priming centrifugal pump was numerically studied. The hydraulic performance and self-priming experiment were carried out. At the same time, the unsteady performances of pressure fluctuation and radial force in the pump were analyzed. The following are the main conclusions.
With the increase in the impeller trim quantity, the maximum efficiency point of the pump moves to the small flow rate condition. Under the design flow rate, when the two stages of impellers are both trimmed by 6%, head of the pump decreases by 13%, and efficiency of the pump decreases by only 1.69 percentage points, while the high-efficiency area is still relatively wide. Therefore, the two-stage self-priming centrifugal pump in the head range of 94–107 m can meet the operating requirements using impeller trim.
With the increase in impeller trim quantity, the radial forces on the wall of radial guide vane and volute are smaller, and the pressure fluctuation in the positive guide-vane outlet flow channel of radial guide vane and the volute flow channel is smaller. Under the design flow rate, when the impeller outlet diameter trims by 6%, the radial forces on the wall of radial guide vane and volute decrease by 70% and 12.8%, respectively. The pressures of the monitoring point P1 in radial guide vane and P5 in volute decrease by 14.2% and 8.4%, respectively. And pressure fluctuation coefficients decrease by 9.1% and 25%, respectively.
With the increase in the impeller trim quantity, the gaps between the first-stage impeller and the radial guide vane and the second-stage impeller and the volute will increase. When the self-priming height is 4 m, the self-priming time will increase. After the two stages of impellers are both trimmed by 6%, the self-priming time of the pump increases by 27 s.
Footnotes
Academic Editor: Takahiro Tsukahara
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (grant no. 51509109), China Postdoctoral Science Foundation (grant no. 2016M600370), Key Research and Development Program of Jiangsu Province of China (grant no. BE2015001-1), the Science and Technology Support Program of Jiangsu Province of China (grant no. BE2014116), Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and Post-Doctoral Research Project of Zhejiang Province of China.