# Analysis of Energy Characteristics and Internal Flow Field of “S” Shaped Airfoil Bidirectional Axial Flow Pump

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Computation Models, Grids and Computational Methods

#### 2.1. Numerical Calculation Models

#### 2.2. Meshing

#### 2.3. Control Equations, Boundary Conditions and Calculation Methods

^{−6}. In principle, the smaller the residual value, the better.

#### 2.4. Analytical Formulae for Numerical Calculation Results

_{net}calculation formula is [11,12,13]:

_{1}and P

_{2}are the average static pressure (Pa) at the inlet and outlet of the axial flow pump channel; ρ is the flow density (kg/m

^{3}); g is the acceleration of gravity (m/s

^{2}); s

_{1}and s

_{2}are the cross section areas of inlet and outlet of axial flow pump (m

^{2}); u

_{1}and u

_{2}are the flow velocity at each point of the inlet and outlet channel section of the axial flow pump (m/s); u

_{t}

_{1}and u

_{t}

_{2}are the normal components of flow velocity at each point of the inlet and outlet channel section of axial flow pump (m/s); Q is axial flow pump flow (m

^{3}/s); T is the rotating torque of impeller (N·m); ω is the impeller rotation angle speed (rad/s).

## 3. Test Device and Test Method

#### 3.1. Test Device

#### 3.2. Test Method

_{1}and P

_{2}are the static pressure (Pa) at the inlet and outlet of the flow field, z

_{1}and z

_{2}are the height (m) of the inlet and outlet of the flow field, u

_{1}and u

_{2}are the flow velocity (m/s) at the inlet and outlet of the flow field, ρ is the real-time water density of the test (kg/m

^{3}), g is the local gravity acceleration (m/s

^{2}), N is the shaft power (kw), M is the pump input torque (N·m), M′ is the pump mechanical loss torque (N·m), n is the pump test speed (r/min), η is the pump model efficiency (%), and Q is the pump flow (m

^{3}/s).

## 4. Numerical Calculation Results and Experimental Verification

#### 4.1. Experimental Verification of Numerical Calculation Energy Characteristics

#### 4.2. Numerical Calculation and Energy Characteristic Analysis

_{f}is the hydraulic loss ratio, h

_{i}is the inlet pipe hydraulic loss (m); h

_{g}is the guide vane body hydraulic loss (m); h

_{o}is the outlet pipe hydraulic loss (m); H is the pump head (m).

_{u}is the uniformity of axial flow velocity distribution in the characteristic section (%); v

_{ai}is the axial velocity of each calculation unit (m/s); n is the number of calculation units. v

_{a}is the axial flow velocity at impeller inlet.

#### 4.3. Analysis of Internal Flow Fields for Numerical Calculations

_{df}, 1.0Q

_{df}, 1.1Q

_{df}(Forward design working flow rate Q

_{df}= 368 L/s) is shown in Figure 10a, Figure 11a and Figure 12a, and the overall streamline of the bidirectional axial flow pump reverse taking 0.9Q

_{dr}, 1.0Q

_{dr}, 1.1Q

_{dr}(Reverse design working flow rate of Q

_{dr}= 316 L/s) is shown in Figure 10b, Figure 11b and Figure 12b. As shown in Figure 10, Figure 11 and Figure 12, forward operation of the inlet pipe for the straight pipe and reverse operation of the inlet pipe for the elbow, forward, and reverse operation of the inlet water flow state are better and the streamline is uniform.

_{d}, 1.0Q

_{d}, 1.1Q

_{d}are shown in Figure 13, Figure 14 and Figure 15.

_{d}, 1.0Q

_{d}, and 1.1Q

_{d}as shown in Figure 16, Figure 17 and Figure 18.

_{d}, 1.0Q

_{d}, and 1.1Q

_{d}is shown in Figure 19, Figure 20 and Figure 21. In this paper, the vortex discrimination criterion is Q-Criterion, which was proposed by Hunt et al. in 1988 [20,21].

## 5. Conclusions

- (1)
- The comparative analysis of the numerical calculation results and tests of the energy characteristics of the bidirectional axial flow pump shows that the predictions of the forward and reverse numerical calculations are relatively accurate, and the error is basically within 5%. Compared with the forward prediction, the accuracy of the reverse numerical calculation is slightly worse, and the numerical calculation results are credible.
- (2)
- The test results show that the bidirectional axial flow pump design working condition flow rate Q = 368 L/s, head H = 3.767 m, and efficiency η = 80.37% in forward operation and bidirectional axial flow pump design working condition flow rate Q = 316 L/s, head H = 3.658 m, efficiency η = 70.37% in reverse operation. The forward operation is about 15% larger than the reverse operation design working condition flow rate, the design head is about 3.70 m, and the design working efficiency is about 10% higher in the forward direction than in the reverse direction.
- (3)
- The numerical calculation results show that under the forward design condition (Q = 368 L/s), the proportion of hydraulic loss is 6.22%, and under the reverse design condition (Q = 316 L/s), the proportion of hydraulic loss is 11.81%, with a difference of about 6%. The uniformity of impeller inlet flow velocity is about 12% higher than that under the reverse operation. The main reason for the difference in hydraulic loss and flow velocity uniformity between forward and reverse operation is that during reverse operation, curved guide vanes are placed in front, which reduces the flow velocity uniformity at the inlet of the impeller, resulting in an increase in the bad flow pattern of the inlet water of the impeller, and because the outlet water has no circulation recovery structure such as guide vanes, the ability of converting kinetic energy into pressure energy of the outlet water is weakened, and the proportion of hydraulic loss is increased.
- (4)
- In the forward operation, the inlet water is straight pipe, and in the reverse operation, the inlet water is elbow. Under the forward and reverse operation, the inlet water flow pattern is relatively good. In the forward and reverse operation, with the increase of flow, the outlet water streamline, the total pressure distribution of outlet water, the uniformity of impeller inlet flow velocity, and the vortex in the impeller domain are improved. The internal flow fields, such as outlet streamline, total outlet pressure distribution, impeller inlet velocity uniformity, and impeller domain vortex, under forward operation are better than those under reverse operation, so the performance of forward operation is better than that of reverse operation.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Schematic diagram of forward and reverse operation of “S” shaped airfoil bidirectional axial flow pump. (Black indicates forward operation, Red indicates reverse operation).

**Figure 5.**Plan of high precision hydraulic machinery test bench. 1. Water inlet tank; 2. Tested pump; 3. Pressure outlet tank; 4. Bifurcated water tank; 5~6. Flow in situ calibration device; 7. Working condition regulating gate valve; 8. Pressure stabilizing rectifier cylinder; 9. Electromagnetic flowmeter; 10. Operation control gate valve; 11. Auxiliary pump unit.

**Figure 7.**Numerical calculation curve of energy characteristics: (

**a**) Forward bidirectional pump impeller; (

**b**) Reverse bidirectional pump impeller; (

**c**) Forward bidirectional pump; (

**d**) Reverse bidirectional pump.

**Table 1.**Parameters of design working conditions of “S” shaped airfoil bidirectional axial flow pump.

Parameters | Forward | Reverse |
---|---|---|

Blade angle | 0° | 0° |

Impeller diameter | (300–0.2) mm | (300–0.2) mm |

Rotating speeds | 1450 rpm | 1450 rpm |

Design flow | 368 L/s | 316 L/s |

Design head | 3.70 m | 3.70 m |

Design point ratio speed | 1187 | 1124 |

Serial Number | N | η (%) | Serial Number | N | η (%) |
---|---|---|---|---|---|

1 | 1,607,288 | 76.4150 | 4 | 3,402,093 | 77.0300 |

2 | 2,143,050 | 76.4745 | 5 | 4,018,220 | 77.0360 |

3 | 2,678,813 | 77.0405 | 6 | / | / |

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**MDPI and ACS Style**

Xie, C.; Feng, A.; Fu, T.; Zhang, C.; Zhang, T.; Yang, F.
Analysis of Energy Characteristics and Internal Flow Field of “S” Shaped Airfoil Bidirectional Axial Flow Pump. *Water* **2022**, *14*, 2839.
https://doi.org/10.3390/w14182839

**AMA Style**

Xie C, Feng A, Fu T, Zhang C, Zhang T, Yang F.
Analysis of Energy Characteristics and Internal Flow Field of “S” Shaped Airfoil Bidirectional Axial Flow Pump. *Water*. 2022; 14(18):2839.
https://doi.org/10.3390/w14182839

**Chicago/Turabian Style**

Xie, Chuanliu, Andong Feng, Tenglong Fu, Cheng Zhang, Tao Zhang, and Fan Yang.
2022. "Analysis of Energy Characteristics and Internal Flow Field of “S” Shaped Airfoil Bidirectional Axial Flow Pump" *Water* 14, no. 18: 2839.
https://doi.org/10.3390/w14182839