# Internal Flow Phenomena of Two-Way Contra-Rotating Axial-Flow Pump-Turbine with Various Numbers of Blades in Pump Mode

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Pump Geometry

_{1}and β

_{2}shown in Figure 2 are not equal. The front and rear impellers for the same hydraulic model mirror relationship, which can ensure the consistent performance of the forward and reverse working conditions, that is, to meet the requirements of a two-way operation. Table 1 shows the design parameters of the test pump, which uses a two-way design that eliminates the need to distinguish between flood and ebb modes during the simulation process for the impellers. The hydraulic model design parameters in Table 1 were designed using the streamline method and adopted an asymmetric design approach. Among them, the shroud and hub of the pump-turbine are both designed with cylindrical surfaces.

#### 2.2. Experimental Methods

#### 2.3. Numeral Methods

#### 2.3.1. Hydraulic Model Components

#### 2.3.2. Meshing

^{3}/h) were obtained (shown in Figure 6). The computational machine we used has 2 intel Gold 6238R CPUs and 128 GB of RAM. When the 56 cores of the CPU are invoked, it takes about 8 h to complete a numerical simulation.

#### 2.3.3. Calculation Method and Boundary Conditions

^{3}. The liquid phase is 25 ℃ water with a dynamic viscosity of 8.899 × 10

^{−4}kg/(m·s). ${\sigma}_{k}$ and ${\sigma}_{\epsilon}$ are the model coefficients. ${C}_{\epsilon 1}$ and ${C}_{\epsilon 2}$ are empirical constants. ${P}_{k}$ and ${P}_{\epsilon}$ are the production terms. ${\epsilon}_{0}$ is the ambient turbulence value that offsets turbulence attenuation. ${f}_{2}$ is the damping function. ${T}_{0}$ is the unit time scale.

^{2}/s).

^{−5}.

#### 2.3.4. Vorticity Equation

^{6}near the blade tip, and the viscous diffusion term $\nu {\nabla}^{2}\stackrel{\rightharpoonup}{\omega}$ is relatively small to be typically disregarded. Thereafter, the Z-axis component of the vorticity equation is as follows:

## 3. Results and Discussion

#### 3.1. Performance Test

#### 3.2. Research on the Various Numbers of Blades under Pump Mode

^{3}/s. At low flow rates and rated flow rates (Q ≤ 108.5 m

^{3}/s), the head of Case2 is greater than that of Case. However, at high flow rates (Q > 108.5 m

^{3}/s), the head of Case2 is smaller than that of Case1. This means that when the blade count of a stage impeller of a contra-rotating axial-flow pump-turbine is increased, its Q–H curve becomes steeper. In all calculation conditions, the head of Case2b is greater than that of Case2a. This means that increasing the blade count of the rear impeller improves the head more than increasing the blade count of the front impeller.

_{f}represents the power of the front impeller, and H

_{r}represents the power of the rear impeller. In Case2a with a higher blade count for the front impeller, Q–H

_{f}curve becomes steeper. The curves of Case1 and Case2b are almost identical until a flow rate of 86.66 m

^{3}/s, where the H

_{f}of Case2b slightly increases. At low flow rates and rated flow rates (Q ≤ 108.5 m

^{3}/s), the head of Case2 is greater than that of Case1, especially for Case2b with 4 blades, which shows a significant improvement in the head.

_{f}represents the power of the primary impeller, and P

_{r}represents the power of the secondary impeller. The Q–P curves of each stage impeller of the different cases under the pump mode have the same trend as the Q–H curves. Since the same motor is used for both stage impellers, it is important to focus on the power of the rear impeller, P

_{r}. At low flow rates and rated flow rates (Q ≤ 108.5 m

^{3}/s), increasing the blade count, especially for the rear impeller, leads to a significant increase in P

_{r}.

_{f}/η

_{r}curves of each stage impeller of the different cases under the pump operating conditions. Here, η

_{f}represents the efficiency of the front impeller, and η

_{f}represents the efficiency of the rear impeller. Case2a shows a significant change in η

_{f}, especially at high flow rates where η

_{f}drops significantly. The Q–η

_{f}curves of Case1 and Case2b almost overlap in all conditions, indicating that the power output of the front impeller is the same with the same blade count in the front impeller. At low flow rates, the Q–η

_{r}curve of Case2b is significantly improved. This indicates that increasing the blade count of the rear impeller can improve its efficiency at low flow rates. At high flow rates, all cases of Case2 show a significant decrease in efficiency, especially Case2b.

^{3}/s), the efficiency of Case2 decreases significantly, and the high-efficiency point of Case2 shifts toward low flow rates. In addition, from Case1 to Case2b to Case2a, the high-efficiency region of the unit under the pump mode gradually narrows. It is precisely because of the increase in the number of blades that the flow-section area decreases, which will cause greater flow obstruction at high flow rates. In Case2, a higher efficiency can be achieved by increasing the blade count of the front impeller. At low flow rates (Q < 108.5 m

^{3}/s), increasing the blade count of the rear impeller can achieve higher efficiency, while increasing the blade count of the front impeller has a negative impact on the efficiency of the unit.

#### 3.3. Streamline Analysis

^{3}/s) for the different cases. In the front impeller, it is difficult to observe significant differences in the streamlines. The red dashed box in Figure 15 represents the area near the LE (leading edge) of the secondary impeller, which is enlarged and shown in Figure 16 for better observation of the impact position of the fluid on the LE of the rear impeller. A red dashed line is added as a reference for the impact position. Compared with Case1, the impact position of Case2a shifts downstream, which is the main reason for the increase in the P

_{r}of Case2a. When the two-stage impellers maintain the same speed, the impact position of the fluid on the rear impeller is not ideal. The impact position of Case2b shifts slightly upstream, which is actually beneficial for the impeller to work. However, the increase in blade count leads to an increase in power, so although the power of the rear impeller of Case2b is higher, its efficiency is not much different from that of Case1.

_{f}of the front impeller of Case2a is the highest at this condition. In Figure 18, the 15 m/s iso-surface area of Case2b is the largest. Comparing this with Figure 16, as the position of the fluid impact on the LE shifts downstream, the area of the 15 m/s iso-surface gradually decreases.

#### 3.4. Vorticity Analysis

## 4. Conclusions

- An increase in the blade count of the impeller stage of a mixed-flow pump-turbine will result in a steeper Q–H curve. Increasing the blade count of the impeller stage has a greater effect on improving the head than increasing the blade count of the previous stage.
- With the increase in the number of impeller blades of a certain stage in the contra-rotating axial-flow pump, the high-efficiency point of the unit under pump mode will shift toward lower flow rates, and the high-efficiency region will also become narrower.
- Varying the number of blades will have an impact on the location of the LE water impact on the rear impeller, which in turn affects the contours of vorticity of the rear impeller near the LE.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 20.**Contours of vorticity and each term on Span 1 of the front impeller. (

**a**) The distribution of the vorticity on Span 1. (

**b**) The contours of the vortex stretching term on Span 1. (

**c**) The contours of the vortex dilatation term on Span 1.

**Figure 21.**Contours of vorticity and each term on Span 2 of the front impeller. (

**a**) The distribution of the vorticity on Span 2. (

**b**) The contours of the vortex stretching term on Span 2. (

**c**) The contours of the vortex dilatation term on Span 2.

**Figure 22.**Contours of vorticity on Span 1 of the front impeller of different cases: (

**a**) Case1; (

**b**) Case2a; (

**c**) Case2b.

**Figure 23.**Contours of vorticity on Span 2 of the front impeller of different cases: (

**a**) Case1; (

**b**) Case2a; (

**c**) Case2b.

**Figure 24.**Contours of vorticity on Span 1 of the rear impeller of different cases: (

**a**) Case1; (

**b**) Case2a; (

**c**) Case2b.

**Figure 25.**Contours of vorticity on Span 2 of the rear impeller of different cases: (

**a**) Case1; (

**b**) Case2a; (

**c**) Case2b.

Design Parameters | Design Value |
---|---|

Flow Q (m^{3}/h) | 108 |

Head H (m) | 1.25 |

Rotating speed n (r/min) | 1450 |

Blade numbers | 3 |

Impeller hub diameter (mm) | 48 |

Impeller shroud diameter (mm) | 145 |

Axial length of impeller blade outer flow line (mm) | 36 |

Axial length of impeller blade inner flow line (mm) | 42 |

Impeller blade thickness (mm) | 3 |

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**MDPI and ACS Style**

An, C.; Chen, Y.; Fu, Q.; Zhu, R.
Internal Flow Phenomena of Two-Way Contra-Rotating Axial-Flow Pump-Turbine with Various Numbers of Blades in Pump Mode. *Water* **2023**, *15*, 3236.
https://doi.org/10.3390/w15183236

**AMA Style**

An C, Chen Y, Fu Q, Zhu R.
Internal Flow Phenomena of Two-Way Contra-Rotating Axial-Flow Pump-Turbine with Various Numbers of Blades in Pump Mode. *Water*. 2023; 15(18):3236.
https://doi.org/10.3390/w15183236

**Chicago/Turabian Style**

An, Ce, Yiming Chen, Qiang Fu, and Rongsheng Zhu.
2023. "Internal Flow Phenomena of Two-Way Contra-Rotating Axial-Flow Pump-Turbine with Various Numbers of Blades in Pump Mode" *Water* 15, no. 18: 3236.
https://doi.org/10.3390/w15183236