*3.1. Test Bench*

In order to test the external and internal characteristics of the pump, a small submersible tubular pump test bench for model tests and pressure pulsation tests was established. The test cycle piping system is shown in Figure 4, which had a length of 4.2 m and a height of 1.2 m (excluding the pressure tank and the suspended height). The main dimensions of the test system are shown in Figure 4 (unit is mm). The pipeline included a thick pipe section with an inner diameter of 200 mm, a tapered section with an inner diameter of 200 mm to 120 mm, and a pipe section with an inner diameter of 120 mm. The test bench layout was divided into two layers. The upper layer included the submersible pump, the pressure tank, the torquemeter, and the motor. From the inlet passage to the outlet passage, the entire submersible tubular pump unit was made of plexiglass for flow visualization and internal flow field measurements based on laser testing technology. The lower part contained an electromagnetic flowmeter, auxiliary pump, butterfly valve, and other pipe accessories. The electromagnetic flowmeter

satisfies the installation requirements as the water inlet pipe was greater than 10 D and the water outlet pipe was longer than 5 D.

**Figure 4.** Single-line diagram of pump test stand.

The external characteristic parameters of the pump device include discharge, lift head, power, and efficiency. The instruments generally used for testing are mainly electromagnetic flowmeters, torque meters, and differential pressure transmitters.

The discharge was measured by an electromagnetic flowmeter. The average discharge obtained during a period of time was used as the discharge value under this operating condition.

Pressure measurement sections A-A and B-B in the system can be seen in Figure 4. The equation for lift head is written as [32]:

$$H = \left(\frac{p\_1}{\rho g} + \frac{V\_1^2}{2g} + Z\_1\right) - \left(\frac{p\_2}{\rho g} + \frac{V\_2^2}{2g} + Z\_2\right) \tag{1}$$

The torque moment and the rotational speed values are read from the tacho-torquemeter directly, and converted to power through Equation (2):

$$P = M\omega, \;\omega = \frac{2\pi n}{60} \tag{2}$$

When the above data are obtained, the efficiency is computed through Equation (3):

$$
\eta = \frac{\rho gQH}{p} \tag{3}
$$

#### *3.2. Pressure Pulsation Measurement*

The pump device pressure pulsation test mainly uses multiple dynamic pressure sensors to collect pulsation data. The micropressure sensor used in this test was a CYG1505GSLF made by Kunshan Shuangqiao Sensor Measurement Controlling Company (Kunshan, China, 2016). The basic parameters are given in Table 2. The SQCJ-USB-36 data acquisition instrument was also produced by Kunshan Shuangqiao Sensor Measurement Controlling Company (Kunshan, China, 2016). The number of analog channels was 36 channels, and the sampling frequency was 100 kHz.

**Table 2.** Parameters of the pressure sensor.


In order to compare the different pressure pulsations in the various flow components of the submersible pump device, dynamic pressure sensors were arranged at the impeller outlet (P1), middle of the guide vane (P2), the guide vane outlet (P3), and the bulb unit (P4, P5 and P6) to monitor the pressure pulsation, as shown in Figure 5. All the measuring points were arranged on the line where the horizontal longitudinal section intersected the wall surface.

**Figure 5.** Location of pressure measurements.

#### **4. Results and Analysis**

#### *4.1. External Characteristics of Pumping System*

The external characteristic data of the submersible pumping system obtained by the model test was compared with the performance of the pumping system predicted by CFD calculation. The comparison results of the two are shown in Figure 6 (the solid square points in the figure are the data points obtained by the model test, and the hollow square points are the data points obtained by the numerical simulation. These points are respectively fitted with a quadratic curve to obtain the final performance curve). It can be seen that the numerical simulation results agree well with the experimental results, especially in the high efficiency area, where the high efficiency point appears in the same flow rate at about 19 L/s, and the corresponding maximum efficiency is 74.4%. Under the small flow condition, the numerical calculation results were higher than the model test values, while under large flow conditions, the model test value was slightly higher than the calculated value. From the comparison of calculated and measured results, the calculated data can be considered accurate and reliable.

**Figure 6.** Hydraulic performance of the pumping system.

#### *4.2. Pressure Pulsation Analysis*

In order to compare the results of the pressure pulsation measurements, the monitoring points set in the numerical calculation were the same as those in the experiment (P1, P2, P3, P4, P5, and P6), and additionally the monitoring points inside the pump, which cannot be measured by testing, were added to obtain more pulsation information for the pump. The detailed location of the monitoring points is shown in Figure 7. Since the actual measurement points are distributed from the plane parallel to the ground plane, this arrangement makes each point on the line appears to coincide, and only one point can be seen in the front view. In order to show the location of the measuring points, Figure 7 is the actual calculation domain rotated 90◦ clockwise along the axis.

**Figure 7.** Pressure monitoring points.

The pressure pulsation data of each point was subjected to fast Fourier transform analysis to obtain the frequency domain diagram of each point. The results were compared with the experimental data in different sections, as shown in Figure 8. (The red points in the figure are the pulsation data points measured experimentally, while the black points are the pulsation data points obtained by numerical calculation. Each point is connected with a straight line to obtain the final pressure pulsation curve.) Only the pressure pulsation values for the six points P1–P6 were taken: P1 is the impeller outlet, P2 is the middle guide vane, P3 is the guide vane outlet, P4 is the middle of the bulb unit, P5 is the bulb unit tapered section, and P6 is the bulb unit tail in the optimum condition (*Q*opt = 19 L/s), where the abscissa is the rotational frequency multiple, *N*F, and the ordinate is the amplitude, A. Here, *N*<sup>F</sup> is defined as follows:

$$N\_{\rm F} = 60 \text{ zF/}n = \text{F/F}\_n \tag{4}$$

Figure 8 shows that the pressure pulsation measurement at the monitoring point P1 has a significant amplitude at the full-fold frequency, and the numerical calculation of the frequency domain map is only due to small adverse effects, such as noise interference. The blade passing frequency (BPF) and its integer multiples have a large amplitude. However, both of them obtain the maximum amplitude at BPF. The amplitude of the pressure pulsation test at the impeller exit monitoring point is 1.14 times the unsteady calculated amplitude. The reasons for the error may be: (1) The influence of dynamic and static interference. (2) The submerged cross-flow pump has a small bulb unit, and the motor is placed outside the pump device and connected to the impeller through the rotating shaft. During the rotation of the impeller, the rotating shaft also drives the water in the inflow passage to rotate, so under test conditions, the pressure pulsation value is too large. (3) There are many interference factors in the test case. (4) There is a certain relationship between the form of the Fourier transform and the selection and length of the window function. However, the overall pressure pulsation test and numerical simulation have a high degree of agreement for the main frequency. At monitoring point P2, due to the restriction effect of the inlet vane on the water flow, the amplitude of the blade frequency is significantly reduced with respect to the impeller outlet, and the amplitudes of the 1x rotation frequency and the 2x rotation frequency do not change much. The amplitude of the model test at the blade frequency is 1.07 times the unsteady calculated amplitude. At the integer frequency of the blade frequency, the amplitude of the test and the numerical calculation is in good agreement, and the model test is caused by the influence of bubbles. The frequency domain map has more components at high frequencies. At monitoring point P3 (the vane outlet), the amplitude of the model test and the unsteady calculation result of the blade frequency are somewhat reduced, and the amplitude of the model test at this point is 1.23 times the unsteady calculated amplitude. The amplitudes of the measurement and the unsteady calculation result are obviously increased with the 12-fold frequency shift, which may cause undesirable flow states. such as backflows and vortexes at the exit of the guide vane.

**Figure 8.** Comparison of numerical calculation results of pressure pulsation for each part with experimental data.

The bulb unit also has a certain inhibitory effect on the pressure pulsation due to the rectifying action of the supports. At monitoring point P4 (in the middle of the bulb unit), the pressure pulsation amplitude is significantly reduced relative to the vane section. At the blade frequency, the amplitude of the pressure pulsation test is 1.5 times the amplitude of the unsteady calculation. The amplitude of the pressure pulsation test is significantly larger than the unsteady calculation result, but the difference between the amplitudes of these two is smaller at 1x frequency. Probably because the monitoring point is far from the impeller, the influence of the impeller on the pressure pulsation is reduced, which leads to a large numerical error in the calculation of the amplitude at the 3x frequency shift. The frequency domain diagram of monitoring point P5 is shown at the blade frequency, and the amplitude of the pressure pulsation test is 2.4 times the amplitude of the unsteady calculation. The amplitude difference between the test and the digital mode gradually increases, and the distance from the pulsating source impeller also increases. The amplitude becomes smaller, and the influence of interference on the test results is more obvious. At the same time, the flow path of the gradual section is widened, and certain bad flow patterns occur when the water flow is fast. The model test has a large amplitude at high frequencies. At the end of bulb section monitoring point P6, the test and numerical calculations have large amplitudes at low frequencies. At the blade frequency, the amplitude of the model test is 2.8 times the unsteady calculated amplitude. Due to the poor flow pattern in the tail of the bulb body, the frequency domain diagram of monitoring point P6 obtained as measured by the pressure pulsation test also has a large amplitude at high frequencies.

In summary, under the optimal working conditions, the pressure pulsation values of the monitoring points obtained by the pressure pulsation test are basically the same as the general trend for the unsteady calculation results. In the impeller and vane parts especially, the monitoring points are at the main frequency and amplitude. The upper abundance is higher, and the amplitude of the blade frequency increases up to 11%. It can be seen that the pressure pulsation test and the pressure pulsation data obtained by the nonfixed constant value simulation are more accurate, which further studies the internal characteristics of the pump device through a nonfixed constant value simulation.

#### **5. Conclusions**

The study presents a numerical simulation and experiment of external characteristics and pressure pulsation of a submersible tubular pumping system. The following results are obtained:


**Author Contributions:** Y.J. conceived and designed the experiments. X.H. participated in numerical simulation and proposed the modification suggestions to the original manuscript. H.C., Y.Z., and S.Z. performed the experiments and simulation. H.C. and Y.Z. analyzed the data. Y.J. wrote the paper. C.L. performed funding acquisition.

**Funding:** This work was supported by a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), Nature Science Foundation of China (Grant No. 51609210), and Nature Science Foundation of Jiangsu Province (Grant No. SBK2019041842).

**Conflicts of Interest:** The authors declare no conflicts of interest.
