Yu-ying Huan, Yao-yao Liu, Xiao-jun Li, Zu-chao Zhu, Jing-tian Qu, Lin Zhe, An-da Han

1. Key Laboratory of Fluid Transmission Technology of Zhejiang Province, Zhejiang Sci-Tech University,Hangzhou 310018, China

2. Ebara Great Pumps Co., Ltd., Wenzhou 325204, China

3. Zhejiang Tiande Pump Co., Ltd., Wenzhou 325800, China

Abstract: Along with the anti-cavitation performance, the high speed and the high power density, are the main trends in the development of centrifugal pumps. At present, the most effective method is to install an inducer in front of the impeller. However,the tip leakage of the inducer results in the vortex cavitation at the blade leading edge of the inducer, and the cavitating flow inside the inducer seriously interferes with the hydraulic behavior of the inducer as well as the impeller with the development of the cavitation, thus to badly affect the operational reliability of the high-speed centrifugal pump. In the present paper, the cavitating flow in a high-speed centrifugal pump with an inducer is investigated by numerical simulations and visual experiments for different cavitation numbers. A typical evolution process of the cavitation is shown, including the inception, the development and the deterioration. A general description of the pump head-drop phenomenon is made through the study of the local and global flow fields,and the relationship between the vapor distribution and the static pressure distribution along the inducer is determined to describe the evolution of the cavitation. This paper intends to provide the foundation for studying the overall cavitation state of a high-speed centrifugal pump, and designing the inducer with a better cavitation resistance.

Key words: Centrifugal pump, inducer, cavitation evolution, visualization experiment

Introduction

The cavitation refers to the process of the formation, the development and the collapse of the vacuoles inside the liquid or at the liquid-solid interface when the partial pressure in the liquid is reduced to the saturated vapor pressure. The cavity volume increases rapidly when the suction pressure decreases to a critical value, to disturb the normal hydraulic performance of the pump and thus to induce the fatal failure of the operability[1-5]. The high-speed centrifugal pumps are prone to cavitation than the ordinary centrifugal pumps due to its high rotational speed. Inducers are used to prevent the head decrease of the main impellers due to the cavitation[6-8]. The overall performance of the pump against the cavitation corrosion can be improved by increasing the pressure,reducing and inhibiting the cavitation at the inlet of the impeller. In order to analyze the cavitation and its influence, many numerical simulations and visualization experiments were carried out.

The cavitation evolution and its effect on the pump performance were extensively studied[9-10]. Zhu and Chen[11]used the PIV technology to study the alternated and fixed cavitation in a centrifugal pump,as well as the development of the cavitation in the impeller. Zhang et al.[12]used the high-speed camera to capture the vortex cavitation in an axial pump and compared the results with the numerical data. Kim and Song[13]utilized the high-frequency dynamic pressure sensor and the high-speed camera photography technology to study the cavitation flow in the inducer,the rotation cavitation of the inducer and the asymmetric blade cavitation. Choi and Kim[14]observed the cavitating flows in a turbopump inducer,the vortex cavitation, the tip leakage vortex cavitation and the complete process of the void formation. Luca and Maria[15]adopted the visual experiment to observe the effects of different cavitation numbers on the cavitation patterns of the inducer under different flow conditions. Kang and Kang[16]studied the effect of the number of blades on the performance of the turbopump and the cavitation instabilities of a turbopump inducer with an identical solidity by comparing the experimental results with the numerical simulation. Pei et al.[17]introduced an algorithm to estimate the static pressure for determining the critical cavitation point of 3% head-drop. Wang et al.[18]investigated the pressure fluctuation in a multistage centrifugal pump based on the whole flow field and made a detailed analysis of the instability of the internal flow field of the pump casing. Liu and Tan[19]studied the effect of the tip clearance on the pressure fluctuation, with a detailed description of the flow characteristics and the vorticity in the gap. Tan et al.[20]explored the effect of the angle on the pump energy performance and the pressure fluctuation by changing the angle of rotation of the blade. Kim et al.[21]numerically investigated the effects of the tip clearance on the performance in a turbopump inducer.Li et al.[22]proposed an improved algorithm-the united algorithm for the cavitation vibration analysis on the basis of the short time Fourier transform (STFT)and the Wigner-Ville distribution (WVD), which could be used to monitor the cavitation performance of centrifugal pumps. Li et al.[23-28]analyzed the cavitating flow at a normal flow rate using the shear stress transport k-ε turbulence model and the Zwart cavitation model to capture the cavitation development and the spatial distribution of vapor structures within the pump. Guo et al.[29-32]studied the rotating cavitation of a centrifugal pump with an inducer by numerical simulations and visual experiments, and their method is employed in our present work to improve the understanding of the cavitation phenomenon of a centrifugal pump.

The primary motivation of this study is to quantify the internal flow characteristics of a highspeed pump under cavitation conditions. This paper consists of visual experiments with a high-speed camera and numerical results with ANSYS-CFX,while the operating points under different cavitation conditions are selected to analyze the effect of the cavitation on the flow patterns. Meanwhile, the cavitation states are analyzed in detail, to help the analysis of the evolution of the cavitating flow during the occurrence, the development and the deterioration of the cavitation.

1. Experimental model and device

1.1 Test pump

The test pump is a single-stage high-speed centrifugal pump made up of a two-blade inducer, an eight-blade open-impeller and a volute, as shown in Fig. 1. The specific speed at the operating point is, the design parameter of the pump is Hd=125m, the rotating speed is nd=7081r/min , and the flow rate is. The complete design parameters are given in Table 1.

Table 1 Parameters for tested impeller and inducer

Fig. 1 (Color online) Outline of the pump

1.2 Experimental apparatus

The test equipment is shown in Fig. 2, which is a closed loop consisting of three parts: the recycle water-flow loop, the model pump and the data acquisition equipment. The storage tank has a volume of 14.1 m3, and the water temperature could be kept relatively stable during the experiment (with the water temperature variation less than 0.5°C within 2 h). The rotary-vane vacuum pump is used to regulate the pressure in the water storage tank. The flow rate is controlled by the outlet butterfly valve and measured by an electromagnetic flowmeter within an error of 2%.The speed is measured using a photoelectrictachometer. Both the suction and discharge average pressure signals are generated by the piezoelectric pressure transducers with the FS accuracy of 0.2%.The ranges of the sensors are -0.1 MPa to 0.1 MPa at the suction and 0 MPa to 2.5 MPa at the pump discharge.

Fig. 2 (Color online) Outline of the pump closed test rig(1-Reservoir tank, 2, 3, 11, 12, 13-Gate valves,4-High-speed camera, 5-Light source, 6-Computers,7-Electromotor, 8-Test pump, 9-Pressure transducer,10-Electromagnetic flowmeter, 14-Vacuum pump)

During the cavitation experiment, the inlet gate valve is adjusted to reduce the absolute pressure at the inlet of the centrifugal pump to a standard atmospheric level at a specified flow rate point. When the vacuum pump is turned on, the air in the reservoir tank is gradually extracted to reduce the inlet pressure of the pump. In the visualization experiment, the exposure time of the high-speed camera is set to 0.2 ms and the frequency is 5 000 Hz. A cold light source is used to illuminate the shooting area.

2. Numerical simulation

2.1 Computing domain

The computing domain is shown in Fig. 2, which is divided into five individual parts: (1) the suction section (Lin/Ds=4), (2) the inducer, (3) the openimpeller, (4) the volute and (5) the discharge section(Lout/Do=5).

2.2 Numerical methods

2.2.1 Governing equations

With the fluid being assumed to be incompressible and homogeneous, the governing equations are as follows:

whereuis the velocity,pis the pressure,ρis the mixture density,μis the viscosity,cαis the phasic volume fraction andNpis the number of phases.

2.2.2 Cavitation model

The cavitation procedure is modelled by the vapour volume fraction mass transfer equation. The conservation equation of the vapor volume fraction takes the form

where αvis the vapour volume fraction, the source terms m˙+and m˙-imply the evaporation and condensation rates when the phase changes.

We adopt the Zwart cavitation model for the interphase mass transfer effects, which is an internal function provided by the CFD package and is defined as[33]:

where Ce=50.00 and Cc=0.01 are the empirical coefficients for the vaporization and condensation rates, respectively, RB=10-6is the bubble radius,pvis the saturated vapour pressure and αnuc=5× 1 0-4is the nucleation site volume fraction.

2.2.3 Calculation domain and boundary condition

For the numerical analysis, the finite volume method is used to discretize the governing equations,the three-dimensional incompressible continuity equation and the DES model. A high resolution scheme with second-order accuracy is used for the advection terms. For the space discretization, the second-order upwind scheme is applied.

The static pressure is provided at the suction inlet of the computational domain, and the vapour volume fraction is supposed to be zero in the cavitation cases to make the pump inlet pressure consistent with the laboratory experimental operation. The mass flow rate is specified according to the outlet boundary condition.The surfaces of the impeller are modelled by employing a rotating domain, whereas the other walls of the pump are stationary. The no-slip and nopenetrating velocity boundary condition is prescribed on all flow passage walls.

The initial calculation is converged under the given condition in calculating the cavitation flow. The subsequent steady and unsteady cavitation calculations are carried out with the decreasing suction pressure. The calculated time step is set as 7.061 × 10-5s,corresponding to a rotational speed of 3° per time-step.

2.3 Grid generation

The hexahedral grid elements for all pump parts are generated with ANSYS ICEM-CFD 16.2, and the mesh is refined near the inducer tip and the volute tongue region. The local mesh sensitivity test is performed for small gaps, such as the inducer tip region. Five cases with different number of grids are used to verify the grid independence under the design conditions. The results are shown in Fig. 3, the calculated head and efficiency change little with the increase of the node number beyond 4.4×106(scheme 4). In order to meet the requirement of the calculation accuracy, scheme 4 is chosen as the computational grid.

Fig. 3 Results of grid independence

3. Results and discussions

3.1 Experimental verification

The measured and predicted performances of the pump are shown in Figs. 4, 5 to validate the calculation accuracy of the current numerical method. Figure 4 shows the comparison between the experimental and predicted results of the cavitating curves at Qd.

Fig. 4 Comparison of the head-drop curves at Qd

Fig. 5 (Color online) Isosurface of 10% vapor volume fraction in cases

Figure 5 shows the vapor volume distribution in cases of NPHSA=3.0 m and NPHSA=1.7 m. The numerical results are in good agreement with the experimental results. In addition, it is observed that the cavitation mainly occurs at the inlet of the inducer.

3.2 Visualization of cavitation evolution

The cavitation development within the highspeed centrifugal pump is shown in Fig. 6, which can be roughly divided into three stages: the cavitation inception, the cavitation development and the deterioration stage. The detailed information about the cavitation evolution is shown in Fig. 7.

Fig. 6 (Color online) Cavitation evolution under different suction pressures

Fig. 7 (Color online) Vapor distribution in the inducer under different NPSHA values (1-Tip leakage vortex cavitation, 2-Sheet cavitation, 3- Cloud cavitation, 4-Backflow vortex cavitation)

Under the cavitation free condition (NPHSA=6.0 m), no vapor is observed in the flow passage. The micro-cavity begins to appear at the tip of the inducer blade when NPHSA=5.0 m, caused by the tip leakage flow. Because the shape of the tip leakage vortex cavitation does not change during the inducer rotation, so the condition of NPHSA=5.0 m can be used as the initial state of the cavitation.

With the cavitation intensifying, although the cavity increases in length with the decrease of the NPSHA values, the cavitation shape and the position of its occurrence do not change significantly. When the NPSHA value drops to 2.0 m, the cavitation shape over the blade would be significantly altered, while the cavitation zone develops downstream the inducer and extends to the hub of the inducer at the same time.Under this condition, with the decrease of the suction pressure, a large number of bubbles are generated near the leading edge to promote the formation of the sheet cavitation on the suction surface. If the NPSHA value approaches 1.5 m, the cavitation zone would extends to the pressure surface and the shedding bubbles would interact with the mainstream in the passage, to form the cloud cavitation.

When the NPSHA value is less than 1.1 m, it is in the cavitation deterioration stage. The corresponding centrifugal pump head fluctuates substantially up and down, with a large amount of backflow cavitation at the inlet of the flow channel. When the NPSHA value is 1.0 m, the flow channels are choked by the generated bubbles, with sharply decreased efficiency and head. Due to the existence of the choked flow in the channel, the inducer loses its ability to increase the pressure, thus a large number of bubbles appear in the flow passage of the open-impeller.

Figure 8 shows the internal cavitation pattern at continuous time intervals when NPHSA=1.5 m.The time interval of each figure is 1.6 ms, which means 68° of the rotation of the inducer and the impeller per time-step. It can be seen that the cavity length on the two blades is different. At t=0 ms, a large number of bubbles are observed on blade 1,while almost no bubbles appear on blade 2. The region of the bubbles on blade 1 gradually expands in size with time from 1.6 ms to 4.8 ms. In contrast, only the tip leakage cavitation occurs on blade 2 during the experimental period. The reason was clarified by Huang et al.[34], it is because the longer cavity extends into the blade passage to increase the incidence angle of the blade, and the incidence angle of the adjacent blade would decrease correspondingly, thus the development of shorter cavities is suppressed. This asymmetric cavitation phenomenon mainly occurs in the stage of the cavitation development and would disappear with the further decrease of the pump suction pressure.

3.3 Numerical analysis of cavitation evolution

3.3.1 Internal flow analysis of cavitation evolution

In Fig. 9, the vapour volume fraction and the pressure distribution along the inducer are presented under different suction pressures. As the suction pressure decreases, a small partial cavity attaches to the suction side of the blade leading edge for the NPSHA value of 5.0 m. The cavity increases in length in all blade leading edges with the decrease of the NPSHA value. The cavity zone grows downstream with the development of the cavitation.

Fig. 9 (Color online) View of the vapor volume fraction and pressure distribution under different suction pressures

When NPHSA=3.0 m, the inlet pressure distribution of the inducer is altered as the cavity zone extends to the inducer channel. Notably, when the value of the NPSHA is below 1.5 m, the trailing edge of the cavity reaches the throat of the inducer channel,and the vapour bubbles appear at the blade pressure surface. The cavitation tends to induce the flow blockage under the fully developed cavitation conditions. However, an obvious asymmetric cavitation is not observed under this NPSHA condition, for which the detailed reasons need to be further studied.

When the NPSHA value is further reduced to 0.9 m,the low-pressure region occupies the entire inducer channel, and the entire induced flow passage is filled with the corresponding cavities. It is noteworthy that a local high-pressure point appears at the tip of the blade (Fig. 9(d)), and it could be considered that a certain collapse of the cavity occurs at this position.

The axial position of the inducer is presented in Fig. 10. Z is the axial distance from the inlet of the inducer, L is the total length of the calculation domain of the inducer. The relative position of the inducer is expressed by Z/L. Thus, the axial position of the inducer leading edge (LE) and the trailing edge (TE) are 0.42 and 0.89, respectively.

In order to analyse the influence of the cavitation on the pressure distribution inside the inducer, the static pressure coefficient Cpis used. The distributions of the static pressure coefficients along the axis of the inducer for different NPSHA values are shown in Fig. 11. The static pressure coefficients Cpis defined as

where p denotes the average pressure, pinis the average pressure at the inducer inlet and UTis the tip velocity of the inducer.

In Fig. 11, the static pressure coefficients of the inducer basically coincide along the axial position when the NPSHA value is larger than 3.0 m. The static pressure coefficients remain unchanged in the region of 0-0.32 at the axial position Z/L, and then de-creases slightly in the region of 0.32-0.45 due to the effect of the inducer. The static pressure coefficient increases continuously and reaches the maximum value at TE (Z / L = 0.45 - 0 .89).

Fig. 10 (Color online) Axial position of the inducer

Fig. 11 (Color online) Static pressure coefficient distribution along the inducer

When the NPSHA value is below 3.0 m, the cavitation zones grow downstream, and the static pressure coefficient of the inducer fluctuates along the axial position. When NPHSA=1.5 m, the static pressure coefficient of the inducer decreases in the range of 0.42-0.65 in the axial position, and turns to increase in the range of 0.65-0.89 in the axial position.When the NPSHA value drops to 0.9 m, the pressure distribution over the blade is significantly altered and the cavitation zone extends to the inducer trailing edge.It can be seen from Fig. 12 that the cavitation tends to induce the flow blockage under the condition.

Fig. 12 (Color online)Vapor volume fraction distribution along the inducer

Figure 12 shows the distribution of the vapour volume fraction along the axial position for different NPSHA values. When NPHSA=6.0 m, the vapour volume fraction in the axial position of the inducer is 0, which indicates that no cavitation occurs in the inducer under this condition. When NPHSA=5.0 m,a peak value of 0.8 occurs in the range of 0.42-0.55Z/L, at the tip of the blade leading edge.

With the decrease of the NPSHA value, the peak value of the vapour volume fraction increases gradually and the cavitation zones grow downstream.When NPHSA=1.5 m, a large amount of cavitation occurs in the range of 0.42-0.55Z/L. Meanwhile, a small partial cavity occurs at the inducer entrance.When the NPSHA value drops to 0.92 m, the value of the vapour volume fraction is greater than 0.1, the cavitation zone extends to the inducer trailing edge.As a result, the flow patterns of the open-impeller are also affected by the cavitation.

3.3.2 Streamline of inducer leading edge

Due to the existence of the tip clearance, the leakage flow goes from the pressure surface to the suction surface and a vortex is generated due to the interaction between the leakage flow in the tip clearance and the passage flow in the inducer. The separated flow is generated on the suction surface,resulting in a local low-pressure zone at the blade leading edge (Figs. 7(a), 9(a)).

In Fig. 13, the streamlines along the axial section of the inducer are plotted and coloured by the2λ criterion, with2λ being defined as the second eigenvalue of the strain-rate and spin tensors, and being used to identify the vortex regions in the inducer[35]. When NPHSA=3.0 m, the tip vortex in the inducer channel is not clearly seen. With the decrease of the NPSHA value, a stronger tip vortex is generated in the middle of the inducer channel, which flows from the pressure side to the suction side. In all cases of the three different values of NPSHA simulated, the tip vortices with a similar strength are captured at the blade leading edge, as is consistent with the visualization results that the cavitation pattern at the blade leading edge is almost unchanged. It should be noted that the development of the cavitation causes a large scale backflow structure at the entrance of the inducer. With the decrease of the inlet pressure,the vortex would be close to the small tip vortex, but they are always separated. One possibility is that there may not be a strong correlation between the tip leakage vortex and the backflow vortex at the inducer inlet.

Fig. 13 (Color online) Streamline colored by 2λ criterion for different NPSHA values

4. Conclusions

(1) The numerical results, including those for the cavitation performance and the pressure distribution,are reasonably consistent with the available experimental data. A typical evolution process of the cavitation, including the inception, the development and the deterioration are reasonably captured in the present study.

(2) The cavitation extends from the tip of the leading edge to the inducer hub and to the trailing edge. The cavitation development enhances the separation flow, the vortex and the flow blockage in the inducer. During the growth of the cavity, the cavitation zone extends to the downstream, affecting the pressure distribution over the blade and the pump head eventually breaks down.

(3) The tip vortex cavitation appears at the blade leading edge and its strength changes little during the cavitation evolution. However, the intensity of the backflow cavitation at the inducer inlet increases with the deterioration of the cavitation. There seems to be no strong relationship between the tip leakage cavitation and the backflow cavitation.