Experimental Research on Pressure Pulsation and Flow Structures of the Low Specific Speed Centrifugal Pump

Abstract

The low specific speed centrifugal pump plays a crucial role in industrial applications, and ensuring its efficient and stable operation is extremely important for the safety of the whole system. The pump must operate with an extremely high head, an extremely low flow rate, and a very fast speed. The internal flow structure is complex and there is a strong interaction between dynamic and static components; consequently, the hydraulic excitation force produced becomes a significant factor that triggers abnormal vibrations in the pump. Therefore, this study focuses on a low specific speed centrifugal pump and uses a single-stage model pump to conduct PIV and pressure pulsation tests. The findings reveal that the PIV tests successfully captured the typical jet-wake structure at the outlet of the impeller, as well as the flow separation structure at the leading edge of the guide vanes and the suction surface. On the left side of the discharge pipe, large-scale flow separation and reverse flow happen as a result of the flow-through effect, producing a strong vortex zone. The flow field on the left side of the pressure chamber is relatively uniform, and the low-speed region on the suction surface of the guide vanes is reduced due to the reverse flow. The results of the pressure pulsation test showed that the energy of pressure pulsation in the flow passage of the guide vane occurs at the f_BPF and its harmonics, and the interaction between the rotor and stator is significant. Under the same operating condition, the RMS value distribution and amplitude at f_BPF of each measurement point are asymmetric in the circumferential direction. The amplitude of f_BPF near the discharge pipe is lower, while the RMS value is higher. A complex flow structure is shown by the larger amplitude and RMS value of the f_BPF on the left side of the pressure chamber. With the flow rate increasing, the energy at f_BPF of each measurement point increases first and then decreases, while the RMS value decreases, indicating a more uniform flow field inside the pump.

1. Introduction

Centrifugal pumps have a significant role in every field, and it is of utmost importance to operate efficiently and steadily in order to ensure the safety of the entire system [1,2,3,4]. One particular type of centrifugal pump, known as the low specific speed centrifugal pump, is extensively utilized in industrial applications due to its ability to handle low flow rates and high heads [5]. However, this particular pump, with its low specific speed, exhibits intricate three-dimensional unsteady flow patterns, characterized by complex hydraulic phenomena. These phenomena include interactions between the impeller and guide vanes, flow separation, secondary flows, and non-uniform flow structures at the outlet of the impeller [6]. To investigate these complex internal flow features, numerous researchers have conducted flow measurements inside centrifugal pumps using techniques such as PIV (Particle Image Velocimetry) and LDA (Laser Doppler Anemometry). Paone et al. [7] first studied the stall phenomenon inside a centrifugal pump using PIV and found that stall cells are generated near the impeller inlet under low flow rate conditions. Keller et al. [8] captured the wake vortex of the centrifugal pump impeller using PIV and analyzed its evolution process in the volute under high flow rate conditions, revealing the flow mechanism of impeller–guide vane interaction from a vortex dynamics perspective. Zhang et al. [9] used PIV to extensively study the flow structures inside low specific speed centrifugal pumps, particularly in the tongue region of the volute, and observed strong impeller–guide vane interaction and jet-wake structures at the impeller outlet, as well as low-speed flow separation regions in the impeller channels under low flow rates. Zhang et al. [10] investigated the absolute and relative velocity distributions inside centrifugal pumps with different impeller designs, including long and short blades using PIV, and found that short blades effectively suppress the “jet-wake” structures at the impeller outlet, thereby improving pump performance. Atif et al. [11] captured the flow field at the impeller outlet of a vaneless centrifugal pump using PIV and found differences in velocity distributions within each impeller channel, indicating that the impeller–guide vane interaction is not entirely identical.

Unsteady flow structures inside centrifugal pumps can induce pressure pulsations, and the energy of pressure pulsations is mainly concentrated at the blade passing frequency (BPF) and its harmonics, as well as at the shaft frequency and its harmonics, which impact the pump’s ability to run safely and consistently [12]. Extensive work has been conducted to investigate the characteristics of pressure pulsations in pumps, aiming to reveal the correlation between pressure pulsations and internal flow. González et al. [13] studied the distribution characteristics of BPF amplitudes along the circumferential direction of the volute and found that the energy of pressure pulsations decreases continuously further away from the tongue region. They preliminarily created a predictive model for BPF amplitudes based on the assumption of an evenly distributed pressure around the volute circumference. Gao et al. [14] extracted pressure pulsation signals along the circumferential direction of the volute in experiments and analyzed the influence of impeller–guide vane interaction on pressure pulsations at different measurement points and flow rates. Pavesi et al. [15] obtained the pressure spectrum characteristics of centrifugal pumps under different speeds and operating conditions using advanced wavelet transform-based time-frequency analysis techniques. They also characterized the cross-correlation among pressure signals at different measurement points using correlation analysis techniques. Lu et al. [16] studied the vibration characteristics of multistage centrifugal pumps under various operating conditions and found that the BPF and its high-order harmonics are the main excitation frequencies for vibrations. Posa et al. [17] used LES (Large Eddy Simulation) to study the effect of guide vane inlet angle variation on pressure pulsations in centrifugal pumps under different operating conditions. Feng et al. [18] studied the influence of different guide vane parameters, including the number of guide vane blades and radial clearances, on pressure pulsations and internal flow structures of pumps. The impeller–guide vane interaction was found to be the primary cause of pressure pulsations at the guide vane inlet, and the evolution of the wake vortex affects the pressure pulsations at the impeller outlet [19]. Kergourlay et al. [20] investigated the suppression effect of short blades on the jet-wake structures and confirmed that a uniform flow field structure at the impeller outlet can reduce the energy of pressure pulsations inside the pump. Ni et al. [21] found that changing the shape of the trailing edge of the guide vanes in a mixed-flow nuclear main pump can reduce the intensity of vortex shedding and alter the flow structure inside the pressure chamber to suppress pressure pulsations. Zhang et al. [22] suggested a design for hydrofoil blades for centrifugal pumps to reduce unstable pressure pulsations. The flow homogeneity at the impeller outlet is improved by a drop in relative velocity in the jet zone at the outflow of the impeller and a reduction in velocity gradients between the pressure and suction sides. Moreover, the impeller outlet’s reduced vortex strength prevents high-energy vortices from being shed from the trailing edge of the blades.

In summary, there is some understanding of the evolution patterns of the internal flow and excitation mechanisms within centrifugal pumps currently. However, the matching complexity of impellers and guide vanes in the low specific speed centrifugal pump is not yet clear, and the mechanism of impeller–guide vane interaction is still uncertain. Research on the correlation between excitation features inside the pump and the evolution of unsteady flow structures is still required. Therefore, a closed-loop test rig of a model pump will be constructed, and high-frequency pressure pulsation sensors will be used to measure the pressure pulsations at the guide vane measurement points. Pressure pulsation signals from the model pump will be collected under various operating conditions, and modern signal analysis techniques will be employed to analyze the characteristics of pressure pulsation amplitudes under different operating conditions. Simultaneously, a visual test rig for the model pump’s internal flow will be developed, and PIV measurement techniques will be applied to collect data on the flow field inside the model pump under different conditions of operation. To understand more about the development of impeller wakes and velocity changes inside the pump, the time-averaged velocity field and vorticity field will be examined. This study aims to provide a clearer understanding of the complex internal flow and pressure pulsation characteristics of this type of pump, and to provide references for the efficient design and control of fluid-excited pressure pulsations in the pump.

2. Experimental Study

2.1. Design of the Model Pump

In order to explore the complex flow structures and flow-induced pressure pulsation characteristics inside the low specific speed centrifugal pump, a single-stage model pump was designed as the research object, with its main design parameters shown in

Table 1. The main design parameters of the pump.

Main Parameters	Value
Flow capacity Qd	20 m3/h
Pump head Hd	25 m
Shaft speed n	1450 rpm
Specific speed ns	35
Blade number of impeller Z	10
Impeller hub diameter Dh	95 mm
Impeller suction diameter Dj	115 mm
Impeller outer diameter D2	300 mm
Impeller exit width b2	6 mm
Blade outlet angle β2	14°
Blade wrap angle φ	145°
Diffuser blade number Zd	8
Diffuser inlet width b3	9.6 mm
Diffuser inlet diameter D3	306 mm
Diffuser inlet angle α3	4°
Diffuser outlet diameter D4	180 mm
Diffuser diffusion angle φd	4°

. In order to accurately obtain the flow field structure within the pump by the PIV measurements, an annular intake chamber was used as the pump inlet, and the volute was designed with an annular cross-section. Figure 1 shows the assembly diagram of the model pump, which mainly includes the annular inlet, impeller, diffuser, and annular volute.

2.2. Pressure Pulsation

A closed-loop test rig was built, as illustrated in Figure 2, to determine the model pump’s pressure pulsation characteristics. To measure the head of the model pump with an accuracy of 0.1%, two pressure gauges were fitted at the entry and exit of the pump. The flow rate of the model pump was measured using an electromagnetic flowmeter under various operating conditions, with an accuracy of 0.2% of the measured value. A torque meter was installed between the motor and suspension to measure the input power of the model pump. The speed of the model pump was adjusted to 1450 rpm under different operating conditions using a frequency converter. The pressure pulsation test system consists of an LMS data acquisition system, LMS Test. Lab 12A software, PCB113B27 pressure sensors (PCB Piezotronics, Inc., Depew, NY, USA), and a computer. It was used to measure the pressure pulsations of the model pump under different operating conditions. Considering the structure of the model pump, pressure pulsation measurement points were arranged at the outlet of each guide vane passage, as shown in Figure 2a. The pressure pulsation sampling frequency range was set to 0–25,600 Hz with a frequency resolution of 0.5 Hz. The sampling time was 3 s, with a time interval of 0.5 s. The outlet valve was adjusted to control the flow rate, with an error controlled within 1%, and the measurement conditions ranged from the shut-off point to 1.8 Q_d.

2.3. Particle Image Velocimetry

To conduct PIV measurements of the flow field inside the pump, the impeller, guide vanes, and annular pressure chamber of the model pump were fabricated using organic glass, as shown in Figure 3a–c. The 2D2C particle imaging velocimetry (PIV) system manufactured by Dantec Dynamics A/S, Copenhagen, Denmark was used to construct the experimental setup for time-averaged flow field measurements of the model pump, as shown in Figure 3. During the experiment, a dual Nd-YAG laser with a pulse energy of 60 mj (Dantec Dynamics A/S, Copenhagen, Denmark Dantec Dynamics A/S, Copenhagen, Denmark) was used as the light source, which was illuminated on the measurement plane through a cylindrical lens. The laser pulse interval was set at 30 μs, with a working frequency of 15 Hz. A CCD camera (Flow Sense EO 2M) (Dantec Dynamics A/S, Copenhagen, Denmark Dantec Dynamics A/S, Copenhagen, Denmark) was used for image acquisition, with a camera resolution of 1600 × 1200 pixels and a capture speed of 15 frames per second. The Dynamic Studio 6.8 intelligent software and synchronization controller were used to synchronize the laser emission and CCD camera exposure times. A shaft encoder was used to achieve phase-locking of the CCD camera. To trigger the CCD camera every two revolutions, the shaft encoder was coupled to a frequency divider, which was subsequently coupled to the PIV synchronization controller.

3. Results and Discussion

3.1. The Performance of the Model Pump

Figure 4 presents the performance of the model pump. From the efficiency–flow rate curve, it can be seen that the optimum efficiency point is located around 1.5 Q_d. At the best efficiency point (BEP) condition, the pump can achieve a maximum efficiency of 42%. The efficiency at the designed operating condition is about 38%, slightly lower than the maximum efficiency. It can be observed from the graph that the pump has a wide high-efficiency region, and the difference between the efficiency at the designed operating condition and the maximum efficiency point is not significant. From the head–flow rate curve, it can be seen that the head decreases monotonically with increasing flow rate. The head at the designed operating condition is around 21 m, lower than the design head.

3.2. Pressure Pulsation Characteristics

In order to explore the complex pulsation characteristics of the pump under different operating conditions, Figure 5 presents the pressure pulsation time-domain signals at the D804, D204, and D404 measurement points under different operating conditions. It can be observed that the time-domain signals at the three measurement points are relatively chaotic, and the pressure pulsations show a certain periodicity under different operating conditions, especially at high flow rate conditions where the periodicity of the pressure pulsations is more pronounced. However, under low flow rate conditions, this periodicity decreases to some extent, indicating that the flow inside the pump becomes more complex and chaotic, usually dominated by large-scale flow separation, which induces complex pressure pulsation characteristics [23]. The amplitude of the pressure pulsations varies significantly under different operating conditions, and it decreases with increasing flow rate, indicating that as the flow rate increases, the flow field inside the pump becomes more uniform. From the pump performance curve, we can also find that the best efficiency point deviates from the high flow rate, which means a more uniform flow pattern at the high flow rate. However, under low flow rate conditions, the amplitude of the pressure pulsations is larger, indicating the deterioration of the flow inside the pump.

The time-domain data were processed using the Fast Fourier transformation (FFT) to acquire the frequency-domain characteristics of the pressure pulsations, as shown in Figure 6, in order to conduct a thorough study of the pressure pulsation signals. It can be observed that the monitoring points captured typical frequencies such as the shaft frequency f_R, its harmonics, and the blade passing frequency f_BPF under different operating conditions. The shaft frequency signal is primarily caused by the imbalance of the rotor system, including misalignment of the shaft system and the non-symmetry of the impeller. The blade passing frequency is mainly caused by the interaction between the rotor and stator. The amplitudes of the shaft frequency and blade passing frequency vary under different operating conditions. In order to quantitatively analyze the unsteady pressure pulsation characteristics at each monitoring point under different operating conditions, the pressure amplitudes at the characteristic frequencies were extracted for analysis.

The distribution of pressure pulsation amplitudes at the blade passing frequency (f_BPF) at various measurement points under various operating conditions is depicted in Figure 7a. It can be observed that the amplitudes of f_BPF at different measurement points showed no significant regularities under different operating conditions. In the same operating condition, the distribution of f_BPF amplitudes is extremely asymmetrical in the circumferential direction. At the 0.2 Q_d operating condition, the f_BPF amplitude is the smallest at all measurement points, while at the 1.0 Q_d operating condition, except for the D104 measurement point, the f_BPF amplitude is the largest at the remaining measurement points. In all operating conditions, the D304 measurement point exhibits a peak in the f_BPF amplitude, while the D504 measurement point has the smallest f_BPF amplitude.

The distribution of pressure pulsation amplitudes at 15 f_R and 22 f_R frequencies under various operating conditions is depicted in Figure 7b,c. It can be seen from the that the D504 measurement point does not exhibit a peak at any characteristic frequency at all operating conditions, and the remaining measurement points show no significant variation in amplitude at the characteristic frequencies. In the same operating condition, except for the D504 measurement point, the distribution of amplitudes at the characteristic frequencies is relatively symmetrical at the other measurement points.

Due to the significant fluctuations in the pressure pulsation amplitudes at different measurement points under different operating conditions, it is necessary to analyze the overall energy characteristics of the pressure pulsation amplitudes at the characteristic frequencies of the measurement points under different operating conditions. The concept of Cumulative Pulsation Energy (C_PE) is introduced and defined as shown in Equation (1).

$$C_{PE}=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{C}_{Pi}^2(N=6)}}$$

(1)

where C_Pi represents the pressure pulsation amplitude at the characteristic frequency of each measurement point and C_PE represents the cumulative pulsation energy of the pressure pulsations at the typical frequencies of all measurement points.

Figure 8 displays the changes in pressure pulsation energy at the typical measurement point frequencies under various operating situations. From the Figure 8, it can be observed that the f_BPF energy accounts for the highest proportion of the pulsation energy of all the typical frequencies for the measurement points, and it increases initially and then decreases with the flow rate increasing. Among them, the pressure pulsation energy at the f_BPF frequency is the highest at the design operating condition and the lowest at 0.2 Q_d.

As shown in Figure 6, there are no peak signals generated in the high-frequency range (800–1000 Hz) of the pressure pulsation spectrum. It is considered that the frequency range of 0–800 Hz represents the full range of pressure pulsations in the model pump. The pulsation energy is closely related to the non-steady flow structures inside the pump. In order to analyze the overall energy variations in the pressure pulsation spectra under different operating conditions, the Root Mean Square (RMS) value of the pressure pulsations is defined for evaluation, as shown in Equation (2) [24]:

$$RMS={\displaystyle \frac{1.63}{2}}\sqrt{{\displaystyle \frac{1}{2}}({\displaystyle \frac{1}{2}}{P}_0^2+{\displaystyle \sum _{n=2}^{n-1}{P}_{n-1}^2+\frac{1}{2}{P}_n^2})}$$

(2)

where P₀ denotes the pressure pulsation amplitude at the starting frequency of the frequency range, P_n denotes the pressure pulsation amplitude at the end frequency of the frequency range, and P_n−1 represents the pressure pulsation amplitude at each frequency within the frequency range.

The distribution pattern of the RMS values of the pressure pulsations at various measurement places under various operating situations is depicted in Figure 9. As the flow rate increases, the RMS values initially rise and subsequently fall, as shown in the Figure 9. Under the same operating conditions, the RMS values are distributed more uniformly in the circumferential direction, similar to the distribution pattern of the shaft frequency. Under low flow rate conditions (0–0.8 Q_d), the RMS values increase, and at 0.8 Q_d, the average increase in the RMS values at each measurement point compared to the shut-off point is 16.1%. Under high flow rate conditions (1.2–1.8 Q_d), except for the D104 measurement point, the increase in the RMS values at the other measurement points with the increase in flow rate is relatively small, and the decrease in the RMS values is not significant. At 1.8 Q_d, the average decrease in the RMS values at each measurement point compared to 1.2 Q_d is 4.24%. The RMS value at the D104 measurement point increases from the shut-off point to 0.8 Q_d and then sharply decreases to 1.2 Q_d, with an average decrease of 29.34% from 0.8 Q_d to 1.2 Q_d. In all operating conditions, the RMS value is the smallest at the D504 measurement point, while it is the largest at the D104 measurement point.

Based on the above, the pressure pulsation spectra of the measurement points in the model pump exhibit peaks at f_R, f_BPF, 15 f_R, and 22 f_R. The peak at f_R is primarily caused by manufacturing and installation errors. The f_BPF pressure pulsation amplitude is mainly due to the interaction between the moving and stationary components. The D504 measurement point has a significant amplitude at f_BPF. The RMS values of the pressure pulsations at the D104 and D204 measurement points are large, while the f_BPF amplitudes are small, especially under low flow rate conditions.

3.3. Internal Flow Structures

The flow field was collected at every 10° interval and =1° in order to get the characteristics of the flow field at various impeller and guide vane positions. In the design operating condition, Figure 10a displays the contour plot and velocity vector plot of the absolute velocity at window A1’s middle portion. From the Figure 10, it can be observed that at T = θ₀, the exit velocity of the impeller is unevenly distributed in the circumferential direction, and a wake region appears at the trailing edge of the blade with a higher velocity. The pressure side of the guide vane blade shows a low-speed region due to the adverse pressure gradient, leading to some fluid entering the impeller passage. At T = θ₀ + 10Δθ, as the impeller blades sweep the guide vane blades, the wake region at the trailing edge of the blade expands, and a low-speed region begins to appear at the leading edge of the guide vane blade, increasing the recirculation region within the impeller passage. As the impeller rotates, the wake region spreads into the impeller passage, resulting in an increase in exit velocity. The velocity distribution in the guide vane passage is uneven, with periodic fluctuations due to the impeller rotation. Significant velocity fluctuations at the guide vane’s trailing edge cause flow separation on the blade’s suction side and create a recirculating vortex at the outlet. Two types of flow are observed at the discharge pipe in the spiral chamber: through flow and recirculating flow. The through flow on the right side of the volute chamber has higher velocity and flows directly into the discharge pipe, producing a recirculation flow upon impacting the right wall of the discharge pipe. The recirculating flow on the left side of the volute chamber has a lower velocity and interacts with the fluid at the exit of the guide vane, resulting in low-speed recirculation and a turbulent flow structure in this region.

To analyze the influence of different operating conditions on the flow structure in the A1 region, Figure 10b shows the absolute velocity field and velocity vector plots under different operating conditions. It can be observed that the exit velocity of the impeller is unevenly distributed in the circumferential direction and varies significantly under different operating conditions. In the design operating condition, due to significant recirculation, the wake region at the impeller exit is not prominent, and there is a large region of low-speed flow separation on the pressure side of the guide vane leading edge, leading to complex flow structure and high flow losses on the left side of the discharge pipe in the volute chamber. Under the high-efficiency operating condition (1.6 Q_d), the flow field at the impeller exit is more uniform, with a distinct wake region. The flow separation region on the suction side of the guide vane is the smallest, and the recirculation flow generated by the impingement of through flow on the right wall of the discharge pipe disappears, resulting in a smoother flow on the left side of the discharge pipe.

In order to quantitatively analyze the velocity distribution in the A1 region, the absolute velocities at different positions of the guide vanes and within the volute chamber under different operating conditions were extracted, as shown in Figure 11. It can be observed that the velocity distribution at the same position is similar under different operating conditions, with increasing velocity as the flow rate increases. The velocity distribution within the guide vane passage is shown in Figure 11a. Generally, the velocity gradually decreases from the inlet to the outlet of the guide vane, then increases and decreases again, which is related to the change in the cross-sectional area of the guide vane passage. The flow separation on the suction side of the guide vane blade leads to a low-speed region at the outlet of the guide vane. Under the design operating condition, the velocity fluctuations within the guide vane passage are significant, with multiple low-speed regions, indicating the presence of a large amount of recirculation and inducing strong pressure pulsations. As the flow rate increases, the velocity distribution improves, the low-speed regions disappear, the flow field becomes more uniform, and the amplitude of the pressure pulsations decreases, which is consistent with the results of the previous section on pressure pulsation testing.

Figure 11b depicts the distribution of absolute velocity at position L2 within the volute chamber. Overall, the velocity decreases in a wave-like pattern as the fluid flows out of the guide vanes and enters the volute chamber, and the amplitude of the fluctuations decreases as the flow rate increases, resulting in a more uniform flow field. There are low-speed regions present at the suction side of the guide vane (L = 0.6~0.8) under all operating conditions with the lowest velocity and the widest range under the design operating condition, and the highest velocity at the high-efficiency point (1.6 Q_d). By comparing the absolute velocity vector plots, it is found that the large-scale flow separation and mixing with recirculating flow on the suction side of the guide vane leads to a decrease in velocity and turbulence in this region. At 1.6 Q_d, the flow separation region is the smallest, resulting in lower hydraulic losses and the highest pump efficiency. In the region of L = 0.9~1.0, a peak in velocity is observed, which is considered to be due to the superposition of recirculating flow and backflow, resulting in an increase in velocity.

The velocity distribution near the discharge pipe, specifically at position L3 within the volute chamber, is shown in Figure 11c. The velocity on line L3 is divided into three regions: the right side of the discharge pipe (L = 0~0.2), the discharge pipe (L = 0.2~0.5), and left side of the discharge pipe (L = 0.5~0.9). It is found that the velocity is higher on the right side of the discharge pipe, where the through flow is present. The through flow impacts the right wall of the discharge pipe, resulting in backflow and a gradual decrease in velocity (L = 0.2). At the discharge pipe, the through flow flows out uniformly with a higher velocity, which increases with the flow rate. On the left side of the discharge pipe, there is a low-speed region due to the impact of the through flow on the left wall of the discharge pipe and its interaction with the recirculating flow. At L = 0.9~1.0, a reflection error caused by the bolt leads to a peak in velocity.

Region A2 on the left side of the annular volute chamber’s velocity vector plot and time-averaged velocity distribution are shown in Figure 12a under the design operating condition. It is evident that there are localized low-speed zones and an uneven velocity distribution in the volute chamber’s left side section. The recirculation generated by the flow separation on the suction side of the guide vane blade mixes with the upstream inflow and flows downstream. There are low-speed regions on the guide vane leading edge and pressure side due to the adverse pressure gradient, and some of the fluid flows into the impeller passage. The velocity on the guide vane suction side and pressure side increases, and the wake region of the blade expands. Figure 12b shows the time-averaged velocity distribution in region A2 under different operating conditions. The velocity distribution in the model pump tends to be more uniform as the flow rate rises, and the flow becomes more stable. The flow separation on the guide vane suction side disappears, and the low-speed region on the guide vane pressure side gradually decreases in size, almost disappearing at 1.8 Q_d. This is similar to the variation pattern of the pressure pulsations in region A2 (Figure 9).

In summary, under the design operating condition, the velocity distribution in all measurement regions (A1, A2) of the model pump is uneven, with large-scale flow separation and localized low-speed regions. This might be connected to the vortices that the guide vanes’ trailing edge sheds. In particular, the left side region of the volute chamber in the vicinity of the discharge pipe (A1) is influenced by the combined effect of through flow and recirculating flow, resulting in the most turbulent flow field and higher hydraulic losses. These phenomena may lead to unstable pressure pulsations. As the flow rate increases, the velocity distribution in the model pump becomes more uniform, and the flow becomes more stable.

To clearly describe the distribution and evolution process of vortex structures inside the model pump, the PIV results were processed to obtain the vorticity distribution in each measurement region. Figure 13a shows the vortex structure distribution in region A1 of the model pump at different moments under the design operating condition. It can be observed that the positive vortex is shed from the pressure side of the impeller blade, while the negative vortex is shed from the suction side of the impeller blade. The shedding of vortices from the trailing edge of the blade is influenced by the squeezing and shearing of the guide vane, leading to an increase in vortex energy and the occurrence of separation. As the impeller rotates, the positive and negative vortices alternately enter the guide vane passage. The positive vortex attaches to the pressure side, while the negative vortex attaches to the suction side. After the periodic shedding of the guide vane trailing edge, there is impact and mixing, leading to dissipation inside the volute chamber. Figure 13b shows the vortex structure distribution in region A1 of the model pump under different operating conditions. It can be observed that as the flow rate increases, the energy of the vortices shed from the impeller wakes decreases, and the region of influence reduces. Due to the higher flow velocity inside the discharge pipe, the energy and range of the vortex structures inside the volute chamber near the discharge pipe increase.

Figure 14a displays the distribution of vortex structures in region A2 under the design operating condition. It can be observed that the evolution of vortex structures in the impeller and guide vanes in region A2 follows a similar pattern as in region A1. The positive vortex experiences interference with the guiding vanes (at at T = θ₀ + 10Δθ), causing squeezing and shearing as well as an increase in vortex energy after shedding from the trailing edge of the blade. Then, the vortex structures continue to shed and dissipate (at T = θ₀ + 30Δθ). As the impeller rotates, the vortex structures exhibit periodic evolution. Positive and negative vortex structures alternate inside the volute chamber, flowing downstream and dissipating. The distribution of vortex formations in region A2 under various operation circumstances is displayed in Figure 14b. There are significant differences in the distribution and energy of vortex structures in region A2 under different operating conditions. Under the design operating condition, the vortex structures in the impeller passage are small and low in energy, and the wake vortices shed from the impeller exit dissipate after interacting with the guide vane blades. There are more high-energy vortex structures in the guide vanes and the volute chamber, resulting in a turbulent flow field. As the flow rate increases, the vortex structures in the impeller passage gradually attach to the pressure and suction sides of the entire blade, the energy of the wake vortices at the impeller exit significantly increases, and they periodically shed over time. The vortex structures in the guide vanes and the volute chamber disappear, resulting in a more uniform flow field, and the flow becomes more stable.

4. Conclusions

This paper investigates the unsteady pressure pulsations and the complex internal flow structure of a low specific speed centrifugal pump based on experimental methods. The main conclusions are as follows:

The energy of pressure pulsations at the outlet of the guide vane passage exhibits peaks at f_BPF and its harmonics, as well as the shaft frequency energy at each measurement point. Under different operating conditions, the circumferential distribution of f_BPF amplitude at each measurement point is asymmetric. The f_BPF amplitude is lower near the discharge pipe in the volute chamber, while it is higher on the left side of the volute chamber due to significant interaction between the moving and stationary components. The energy of pressure pulsations at f_BPF decreases after an initial increase with increasing flow rate.

The RMS values of pressure pulsations exhibit an asymmetric circumferential distribution under the same operating conditions, with larger RMS values on the left side of the discharge pipe. The flow structures in this region are more complex, resulting in large pressure fluctuations. The RMS values decrease as the flow rate increases, indicating a more uniform and stable flow field.

Under the design operating condition, the velocity distribution is uneven in regions A1 and A2. The flow structures inside the impeller and guide vanes are similar, with the formation of a wake region at the impeller exit. Low-speed regions are observed at the leading edge and pressure side of the guide vanes, resulting in flow separation due to adverse pressure gradient forces. Some of the fluid flows into the impeller passage. Region A1 is located near the discharge pipe and is influenced by the interaction between recirculating flow and through flow, resulting in large-scale flow separation and vortex recirculation on the left side of the discharge pipe. Region A2 is located on the left side of the volute chamber, where the flow field is more uniform. The recirculation generated by flow separation on the suction side of the guide vane is influenced by the upstream inflow, leading to a reduction in the size of the low-speed region and flow downstream inside the volute chamber. Under high flow rate conditions (1.4 Q_d~1.8 Q_d), the wake region of the impeller becomes more pronounced and the flow separation region on the suction side of the guide vane decreases, resulting in a more uniform flow structure inside the volute chamber.

Under the design operating condition, the vortex distribution and the evolution of vortex structures in regions A1 and A2 of the impeller and guide vanes are similar. After shedding from the trailing edge of the blade, the wake vortices experience squeezing and shearing from the guide vane blades, resulting in an increase in energy and separation. As the impeller rotates, positive and negative vortices alternately enter the guide vane passage, leading to periodic shedding from the trailing edge of the guide vanes. The distribution of vorticity in the volute chamber is uneven in regions A1 and A2, with a large number of positive and negative vortex structures. The vortex structures inside the discharge pipe exhibit the highest energy. Under high flow rate conditions, the intensity of the wake vortices shed from the blade’s trailing edge decreases, and there are fewer vortex structures in the guide vane passages and the volute chamber, resulting in a more ordered flow.