Investigation on Pressure Fluctuation of the Impellers of a Double-Entry Two-Stage Double Suction Centrifugal Pump

Abstract

Double-entry two-stage double-suction centrifugal pumps with high flow rates and high heads are used in some large water supply applications. The pressure fluctuation of the impeller is a key factor influencing the vibration in centrifugal pumps. In this paper, the pump is simulated and verified by experiments, and the pressure fluctuation distribution of two stage impellers is obtained. The study on the time domain and frequency domain of the two-stage impellers demonstrates that the pressure fluctuation of the first-stage single-suction impeller is affected by the twin volute. At 1.0 Q, the dominant frequency on the blade suction side and pressure side is twice the rotation frequency. The main frequency of pressure fluctuations at the outlet side of the blade at a low flow rate is higher than that at the design flow rate. Pressure fluctuations in the second-stage impeller are influenced by the inter-stage passage. The dominant frequency amplitudes grow incrementally along the streamlined direction. In the second-stage double-suction impeller, the dominant frequency amplitude at 0.6 Q is approximately twice that of 1.0 Q. Research in this paper can guide the design and operation of a two-stage pump.

1. Introduction

The Double-entry Two-stage double-suction centrifugal pump (DTDCP) is suctioned on both sides and pressured out from the center. The first-stage impeller with a left-right symmetrical distribution structure is a single-suction type, and the second- stage impeller in the middle is a double-suction type. The two-stage impellers are connected through internal channels. This pump not only inherits the characteristics of a double-suction centrifugal pump with a large flow but also highlights the features of a high head, which is extensively applied to long-distance water conveyance projects and high-lift irrigation projects [1,2]. For example, in China, the Yuxi Three Lakes Ecological Protection Water Resources Allocation Project in Yunnan Province, the Shanxi Jiamakou Yellow River Diversion Project, and the Xifan Yellow River Diversion Project have all adopted this pump type, and the single pump head of more than 150 m.

Many scholars have investigated the flow feature of centrifugal pumps impeller. The distribution of radial force in a single-stage double-suction centrifugal pump was studied by Wang [3] and Shadab [4]. It was concluded that the double-volute type centrifugal pump has less radial force. The rotor-stator interaction (RSI) of guide-vane centrifugal pump was studied by Posa [5], and he paid more attention to the impeller flow field which can influence the downstream guide vane. In the research of centrifugal pump impellers, stall [6,7], cavitation [8,9] and fluid-structure coupling [10,11] are also phenomena that many scholars pay attention to. Among them, the pressure fluctuation in the impeller is an important index to study these phenomena. Thus, for centrifugal pumps, the impeller pressure fluctuation is an important parameter. For a centrifugal pump with single-stage and single-suction, Zeng [12] studied pressure fluctuation in centrifugal pumps by experiments and discovered a larger amplitude in the tongue area, meanwhile, the volute structure affects the pressure fluctuation at the corresponding position. Sonawat [13] made a study of pressure fluctuation near the blade position of centrifugal pump through experiments and drew the conclusion that the aptitude of the impeller is related to the blade placement angle as well as the number of blades. Chalghoum [14] studied the interaction between the impeller blade and each tongue of the volute, and discovered the radial force arising from the imbalance of the pressure field will affect the pressure fluctuation and have a greater impact on the tongue. Zhang [15] studied the flow-induced vibration of centrifugal pumps at diverse guide vane openings. The study showed that the BPF (blade passing frequency) is the main frequency in guide vane, and the occurrence of low-frequency pressure fluctuation is associated with the periodic large-scale turbulence of the guide vane. For single-stage double-suction pumps, Gangipamula [16] carried out an analysis of pressure fluctuation, finding that the pressure reached the maximum when impeller and tongue overlapped. The outlet strain and the axial and radial vibration of a pump were tested by Fu [17]. The test results show that the vibration is affected by the interaction between the rotating impeller and the stationary blade. For multistage pumps, Tan [18] determined the optimal clocking position by comparing the pressure fluctuation when the different stages of impellers were at different axial arrangement positions. Ping [19] established a new design method for a multistage pump with pressure fluctuation as the key index. At present, research on pressure fluctuation of a two-stage double-suction centrifugal pump impeller is rare. The impeller regions of DTDCP consist of two parallel single-suction impellers and a double one. Investigation on pressure fluctuation in this region is significant to guide the operation.

As computer science has found its way into research, more and more experts have applied Computational Fluid Dynamics (CFD) to study the rotating machines flow field [20,21,22,23]. Wang [24] analyzed the pressure fluctuation on the pressure and suction sides of the blade in a single-stage pump using the RNG k-ε turbulence model in diverse flow rate situations. Barrio [25] analyzed the characteristics of the pressure of 6 monitoring points near the centrifugal pump volute tongue in diverse flow rates and found the position of monitoring points is important for results. Tarodiya [26] using the sliding mesh method, obtained the impeller pressure fluctuation characteristics in a single-stage pump. The quality of the grid [27], together with the scale of time step [28], also influences calculation accuracy. Time domain analysis [29] and frequency domain analysis [30] were used by the majority of scholars to do the post-processing of pressure fluctuation when discussing the results.

In this paper, the unsteady flow field of a DTDCP is calculated using CFD. Furthermore, the pressure fluctuation of pump impeller regions is emphatically investigated.

2. Physical Configuration and Numerical Model

2.1. Calculation Domain

The DTDCP of this research was operated in Shanxi, China. The basic parameters are represented in

Table 1. Pump Parameters.

Parameters	Values
D1	1050 mm
Z1	6
D2	1000 mm
Z2	6
n	$750 \mathrm{r}\cdot {\min }^{-1}$
Q	$8640 {\mathrm{m}}^3\cdot {\mathrm{h}}^{-1}$
H	158 m

.

The calculation domain includes the symmetrically arranged suction chambers, the symmetrically arranged first-stage single-suction impellers, the symmetrically arranged inter-stage flow channels, a second-stage double-suction impeller, a double-volute, and extended sections whose lengths are 2 times the diameter of import. The calculation domain is shown in Figure 1.

The flowchart of the study process is shown in Figure 2. First, a three-dimensional water body area is established; second, grid division is conducted, and boundary conditions are set according to actual operating conditions. After grid independence verification, the energy characteristic curve of the centrifugal pump is obtained by steady simulation and verified with the test results. Finally, the pressure fluctuation characteristics inside the centrifugal pump impeller are obtained by unsteady calculation.

2.2. Grid and Boundary Conditions

Taking into account the complex structure of the DTDCP, the unstructured grid is used, as shown in Figure 3. The extended pipe is used and is specified as the velocity inlet condition. The outlet is set to free flow condition for the flow in the pump has been fully developed. The RNG k-ε turbulence pattern is used to deal with the high strain rate of the pump [31,32]. In addition to the inlet, outlet, and interfaces between sub-basins, the other surfaces are defined as wall boundaries. And the wall boundary has no-slip wall circumstance [33,34]. The sliding mesh is introduced for the rotor-stator interface. For the pump, when the water flows through the surface, the flow near the wall region has a large velocity gradient, due to the effect of the viscosity. With the purpose of ensuring the reliability of the calculation, taking the near-wall grid into account is necessary. To do this, the first layer of the grid is validated. After testing, 30< y⁺ < 300, which means the calculation is reliable.

The number of grids is added at the tongue region of semi-spiral suction chamber and double-volute, blade surface. The calculation domain with different grid numbers is simulated by applying the RNG k-ε turbulence pattern. From Figure 4, at the design flow rate, the head rises when grids elements increase from 3.56 million to 4.85 million. The variation of heads is scarce when grid elements increase to 6.43 million. In conclusion, the elements of grids make a small difference to the results when they continue to increase. Therefore, the elements of grids of the pump will be controlled at about 6.43 million, and the corresponding number of nodes is 3.8 million.

In the unsteady simulation, the chief purpose of the study is to obtain the characteristics of the pressure fluctuation. There are no differences between the unsteady cases and steady cases in turbulence model and boundary conditions. The measured time step is 0.00133 s, which is just 1/60 of the impeller rotational period. The result of the steady calculation is taken as the initial value of the unsteady calculation The root means square (RMS) residuals are set to below 10⁻⁵. The cases are run in the High-Performance Computing Center of Hohai University, using 256 GB of memory and 128 cores for parallel computing. The numerical calculation is carried out on ANSYS CFX 2020.

2.3. Monitoring Points

Taking into account the data storage and computing speed, the number of monitoring points located in both impellers is 36. The monitoring points are presented in Figure 5. The single-suction impellers are matched with twin volutes. The double-suction impeller is matched with a double-volute. The monitoring points 1 to 3, 4 to 6, and 7 to 9 are respectively arranged on the front shroud, middle streamline, and hub. The SS, SP, DS, and DP are shortened for the Single-suction impeller suction side, single-suction impeller pressure side, double-suction impeller suction side, and double-suction impeller Pressure side. Three typical operating conditions (0.6 Q, 1.0 Q, 1.1 Q) are analyzed. The pressure coefficient Cp [35] is introduced to contrast pressure at different positions.

$$Cp=\Delta p/(0.5\rho u^2)$$

(1)

$$u=\frac{\pi Dn}{60}$$

(2)

where, Δp is the difference between the pressure and its average value, u is the circumferential velocity at the impeller outlet, ρ is the fluid density, D is the impeller outlet diameter, and n is the rated speed of the centrifugal pump. For the first stage and the second stage of the pump, the denominator of the pressure coefficient will be calculated according to the different impeller outlet diameters.

3. Results and Discussion

3.1. Pump General Performance

The external characteristics of the pump were tested on the simple opening test rig. The circuit diagram designed for testing is presented in Figure 6, including a large circulating pool, a pump and motor for the test, pipelines at the pump inlet, filters, pump outlet pipelines, pressure sensors, flow meters, and electric flow regulating valves as well as other auxiliary systems. The flow rate, pressure of entry and vent, velocity, head, power, efficiency, and NPSH can be obtained from the test rig. The comprehensive measurement error of the test device is ±0.5%.

The calculated values and experimental values of performance characteristics are displayed in Figure 7. At the rated flow rate condition, the experiment outcomes indicate that the head of the pump is 158 m and the unit efficiency is 84.5% while the result of numerical simulation calculation is 155.3 m and the unit efficiency is 82%. The head relative error is 1.7%, while the efficiency relative error is 3%. The efficiency relative error is slightly larger because the seal friction loss and bearing friction loss are unable to accurately estimate when simulated. On the whole, the simulation data fits well with the experimental value. The error of the efficiency and the head between the experimental and numerical simulations are reasonable.

3.2. Characteristics of Pressure Fluctuation of First-Stage Single Suction Impeller

The unsteady numerical simulations are stable after six loops, showing periodicity obviously. The convergence accuracy reaches 10⁻⁵ at the eighth loop. The data were chosen from the ninth loop to the tenth loop.

From Figure 8, the pressure fluctuation of the suction sides and pressure sides shows the periodicity. The period is 0.04 s, which is the time of a blade through a volute tongue. For the first-stage single-suction impeller, it is required 0.08 s to turn a circle. There are two max peaks in a circle due to the two tongues of the twin volute. From (a) to (c) in Figure 8, it is shown that the pressure fluctuation near the front shroud is larger at the same radius of the blade suction side. The peak-to-peak value of outlet near the front shroud is 0.58. Compared with the suction side, the blade monitoring points are situated at the equivalent radius, the pressure near the hub changes obviously, and the peak-to-peak value is 0.62.

Frequency domain characteristics could be derived through fast Fourier transform (FFT). As shown in Figure 9, The dominant frequency is 2 times the rotational frequency (f_r = 12.5 Hz). Among the monitoring points of the blade suction side, the dominant frequency amplitude of point SS3 is the highest, while the frequency of point SS4 is the smallest. The dominant frequency amplitude of SS3 is 1.2 times that of point SS6 while it is 2 times that of point SS4. For all monitoring points on the blade pressure side, the dominant frequency amplitude at SP9 is the maximum while point SP4 is the smallest. The numerical value of point SP9 is 1.6 times that of SP3, while it is about 2.8 times that of point SP4. Comparing the values of the blade, the maximum amplitude on the pressure side is 1.3 times that on the suction side.

Time domain characteristics at SP6 point can be obtained from Figure 10. The pressure fluctuation is periodic at three typical flow rate conditions. The waveform is relatively stable at design and large flow rate conditions while the waveform of the pressure fluctuation shows a larger change at low flow rate conditions. Figure 11 shows the frequency domain diagram of blade pressure side at three flow rate conditions. The dominant frequency at each monitoring site on the pressure side is twice the rotational frequency at the low flow rate.

3.3. Comparison of Pressure Fluctuation of Two Single-Suction Impellers

Reference [36] investigated the pressure fluctuation of a single-stage single-suction centrifugal impeller. Figure 12 presents the results comparing the pressure characteristics of corresponding monitoring sites at three flow rates. Overall, the trend is consistent. The dominant frequency amplitude grows from entrance to exit. The dominant frequency amplitude of the exit reaches the maximum in cases of low flow rate, while that reaches the minimum at high flow conditions. The spread rule of the blade trailing edge is different. In reference [36], the maximum amplitude at 0.6 Q is about 6 times that at 1.0 Q. The maximum amplitude near the edge pressure side of the blade outlet at 0.6 Q is about twice that of the design conditions in this paper. Differing from the straight suction chamber of single-stage single-suction, the spiral suction chamber of the pump causes such differences.

It is the change of pressure with time that is the essence of pressure fluctuation, so pressure can directly reflect the intensity of pressure fluctuation. Figure 13 shows the static pressure of the impeller and twin volute at three operating modes. It can be concluded that the pressure of single-suction impeller in this paper is uneven, and the pressure gradient is relatively huge. It is mainly due to the connection between impeller and twin volute, and the sharp impact of liquid flow on tongue and the wall surface to form a vortex, which leads to pressure distribution unevenly in the section, and a larger gradient. The instability of the blade outlet will cause the generation of radial force, and the flow asymmetry in the rotating impeller will cause the imbalance of radial force. The jet-wake flow phenomenon at the impeller outlet can be discovered. This phenomenon makes the dynamic radial force vary with time making the internal flow of hydraulic machinery unstable. The asymmetry of internal flow is mainly due to the obvious hydraulic action between the blade and the channel, and the obvious disturbance of the rotor-stator interaction to the internal area. The uneven and asymmetric pressure on the impeller blade leads to the unstable variation of radial force in unsteady circumstances. With the design, the static pressure near the blade outlet should be relatively well-distributed, and the pressure gradient small, which reveals that the flow uniformity is related to flow rate, thus influencing the radial force.

The flow channel establishes the connection between twin volute and second-stage impeller, which is a region with serious hydraulic loss. Observe the flow pattern at three working conditions, as shown in Figure 14. It is a double helix structure. Due to the space distortion of the bridging channel, the water flows through the bridging channel and enters the inter-stage flow channel, causing certain vortices. There are vortices and obvious low-speed areas in the three working conditions, among which, the low-speed areas less than 6 m/s in the inter-stage flow passage at the same time account for 48%, 35%, and 28%, respectively, in three working conditions; The low-speed area occurs at the inlet of low-flow rate. In addition, the vortex area at the large flow rate is small; This proves with the decrease in rate, the flow field in the inter-stage is turbulent, which will influence upstream and downstream pressure fluctuations.

3.4. Characteristics of Pressure Fluctuation of Second-stage Double-Suction Impeller

The pressure fluctuation of the second-stage double-suction impeller is periodic. Figure 12 shows that the frequency of the suction side is 2 times the rotational frequency. On the suction side, the dominant frequency amplitude of the outlet is greater than that of the inlet. The amplitude of DS6 is the largest in all monitoring points, while DS5 is the minimum. Figure 15a for point DS6 is 1.5 times that of point DS5. The dominant frequency of the entry and exit is 2 times the rotational frequency. It is different at the same position between these two types of impellers. The dominant frequency amplitude of point DS8 is 1.3 times that of point SS8. In the pressure sides, the numerical value of DS3 is the most. The numerical number of point DP9 is 40% larger than that of point DP6, which is about 2.3 times of point DP4. Compared with the monitoring points at the same position on both sides, the dominant frequency amplitude on the pressure side is greater than that of the suction side. The pressure coefficient of the monitoring point DP9 at 2 times the impeller rotational frequency is 0.06841, which is larger than that of the monitoring point DS3.

From Figure 16, the dominant frequency at the low flow-rate condition is higher than other conditions. The value at 0.6 Q is 5 times that at 1.0 Q. In comparison with the first-stage single-suction impeller, the dominant frequency of the shroud inlet of the second-stage impeller is about 3 times that of the first-stage impeller at the low flow rate condition. It means that the flow Regime of inter-stage flow channel has a great influence on the double-suction impeller.

From Figure 17, It can be found that there is an obvious wake jet flow phenomenon at the outlet, under the three working conditions. Since the double-suction impeller is used, the flow at the outlet has obvious symmetry. Because the pressure variation in the pressure chamber is affected by the jet wake, and there are dynamic and static disturbances, the amplitude of the pressure pulsation energy is large. At 0.6 Q, the flow is relatively turbulent. Besides, the outlet pressure gradient is relatively larger due to the impact of water on the wall, so the amplitude of the corresponding pressure fluctuation is also large.

4. Conclusions

In this article, the pressure fluctuation characteristics of the impeller of the double-entry two-stage double-suction centrifugal pump are studied by numerical simulation method:

(1)

The pressure fluctuation characteristics of the first-stage single-suction impeller are obtained. In the first-stage single-suction impeller, the pressure fluctuation changes periodically with time. The dominant frequency of the impeller regions is 2 times the rotational frequency. The dominant frequency amplitude increases from the blade inlet to the blade outlet. The value of the blade outlet is about 2 times that of the blade inlet. Among the three typical conditions, the dominant frequency amplitude at 0.6 Q is the maximum, which is about three times that of 1.0 Q.

(2)

The effects of a taper pipe suction chamber and semi-spiral suction chamber on the pressure pulsation of a single-suction impeller are compared. Both the impellers show that along the streamline direction, the dominant frequency amplitude of pressure fluctuation increases. The dominant frequency amplitude of the same region reaches a maximum when the flow rate is low. Different from the straight chamber of the single-stage single-suction centrifugal pump, the semi-spiral suction chamber of the pump affects the dominant frequency amplitude of the first-stage single-suction impeller.

(3)

The pressure fluctuation characteristics of the second-stage double-suction impeller are obtained. In the second-stage double-suction impeller, the dominant frequency is twice that of the rotational frequency. It increases from the blade entrance to the blade outlet. At 0.6 Q, the dominant frequency amplitude is about twice that at 1.0 Q. The dominant frequency amplitude of the blade pressure side inlet is about 5 times that of the first-stage single-suction impeller due to the differences of the suction chambers.

The research results obtained in this paper have guiding significance for the design and safe and stable operation of large flow, high head double-suction centrifugal pumps. However, some problems need to be further studied in the future, especially carrying out the pressure fluctuation test and using more accurate simulation methods.