# Influence of Cross-Sectional Flow Area of Annular Volute Casing on Transient Characteristics of Ceramic Centrifugal Pump

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## Abstract

The annular volute is typically used in a slurry pump to reduce the collisions between solid particles and the volute tongue and to achieve a better resistance to blocking. However, only limited studies regarding annular volutes are available, and there is no systematic design method for annular volutes. In this study, the influence of volute casing cross-sectional flow area on the hydraulic loss, pressure pulsations, and radial force under varying working conditions in a centrifugal ceramic pump are discussed in detail. Experimental tests were conducted to validate the numerical results. The results indicated that, when the volute casing flow area increases, the hydraulic performance decreases marginally under the rated working conditions, but increases at the off-design points, specifically under large flow condition. However, the volute casing with a larger flow area has a wider high-efficiency region. In addition, the increase in the volute casing flow area will decrease the pressure pulsations in the volute, regardless of the working condition, and decrease the radial force on the shaft, therefore, providing an improved pump operational stability. It is anticipated that this study will be of benefit during the design of annular volutes.

## Keywords

Annular volute Centrifugal pump Cross section Transient characteristics Pressure pulsation Radial force## 1 Introduction

As far as the authors are aware, only limited studies have been reported in open literature considering centrifugal pumps with annular volutes, although numerous studies have reported the transient characteristics of conventional spiral volute casings. In this study, the influence of the cross-sectional area of the annular volute of a ceramic centrifugal pump on the transient characteristics and the pump hydraulic performance are investigated. Two volute casings were custom-built to experimentally validate the numerical results. It is anticipated that this study will be of benefit in the design of ceramic slurry pumps.

## 2 Pump Geometry

*Q*of 100 m

^{3}/h and a rotational speed

*n*of 2900 r/min. The impeller is semi-open, namely without a front shroud, and has four backward-curved blades and 12 backward-curved back blades outside the back shroud. As opposed to the spiral volute casing used in conventional centrifugal pumps, the annular volute casing has a fixed cross-sectional area and a greater gap between the tongue and impeller exit. The cross-sectional area of the annular volute casing of the original case was designed to be identical to cross section VIII of the spiral volute casing, as shown in Figure 1, based on the velocity coefficient method [26]. The primary geometric dimensions of the ceramic pump are presented in Table 1.

Primary geometric dimensions

Parameter | Value |
---|---|

Suction branch diameter | 0.1 |

Discharge branch diameter | 0.08 |

Impeller eye diameter | 0.09 |

Impeller exit diameter | 0.21 |

Leading edge width | 0.041 |

Trailing edge width | 0.028 |

Leading edge blade angle | 20 |

Trailing edge blade angle | 26 |

Blade wrap angle | 120 |

Back blade width | 0.005 |

Volute chamber width | 0.063 |

Diameter to volute tongue | Varying |

## 3 Numerical Method

### 3.1 Calculation Domain and Grid Generation

Grid independence analysis

Grid number | 2071856 | 3115696 | 4021768 | 5013874 |
---|---|---|---|---|

Head | 47.38 | 48.02 | 48.43 | 48.61 |

Efficiency | 59.26 | 59.87 | 60.22 | 60.49 |

### 3.2 Pre-processing

The transient flow through the modeled pump was simulated using the commercial software ANSYS CFX 14.5, which utilized the finite volume method to solve the unsteady three-dimensional Navier–Stokes equations. Because of the fast convergence and the accurate hydraulic performance achieved compared to other turbulence models, the standard *k*-*ε* model was selected to complete the turbulence equation, with the standard wall function for the treatment of the flow in the boundary layer based on the refined grids [27]. All the solid walls in the computational domain were set as no-slip walls with a roughness of 0.2 mm. The surfaces of the impeller and back blades were set in a rotating reference frame with a rotational speed identical to the nominal operating speed of the pump [28, 29]. All the other surfaces were set in a stationary frame. The transient rotor–stator model was attached to the interfaces between the rotating and stationary regions. An axial velocity, based on the variation of the flow rate, was provided at the inlet boundary located at the suction branch. In addition, the outlet boundary was set as an opening with a specified static pressure in the case of the upstream influence of backflow on the primary flow domain. A high-resolution technique was used for the discretization of the advection scheme and turbulence terms. The second-order backward Euler method was applied for the transient scheme. The convergence criterion was set as 1 × 10^{−5} for the scaled residuals, with at least 20 iterations per time step. The time step was set as 0.000172414 s, as this provided a blade rotation of 3° between iterations, which means an impeller rotational period covers 120 time steps. Ten impeller revolutions were required when the flow reached a clear periodic regime. The data of one additional impeller revolution was then extracted to analyze the transient flow characteristics for each case. The data include the maximum, minimum, time-average, and standard deviation of the selected flow variables, including static pressure, total pressure, relative velocity, and absolute velocity.

## 4 Validation of CFD Results

*Q*-

*H*and

*Q*-

*η*curves, showing a good quantitative agreement with the relative errors in heads smaller than 1.5%, and efficiency smaller than 3%, under the rated working condition. However, the difference between the simulation the test results increases when the flow rate offsets away from the rated working condition. Specifically, at a flow rate of 30 m

^{3}/h, the difference in the head and efficiency were 4.8% and 8.2%, respectively. This is, in all probability, because of the limitation of the turbulence model in dealing with the significant vortex and backflow. In addition, the head curve of the case with the greater cross-sectional area exhibits a flat and rightward decreasing tendency overall, and the head curve of the case with the smaller cross-sectional area in the low flow rate region decreases slowly. It can be reasonably surmised that the small volute casing cross-sectional area could cause a hump in the pump head curve, which will result in a surge in the pipe system. At the rated working condition, the hydraulic performance decreases marginally with increasing volute casing flow area. While the pump operation offsets away from the rated working condition, the case with a greater volute casing flow area exhibits improved hydraulic performance. In addition, the high-efficiency region widens with increasing volute casing flow area. In summary, from the comparisons it can be concluded that the numerical simulation can be considered adequate to investigate the unsteady flow behavior in the pump.

## 5 Results and Discussion

### 5.1 Hydraulic Loss in Volute Casing

### 5.2 Analysis of Flow Rate Distribution at Cross-Sections

^{3}/h, 100 m

^{3}/h, and 170 m

^{3}/h. It should be noted that cross section I (Figure 1) is located at 3° backward of the volute tongue. The other seven cross-sections have an equivalent deviation angle of 60°. Cross section 9 represents the throat cross section and cross section 11 the outlet of the pump. It can be seen that the flow rate increases from cross section I to cross section VIII regardless of the flow rate variation for all three cases. In addition, the increase in flow rate from cross section I to the throat cross section increases with increasing flow rate at the pump inlet. The flow rate at cross section I comprises two parts that can be observed in Figure 7. One part is the flow discharged from the impeller, and the other part is the flow from cross section VIII that flows back into the volute casing through the gap between the volute tongue and impeller periphery. When the pump operates at the low flow condition with a flow rate of 30 m

^{3}/h, the bulk of the fluid circulates in the volute casing, as can be seen in Figure 7(a). Backflow occurs in the diffuser because of the significant pressure gradient and circulating flow. When the pump operates under the large flow condition with a flow rate of 170 m

^{3}/h, the flow rate through the cross section I decreases significantly, as can be seen in Figure 6(c). The backflow occurs at positions backward from cross section I. In addition, it can be seen that the flow rate through cross section VIII is smaller than the pump flow rate. Therefore, a part of the fluid discharged from the impeller passage close to the volute tongue flows toward the throat cross section, resulting in the backflow, which can be seen in Figure 7(c). By comparing the flow rates of the three cases at the volute cross-sections, it can be observed that the increase in the volute flow area can increase the volute flow capacity, which accordingly shifts the maximum efficiency point offsets toward the large flow condition.

### 5.3 Pressure and Velocity Distribution in Volute Casing

^{3}/h for the three cases. By comparing Figure 10(a) and Figure 8(a), it can be observed that the velocity from cross section I to cross section IV increases even with a decrease in the pump flow rate. The reason for this can be seen in Figure 6. Although the flow rate of pump decreases, the flow at cross section VIII remains approximately constant. Only the flow rate at the throat cross section decreases significantly, and the bulk of the fluid circulates in the volute through cross section I, as can be seen in Figure 7, resulting in the velocity in the volute increasing even though the pump flow rate decreases. Because the bulk of the fluid circulates in the volute, the static pressure gradient from cross section VIII to cross section I decreases with decreasing pump flow rate. By comparing the three cases, it can be observed that the static pressure remains increasing and the circumferential distribution of static pressure at the volute casing inlet becomes more uniform with the increase in the volute casing flow area, similar to the nominal flow rate condition. In addition, the total pressure increases as a whole with increasing casing flow area. As shown in Figure 11, there is only one vortex at cross section I and the area of the vortex decreases with increasing volute casing flow area. Two asymmetric vortices can be observed at the throat cross section for all the three cases because the flow rate offsets at a distance from the designed point. The area of the left vortex decreases with increasing volute casing flow area. Under the effect of the nonuniform circumferential static pressure distribution at the volute casing inlet and the vortex structure at the cross sections, the volute with a greater flow area has a better hydraulic performance under the small flow condition.

^{3}/h for the three cases. It can be seen that the velocity distribution at the volute inlet in the flow direction exhibits a significant gradient, especially from cross section VIII to cross section I. The reason, as can be seen in Figure 6, is that the bulk of the fluid enters the diffuser through the throat cross section instead of circulating in the volute because of the large pump flow rate. The greater volute flow area results in a greater fluid capacity, which will decrease the velocity in the volute, especially the velocity at cross section VIII. The lower velocity at cross section VIII results in a smaller velocity gradient from cross section VIII to cross section I, which results in a smaller static pressure gradient. As discussed above, the total pressure at cross section I decreases with increasing volute casing flow area. The reason has been analyzed before. The high-energy flow discharged from the impeller passage close to the volute tongue flows toward the throat cross section to supplement the flow rate, resulting in a greater total pressure in cross section I. Because of the lack of fluid flow into the volute casing, the total pressure from cross section II to cross section V decreases with increasing volute casing flow area. However, the total pressure decreases more sharply from cross section VII to the throat cross section because of the greater velocity gradient for the volute with the smaller flow area. As can be seen in Figure 13, the vortex structure at the cross-sections are approximately identical. Therefore, the backflow at cross section I and the significant velocity gradient from cross section VIII to the throat cross section are the primary reasons for the poorer hydraulic performance of the volute with the smaller flow area.

### 5.4 Pressure Pulsations in Annular Volute

*C*

_{p}is defined as:

*u*

_{2}is the circumferential component of the absolute velocity at the impeller periphery.

*t*

_{0}represents the starting time for one impeller period of the transient simulation, and

*N*is the sample number during the last revolution period.

### 5.5 Radial Force

## 6 Conclusions

- (1)
When the volute casing flow area increased, the hydraulic performance decreased marginally at the rated working condition but increased at off-design points, specifically under the large flow condition. However, the volute casing with a larger flow area had a wider high-efficiency region.

- (2)
The nonuniform circumferential static pressure distribution at the volute casing inlet and the vortex structure at the cross-sections were the primary reasons for the hydraulic loss in the volute under the rated and small flow conditions. However, for the large flow condition, the backflow at cross section I and the large velocity gradient from cross section VIII to the throat cross section were the primary reasons.

- (3)
The greatest pressure pulsation occurred approximately 30° backward of the volute tongue. An increase in the volute flow area decreased the pressure pulsations in the volute regardless of the working condition, and decreased the radial force on the shaft, which resulted in an improved operational stability of pump.

It is anticipated that this study would be of benefit during the design of annular volutes. The annular volute cross-sectional area should be appropriately greater than cross section VIII of the spiral volute casing to achieve an improved hydraulic performance under large flow condition and an improved pump operational stability. However, it should be noted that a greater annular volute cross-sectional area will require a larger pump, which will increase material costs and make transportation more logistically difficult. Therefore, the cross-sectional area of the annular volute should be comprehensively considered during the design.

## Notes

### Authors’ Contributions

YT was in charge of the whole trial; YT wrote the manuscript; SY, JL, and FZ assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.

### Authors’ Information

Yi Tao, born in 1988, is currently a lecturer at *Wuxi Vocational Institute of Arts and Technology, China.* He received his PhD degree from *National Research Center of Pumps and System Engineering and Technology, Jiangsu University, China*. His research interests include solid–liquid two-phase flow and design of slurry pumps.

Shouqi Yuan, born in 1963, is currently a professor and a PhD candidate supervisor at *National Research Center of Pumps and System Engineering and Technology, Jiangsu University, China*. He has received 16 prizes for science and technology advancement at province or ministry level. He has published 3 books and more than 240 papers. His research interests include the theory, design and CFD of pumps and fluid machinery.

Jianrui Liu, born in 1952, is currently a professor and a PhD candidate supervisor at *National Research Center of Pumps and System Engineering and Technology, Jiangsu University, China*. His research interests include fluid machinery engineering

Fan Zhang, born in 1987, is currently a PhD at *National Research Center of Pumps and System Engineering and Technology, Jiangsu University, China*. His research interests include flow characteristics in fluid machinery.

### Competing Interests

The authors declare no competing financial interests.

### Funding

Supported by National Natural Science Foundation of China (Grant No. 51779107), Jiangsu Provincial Natural Science Foundation of China (Grant No. BK20170548), Postdoctoral Science Foundation of China (Grant No. 2017M611724), and Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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