# Research on Influence of Rotation Center Eccentricity on Radial Force of Single-Blade Centrifugal Pump

^{*}

## Abstract

**:**

_{d}, which is about 17%. The study may prove helpful to designers and pump manufacturers to find a path forward for an optimal eccentricity to minimize the radial force.

## 1. Introduction

## 2. Numerical Calculations

#### 2.1. Calculate Model

_{d}= 20 m

^{3}/h, head H = 11 m, rotation speed n = 2940 r/min, and specific speed n

_{s}= 132. The main geometric parameters are as follows: impeller inlet diameter D

_{j}= 45 mm, outlet diameter D

_{2}= 125 mm, outlet width b

_{2}= 30 mm, blade angle φ = 360°, and volute base circle diameter D

_{3}= 135 mm. Bladegen and Pro/E were used for the 3D modeling of the model. The model pump is shown in Figure 1, including the chamber, impeller, volute, inlet, and outlet sections. To ensure the stability of the numerical calculations, the extended inlet and outlet sections are five times the inlet and outlet diameters.

#### 2.2. Meshing

#### 2.3. Turbulence Model and Boundary Conditions

^{−4}s (3° per time step) for the simulation. Ten revolutions were calculated and the total time was 2.011 × 10

^{−1}s. The convergence accuracy was set as 10

^{−5}.

## 3. Experimental Verification

#### 3.1. External Characteristic Verification

#### 3.2. Pressure Distribution

## 4. Results and Analysis of Numerical Calculation

#### 4.1. Influence of Impeller Eccentricity on Radial Force

_{r}is radial force and p is the pressure acting on the impeller surface A.

_{x}is consistent. F is negative, and the time of the radial force peak and trough of each impeller is the same, without an obvious phase difference. The radial force x component is larger when the impeller is non-eccentric and the eccentricity is (−1,0), and the peak value of radial force is the largest and the pulsation is the strongest when the impeller eccentricity is (−1,0). When the shaft center of the impeller offsets 1 mm to the positive direction of the x-axis, that is, the eccentricity is (1,0), the x component radial force and pulsation are reduced to a certain extent, and the time average is reduced by 24% compared with the maximum value. When the impeller eccentricity is (0,1) and (0,0.5), the difference between the x component of the radial force is small. It can be seen from Figure 9b that eccentricity has little effect on the period and phase of the radial force y component F

_{y}, but the radial force y component increases when the impeller shaft center is eccentric to the volute tongue. It can be seen from the graph that the F

_{y}value is larger when the eccentricity is (0,1) than when the eccentricity is (0,0.5), the value is the largest, while the F

_{y}value is the smallest, when the eccentricity is (0,−1), and the minimum value is 11% smaller than the mean value when at the maximum value. Viewing the fluctuation of F

_{y}, the peak value is maximum when eccentricity is (0,1) and (−1,0). Figure 9c is the curve of a radial force varying with time. The diagram shows that impeller eccentricity has little effect on the period and peak phase of radial force. When the impeller eccentricity is (1,0), the radial force is the smallest, and the mean value is reduced by 8.8% compared with the maximum value, but the peak value is increased compared with the non-eccentric impeller, which means that the impeller eccentricity leads to the increase of radial force pulsation.

#### 4.2. Balance Radial Force through Impeller Eccentricity

_{x}of an eccentric impeller is significantly reduced, the time-averaged value is 35% lower than that of a non-eccentric impeller, but the radial force y component F

_{y}changes little, the radial force F

_{r}decreases, and the time-averaged value decreases by 6% at a low flow rate, which is 0.6 Q

_{d}. When the flow rate is 1.0 Q

_{d}, the reduction effect of the radial force of the eccentric impeller is more obvious, in which the time-averaged value of the x component F

_{x}is 27.5% lower than that of the non-eccentric impeller. The peak value of the radial force y component F

_{y}wave is similar, but the trough value is significantly reduced, with the time-averaged value reduced by 14.7% and the time-averaged value of the radial force F

_{r}reduced by 17%. When the flow rate is 1.4 Q

_{d}, the x component F

_{x}decreases significantly, and the mean value is 11.4% lower than that of the non-eccentric impeller. The peak value of the radial force y component F

_{y}increases significantly, the mean value of F

_{y}decreases by 15.8%, and the mean value of the radial force F

_{r}decreases by 12.5%.

## 5. Conclusions

- (1)
- Compared with the case without eccentricity, when the eccentricity coordinates of the impeller are (1,0) and (0,−1), the radial force on the impeller is reduced by 10.8% and 8.1%, respectively, which means the offset of the impeller center to the x-positive direction and y-negative direction can effectively reduce the radial force.
- (2)
- The hydraulically induced radial force of the impeller fluctuates periodically with the impeller rotation. The radial force varies with the impeller rotation, the curve being a distorted circle deviating from the center, and the radial force increases when the center of the impeller is close to the volute tongue.
- (3)
- The mean time of radial force on the impeller decreases after eccentricity (2,−2) under different conditions. It decreases by 17% under designed conditions 1.0 Q
_{d}, 12.5% under large flow conditions 1.4 Q_{d}, and 6% under small flow conditions 0.6 Q_{d}, which means the way is feasible.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Hirschberger, M.; Kuhlmann, J.; Benra, F.K. Designing high-power sewage water pumps. World Pumps
**2009**, 2009, 20–25. [Google Scholar] [CrossRef] - Nishi, Y.; Fujiwara, R.; Fukutomi, J. Design method for single-blade centrifugal pump impeller. J. Fluid Sci. Technol.
**2009**, 4, 786–800. [Google Scholar] [CrossRef] [Green Version] - Aoki, M. Instantaneous interblade pressure distributions and fluctuating radial thrust in a single-blade centrifugal pump. Bull. JSME
**1984**, 27, 2413–2420. [Google Scholar] [CrossRef] - Nishi, Y.; Fukutomi, J. Effect of Blade Outlet Angle on Unsteady Hydrodynamic Force of Closed-Type Centrifugal Pump with Single Blade. Int. J. Rotating Mach.
**2014**, 2014, 1–16. [Google Scholar] [CrossRef] [Green Version] - Meng, D.; Jiang, T.; Deng, H.; Hou, G. Numerical Simulation Research on Radial Force of Centrifugal Pump with Guide Vanes. Shock. Vib.
**2021**, 2021, 6638123. [Google Scholar] [CrossRef] - Al-Obaidi, A.R. Influence of guide vanes on the flow fields and performance of axial pump under unsteady flow conditions: Numerical study. J. Mech. Eng. Sci.
**2020**, 14, 6570–6593. [Google Scholar] [CrossRef] - Cui, B.; Li, J.; Zhang, C.; Zhang, Y. Analysis of Radial Force and Vibration Energy in a Centrifugal Pump. Math. Probl. Eng.
**2020**, 2020, 6080942. [Google Scholar] [CrossRef] - Cui, B.; Li, X.; Rao, K.; Jia, X.; Nie, X. Analysis of unsteady radial forces of multistage centrifugal pump with double volute. Eng. Comput.
**2018**, 35, 1500–1511. [Google Scholar] [CrossRef] - Jiang, W.; Li, G.; Liu, P.F.; Fu, L. Numerical investigation of influence of the clocking effect on the unsteady pressure fluctuations and radial forces in the centrifugal pump with vaned diffuser. Int. Commun. Heat Mass Transfer.
**2016**, 71, 164–171. [Google Scholar] [CrossRef] - Cao, W.D.; Yao, L.J.; Liu, B.; Zhang, Y.N. The influence of impeller eccentricity on centrifugal pump. Adv. Mech. Eng.
**2017**, 9, 1687814017722496. [Google Scholar] - Tan, L.W.; Yang, Y.F.; Shi, W.D.; Chen, C.; Xie, Z.S. Influence of Blade Wrap Angle on the Hydrodynamic Radial Force of Single Blade Centrifugal Pump. Appl. Sci.
**2021**, 11, 9052. [Google Scholar] [CrossRef] - Chen, J.F.; Shi, W.D.; Zhang, D.S. Influence of blade inlet angle on the performance of a single blade centrifugal pump. Eng. Appl. Comput. Fluid Mech.
**2021**, 15, 462–475. [Google Scholar] [CrossRef] - Al-Obaidi, A.R. Analysis of the Effect of Various Impeller Blade Angles on Characteristic of the Axial Pump with Pressure Fluctuations Based on Time- and Frequency-Domain Investigations. Iran. J. Sci. Technol. Trans. Mech. Eng.
**2021**, 45, 441–459. [Google Scholar] [CrossRef] - Tan, L.; Shi, W.; Zhang, D.; Wang, C.; Zhou, L.; Mahmoud, E. Numerical and experimental investigations on the hydrodynamic radial force of single-channel pumps. J. Mech. Sci. Technol.
**2018**, 32, 4571–4581. [Google Scholar] [CrossRef] - Zhou, R.; Yang, J.; Liu, H.L.; Dong, L. Effect of Volute Geometry on Radial Force Characteristics of Centrifugal Pump during Startup. J. Appl. Fluid Mech.
**2022**, 15, 25–36. [Google Scholar] - Yuan, Y.; Yuan, S.Q.; Tang, L.D. Numerical Investigation on the Mechanism of Double-Volute Balancing Radial Hydraulic Force on the Centrifugal Pump. Processes
**2019**, 7, 689. [Google Scholar] [CrossRef] [Green Version] - Hao, Y.; Tan, L. Symmetrical and unsymmetrical tip clearances on cavitation performance and radial force of a mixed flow pump as turbine at pump mode. Renew. Energy
**2018**, 127, 368–376. [Google Scholar] [CrossRef] - Jia, X.; Yuan, S.; Zhu, Z.; Cui, B. Numerical study on instantaneous radial force of a centrifugal pump for different working conditions. Eng. Comput.
**2020**, 37, 458–480. [Google Scholar] [CrossRef] - Al-Obaidi, A.R. Investigation of the influence of various numbers of impeller blades on internal flow field analysis and the pressure pulsation of an axial pump based on transient flow behaviour. Heat Transfer.
**2020**, 49, 2000–2024. [Google Scholar] [CrossRef] - Xiaoqing, C.; Ri, Z.; Yongtao, H.; Dan-Qing, Y. Optimization Design of Deep—Well Centrifugal Pump based on CFX Orthogonal Test. Fluid Mach.
**2015**, 43, 22–25, (In Chinese with English abstract). [Google Scholar] - Lang, T.; Shi, W.D.; Chen, K.Q.; Li, W.; Cheng, C. Research on the Flow Field and Abrasion Characteristics in Sewage Pump with Pre-mixing Device. Fluid Machinery
**2015**, 43, 29–33, (In Chinese with English abstract). [Google Scholar] - ANSYS CFX Tutorials 14.5; ANSYS, Inc.: Canonsburg, PA, USA, 2012.
- Benenra, F.K.; Dohmen, H.J.; Schneider, O. Calculation of hydrodynamic forces and flow-induced vibrations of centrifugal sewage water pumps. Fluids Eng. Div. Summer Meet.
**2003**, 36975, 603–608. [Google Scholar] - González, J.; Parrondo, J.; Santolaria, C.; Blanco, E. Steady and unsteady radial forces for a centrifugal pump with impeller to tongue gap variation. J. Fluids Eng.
**2006**, 128, 454–462. [Google Scholar] [CrossRef]

**Figure 1.**Model pump. (

**a**) Calculation domains. (

**b**) Cross-section of the pump model. 1. Inlet, 2. Impeller, 3. Chamber, 4. Volute, 5. Outlet.

**Figure 3.**Experiment setup. 1. Outlet valve, 2. Electromagnetic flowmeter, 3. Inlet valve, 4. Outlet pressure transducer, 5. Inlet pressure transducer, 6. Test pump.

**Figure 6.**Comparison of pressure distribution at design flowrate. (

**a**) Monitoring point V1. (

**b**) Monitoring point V2. (

**c**) Monitoring point V3. (

**d**) Monitoring point V4.

**Figure 8.**Pressure contours at different moments. (

**a**) When the impeller has no eccentricity. (

**b**) Model a.

**Figure 9.**Time–Domain Diagram of the Radial Force on the Impeller. (

**a**) Radial force component in the x-direction; (

**b**) Radial force component in the y-direction; (

**c**) Radial force.

**Figure 10.**The Radial Force on the Impeller at 1.0 Q

_{d}. (

**a**) non-eccentricity; (

**b**) impeller eccentricity (2,−2).

**Figure 11.**Pressure contours at different moments when impeller eccentricity is (2,−2) and flow rate is 1.0 Q

_{d}. (

**a**) 0°. (

**b**) 90°. (

**c**) 180°. (

**d**) 270°.

**Figure 12.**Comparison of Radial Forces Under Different Operating Conditions. (

**a**) 0.6 Q

_{d}. (

**b**) 1.0 Q

_{d}. (

**c**) 1.4 Q

_{d}.

**Figure 13.**Frequency domain diagram of radial force on impeller under different flow conditions at rated speed. (

**a**). F

_{x}. (

**b**). F

_{y}. (

**c**) F

_{r}.

Grid number | 618,866 | 1,162,332 | 1,457,264 | 2,727,422 | 2,899,675 |

Head (m) | 12.38 | 12.35 | 12.18 | 12.20 | 12.19 |

Model a | Model b | Model c | Model d | Model e | Non-Eccentricity | |
---|---|---|---|---|---|---|

F_{x} | −0.0799 | −0.0953 | −0.0920 | −0.0755 | −0.0823 | −0.1047 |

F_{y} | 0.1779 | 0.1720 | 0.1573 | 0.1631 | 0.1728 | 0.1702 |

F_{r} | 0.1963 | 0.1988 | 0.1846 | 0.1812 | 0.1929 | 0.2008 |

0.6 Q_{d} | Non-Eccentricity 0.6 Q _{d} | 1.0 Q_{d} | Non-Eccentricity 1.0 Q _{d} | 1.4 Q_{d} | Non-Eccentricity 1.4 Q _{d} | |
---|---|---|---|---|---|---|

F_{x} | −0.0801 | −0.1241 | −0.0759 | −0.1047 | −0.0738 | −0.0833 |

F_{y} | 0.1784 | 0.1662 | 0.1452 | 0.1702 | 0.1505 | 0.1788 |

F_{r} | 0.1961 | 0.2078 | 0.1664 | 0.2008 | 0.1747 | 0.1997 |

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**MDPI and ACS Style**

Wang, C.; Tan, L.; Shi, W.; Chen, C.; Francis, E.M.
Research on Influence of Rotation Center Eccentricity on Radial Force of Single-Blade Centrifugal Pump. *Water* **2022**, *14*, 2252.
https://doi.org/10.3390/w14142252

**AMA Style**

Wang C, Tan L, Shi W, Chen C, Francis EM.
Research on Influence of Rotation Center Eccentricity on Radial Force of Single-Blade Centrifugal Pump. *Water*. 2022; 14(14):2252.
https://doi.org/10.3390/w14142252

**Chicago/Turabian Style**

Wang, Chuanlong, Linwei Tan, Weidong Shi, Cheng Chen, and Egbo Munachi Francis.
2022. "Research on Influence of Rotation Center Eccentricity on Radial Force of Single-Blade Centrifugal Pump" *Water* 14, no. 14: 2252.
https://doi.org/10.3390/w14142252