5.1. Validation Experiment
A validation experiment was carried out to ensure the reliability of the numerical results.
Figure 11 shows the experimental pump, and
Figure 12 shows the test rig. The characteristic test of the original vertical inline pump was carried out on the open-loop in National Research Center of Pumps, Jiangsu University. The measurement errors of head and efficiency were less than ±2%, and the figure for flowrate was less than ±2%. The WIKA pressure sensor was used to measure the inlet and outlet pressure of the pump, with the range of 0–1.6 bar and 0–4 bar respectively. The flow rate of the pump was obtained by the electromagnetic Flowmeter (KROHNE-UFM 3030), and the input power of the pump was recorded by the power meter. In the experiment, the variable frequency drive controlled the rotational speed of the motor, and the flow rate was adjusted by adjusting the throttle valve. At the same time, repeated tests were carried out to ensure the reliability of the results.
As shown in
Figure 13, dimensionless parameters show both the test results and the calculated results. The computational results showed good agreement with the experimental results. The head coefficient is defined as Formula (2), and the flow coefficient used in the diagram is defined, as follows:
where:
: volume flow rate, ;
: impeller outlet diameter, m;
: impeller outlet width, m; and,
: tangential velocity at impeller outlet, m/s.
5.2. Data Mining Analysis
The cases generated in the optimization process were adopted in order to analyze the correlation between these 40 variables and the objective functions. A data mining analysis based on multiple linear regression was carried out. The regressions for models of efficiencies at the part-load condition and nominal condition are 0.96 and 0.934, respectively, indicating that the results had great reliability.
The data were sorted in descending order with reference to the absolute sum of standardized coefficients for models of efficiency at the part-load condition and nominal condition. It was found that the blade angle and the blade number have great influence on the performance of the vertical inline pump. Specifically, the outlet blade angle (y19) has the greatest effect on pump performance and the increase of this value has a negative influence on the efficiencies of both operating conditions. The increase of the blade number (z) has a slight positive effect on the performance under the part-load condition, while it has a strong negative effect on the performance under the nominal flow condition.
5.3. Pareto Frontiers Analysis
The calculated Pareto frontiers are shown in
Figure 14, and the performance data is given in
Table 2, and the main design parameters are shown in
Table 3. When compared with the original model, the optimized cases have higher efficiency and the heads can also satisfy the design conditions. For the part-load condition, the maximum efficiency increase after optimization is 8.06%. When compared with the original model, the optimized cases have obvious decreases in terms of input power, and the heads do not have obvious fluctuation. For nominal flow conditions, the maximum efficiency increase after optimization is 7.33%. In terms of input power and head, there is a great difference between different results.
As shown in
Figure 14, the efficiency of the part-load condition decreases with the increase of efficiency for the nominal flow rate. When the efficiency of
is less than 76%, there is a slight decrease in efficiency at part-load conditions. However, when the efficiency of the design flow rate is higher than 76%, the efficiency at part-load rapidly decreases with the increase of the efficiency at the nominal condition.
According to the design parameters of the Pareto solutions in
Table 3, the case with higher efficiency at part-load condition usually has an inlet pipe with a relatively longer transverse length (
x0 in the table indicates the transverse length of the inlet bend, the same as below), an impeller with smaller inlet blade angle, and a larger outlet blade angle (
y14 indicates inlet blade angle and
y19 indicates outlet blade angle, the same below). The case with better performance at nominal flow condition shows that it generally has an inlet pipe with smaller transverse length and the impeller outlet angle is smaller. The design schemes with more blades (the number of blades is more than six) commonly have better comprehensive performance.
Three representative cases were selected and compared with the original case in order to further study the reasons for the performance improvement of the vertical inline pump after optimization, and their numbers were 1, 8, 12 respectively.
5.4. Performance Comparison
A performance comparison between the three selected optimized cases and the original case based on transient calculation was carried out. The time step was set as
s, which is the time that is required for the impeller to rotate three degrees, and the mean value of the last 20 positions was utilized in the analysis.
Table 4 lists the main design variables of these four cases and the
Table 5 gives the performance characteristics (where Optimized Case (1), (2), (3) refer to Pareto solutions 1, 8, and 12 in
Table 2 respectively).
As shown in
Table 5, the optimized cases show better performance and stability than the original model from 0.5 to 1.5 times design flow rate conditions. However, with the further increase of the flow, the stability of the optimized cases is poor, and the optimization model (1) has a steep drop in efficiency.
Figure 15 shows a comparison of profiles for inlet pipe between the three selected models and the original case. The black line represents the original model, blue represents the optimized case (1), red represents the optimized case (2), and pink represents the optimized case (3). As shown in the diagram, the transverse length of the inlet pipe of the optimized models is longer, and the relative position of the second bend is further away from the outlet. Specifically, the transverse lengths of the three optimization models decrease in turn, with optimized case (1) being the longest, whereas optimized case (3) is the shortest. The curvature of the first bend of the optimized case (1) is relatively smaller, and the transition section between the first bend and the second bend is longer.
5.5. Hydraulic Head Distribution
The head distributions of the original model and the optimized cases were analyzed in order to study the flow losses in different parts, and the results are shown in
Table 6. The head value was calculated using the formula below:
where, subtitle 1, 2 represent the inlet and the outlet of each component (as shown in
Figure 16), respectively.
For the overload condition, the input power for the three optimized cases is significantly reduced. The workability of the impeller for optimized case (1) under the over-load condition is poor and, therefore, the input power of this case is obviously lower than the others. For the inlet pipe, the hydraulic losses are mainly composed of the impact losses and the friction losses under the design flow and the large flow condition. The optimized cases have more hydraulic losses in the inlet pipes, as the length of the inlet pipe of the optimized case is longer than the original one. The data for other parts is not much different (in addition to the optimization model (1)), but the input power is significantly reduced, so that the efficiency of the optimized cases (2) and (3) is better than the original model under large flow conditions.
In the same way, under the design flow condition, the input power of the three optimized cases is lower than that of the original case, and the hydraulic losses inside the volute and the delivery pipe are reduced, so the performance of the optimized model under the nominal condition is superior to the original model.
Under the part-load condition, the working ability of the optimized impeller had a slight decrease, but, at the same time, the losses in other flow channels reduce for different degrees, so the total head still meets the design requirements. For the optimized case (1), the hydraulic losses in the inlet pipe are significantly reduced when compared with the original model, and the figure for the volute is also lower than the original one. For the optimized cases (2) and (3), the hydraulic losses in the volute have a significant decrease, and the figures for inlet pipe are similar to the original case. Meanwhile, the input power of the three optimized cases under the small flow condition is obviously lower than that of the original model, so the efficiencies of the three optimized cases at the part-load condition are improved.