Efficiency improvement and evaluation of a centrifugal pump with vaned diffuser

Transcription

1 Research Article Efficiency improvement and evaluation of a centrifugal pump with vaned diffuser Advances in Mechanical Engineering 2019, Vol. 11(3) 1 12 Ó The Author(s) 2019 DOI: / journals.sagepub.com/home/ade Kai Wang 1,2, Yu-cheng Jing 1, Xiang-hui He 3 and Hou-lin Liu 1 Abstract In order to enhance the efficiency of centrifugal pump, the structure of a centrifugal pump with vaned diffuser, whose specific speed is 190, was numerically improved by trimming back-blades of impeller and smoothing sharp corner in annular chamber. The energy performance, the internal flow field, the axial force, the radial force, and the pressure pulsation of the pump were analyzed. Results show that efficiency of the improving scheme 1 under the design flow rate is 77.47%, which can balance 69.82% of the axial force, while efficiency of the improving scheme 2 under the design flow rate is the maximum, which could still balance 62.74% of the axial force. The pressure pulsations of the improving scheme 2 at the typical monitoring points are less than that of the improving scheme 1 and the original scheme. The difference of the radial force peak between the improving scheme 1 and the improving scheme 2 is very small. The vector distributions of the radial force of the improving scheme 1 and the improving scheme 2 are more uniform than that of the original scheme. Considering the efficiency, pressure pulsation, and axial force, experiment measurements on the improving scheme 2 were carried out to verify the effectiveness of the improvement result. Results of energy performance experiment show that efficiency of the improving scheme 2 under the design flow rate is 76.48%, which is 5.26 percentage points higher than that of the original scheme. Keywords Centrifugal pump with vaned diffuser, efficiency improvement, axial force, radial force, pressure pulsation Date received: 2 October 2018; accepted: 2 January 2019 Handling Editor: Assunta Andreozzi Introduction Centrifugal pump is a kind of hydraulic machinery widely used in agriculture, industry, nuclear power, and other fields. It is of great practical significance to improve the efficiency and optimize the performance of the centrifugal pump. 1 5 Derakhshan et al. 6 redesigned the blade shape of a centrifugal pump to improve its hydraulic efficiency by using a gradient-based optimization algorithm coupled with a three-dimensional (3D) Navier Stokes flow solver. Yang 7 improved the hydraulic efficiency by optimizing the impeller of highspecific-speed centrifugal pump. Cao et al. 8 studied the effect of axial clearance on the efficiency of a shrouded centrifugal pump with model tests and numerical simulation. They found that the volumetric efficiency is the key factor why the gross efficiency changes with axial clearance. Lipej et al. 9 studied the effect of wall roughness on the efficiency of centrifugal pump. Li et al. 10 investigated the effect of the blade-loading 1 National Research Center of Pumps and Pumping System Engineering and Technology, Jiangsu University, Zhenjiang, China 2 Institute of Fluid Engineering Equipment, Jiangsu Industrial Technology Research Institute (JITRI), Zhenjiang, China 3 TE Connectivity (Suzhou) Ltd., Suzhou, China Corresponding author: Kai Wang, National Research Center of Pumps and Pumping System Engineering and Technology, Jiangsu University, Zhenjiang , China. wangkai@ujs.edu.cn Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License ( which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages ( open-access-at-sage).

2 2 Advances in Mechanical Engineering Figure 1. Structure of the centrifugal pump with vaned diffuser. Table 1. Main structure parameters of the pump. Structure parameters Values Inlet diameter of impellers D j (mm) 165 Diameter of impellers D 2 (mm) 254 Outlet width of impellers b 2 (mm) 45 Blade numbers of impeller Z 1 5 Blade wrap angle of impeller u i ( ) 95 Inlet diameter of vaned diffuser D 3 (mm) 260 Outlet diameter of vaned diffuser D 4 (mm) 450 Blade numbers of vaned diffuser Z 3 6 Blade wrap angle of vaned diffuser u d ( ) 110 Inlet diameter of pump suction section D s (mm) 150 Outlet diameter of pump discharge section D d (mm) 125 distribution on head, radial force, and pressure pulsation of a low-specific-speed centrifugal pump with cylindrical impeller blades and analyzed the effect of the variation of the aft-loading point on hydrodynamic performance of the pump. Wang et al. 11 proposed a method to optimize the design of a typical multistage centrifugal pump based on energy-loss model and computational fluid dynamics (CFD) and assessed interactive relationships among the different types of energy losses. Dong et al. 12 studied the performance characteristics of a super-low-specific-speed centrifugal pump with different front streamline sweep angles of the impeller blades and analyzed the effect of the blade design aspect on internal flow field, pressure pulsation, and interior and exterior acoustics of the pump. Wang et al. 13 analyzed the energy characteristics, pressure pulsation, vibration, and noise characteristic of a fivestage centrifugal pump under different flow rate. Vaned diffuser is one of the most important flowpassage parts of the centrifugal pump, which has a direct effect on the performance of the pump. The back-blades of the impeller are radial blades on the back shroud of the centrifugal pump impeller, whose main role is to balance the axial force and axial seal. In recent years, some scholars have performed a lot of research on the vaned diffuser of the centrifugal pump by experiment and numerical simulation Sun et al. 19 analyzed the pressure fluctuations in a pump turbine with different guide vane s opening angle and found that pressure fluctuation under design-opening angle were much lower than those under off-designopening angle. The main source of pressure fluctuation between runner and guide vanes is rotor/stator interaction. Li et al. 20 found that the change of the number and width of impeller back pump-out vanes in the screw centrifugal pump has great influence on the distribution of the pressure in seal chamber and volute casing. Huang and Liu 21 employed CFD method to indicate that the key cause of low-frequency pressure pulsation is the eddies generated due to streamline distortion. Based on the detached eddy simulation (DES) model, Zhou et al. 22 put forward the impeller design method to optimize the anti-missile blade, reduce the flow loss between the guide vanes, and improve the performance of a multistage centrifugal pump. Because the back-blades and sharp corner in annular chamber directly affect the flow field of the pump, their cumulative effect on the pump performance was studiedinthisarticle.toimprovetheefficiencyofa centrifugal pump with vaned diffuser, two improving schemes were proposed by trimming back-blades of impeller and smoothing sharp corner in annular chamber. The energy performance, the internal flow field, the axial force, the radial force, and pressure fluctuation of the pump were analyzed with numerical simulation method. Finally, the energy performance of the improving scheme 2 was experimentally validated. Improving schemes Centrifugal pump with vaned diffuser Design parameters of a centrifugal pump with vaned diffuser are as follows. Design flow rate Q d is 270 m 3 /h, head of the pump H is 15 m, efficiency of the pump h is 75%, rotation speed p n is 1450 r/min, and specific speed n s (n s =(3:65n ffiffiffiffi Q )=H 3=4, where units of flow rate, rotational speed, and head are m 3 /s, r/min, and m, respectively) is 190. Structure diagram of the centrifugal pump with vaned diffuser is shown in Figure 1, and the main geometric parameters of the pump are shown in Table 1. Experiment of energy performance Experiment bench of the centrifugal pump with vaned diffuser is shown in Figure 2. Experimental equipment on energy performance of the pump includes a motor,

3 Wang et al. 3 Figure 2. Experiment bench of the pump: (a) schematic diagram of the experiment bench and (b) experiment bench. transmitters, and digital power meter, respectively, in the experiment. All experimental data were managed and analyzed by a data acquisition instrument. Figure 3 shows experimental results of energy performance of the pump. It can be observed from Figure 3 that under the design flow rate, head of the pump is m and efficiency of the pump is only 71.47%. Therefore, it is necessary to improve its structure so that its efficiency can reach the design requirement. Figure 3. Energy performance curve in the pump. a flow meter, two pressure transmitters, a three-phase pulse width modulation (PWM) digital power meter, and so on. The flow rate, head, and power were measured several times by the flow meter, pressure Improving schemes In order to improve efficiency of the centrifugal pump with vaned diffuser, the back-blades of the impeller were trimmed to reduce the power consumption. Improving schemes are shown in Figure 4. Moreover, the chamfer of the annual chamber in the original scheme was made with sharp corner. In order to improve the internal flow field of the pump, sharp

4 4 Advances in Mechanical Engineering Numerical simulation method Grid independence analysis The 3D model and assembly of the pump were carried out by Pro/E software. ICEM software was chosen for hexahedral mesh generation, as shown in Figure 6. In order to select the appropriate grid number, mesh sensitivity analysis was carried out. Table 2 shows results of grid independence analysis. As can be seen from Table 1, with the increase of grids number, head and efficiency of the pump will be stable at a certain value and the change is very small. Therefore, considering the calculation time, scheme 4 was selected for the subsequent simulation. Figure 4. Trimming back-blades of impeller. Figure 5. Smoothing sharp corner in annular chamber. corner in annular chamber in the improving schemes was smoothed (shown in Figure 5), whose radius is 50 mm. Therefore, according to the previous figures, three schemes were as follows: 1. Original scheme: the outlet diameter of the back-blades is 208 mm and the width is 8.4 mm. 2. Improving scheme 1: the outlet diameter of the back-blades is 179 mm, the width is 7.4 mm, and sharp corner in annular chamber is smoothed. 3. Improving scheme 2: the outlet diameter of the back-blades is 150 mm, the width is 6.4 mm, and sharp corner in annular chamber is smoothed. Boundary conditions The numerical simulation was carried out by ANSYS CFX software. The fluid medium chosen was water. The impeller and back-blades of impeller were arranged in a rotation domain with a rotational speed of 1450 r/ min. Other domains were set to be static domains. There are three pairs of static and dynamic interfaces: impeller and gap, back-blades of impeller and gap, and impeller and suction chamber. Other interfaces were defined as static interfaces. The inlet pressure was set as the total pressure of 1 atm, and the outlet was set to be the calculated mass flow rate. The walls were set as noslip condition, and the roughness was mm. Applicability of turbulence model Standard k-e model, shear stress transport (SST) model, k-v model, and renormalization group (RNG) k-e model were used to analyze the applicability of turbulence model. Except for the choice of turbulence model, other settings are the same in the numerical simulation setting. The simulated head and efficiency of the pump under the design flow rate are compared with the experimental results, as shown in Table 3. As can be seen from Table 3, the relative error of head and efficiency of the four turbulence models under the design flow rate are larger than experiment values. Compared with each turbulence model, the relative error of standard k-e model is smaller. The relative error of head is 6.7%, and the relative error of efficiency is 2.4%. The relative error of SST model is the largest. The relative error of head is 9.2%, and the relative error of efficiency is 8.7%. Therefore, standard k-e model was chosen for the subsequent simulation. Arrangement of monitoring points of pressure pulsation In order to analyze the pressure pulsation in the pump, the monitoring point P1 at outlet of the impeller, the

5 Wang et al. 5 Figure 6. Mesh generation. Table 2. Grid independence analysis. No. Grid number Head (m) Efficiency (%) Table 3. Comparison of turbulence model. Turbulence model Head Simulation value (m) Experiment value (m) Relative error (%) Standard k-e SST k-v RNG k-e Turbulence model Efficiency Simulation value (%) Experiment value (%) Relative error (%) Standard k-e SST k-v RNG k-e SST: shear stress model; RNG: renormalization group

6 6 Advances in Mechanical Engineering Efficiency of the improving scheme 1 is 77.47%, which is 4.25% higher than that of the original scheme. Figure 7. Distribution of monitoring points of pressure pulsation. Internal flow field Figure 9 shows the absolute velocity distribution and streamlines in the middle section under the design flow rate. As can be seen from Figure 9, the absolute velocity distributions in the three schemes are gradually increased from the impeller inlet. They reach the maximum at the impeller outlet. In the original scheme, a high-pressure area appeared on the suction surface of the impeller near the outlet. The internal flow of the improving scheme 1 and improving scheme 2 are uniform and stable. The high-pressure area is very small and can be neglected. A distinct low-pressure area appeared at downstream of the right side of the annual chamber in the original scheme. A wake zone without fluid flow appeared near the low-pressure area. For the two improving schemes, the impact of the flow is weak, which can reduce flow loss to some extent. Figure 8. Energy performance curve with numerical simulation. monitoring point P2 at outlet of the vaned diffuser, the monitoring point P3 at the annular chamber near the chamfer, and the monitoring point P4 at the outlet were selected, which are shown in Figure 7. Because the rotation speed of the pump n is 1450 r/ min in this experiment, axis-passing frequency of the pump is 25 Hz. Due to the impeller with five blades, the blade-passing frequency of the impeller is 125 Hz (i.e. 5th harmonic of axis-passing frequency). Numerical results and analysis Energy performance Figure 8 shows the energy performance curves of the three schemes. Compared with the original scheme, efficiency of improving scheme 1 and improving scheme 2 are greatly increased. Efficiency of the improving scheme 2 is 79.59%, which is the maximum and is 6.37% higher than that of the original scheme. Axial force The axial forces of the three schemes under the different flow rate are shown in Figure 10. The axial force decreases with the increase of flow rate. In contrast to the three schemes, the parameters of the back-blades of impeller in original scheme are most appropriate. Because the ability to balance the axial force gradually decreases after trimming the diameter and width of the back-blades of impeller. Under the design flow rate, the axial force of the model without back-blades is 3000 N. The original scheme can balance 89.47% of the axial force, while the improving scheme 1 can balance only 69.82% of the axial force and the improving scheme 2 can balance only 62.74% of the axial force. The difference of the axial force between improving scheme 1 and improving scheme 2 is 7.08 percentage points. Although trimming the back-blades of the impeller reduces their ability to balance axial force, it can greatly improve efficiency. Therefore, the improving scheme 2, which is better than improving scheme 1, was chosen to perform the subsequent experiment verification. Radial force Figure 11 shows time domain and frequency domain of the radial force in the impeller under the design flow rate. It can be seen from Figure 11 that the time domain and frequency domain of radial force in the three schemes are exactly the same when the impeller rotates for one circle, while the magnitude is different. It can be seen from Figure 11(a) that the peak value of the pressure pulsation peak can be arranged in order: original scheme.improving scheme 1.improving scheme 2.

7 Wang et al. 7 Figure 9. Absolute velocity distribution in middle section: (a) original scheme, (b) improving scheme 1, and (c) improving scheme 2. Figure 10. Axial force under different flow rate. The peak value of scheme 1 is 12% smaller than that of the original scheme. The peak value of the improving scheme 2 is 20% smaller than that of the original scheme. It can be seen from Figure 11(b) that the dominant frequency of the three schemes is 25 Hz (i.e. axispassing frequency) and the second frequency is 600 Hz. Amplitude of the frequency domain of the improving scheme 1 is 83.6% of the original scheme. Amplitude of the frequency domain of the improving scheme 2 is 74.5% of the original scheme. Figure 12 shows time domain and frequency domain of the radial force in the annual chamber under the design flow rate. As can be seen from Figure 12(a), the radial forces of the three schemes are exactly the same. There are five peaks and troughs, which is corresponding to the blade number of the impeller. The difference of the radial force peak between the improving scheme 1 and the improving scheme 2 is very small. But at the same angle, pressure value of the original scheme is the minimum. This is due to the reduction of the energy loss when the back-blades of the impeller is trimmed, which results in the increase of the outlet pressure. Figure 11. Radial force in the impeller: (a) time domain and (b) frequency domain. From Figure 12(b), it can be seen that the dominant frequency of the three schemes is 120 Hz. Amplitude of blade frequency of the radial force in the improving scheme 1 and the improving scheme 2 is 6.6% lower than that of the original scheme. Therefore, although the pressure value of the improving scheme 1 and the

8 8 Advances in Mechanical Engineering Figure 12. Radial force in the annular chamber: (a) time domain and (b) frequency domain. Figure 14. Pressure pulsation at P1: (a) time domain and (b) frequency domain. Figure 13. Radial force vector in the annular chamber. improving scheme 2 increased, the pressure pulsation conditions are improved. Figure 13 indicates radial force vector in the annular chamber. As can be seen from Figure 13, the radial force vectors of the three schemes are all hexagonal, which is corresponding to the blade number of the vaned diffuser. In one rotating period, hexagon repeats five times which is corresponding to the blade number of the impeller. Therefore, the radial force in the annular chamber is the result of rotor stator interference between the impeller and the vaned diffuser. Each blade of impeller sweeps over a stationary blade of vaned diffuser which leads to a radial force peak. The difference of radial force vector between the improving scheme 1 and the improving scheme 2 is very small. The radial forces of the two schemes are more evenly distributed in the four quadrants. The radial force of the original scheme is partial to the X direction. Theoretically, the radial force distribution is uniform, indicating that the force in each direction is more uniform, and there will be no large vibration impact. However, the original scheme with uneven radial force distribution is easy to generate stress on one side. It leads to greater stress concentration in the annular chamber which is unfavorable to the long-term smooth running of the pump. Pressure pulsation The result of numerical simulation on each monitoring point shows the static pressure at different time. In order to accurately compare the pressure of each

9 Wang et al. 9 Figure 15. Pressure pulsation at P2: (a) time domain and (b) frequency domain. Figure 16. Pressure pulsation at P3: (a) time domain and (b) frequency domain. monitoring point, the pressure pulsation coefficient C p is introduced C p = 2(p p) ru 2 where p is the static pressure of the monitoring point, p is the average static pressure for the impeller rotating one circle, and u is the circumferential velocity of the impeller. Figure 14 shows the time domain and frequency domain of the pressure pulsation at the monitoring point P1. As can be seen from Figure 14(a), the pulsations in the three schemes are exactly the same, which have five peaks and troughs. The time to enter the peaks (i.e. the high-pressure area) is longer than the time to enter the troughs (i.e. the low-pressure area). It indicates that high-pressure area at the outlet of impeller is larger. As shown in Figure 14(b), the dominant frequency of the three schemes is 150 Hz (i.e. 6th harmonic of axis-passing frequency, or blade-passing frequency of the vaned diffuser). The amplitude difference of the pressure pulsation between the three schemes is very small. Therefore, trimming back-blades of impeller does not affect the change trend of the pressure pulsation at the outlet of the impeller and has little influence on its amplitude. Figure 15 gives the time domain and frequency domain of the pressure pulsation at the monitoring point P2. The pulsation rule of time domain and frequency domain are basically the same in the three schemes. The order of the peak value of pressure pulsation is as follows: improving scheme 2.improving scheme 1.original scheme. The difference of the peak value of pressure pulsation between the improving scheme 2 and the original scheme is the largest. The peak value of pressure pulsation is 0.14% larger than that of the original scheme. The pressure pulsation coefficients of the three schemes are compared. The dominant frequency of the three schemes is 120 Hz, which is the blade-passing frequency of the impeller. The order of the amplitudes of the pressure pulsation coefficients is as follows: original scheme.improving scheme 1.improving scheme 2. The amplitude of the pressure pulsation in the improving scheme 1 is 94.4% of the original scheme and improving scheme 2 is 93.2% of the original scheme. The difference between the

10 10 Advances in Mechanical Engineering Figure 17. Pressure pulsation at P4: (a) time domain and (b) frequency domain. annular chamber. The pressure pulsation signal is also affected by the outlet diffuser section. Figure 16 shows the time domain and frequency domain of the pressure pulsation at the monitoring point P3. As can be seen from Figure 16, the pulsation rules of the pressure values in the three schemes also are the same. The order is as follows: original scheme.improving scheme 1.improving scheme 2. The peak value of pressure pulsation in the improving scheme 2 is 0.52% lower than that of the original scheme. Variation rule of the amplitude of pressure pulsation coefficient is the same as that of the pressure value. The dominant frequency of the three schemes is 120 Hz. Figure 17 shows the time domain and frequency domain of the pressure pulsation at the monitoring point P4. As can be seen from Figure 17(a), the pressure values of the improving scheme 1 and the improving scheme 2 are obviously larger than that of the original scheme. The pressure value of the improving scheme 1 is 16.4% larger than that of the original scheme and the improving scheme 2 is 16.8% larger than that of the original scheme. The increase of the outlet pressure is due to the decrease of energy loss after structural optimization. The magnitude of the pressure pulsation frequency in Figure 17(b) is in the order as follows: original scheme.improving scheme 1.improving scheme 2. The improving scheme 1 is 12.85% less than that of the original scheme and the improving scheme 2 is 14.2% less than that of the original scheme. The dominant frequency is the bladepassing frequency of the impeller. Figure 18. Comparison of energy performance. improving scheme 1 and the improving scheme 2 is very small. Therefore, the pressure pulsation of the monitoring point at outlet of the vaned diffuser is mainly affected by the rotor stator interference at outlet of the impeller. The monitoring point of the vaned diffuser outlet is closer to the outlet diffuser section of the Experiment verification In order to verify the feasibility of structural improvement, experimental measurements on the improving scheme 2 were carried out. The energy performance curves of the original scheme and the improving scheme 2 are shown in Figure 18. As can be seen from Figure 18, the differences between head and efficiency of the pump before and after optimization are very small under the small flow rate. With increase of the flow rate, the difference also increases. Under the design flow rate, the efficiency of the improving scheme 2 is 76.48%, which is 5.26 percentage points higher than that of the original scheme. The effect of structural improvement is very obvious. Conclusion The structure of a centrifugal pump with vaned diffuser has been improved. Numerical analysis and experimental verification have been carried out. Some conclusions are as follows:

11 Wang et al Trimming back-blades has a certain influence on the axial force in the pump. Under the design flow rate, the original scheme can balance 89.47% of the axial force, the improving scheme 1 can balance 69.82% of the axial force, and the improving scheme 2 can balance 62.74% of the axial force. 2. The frequency-domain amplitude of radial force of the improving scheme 1 is 83.6% of the original scheme, while the frequency-domain amplitude of radial force of the improving scheme 2 is 74.5% of the original scheme. After structural improvement, the radial force in the annular chamber increases. But the pulsation of frequency domain is improved, and the vector distribution is more uniform than that of the original scheme. 3. In the two improving schemes, the pressure pulsation coefficients at the four monitoring points are less than that of the original scheme. 4. Although trimming the back-blades of the impeller reduces their ability to balance axial force, it can greatly improve efficiency. Experimental results of the improving scheme 2 show that the efficiency of the improving scheme 2 under the design flow rate is 76.48%, which is 5.26 percentage points higher than that of the original scheme. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Key Research and Development Program of China (grant no.: 2016YFB ), the National Natural Science Foundation of China (grant nos.: and ), and Six Talent Peaks Project in Jiangsu Province of China (grant no.: 2018-GDZB-154). ORCID id Kai Wang References 1. Ren T, Yan YQ and Liang WK. Application of CFD to optimization design for centrifugal pump. J Drain Irrig Mach Eng 2007; 25: Wang K, Liu H, Yuan S, et al. Optimization method for hydraulic performance of centrifugal pump at multioperation points. J Drain Irrig Mach Eng 2012; 30: Zhang Y, Zhu Z, Cui B, et al. Experimental investigation of external performance of prototype centrifugal pump during startup period. J Mech Eng 2013; 49: Yuan S, Wang W, Pei J, et al. Multi-objective optimization of low-specific-speed centrifugal pump. Trans Chin Soc Agric Eng 2015; 39: Heo MW, Ma SB, Shim HS, et al. High-efficiency design optimization of a centrifugal pump. J Mech Sci Technol 2016; 30: Derakhshan S, Mohammadi B and Nourbakhsh A. Efficiency improvement of centrifugal reverse pumps. J Fluid Eng 2009; 131: Yang CT. Hydrodynamic efficiency improvement of high-specific-speed centrifugal pump impeller. Appl Mech Mater 2014; 467: Cao L, Zhang Y, Wang Z, et al. Effect of axial clearance on the efficiency of a shrouded centrifugal pump. J Fluid Eng 2015; 137: Lipej A, Muhič S and Mitruševski D. Wall roughness influence on the efficiency characteristics of centrifugal pump. J Mech Eng 2017; 63: Li X, Gao P, Zhu Z, et al. Effect of the blade loading distribution on hydrodynamic performance of a centrifugal pump with cylindrical blades. J Mech Sci Technol 2018; 32: Wang C, Shi W, Wang X, et al. Optimal design of multistage centrifugal pump based on the combined energy loss model and computational fluid dynamics. Appl Energ 2017; 187: Dong L, Zhao Y, Liu H, et al. The effect of front streamline wrapping angle variation in a super-low specific speed centrifugal pump. Proc IMechE, Part C: J Mechanical Engineering Science 2018; 232: Wang K, Xia C, Zhang Z, et al. Experimental investigation of pressure fluctuation, vibration and noise in a multistage pump. Shock Vib 2018; 2018: Liu H, Cui J, Tan M, et al. CFD calculation of clocking effect on centrifugal pump. Trans Chin Soc Agric Eng 2013; 29: Junaidi MAR, Kumari NBVL, Samad MA, et al. CFD simulation to enhance the efficiency of centrifugal pump by application of inner guide vanes. Mater Today Proc 2015; 2: Wang K, Lu X, He X, et al. Experimental investigation of vibration characteristics in a centrifugal pump with vaned diffuser. Shock Vib 2018; 2018: Yuan D, Han Y, Cong X, et al. Design and optimization of new-type space guide vanes for multistage centrifugal pump. J Drain Irrig Mach Eng 2015; 33: Zhu X, Jiang W, Li G, et al. Numerical analysis of hydraulic performance in centrifugal pump with vane diffuser. Trans Chin Soc Agric Mach 2016; 47: Sun YK, Zuo ZG, Liu SH, et al. Numerical study of pressure fluctuations in different guide vanes opening angle in pump mode of a pump turbine. IOP Conf Ser: Earth Env Sci 2012; 15: Li R, Gao Y, Cheng X, et al. Numerical calculation for effects of impeller back pump-out vanes on axial thrust in screw centrifugal pump. J Mech Eng 2012; 48:

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