Study on the Cavitation Performance in the Impeller Region of a Mixed-Flow Pump Under Different Flow Rates

Abstract

Mixed-flow pumps, optimized for marine engineering, provide a balance of high efficiency and adaptability, accommodating varied flow and head demands across challenging oceanic settings and are essential for reliable operations in tidal energy and subsea applications. The primary purpose of this paper is to perform a numerical analysis of the cavitation flow characteristics of the mixed-flow pump under differing operational circumstances. The cavitation simulation was implemented to explore the cavitation bubbles evolution and the pressure pulsation characteristics in the impeller region under diverse flow rates, utilizing the Shear Stress Transport (SST) turbulence model and the Zwart-Gerber-Belamri cavitation model as a foundation. The findings indicate that cavitation bubbles initially distribute at the leading edge of blade suction surfaces at the cavitation growth stage. The bubbles spread gradually with the decline of the available net positive suction head (NPSH_a). At the same time, many bubbles appear in the area below the blade and extend to the rim of the suction side of blades. As the flow rate decreases, the critical net positive suction head (NPSH_c) gradually declines. The dominant pressure pulsation frequency at the impeller inlet is the blade passing frequency, and the vibration at the impeller shroud inlet is more intense than that at the hub. The dominant frequency at the impeller outlet is mainly the blade passing frequency. With the development of cavitation, it changes to impeller rotation frequency at low flow rates, while the dominant frequency remains unchanged at high flow rates.

1. Introduction

Mixed-flow pumps have gained widespread adoption in many realms, such as farmland drainage and irrigation [1], waterlogging and flood prevention [2], water conservancy projects [3], sewage treatment [4], and power station cooling systems [5]. A typical area for application is marine engineering, where pumps are required to offer a combination of high efficiency and versatility. They are designed to handle a wide range of flow rates and head variations, making them ideal for diverse oceanographic conditions. Their substantial high-efficiency operating zone ensures energy-saving performance, while their stable and reliable operation is crucial for demanding and often harsh marine environments, such as in tidal energy conversion systems and submarine ventilation processes [6]. However, the occurrence of the cavitation phenomenon will have negative effects on its performance. Cavitation will not only lead to the deterioration of hydraulic performance but also erode the flow-passing parts, destroy the flow passage, and generate vibration and noise [7,8,9,10,11]. Therefore, conducting thorough research into cavitation phenomena within pumps is of great significance for enhancing their stability and reliability.

Many academics have analyzed and predicted the internal cavitating flow field for the mixed-flow pump [12,13,14], and investigated the effects of blade stacking [15], tip clearance [16], blade thickness [17], the number of blades [18], the incident angle [19,20], and the blade leading edge shape [21] on cavitating flow characteristics. Through the optimized design of blade shapes, it is possible to enhance both efficiency and cavitation performance [22,23,24,25,26]. Huang et al. [27,28] researched pressure pulsation under cavitation conditions and discovered that the acceleration of cavity volume is the primary source of pressure pulsation. Xu et al. [29] concluded through model experiments that the power spectrum density method can offer a more precise depiction of the cavitating flow in pumps compared to traditional time-frequency domain analysis. Regarding the cavitation leakage vortex caused by the tip clearance, Han et al. [30,31] summarized the categories and evolution processes. Li et al. [32,33] analyzed the path of the tip leakage vortex and energy dissipation mechanism. Lu et al. [34] studied the association between cavitation and vibration under the conditions of both steady-state operation and rapid start-up procedures. Based on this association, they proposed a means for identifying the occurrence of cavitation. There is a close relationship between cavitation and vibration, which has been studied by many scholars. Hao et al. [35] studied the impact of the blade tip gap on the impeller radial thrust under cavitation conditions. Yang et al. [36,37] concluded from experiments that, upon the occurrence of cavitation, there is a fluctuation in pressure and vibration amplitudes, specifically near the blade passing frequency. By experimental analysis, Liu et al. [38] found that the noise and vibration have a regularity under cavitation conditions.

Currently, the focus of research on the cavitation in mixed-flow pumps is on investigating both the cavitation bubbles evolution and the noise and vibration induced by cavitation. There have been few studies on pressure pulsations under cavitation conditions, most of which were model experiments. Therefore, the present study adopts the method of numerical simulation to research the cavitating flow and pressure pulsation properties in the impeller region under diverse flow rates, providing references for the safe operation and operating condition selection of pump units.

2. Numerical Model and Settings

2.1. Physical Model and Meshing

A mixed-flow pump equipped with guide vanes serves as the basis for the computational analysis in this paper. The geometry of the pump is displayed in Figure 1, and the sectional view is shown in Figure 2. The primary design factors are listed in

Table 1. Primary design factors.

Qd (L/s)	n (r/min)	D (mm)	Zi	θ (°)	Zg
295.92	1306	320	4	−2	7

, and their values are derived from the parameters of the model test. The model pump is structured with four separate segments: an inlet pipe, an impeller, a guide vane, and an outlet pipe. The three-dimensional modeling software UG NX 12.0 is employed for geometric modeling.

The commercial software ICEM-CFD 2021 R1 is applied to perform finite volume meshing for the model pump. Hexahedral structured grids are adopted for the inlet and outlet pipes of the model pump. Considering the complexity of the geometric structure, impeller and guide vane regions are meshed by tetrahedral unstructured grids with strong adaptability. To perform grid independence verification, simulations are conducted using different numbers of grid elements, and the sensitivity of head to grid elements is analyzed [39]. As shown in

Table 2. Grid independence verification.

Scheme	1	2	3
grid elements (million)	1.05	2.69	3.58
H (m)	10.64	10.71	10.73

, when the number of grid elements increases to 2.69 million, there is minimal change in the head, indicating that the impact of further increases in grid elements on the results is negligible. The total grid number is identified as 2.69 million. Figure 3 exhibits the grid of the calculation domain for each hydraulic component.

2.2. Numerical Method

2.2.1. Turbulence Model

The Shear Stress Transport (SST) model is chosen as the turbulence model, which has the strengths of the k-ω model and the k-ε model [40]. This model has high precision in dealing with the calculation of low Reynolds numbers near the wall surface. The equations are given as follows:

$$v_t={\displaystyle \frac{{\alpha }_{1}k}{\max ({\alpha }_1\omega ,S{F}_2)}}=\rho {\displaystyle \frac{k}{\omega }}$$

(1)

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho U_{j}k\right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left(\left(\mu +{\displaystyle \frac{{\mu }_t}{\sigma k}}\right){\displaystyle \frac{\partial k}{\partial x_j}}\right)+P_k-{\beta }^{\prime }\rho k\omega +P_{kb}$$

(2)

$${\displaystyle \frac{\partial \left(\rho \omega \right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho U_j\omega \right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left(\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\omega }}}\right){\displaystyle \frac{\partial \omega }{\partial x_j}}\right)+\alpha {\displaystyle \frac{\omega }{k}}{P}_k-\beta \rho {\omega }^2+P_{\omega b}$$

(3)

where P_k represents the turbulence production term, σ_k = σ_ω = 2; β = 0.075; β′ = 0.09; α = 5/9.

2.2.2. Cavitation Model

The Zwart-Gerber-Belamri model is utilized to solve the cavitation phenomena founded upon the Rayleigh-Plesset equation [41], concentrating on the effect of bubble volume variation during the growth stages of cavitation. The expressions of gas-liquid two-phase transfer and transport are described as follows:

$${\displaystyle \frac{\partial }{\partial t}}({\alpha }_v{\rho }_v)+\nabla ({\alpha }_v{\rho }_v{u}_v)=R_e-R_c$$

(4)

$$R_e=F_{vap}{\displaystyle \frac{3{\alpha }_{ruc}(1-{\alpha }_v){\rho }_v}{R_B}}\sqrt{{\displaystyle \frac{2}{3}}{\displaystyle \frac{P_v-P}{{\rho }_l}}} \mathrm{if} P<P_v$$

(5)

$$R_c=F_{cond}{\displaystyle \frac{3{\alpha }_v{\rho }_v}{R_B}}\sqrt{{\displaystyle \frac{2}{3}}{\displaystyle \frac{P-P_v}{{\rho }_l}}} \mathrm{if} P>P_v$$

(6)

where α_v is vapor volume fraction, ρ_v is vapor density, R_e and R_c are mass transfer source terms connected to the growth and collapse of the vapor bubbles, respectively, R_B is the bubble radius, α_ruc is the nucleation site volume fraction, F_vap is the evaporation coefficient, and F_cond is the condensation coefficient. Default constants for the Zwart-Gerber-Belamri model cavitation model are listed as R_B = 1 × 10⁻⁶ m, α_ruc = 5 × 10⁻⁴, F_vap = 50, and F_cond = 0.01.

2.2.3. Boundary Conditions

ANSYS-CFX 2021 R1 software is utilized for performing numerical calculations. First, a steady-state calculation is performed for the mixed-flow pump. The boundary conditions are displayed in

Table 3. The settings of boundary conditions.

Item	Setting
inlet boundary condition	total pressure inlet
outlet boundary condition	mass flow outlet
the reference pressure	0 Pa
the interfaces between rotating and stationary domains	frozen rotor interface
the solid walls	no slip wall

.

At the inlet boundary condition, the volume fraction of liquid water is 1, while that of water vapor is 0. This setting allows liquid water to be converted into water vapor at low pressure rather than introducing water vapor from the outside. The water temperature is 25 °C. At this temperature, the saturation pressure of water is 3574 Pa, and the mean diameter of the vapor bubbles is 2 × 10⁻⁶ m. The cavitation conditions in the impeller domain can be controlled by gradually reducing the inlet total pressure. To study the cavitation under various flow rates, three flow rates are selected: low (0.9 Q_d), designed (Q_d), and high (1.1 Q_d). The designed flow rate Q_d is 295.92 L/s.

Then, the unsteady calculation is carried out to analyze the typical cavitation monitoring points under different flow rates. The transient frozen rotor is used to handle interfaces between the rotating and stationary domains. The outcomes from the steady calculation are adopted as the initial values for subsequent unsteady calculations. The timestep is set to 0.0003828 s, i.e., the duration required for the impeller’s three-degree rotation. The total number of steps is 960, representing 8 cycles of the impeller, and the total time is 0.367534 s. After stabilization, the data from the last 4 impeller cycles are used for analysis and processing [42].

3. Results and Discussion

3.1. Study on Cavitation Performance Under Steady Calculation

3.1.1. External Characteristic Analysis

To confirm the precision of numerical calculation results, a comparison is made between numerical calculation outcomes of external characteristics and corresponding experimental outcomes. The experimental data are from the experimental platforms of Jiangsu University in China. The various related variables, measuring instruments, and their measurement accuracies are shown in

Table 4. Measurement methods and accuracies.

Variable	Measuring Instrument	Measurement Accuracy
flow rate (m3/s)	electromagnetic flowmeter	±0.2%
pressure difference between the inlet and outlet of the pump (Pa)	differential pressure transmitter	±0.1%
rotational speed (r/min)	torque and speed sensor	±0.1%
torque (N∙m)	torque and speed sensor	±0.1%

.

Head is the pressure difference between the inlet and outlet of the pump, and the formula is as follows:

$$H={\displaystyle \frac{p_{\mathrm{out}}-p_{\mathrm{in}}}{\rho g}}$$

(7)

where P_out is the outlet pressure of the pump, P_in is the inlet pressure of the pump.

By measuring the flow rate, pressure difference, rotational speed, and torque, the hydraulic efficiency η of the test pump can be calculated using the following formula:

$$\eta ={\displaystyle \frac{\rho gQH}{M\omega }}$$

(8)

where M is the torque of the impeller, ω is rotational speed.

Figure 4 demonstrates that the results of the numerical simulation have a small error compared to the experimental results, and they are consistent in terms of trends. It is noticeable that the numerical simulation models and methods employed in this paper have high reliability.

3.1.2. Cavitation Performance Analysis

Available net positive suction head (NPSH_a) is commonly applied to explain the pump cavitation condition [43]. It represents the abundant energy of the liquid at the pump inlet, which exceeds the vaporization pressure at the temperature at that time. It is expressed by the formula as below:

$$NPS{H}_a={\displaystyle \frac{p_s-p_v}{\rho g}}+{\displaystyle \frac{v_s^2}{2g}}$$

(9)

where P_s is the pressure of the pump inlet, P_v is the vaporization pressure of water flow at the working temperature, and vs. is the velocity of water flow of the pump inlet. In this paper, the working temperature is 25 °C, P_v = 3574 Pa.

Based on the efficiency and NPSH_a obtained from numerical simulations, the performance curves of cavitation are plotted as shown in Figure 5. When the efficiency decreases by 1%, the value of NPSH_a is taken as the critical net positive suction head expressed by NPSH_c and marked with black dots in the figure [44].

According to Figure 5, when the NPSH_a is high, there is almost no change in the efficiency under different flow rates. With the gradual reduction of NPSH_a, the efficiency increases slightly under low flow rates (0.9 Q_d) and design flow rates (Q_d). This phenomenon results from the few cavitation bubbles in the pump, which lubricate the flow passage to some degree [45]. 1.1 Q_d is the first to reach NPSH_c. Generally speaking, upon reduction of the flow rate, NPSH_c will decrease. When the NPSH_a continues to drop below NPSH_c, the cavitation in the impeller becomes more intense, and the efficiency drops sharply, causing substantial harm to the pump’s ability to operate safely.

3.1.3. Study on Cavitation Bubbles in the Impeller

• Cavitation Bubbles at 0.9 Q_d

Figure 6 depicts a projection of the pump onto the xy-plane, viewed from the impeller inlet. It illustrates the bubble development at the impeller shroud under different inlet pressures at 0.9 Q_d. It is apparent that cavitation does not occur at the impeller shroud when NPSH_a is 10.4 m. When NPSH_a decreases to 5.0 m, extensive cavitation bubbles appear in the area below the blade. When NPSH_a further reduces to 4.0 m, the vapor volume fraction is approximately 0.7 [46].

Figure 7 shows that the cavitation bubbles primarily emerge at the blade leading edge when cavitation occurs. The vapor volume fraction is approximately 0.2 when NPSH_a is 10.4 m, causing almost no reduction in efficiency. When NPSH_a decreases to 5.0 m, the cavitation bubbles have developed and expanded due to the reduction in pressure. New cavitation bubbles also appear at the rim of the blades, spreading from the bubbles at the impeller shroud. This partially blocks the impeller channel, affecting the flow area. At this moment, the vapor volume fraction is around 0.7, and the efficiency decreases by about 1%. This is considered to reach the NPSH_c. When NPSH_a further decreases to 4.0 m, the development of cavitation bubbles becomes more severe. Nearly half of the area on the suction surfaces has been occupied by cavitation bubbles, and there is a trend of merging and intersecting between cavitation bubbles at the leading edge and the rim of suction surfaces, seriously blocking the passage and affecting the fluid’s flow capacity. It results in a significant drop in efficiency, indicating the severe stage of cavitation.

Figure 8 exhibits the cavitation performance curve and the cavitation region volume within the impeller at 0.9 Q_d [13]. Upon the reduction of NPSH_a, the volume steadily rises, and the trend is opposite to that of the cavitation performance curve. After reaching the NPSH_c, there is a steep increase in the rate at which the cavitation region’s volume grows.

2.

Cavitation Bubbles at 1.0 Q_d

The development of bubbles at the impeller shroud at 1.0 Q_d is shown in Figure 9. The distribution and trend are generally consistent with those observed at 0.9 Q_d. At the cavitation growth stage, when NPSH_a is 11.0 m, no cavitation occurs at the impeller shroud. As NPSH_a decreases, many bubbles appear in the region below the blades. The vapor volume fraction primarily ranges from 0.6 to 0.8.

As displayed in Figure 10, when NPSH_a is 11.0 m, a few cavitation bubbles first occur at the leading edge, with little effect on efficiency. This indicates the growth stage of cavitation. As NPSH_a decreases to 5.6 m, the efficiency drops by 1%, and cavitation bubbles emerge on the blade leading edge and rim. The bubbles increase, and the vapor volume fraction is primarily around 0.6. These bubbles disrupt the flow within the flow passage. As NPSH_a continues to decline, reaching 5.0 m, the area of cavitation bubbles expands significantly, causing a 2% decrease in efficiency and adversely affecting normal operation.

From Figure 11, the variation trend of the cavitation region volume at 1.0 Q_d is consistent with that at 0.9 Q_d. As NPSH_a gradually decreases, the growth rate of bubbles accelerates, indicating the trend is opposite to that of the cavitation performance curve.

3.

Cavitation Bubbles at 1.1 Q_d

The evolution of bubbles at the impeller shroud at 1.1 Q_d is shown in Figure 12. The distribution and changes are slightly different from that of 0.9 Q_d. When NPSH_a is 13.0 m at the growth stage of cavitation, bubbles don’t occur at the impeller shroud. As the cavitation reaches the critical net positive suction head (NPSH_a = 7.2 m), cavitation bubbles appear below the blade but do not extend to the blade rim. The vapor volume fraction and distribution area continue to expand as NPSH_a decreases further. When NPSH_a reaches 6.0 m, the vapor volume fraction increases to approximately 0.7.

From Figure 13, when NPSH_a is 13.0 m, few cavitation bubbles appear at the leading edge. The vapor volume fraction is minimal, indicating the growth stage of cavitation. When NPSH_a decreases to 7.2 m, the efficiency drops by 1%, accompanied by an increase in cavitation bubbles. Unlike at 0.9 Q_d and 1.0 Q_d, the cavitation bubbles are distributed only at the leading edge. The bubble volume fraction is around 0.4. As NPSH_a further decreases to 6.0 m, the bubbles continue to expand, and new cavitation bubbles emerge at the rim of the suction surface. At this point, the bubble volume fraction remains around 0.5, resulting in a 3% decrease in efficiency.

It is obvious that with the steady decline of NPSH_a, the cavitation region volume continuously expands in Figure 14. The growth rate of bubbles rapidly accelerates, leading to a sharp decrease in efficiency.

3.2. Analysis of Unsteady Cavitation Flow Field

3.2.1. Unsteady Computation Settings

The steady calculation outcomes under each cavitation condition are adopted as the initial values for subsequent unsteady calculation. As depicted in Figure 15, three monitoring points for pressure pulsation are established at each of the inlet and outlet of the impeller, spanning from the shroud to the hub.

Considering that in the course of operating the pump device, the pressure values at the impeller are generally high, resulting in less pronounced pressure pulsation characteristics. To more clearly demonstrate the effect of cavitation on pressure pulsation, the dimensionless pressure coefficient is adopted to study pressure pulsation. The equation for pressure coefficient C_p is given below [47]:

$$C_p={\displaystyle \frac{p-\overline{p}}{\overline{p}}}$$

(10)

where p is the static pressure at monitoring points, $\overline{p}$ is the average static pressure over the last four cycles of impeller rotation.

3.2.2. Study on Pressure Pulsation Characteristics of Impeller Under Cavitation Conditions

• Pressure Pulsation Characteristics of 0.9 Q_d

  (1)

  Pressure Pulsation at Impeller Inlet

An analysis is conducted on time-mean pressure pulsations recorded at three monitoring points located on the inlet section in order to investigate the behavior of pressure fluctuations. Figure 16 shows the pulsation time-domain waveform under various working conditions. It can be observed that in the course of cavitation, the pulsation patterns at the impeller inlet are generally consistent. The amplitude at P3 is the smallest, while that at P1 is the largest, showing that the vibration at the impeller shroud inlet is more intense. As the cavitation continues to deepen, the amplitudes at all three monitoring points increase continuously. The growth rate at P3 is the fastest.

To further explore the pressure pulsation characteristics, fast Fourier transform (FFT) is utilized [48]. Its function is to transform the time domain pulsation under different working conditions into frequency domain signals [49]. Then, frequency components of the pressure pulsation are studied, as illustrated in Figure 17.

Because n is 1306 r/min and Z_i is 4 in this model pump, the impeller rotation frequency is 21.77 Hz, and the blade passing frequency is 87.07 Hz [50]. It is evident that the frequency domain characteristics of each monitoring point are basically consistent under the same cavitation condition, and the dominant frequency is mainly the blade passing frequency. Therefore, the primary influence on the pressure fluctuations observed at the impeller inlet during cavitation stems from the impeller’s rotation. Upon the intensification of cavitation, the pulsation amplitude corresponding to the rotation frequency becomes increasingly larger. The pulsating amplitude corresponding to the blade passing frequency at P2 and P3 increases slowly, while it at P1 increases first and then decreases.

• (2)

  Pressure Pulsation at Impeller Outlet

Pulsation time-domain features of three points at the impeller outlet are analyzed. Figure 18 shows pulsation time-domain waveforms under various degrees of cavitation. It is observable that the pressure pulsation at P6, located near the hub at the outlet, is very disorderly, and the amplitude is the largest. In the growth stage of cavitation, NPSH_a = 10.4 m, the waveform of P4 and P5 monitoring points can still be stable. During one rotation cycle of the impeller, it exhibits four peaks and four troughs, representing the number of blades. When cavitation becomes serious, the amplitude increases. The waveform is no longer stable, and the phenomenon of secondary wave peaks is serious.

The time-mean pressure pulsation measured at the impeller outlet is converted into frequency domain signals by FFT. Figure 19 reveals the frequency components. During the early phase of cavitation, the dominant frequency is mainly blade passing frequency. As cavitation progresses, the dominant frequency shifts to the impeller rotation frequency. The corresponding amplitude increases sharply, while the amplitude of blade passing frequency increases very little, suggesting impeller blades have a relatively small influence on the outlet pressure pulsation at this stage.

2.

Pressure Pulsation Characteristics of 1.0 Q_d

(1)

Pressure Pulsation at Impeller Inlet

Following the aforementioned research approach, characteristics of time-mean pressure pulsation at the impeller inlet are first studied. Figure 20 presents the time-mean pressure pulsation waveforms at the impeller inlet under various degrees of cavitation. Comparable to the fluctuations in pressure pulsation recorded under the 0.9 Q_d condition, P3 has the smallest pulsation amplitude among inlet monitoring points. In contrast, P1 has the largest amplitude, indicating that the vibration near the hub at the impeller inlet is relatively light. With the deepening of the level of cavitation, the amplitudes at all three monitoring points continue to increase.

Figure 21 shows the frequency component of pressure pulsation at the impeller inlet. Similar to the 0.9 Q_d behavior, the blade passing frequency is the dominant frequency at each monitoring point. Additionally, as cavitation develops, the amplitude at the impeller rotation frequency increases rapidly. Differently, pulsation amplitudes corresponding to the blade passing frequency at monitoring points rise and subsequently decline.

• (2)

  Pressure Pulsation at Impeller Outlet

Figure 22 displays the pulsation waveforms located at the impeller outlet. It is plain to see that during the growth stage of cavitation NPSH_a = 11.0 m, the waveforms at each monitoring point are relatively stable. Among monitoring points, the pulsation amplitude at P6 is the smallest, while the amplitude at P4 is the largest. As cavitation further develops, the secondary wave peak phenomenon becomes more pronounced, and the amplitudes at each monitoring point become relatively similar.

Figure 23 displays the frequency component of pressure pulsation at three cavitation conditions. In the growth stage of cavitation, the dominant frequency of each monitoring point is the blade passing frequency. As cavitation becomes more severe, the dominant frequency changes to rotation frequency. The amplitude at the rotation frequency increases sharply, while the amplitude at the blade passing frequency undergoes minimal change.

3.

Pressure Pulsation Characteristics of 1.1 Q_d

(1)

Pressure Pulsation at Impeller Inlet

The time-mean pressure pulsation waveforms located at the impeller inlet are plotted in Figure 24. Under different cavitation intensities, the pulsation patterns at the impeller inlet are generally consistent. It is noticeable that the amplitude at P1 is the largest, while the amplitude at P3 is the smallest. As the degree of cavitation continues to deepen, the amplitudes at all three monitoring points increase, followed by a decrease.

The frequency component of pressure pulsations is depicted in Figure 25. The dominant frequency during the cavitation process is the blade passing frequency. Upon the augmentation of cavitation intensity, pulsating amplitudes at blade passing frequency rise rapidly at first and then decrease slowly.

• (2)

  Pressure Pulsation at Impeller Outlet

Figure 26 demonstrates waveforms of the time-mean pressure pulsation located at the impeller outlet throughout multiple phases of cavitation. During the cavitation process, the waveforms at the impeller outlet maintain a distinct and consistent periodic pattern. Under the same operating conditions, P4, which is located close to the impeller shroud, exhibits the largest pulsation amplitude.

As detailed in Figure 27, the dominant frequency at the impeller outlet during the development of cavitation remains the blade passing frequency. The potential reason for this is that, during the cavitation process at high flow rates, a reduced number of bubbles form on the blade suction surface in comparison to low flow conditions, thereby enabling the blade to retain a notable influence on the fluid. The pulsation amplitudes at each point, corresponding to the blade passing frequency, all display a tendency to first rise and then fall.

4. Conclusions

In this study, the cavitation flow characteristics of a mixed-flow pump under various flow rates are investigated. The primary conclusions obtained are outlined as follows:

(1)

The volume of the cavitation zone progressively enlarges and the bubble growth rate accelerates with the decline in NPSH_a, leading to a continuous decline in efficiency. When NPSH_a falls below NPSH_c, efficiency declines sharply. Overall, the NPSH_c decreases under various operating conditions as the flow rate reduces.

(2)

Cavitation bubbles are initially distributed at the blade leading edge at the growth stage of cavitation. As NPSH_a decreases, the bubble area gradually increases. Meanwhile, a substantial amount of bubbles appear in the impeller shroud and extend to the blade rim. This seriously affects the smooth flow through the channel, contributing to a decrease in pump efficiency. Under the working condition of a large flow rate (1.1 Q_d), the impeller shroud below the blade is the main distribution area of cavitation.

(3)

During the cavitation process at different flow rates, P3 near the hub exhibits the smallest pressure pulsation amplitude, while the amplitude at P1 near the shroud is the largest among the impeller inlet monitoring points, revealing that the vibration at the impeller shroud inlet is more severe. The dominant frequency at the impeller inlet is the blade passing frequency. As the degree of cavitation gradually intensifies, the pulsation amplitude corresponding to the impeller rotation frequency keeps growing under conditions of 0.9 Q_d and 1.0 Q_d.

(4)

At the growth stage of cavitation under conditions of 0.9 Q_d and 1.0 Q_d, the dominant frequency at the impeller outlet is primarily the blade passing frequency. As the severity of cavitation increases, the dominant frequency transforms into the impeller rotation frequency, accompanied by a sharp increase in amplitude. However, for the blade passing frequency, the increase is minimal, implying that the impeller blade has a relatively small influence on pressure pulsations at the outlet at this period. Under the operating condition of 1.1 Q_d, the dominant frequency of pressure pulsation remains the blade passing frequency, unaffected by the intensification of cavitation.

These conclusions can provide certain references for the cavitation research of mixed-flow pumps. In the future, more research can be carried out, especially on flow visualization and pressure pulsation tests.