# Investigation on Stall Characteristics of Centrifugal Pump with Guide Vanes

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## Abstract

**:**

## 1. Introduction

## 2. Research Object and Numerical Calculation Method

^{−4}s, which is 1/360 of the rotation period. The convergence residual is set to 1.0 × 10

^{−5}. This calculation is carried out on the rack server of Hohai University. The servers all use 64-bit high-performance processors and 12 dual computing nodes, including 24 Intel E5-2600 eight-core processors and 192 CPU cores. Each node contains 64 GB of memory, and the total system memory is 678 GB.

_{SAS}to the ω equation:

## 3. Prediction of Centrifugal Pump Performance Curve

_{d}, where Q

_{d}is the flow under design conditions. In order to stabilize the flow field at the pump inlet, a rectifier is placed in the pipe section at the inlet of the resistance plate and impeller [40].

_{d}–0.3 Q

_{d}, in which the hump peak point is 0.3 Q

_{d}, and the wave trough is 0.2 Q

_{d}. The difference is that the SAS model observed the occurrence of the hump phenomenon at 0.5 Q

_{d}–0.6 Q

_{d}, in which the peak point is 0.6 Q

_{d}, and the wave trough point is 0.5 Q

_{d}. The double-hump phenomenon of guide vane centrifugal pump predicted by the SAS model is also observed in the pump turbine [41].

## 4. Characteristic Analysis of Double Humps

_{2}·U

_{2}) and impeller inlet velocity moment (Cu

_{1}·U

_{1}). In the process of numerical simulation, Euler energy and Euler head can be obtained through equations [41]:

_{d}to 0.5 Q

_{d}, the Euler head decreases slowly; when the flow decreases from 0.5 Q

_{d}to 0.4 Q

_{d}, the Euler head decreases rapidly. For the Euler head calculated by SST k-ω, when the flow rate changes from 1.0 Q

_{d}to 0.6 Q

_{d}, the Euler head decreases slowly; when the flow decreases from 0.6 Q

_{d}to 0.5 Q

_{d}, the Euler head decreases rapidly. The hump area is observed at 0.2 Q

_{d}–0.3 Q

_{d}of Euler head calculated by the two models, where the peak point is 0.3 Q

_{d}, and the trough is 0.2 Q

_{d}.

_{d}, to 0.6 Q

_{d}, the head loss decreases slowly; when the flow decreases from 0.6 Q

_{d}, to 0.5 Q

_{d}, the hydraulic loss increases rapidly. For the Euler head calculated by SST k-ω, when the flow rate changes from 1.0 Q

_{d}to 0.5 Q

_{d}, the Euler head decreases slowly; when the flow decreases from 0.5 Q

_{d}, to 0.4 Q

_{d}, the hydraulic loss increases rapidly. Under each working condition, the hydraulic loss calculated by SAS model is greater than SST k-ω. Due to the entropy, generation of the wall area is calculated more accurately by the SAS model, so the hydraulic loss obtained is greater than SST k-ω.

_{d}–0.6 Q

_{d}hump area close to the design working condition. From the peak point (0.6 Q

_{d}) to the trough point (0.5 Q

_{d}) in the hump area, the hydraulic loss of each component suddenly increases, in which the impeller and guide vane increase greatly, while the corresponding Euler head changes little. Therefore, the hump here is mainly caused by hydraulic loss. During the 0.5 Q

_{d}–0.6 Q

_{d}operating condition, there is no hump area calculated by the SST k-ω model because the hydraulic loss of components does not change much. When the flow rates decrease from 0.5 Q

_{d}to 0.4 Q

_{d}, the hydraulic loss increases rapidly, but the calculated Euler head increases at this time, offsetting the occurrence of the hump area. In the hump area of 0.2 Q

_{d}–0.3 Q

_{d}, the Euler head calculated by the two models decreases, and the hydraulic loss increases. Therefore, the hump area is the result of the joint action of Euler head and hydraulic loss.

_{d}, the stall passage of the impeller calculated by the two models does not change much. However, in the guide-vane passage, a separation vortex at the back of the guide vane is observed in the flow field calculated by the SAS model, which indicates that the loss of the guide vane begins to increase at this time. At 0.5 Q

_{d}, the stall vortex is obvious in the impeller calculated by the two models. There are relatively large stall cells calculated by the SST k-ω model in channels A, C, and E, and they are all located on the suction surface of the impeller blade head and in the middle of the impeller pressure surface. There are also stall cells calculated by the SAS model in the flow channels in A, C, and E channels, which is similar to SST k-ω. The difference is that the previous two small vortices become a larger one, which is located near the suction surface of the impeller inlet, and the size of the stall cells almost blocks the entire flow passage. At 0.3 Q

_{d}, the flow pattern of the impeller calculated by the two models becomes worse. From the results calculated by SST k-ω, the relatively large stall vortices are observed in channels A, C, and E, while the flow in the other three channels is relatively stable. Stall cells appear in all six channels from the results calculated by the SAS model, which is consistent with the phenomenon observed in the external characteristic curve in Figure 3. When the pump operates at 0.3 Q

_{d}, the head curve is at the trough of the wave, which indicates that the hump in the head flow curve is largely caused by the stall in the impeller flow passage.

## 5. Clocking Effect of Guide-Vane Centrifugal Pump under Stall Characteristics

_{d}–0.3 Q

_{d}and 0.5 Q

_{d}–0.6 Q

_{d}.

_{d}is shown in Figure 11. The clocking position has a great influence on the flow structure of the guide vane, and different sizes of reflux areas are generated in the flow passage, which is due to the flow separation occurring at the pressure side of the guide vane. Meanwhile, part of the fluid in the guide-vane flow passage flows out of the volute outlet, and part of the fluid enters the volute flow passage. In addition, the velocity direction on the right side of the volute outlet and the vortex structure on the left side is obviously affected by the guide-vane position. In the head curve, the head difference is large at 0.3 Q

_{d}because the flow structure at the outlet of the guide vane close to the volute outlet is greatly affected by the position of the guide vane, which results in flow separation at the volute outlet, causing hydraulic loss.

_{d}. In the middle of the impeller, Figure 12a shows that the guide-vane position at stall condition has a significant impact on the instability characteristics of pressure fluctuation caused by rotor–stator interaction. When the guide vane is installed at position 1, the amplitude of the blade is at a relatively stable minimum; when the guide vane is at position 3, the pressure fluctuation amplitude of the blade has strong instability, which is greatly affected by the rotating position of the impeller. Due to the existence of the vortex at the inlet of the blade suction side, the pressure fluctuation amplitude is enhanced, and the peak-to-peak value is large. In the vaneless region, which is the gap between the impeller and the guide vanes, the flow interference is strong, and the pressure fluctuation signals are relatively greater, and the peak-to-peak value of the pressure fluctuation is the largest. Therefore, when the stall cell moves to the monitoring point, the pressure decreases rapidly, and after the stall cell falls off, the pressure value rises again. Stall cells periodically form, develop, and fall off, inducing low-frequency pressure fluctuations.

_{d}. The clocking position of the guide vane has a significant impact on the dominant frequency and corresponding amplitude of the volute. In the four clocking positions, the dominant frequency at the volute tongue is blade frequency (75 Hz), and the secondary frequency is low frequency. When the guide vane is installed at clocking position 1, the fluctuation amplitude of the dominant frequency is maximum, and when it is installed at clocking position 3, the fluctuation amplitude of the dominant frequency is minimum. The amplitude of dominant frequency fluctuation at clocking position 3 is 1.3 times of that at clocking position 1. At the outlet of the volute, one time of the dominant frequency corresponding to clocking position 1 is the blade frequency (75 Hz), and the dominant frequency at other clocking positions is the low frequency. From Figure 11, it can be seen that the streamline at clocking positions 2, 3, and 4 is twisted at the outlet of the volute, while the streamline at the outlet corresponding to timing position 1 is relatively smooth. Therefore, the timing position affects the flow at the outlet of the volute so that the volute will produce a low-frequency fluctuation.

## 6. Conclusions

- (1)
- The double-hump characteristic was found in the head discharge curve by using the SAS model. Comparing the flow field characteristics at different flow rate conditions, it was found that the hump area close to the optimal working condition is caused by hydraulic loss, and the hump area far away from the optimal working condition point is caused by the combined action of Euler head and hydraulic loss. The SAS model can accurately calculate the wall friction loss, thus predicting the double hump phenomenon.
- (2)
- The pressure fluctuation and head characteristics at different clocking positions under stall conditions were obtained. It was found that when the guide vanes outlet in line with the volute tongue, the flow pattern of the volute and guide vane is good, so the head is high due to small hydraulic loss, and the pressure fluctuation is low.
- (3)
- The mechanism of clocking effect in the centrifugal pump with guide vanes was obtained by simplifying the hydrofoil. Based on the simplified hydrofoil, it can be found that the disturbance of wake to the boundary layer will affect the boundary layer transition and then affect the friction stress of the blade, resulting in the change of flow field pressure amplitude. When the downstream hydrofoil head area is always interfered with by the upstream hydrofoil wake, the wake of the low-energy fluid is mixed with the boundary layer of the same low-energy fluid. At this time, the boundary layer is in a turbulent state to avoid laminar flow separation, causing small vibration of the downstream hydrofoil, so the position where the guide vane’s outlet is in line with the volute tongue is most recommended.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Q_{d} | Design flow | SAS | Scale adaptive simulation |

Cu | Circumferential component of absolute velocity | LES | Large eddy simulation method |

U | Circumferential velocity | RANS | Reynolds average method |

H_{Enter} | Euler head | C_{p} | Pressure coefficient |

ΔCu·U | Euler energy | ω | Angular velocity |

## References

- Wang, C.; Wang, F.; Li, C.; Chen, W.; Wang, H.; Lu, L. Investigation on energy conversion instability of pump mode in hydro-pneumatic energy storage system. J. Energy Storage
**2022**, 53, 105079. [Google Scholar] [CrossRef] - Zhou, P.; Wang, F.; Mou, J. Investigation of rotating stall characteristics in a centrifugal pump impeller at low flow rates. Eng. Comput.
**2017**, 34, 1989–2000. [Google Scholar] [CrossRef] - Feng, J.; Ge, Z.; Yang, H.; Zhu, G.; Li, C.; Luo, X. Rotating stall characteristics in the vaned diffuser of a centrifugal pump. Ocean Eng.
**2021**, 229, 108955. [Google Scholar] [CrossRef] - Ye, C.L.; Wang, C.Y.; Zi, D.; Tang, Y.; van Esch, B.; Wang, F.J. Improvement of the SST γ-Re
_{θt}transition model for flows along a curved hydrofoil. J. Hydrodyn.**2021**, 33, 520–533. [Google Scholar] [CrossRef] - Stenning, A.H.; Kriebel, A.R. Stall propagation in a cascade of airfoils. Trans. Am. Soc. Mech. Eng.
**1958**, 80, 777–789. [Google Scholar] [CrossRef] - Emmons, H.W.; Pearson, C.E.; Grant, H.P. Compressor surge and stall propagation. Trans. Am. Soc. Mech. Eng.
**1955**, 77, 455–467. [Google Scholar] [CrossRef] - Day, I.J. Stall, surge and 75 years of research. ASME J. Turbomach.
**2016**, 138, 011001. [Google Scholar] [CrossRef] - Zhang, N.; Gao, B.; Ni, D.; Liu, X. Coherence analysis to detect unsteady rotating stall phenomenon based on pressure pulsation signals of a centrifugal pump. Mech. Syst. Signal Process.
**2021**, 148, 107161. [Google Scholar] [CrossRef] - Huang, X.-B.; Liu, Z.-Q.; Li, Y.-J.; Yang, W.; Guo, Q. Study of the internal characteristics of the stall in a centrifugal pump with a cubic non-linear SGS model. J. Hydrodyn.
**2019**, 31, 788–799. [Google Scholar] [CrossRef] - Wang, C.; Wang, F.; Xie, L.; Wang, B.; Yao, Z.; Xiao, R. On the Vortical Characteristics of Horn-Like Vortices in Stator Corner Separation Flow in an Axial Flow Pump. J. Fluids Eng.
**2021**, 143, 061201. [Google Scholar] [CrossRef] - Abusorrah, A.M.; Mebarek-Oudina, F.; Ahmadian, A.; Baleanu, D. Modeling of a MED-TVC desalination system by considering the effects of nanoparticles: Energetic and exergetic analysis. J. Therm. Anal. Calorim.
**2021**, 144, 2675–2687. [Google Scholar] [CrossRef] - Hassan, M.; Mebarek-Oudina, F.; Faisal, A.; Ghafar, A.; Ismail, A. Thermal energy and mass transport of shear thinning fluid under effects of low to high shear rate viscosity. Int. J. Thermofluids
**2022**, 15, 100176. [Google Scholar] [CrossRef] - Wang, C.; Wang, F.; Li, C.; Ye, C.; Yan, T.; Zou, Z. A modified STRUCT model for efficient engineering computations of turbulent flows in hydro-energy machinery. Int. J. Heat Fluid Flow
**2020**, 85, 108628. [Google Scholar] [CrossRef] - Posa, A. LES investigation on the dependence of the flow through a centrifugal pump on the diffuser geometry. Int. J. Heat Fluid Flow
**2021**, 87, 108750. [Google Scholar] [CrossRef] - Sano, T.; Yoshida, Y.; Tsujimoto, Y.; Nakamura, Y.; Matsushima, T. Numerical Study of Rotating Stall in a Pump Vaned Diffuser. J. Fluids Eng.
**2002**, 124, 363–370. [Google Scholar] [CrossRef] - Braun, O. Part Load Flow in Radial Centrifugal Pumps. Ph.D. Thesis, EPFL, Lausanne, Switzerland, 2009. [Google Scholar]
- Lucius, A.; Brenner, G. Unsteady CFD simulations of a pump in part load conditions using scale-adaptive simulation. Int. J. Heat Fluid Flow
**2010**, 31, 1113–1118. [Google Scholar] [CrossRef] - Zhang, N.; Jiang, J.; Gao, B.; Liu, X. DDES analysis of unsteady flow evolution and pressure pulsation at off-design condition of a centrifugal pump. Renew. Energy
**2020**, 153, 193–204. [Google Scholar] [CrossRef] - Ji, L.; Li, W.; Shi, W.; Tian, F.; Agarwal, R. Effect of blade thickness on rotating stall of mixed-flow pump using entropy generation analysis. Energy
**2021**, 236, 121381. [Google Scholar] [CrossRef] - Kan, K.; Zheng, Y.; Chen, Y.; Xie, Z.; Yang, G.; Yang, C. Numerical study on the internal flow characteristics of an axial-flow pump under stall conditions. J. Mech. Sci. Technol.
**2018**, 32, 4683–4695. [Google Scholar] [CrossRef] - Krause, N.; Pap, E.R.; The´ venin, D. Influence of the blade geometry on flow instabilities in a radial pump elucidated by time-resolved particle-image velocimetry. In Proceedings of the Turbo Expo: Power for Land, Sea, and Air, Montreal, Canada, 14–17 May 2007; ASME: New York, NY, USA, 2007; Volume 47950, pp. 1659–1668. [Google Scholar]
- Berten, S.; Dupont, P.; Fabre, L.; Kayal, M.; Avellan, F.; Farhat, M. Experimental investigation of flow instabilities and rotating stall in a high-energy centrifugal pump stage. In Proceedings of the Fluids Engineering Division Summer Meeting, Vali, CO, USA, 2–6 August 2009; Volume 43727, pp. 505–513. [Google Scholar]
- Chudina, M. Noise as an indicator of cavitation in a centrifugal pump. Acoust. Phys.
**2003**, 49, 463–474. [Google Scholar] [CrossRef] - Johnson, D.A.; Pedersen, N.; Jacobsen, C.B. Measurements of rotating stall inside a centrifugal pump impeller. In Proceedings of the Fluids Engineering Division Summer Meeting, Houston, TX, USA, 19–23 June 2005; Volume 41987, pp. 1281–1288. [Google Scholar]
- Ye, W.; Huang, R.; Jiang, Z.; Li, X.; Zhu, Z.; Luo, X. Instability analysis under part-load conditions in centrifugal pump. J. Mech. Sci. Technol.
**2019**, 33, 269–278. [Google Scholar] [CrossRef] [Green Version] - Ren, X.; Fan, H.; Xie, Z.; Liu, B. Stationary stall phenomenon and pressure fluctuation in a centrifugal pump at partial load condition. Heat Mass Transf.
**2019**, 55, 2277–2288. [Google Scholar] [CrossRef] - Takamine, T.; Furukawa, D.; Watanabe, S.; Watanabe, H.; Miyagawa, K. Experimental Analysis of Diffuser Rotating Stallin a Three-Stage Centrifugal Pump. Int. J. Fluid Mach. Syst.
**2018**, 11, 77–84. [Google Scholar] [CrossRef] - Liu, X.-D.; Li, Y.-J.; Liu, Z.-Q.; Yang, W.; Tao, R. Dynamic evolution process of rotating stall vortex based on high-frequency PIV system in centrifugal impeller. Ocean Eng.
**2022**, 259, 111944. [Google Scholar] [CrossRef] - Pavesi, G.; Cavazzini, G.; Ardizzon, G. Time–frequency characterization of the unsteady phenomena in a centrifugal pump. Int. J. Heat Fluid Flow
**2008**, 29, 1527–1540. [Google Scholar] [CrossRef] - Takao, S.; Konno, S.; Ejiri, S.; Miyabe, M. Suppression of Diffuser Rotating Stall in A Centrifugal Pump by Use of Slit Vane. In Proceedings of the Fluids Engineering Division Summer Meeting, Online, 10–12 August 2021; American Society of Mechanical Engineers: New York, NY, USA, 2021; Volume 85291, p. V002T03A007. [Google Scholar]
- Yan, H.; Heng, Y.; Zheng, Y.; Tao, R.; Ye, C. Investigation on Pressure Fluctuation of the Impellers of a Double-Entry Two-Stage Double Suction Centrifugal Pump. Water
**2022**, 14, 4065. [Google Scholar] [CrossRef] - Griffini, D.; Insinna, M.; Salvadori, S.; Martelli, F. Clocking Effects of Inlet Nonuniformities in a Fully Cooled High-Pressure Vane: A Conjugate Heat Transfer Analysis. J. Turbomach.
**2015**, 138, 021006. [Google Scholar] [CrossRef] - Benigni, H.; Jaberg, H.; Yeung, H.; Salisbury, T.; Berry, O.; Collins, T. Numerical Simulation of Low Specific Speed American Petroleum Institute Pumps in Part-Load Operation and Comparison with Test Rig Results. J. Fluids Eng.
**2012**, 134, 024501. [Google Scholar] [CrossRef] - Gu, Y.; Pei, J.; Yuan, S.; Wang, W.; Zhang, F.; Wang, P.; Liu, Y. Clocking effect of vaned diffuser on hydraulic performance of high-power pump by using the numerical flow loss visualization method. Energy
**2019**, 170, 986–997. [Google Scholar] [CrossRef] - Wang, W.; Pei, J.; Yuan, S.; Yin, T. Experimental investigation on clocking effect of vaned diffuser on performance characteristics and pressure pulsations in a centrifugal pump. Exp. Therm. Fluid Sci.
**2018**, 90, 286–298. [Google Scholar] [CrossRef] - Tan, M.; Lian, Y.; Wu, X.; Liu, H. Numerical investigation of clocking effect of impellers on a multistage pump. Eng. Comput.
**2019**, 36, 1469–1482. [Google Scholar] [CrossRef] - Menter, F.R. Improved Two-Equation k-Turbulence Models for Aerodynamic Flows; NASA Technical Memorandum, 103975(1_), 3t; NASA: Washington, DC, USA, 1992.
- Hellsten, A. Some improvements in Menter’s k-omega SST turbulence model. In Proceedings of the 29th AIAA, Fluid Dynamics Conference, Albuquerque, NM, USA, 15–18 June 1998; p. 2554. [Google Scholar]
- Menter, F.R.; Egorov, Y. SAS turbulence modelling of technical flows. In Direct and Large-Eddy Simulation VI; Springer: Dordrecht, The Netherlands, 2006; pp. 687–694. [Google Scholar]
- Pedersen, N. Experimental Investigation of Flow Structures in a Centrifugal Pump Impeller Using Particle Image Velocimetry. Ph.D. Thesis, Technical University of Denmark, Kongens Lyngby, Denmark, 2000. [Google Scholar]
- Li, D.; Song, Y.; Lin, S.; Wang, H.; Qin, Y.; Wei, X. Effect mechanism of cavitation on the hump characteristic of a pump-turbine. Renew. Energy
**2020**, 167, 369–383. [Google Scholar] [CrossRef] - Yan, H.; Zhang, H.; Zhou, L.; Liu, Z.; Zeng, Y. Optimization design of the unsmooth bionic structure of a hydrofoil leading edge based on the Grey–Taguchi method. Proc. Inst. Mech. Eng. Part M J. sEng. Marit. Environ.
**2022**, 14750902221128140. [Google Scholar] [CrossRef]

**Figure 6.**Calculation of Head Loss of Each Component of Guide-Vane Centrifugal Pump. (

**a**) Inlet pipe; (

**b**) Impeller; (

**c**) Guide vane; (

**d**) Volute.

**Figure 7.**Pressure Contour and Streamline of Centrifugal Pump Calculated by SAS model. (

**a**) 0.3 Q

_{d}; (

**b**) 0.5 Q

_{d}; (

**c**) 0.7 Q

_{d}.

**Figure 8.**Pressure Contour and Streamline of Centrifugal Pump Calculated by SST k-ω model. (

**a**) 0.3 Q

_{d}; (

**b**) 0.5 Q

_{d}; (

**c**) 0.7 Q

_{d}.

**Figure 9.**Clocking Position of the Pump. (

**a**) Clocking position 1; (

**b**) Clocking position 2; (

**c**) Clocking position 3; (

**d**) Clocking position 4.

**Figure 11.**Velocity Streamline at Different Clocking Positions. (

**a**) Clocking position 1; (

**b**) Clocking position 2; (

**c**) Clocking position 3; (

**d**) Clocking position 4.

**Figure 12.**Pressure Fluctuation of Impeller and Guide Vane. (

**a**) Monitor point R2; (

**b**) Monitor point S2.

**Figure 13.**Pressure Fluctuation of Volute. (

**a**) Monitor point W1 near tongue; (

**b**) Monitor point W8 near outlet.

**Figure 17.**Pressure Distribution of Different Monitoring Points with Valve Opening. (

**a**) Monitoring point P1; (

**b**) Monitoring point P2; (

**c**) Monitoring point P3; (

**d**) Monitoring point P4.

**Figure 18.**Vorticity Distribution at Different Time Sequence Positions. (

**a**) Position 1; (

**b**) Position 2; (

**c**) Position 3; (

**d**) Position 4.

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**MDPI and ACS Style**

Ye, C.; An, D.; Huang, W.; Heng, Y.; Zheng, Y.
Investigation on Stall Characteristics of Centrifugal Pump with Guide Vanes. *Water* **2023**, *15*, 21.
https://doi.org/10.3390/w15010021

**AMA Style**

Ye C, An D, Huang W, Heng Y, Zheng Y.
Investigation on Stall Characteristics of Centrifugal Pump with Guide Vanes. *Water*. 2023; 15(1):21.
https://doi.org/10.3390/w15010021

**Chicago/Turabian Style**

Ye, Changliang, Dongsen An, Wanru Huang, Yaguang Heng, and Yuan Zheng.
2023. "Investigation on Stall Characteristics of Centrifugal Pump with Guide Vanes" *Water* 15, no. 1: 21.
https://doi.org/10.3390/w15010021