# Experimental Investigation on Transient Pressure Characteristics in a Helico-Axial Multiphase Pump

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## Abstract

**:**

## 1. Introduction

## 2. Basic Conditions of Pumps and Test Rig

#### 2.1. Helico-Axial Pump Structure

#### 2.2. Water-Air Two-Phase Test Rig

#### 2.3. Performance Parameter Definition

_{in}, outlet pressure p

_{ou}

_{t}, rotation speed n, and shaft torque M as Equations (2)–(4).

_{g}and H

_{l}, which are defined as Equation (7) and Equation (8). The total pump head H could be calculated by the two parts as Equation (9).

_{g}can be transformed into Equation (10).

#### 2.4. Pressure Fluctuation Monitoring System

## 3. Energy Performances of the Helico-Axial Pump Under Single-Phase and Multiphase Conditions

#### 3.1. Single-Phase Performance

_{d}and design head H

_{d}, and the efficiency curve was normalized by best efficiency value.

_{d}. The pump head under design flow rate is 1.1 H

_{d}and the highest head is about 1.43 H

_{d}under 0.5 Q

_{d}. The head curve shows a slight hump shape under partial load. The reason could be the relatively larger radius of pump shell which could lead to disorder under partial load. The best efficiency point is under the design flow rate, which means that the design of the pump is appropriate for the target.

#### 3.2. Multiphase Performance

## 4. Transient Pressure Characteristics in the Helico-Axial Pump

#### 4.1. Spectral Analysis on the Single-Phase Conditions

_{d}, design flow rate Q

_{d}, and the overload condition 1.2 Q

_{d}were selected as the representative working conditions to investigate the spectral characteristics of the helico-axial pump. The spectral diagrams are shown as Figure 8 with the x axis nondimensionlized by impeller rotation frequency f

_{i}.

_{i}, which could be calculated as rotating revolution per minute. The dominant frequency values reflect that the main fluctuation in the impeller is caused by the regular rotation. The two points, P1 and P2, near impeller inlet have dominant frequency of 4 f

_{i}and 8 f

_{i}in most conditions and the three latter points, P3 to P5, mainly show a fluctuation of 8 f

_{i}and 16 f

_{i}. This phenomenon agrees with the structure of the impeller: four main blades at inlet and eight blades (main blades and splitter blades) at outlet. In conclusion, the blade passing frequency f

_{BPF}, calculated as the product of rotation frequency and blade number, is the main pressure pulsation frequency source, and the maximum fluctuation amplitude appears at f

_{BPF}and 2 f

_{BPF}under the different flow rate conditions.

_{BPF}and higher multiples of rotation frequency tend to be intensified. The high-frequency fluctuation under larger flow rates may be stimulated by the attack of the flow to the flow components.

_{nd}is calculated as follows:

_{d}is higher than the others. Under partial load of 0.8 Q

_{d}, the highest amplitude appears at the impeller inlet, which indicates that the inner-flow pattern is nonuniform with backflow and flow separation. For the design flow rate, the pressure fluctuations of the five points are relatively even: the highest value appears at the first two points, and after the flow enters the splitter-blade region, the fluctuation is restrained. The fluctuation distribution under 1.2 Q

_{d}has many more differences from the other two flow rates. The fluctuation amplitude keeps increasing from the inlet and maximizes at the point P3. P3 is set near the leading edge of the splitter blade, so the increase of P3 fluctuation amplitude indicates that there are some uneven flow structures or flow impacts at the inlet of the splitter blades. The reason for the phenomenon could be the sudden decreasing of passing area, which is caused by the increase of blade number.

#### 4.2. Spectral Analysis on the Multiphase Conditions

_{d}were chosen to further analyze the pressure fluctuation performance. In the seven selected GVF conditions, the GVF had a range of 6.7% to 38.4%, the GVF values are shown as Table 2, and the pressure fluctuation distributions are listed as Figure 10 and Figure 11. The curves are concluded with the position of monitoring points.

_{i}, especially at the multiples of the blade passing frequency f

_{BPF}and 2 f

_{BPF}. This phenomenon proves that the main fluctuation in these conditions is still caused by the blade passing. Interestingly, the fluctuations under every multiple of rotation frequency are strengthened while the single-phase condition mainly has the peaks under multiples of blade passing frequencies. The stimulation of these fluctuation peaks is the consequence of relative movement of the two phases, and the variation of gas phase form in each passage.

_{BPF}, which indicates consistency with the impeller blade number. The fifth point P5 has a dominant frequency of 2 f

_{BPF}and the amplitude values are smaller. This may be caused by the influence of the volute tongue on the point near impeller outlet. As the GVF increases, the low frequency noises become prominent, especially in P5. The phenomenon indicates that under higher GVF conditions, the influence of the impeller rotation is weakened, and irregular fluctuations make significant influence on the multiphase flow near the impeller passages outlet.

## 5. Correlation of Inner-Flow Pattern and Pressure Field

_{d}. It could be observed that in every working condition, the inner-flow region is mainly in a uniform condition with foam shape. The foam shape flow form is a uniformly mixed-flow pattern of liquid-gas flow, which consists of tiny bubbles and well-mixed two-phase condition. This indicates the good mixing performance of the helico-axial pump under liquid-gas flow, while there are differences among the conditions: as the GVF increases, the inner region becomes lighter, which is owed to the increase of bubble size and bubble number. Under the two lower GVF conditions, no separation could be observed in the whole flow region. A gas gathering region could be seen near the leading edge of the blade. Under higher GVF conditions, some big bubbles could be found near the upstream region, where the pressure is lower than the downstream region and the gas phase is not severely compressed. Additionally, the separation could be captured clearly in the 38.4% GVF condition in the downstream region. The increase of gas component and the larger pressure difference in the downstream region lead to the gathering of gas phase in low pressure region, which is the suction side of the blades. Due to the centrifugal force gradient, the hub region is also an accumulation area for gas. The gathering of gas to the hub and blade suction side form an annular flow pattern in the downstream region, which consists of a gas column near the hub and a liquid film in the shroud. The annular flow is a severe separated flow pattern of liquid and gas, which deteriorates the pump performances and blocks the passage.

_{g}+ Q

_{l}= Q

_{d}).

_{i}is the single-stage head of the corresponding stage and H is the total pump head.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

_{h}of test rig could be divided into two parts, the system uncertainty E

_{s}and random uncertainty E

_{r}. The system error could be calculated according to flowrate measurement error E

_{Ql}and E

_{Qg}, head measurement error E

_{H}, torque and speed measurement uncertainty E

_{M}and E

_{n}.

_{Ql}= 0.5%, while the float flowmeter has an uncertainty E

_{Q}

_{g}= 1.0%. The torque and speed measurement uncertainty E

_{M}= E

_{n}= 0.25%. E

_{H}consists of dynamic head measurement uncertainty E

_{d}and static head measurement uncertainty E

_{j}. In the present work, the inlet and outlet pipelines are in the same diameter, so the dynam ic head can be ignored as E

_{d}= 0. The E

_{j}can be calculated by pressure sensor uncertainty E

_{ps}and the pressure transmitter uncertainty E

_{pT}, where E

_{ps}= 0.25% and E

_{pT}= 0.1%. So E

_{H}can be calculated as follows:

_{s}could be calculated by the uncertainty values as follows:

_{r}as follows:

## Appendix B

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**Figure 1.**Structure of the three-stage helico-axial pump (

**a**) Three-dimensional structure of pump; (

**b**) Test pump model.

**Figure 4.**Adoption of pressure fluctuation sensors (

**a**) Reserved holes for the sensors; (

**b**) assembly of the sensors.

**Figure 7.**Hydraulic performances under different GVF conditions (

**a**) dimensionless head curves; (

**b**) efficiency curves.

**Figure 8.**Spectral analysis on the single-phase conditions under (

**a**) 0.8 Q

_{d}, partial load spectral domain graph; (

**b**) 1.0 Q

_{d}, design flowrate spectral domain graph; (

**c**) 1.2 Q

_{d}, overload spectral domain graph.

**Figure 12.**Photograph of the inner field under (

**a**) GVF = 10.3%; (

**b**) GVF = 18.5%; (

**c**) GVF = 25.9%; (

**d**) GVF = 38.4%.

**Figure 14.**Dimensionless pressure fields of multiphase conditions (Q

_{l}+ Q

_{g}= Q

_{d}) (

**a**) GVF = 10.3%; (

**b**) GVF = 18.5%; (

**c**) GVF = 25.9%; (

**d**) GVF = 38.4%.

Parameters | Symbol | Value |
---|---|---|

Design head | H_{d} | 45 m |

Design flow rate | Q_{d} | 70 m^{3}/h |

Rotation speed | n | 2950 rpm |

Axial length (Single-stage) | l | 125 mm |

Number of impeller main blade | Z_{i} | 4 |

Number of diffuser blade | Z_{d} | 11 |

GVF | Head (m) |
---|---|

6.7 | 43.8 |

10.3 | 45.7 |

14.3 | 44.2 |

18.5 | 44.4 |

25.9 | 33.4 |

33.3 | 28.2 |

38.4 | 24.5 |

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## Share and Cite

**MDPI and ACS Style**

Xu, Y.; Cao, S.; Sano, T.; Wakai, T.; Reclari, M.
Experimental Investigation on Transient Pressure Characteristics in a Helico-Axial Multiphase Pump. *Energies* **2019**, *12*, 461.
https://doi.org/10.3390/en12030461

**AMA Style**

Xu Y, Cao S, Sano T, Wakai T, Reclari M.
Experimental Investigation on Transient Pressure Characteristics in a Helico-Axial Multiphase Pump. *Energies*. 2019; 12(3):461.
https://doi.org/10.3390/en12030461

**Chicago/Turabian Style**

Xu, Yun, Shuliang Cao, Takeshi Sano, Tokiya Wakai, and Martino Reclari.
2019. "Experimental Investigation on Transient Pressure Characteristics in a Helico-Axial Multiphase Pump" *Energies* 12, no. 3: 461.
https://doi.org/10.3390/en12030461