# Experimental Investigations on the Inner Flow Behavior of Centrifugal Pumps under Inlet Air-Water Two-Phase Conditions

^{1}

^{2}

^{*}

## Abstract

**:**

_{i}) up to pump shut-off condition. Visualizations were also performed on the flow patterns of a whole impeller passage and the volute tongue area to physically understand pump performance degradation. The results showed that liquid flow modification does not follow head modification as described by affinity laws, which are only valid for homogeneous bubbly flow regimes. Three-dimensional effects were more pronounced when inlet void fraction increased up to 3%. Bubbly flow with low mean velocities were observed close to the volute tongue for all α

_{i}, and returned back to the impeller blade passages. The starting point of pump break down was related to a strong inward reverse flow that occurred in the vicinity of the shroud gap between the impeller and volute tongue area.

## 1. Introduction

## 2. Experimental Set-Up and Model Pump Parameter

_{i}defined by Equation (3) at the pump inlet was always kept constant and the proportional valve was adjusted to increase the pure water flow rate during each test procedure in order to have an overall performance curve for different values of α

_{i}. The open-type tank could be moved up and down to keep the pump inlet pressure constant to achieve the same inlet bubble diameter. The rotational speed of the pump was controlled by a frequency converter to maintain stability. Measurement uncertainties were evaluated as 1.2% error on the pump head, 2.4% on hydraulic efficiency, 0.1% on rotational speed, and 0.2% on α

_{i}.

_{d}was 25 m

^{3}/h, design head was 8.5 m, and the design rotational speed was 1450 r/min. Other corresponding main geometrical and flow parameters of the pump are shown in the last row of Table 1. Three-dimensional design impeller matching with a vaneless spiral volute was used to achieve a better pump performance. In order to improve the photographic accuracy, an unshroud impeller and a rectangular cross section volute passage were used together with the flat casing surface. The gap between the pump body and the blade tip was 0.5 mm. The outer surface of the inlet and outlet pipes was made into a square shape for observing the possible inner flow details. The experimental scene and pump model are shown in Figure 2.

## 3. Pump Performance Changes under Air-Water Two-Phase Flow

_{i}). Then, similar procedures were used to obtain the overall pump performance curves under different α

_{i}by increasing the air content. In order to evaluate the pump handling ability of air content, regardless of rotational speed, all performance parameters were dimensionless.

#### 3.1. Overall Pump Performance at Two Different Rotational Speeds

_{i}on pump performance were that both head and efficiency degraded for both of the two rotational speed. Low flow rate was more sensitive to air content. The degradation slope increased with the decreasing flow rate coefficient when α

_{i}increased. The pump performance degradation at 1000 r/min was worse compared to 1450 r/min, which means that the affinity laws for the pump performance under a higher void of gas-liquid two-phase flow was no longer valid. This result is quite well-known since rotational speed is an important factor that allows the pump to work better when handling two-phase flow.

_{th}are given in Figure 5 for both rotational speeds. Both images show the same theoretical head coefficient change for one-phase flow conditions (only water). However, global efficiency decreased for the lowest rotational speed because of a low Reynolds number (based on impeller outlet speed and radius) that may reach a limiting value of 10

^{5}for flow rates below 70% of nominal conditions. A unique curve was obtained for all inlet void fraction values up to 5% for 1450 r/min and 4% for 1000 r/min. Explanation of such an important result can be found in Si et al. [19,20]. These values also corresponded to severe pump head degradation that can be observed for a flow coefficient range value between φ = 0.055 and φ = 0.065.

#### 3.2. Chnages in Pump Performance Degradation

#### 3.2.1. Change in Water Flow Rate and Head Coefficient with Increased α_{i}

_{i}was less than 3% when it started to drop sharply. This can also be observed for the pump head coefficient in Figure 7.

_{tp}, defined as φ

_{tp}/φ

_{0}and shown in Figure 8, for the two different rotational speeds. Some slight modifications of the curve slope can be observed for different inlet void fractions depending on the initial flow rate conditions. Two distinct zones can be observed: the first one corresponds to α

_{i}between 0% and 4% for n = 1450 r/min and from 0% to 3% for n = 1000 r/min. The smaller the initial flow rate, the smaller the flow rate degradation for both rotational speeds. For higher values of the inlet void fraction (second zone), the slope is much important and a sharp decrease in the liquid flow rate can be observed. This decrease is less pronounced when the initial flow rate is big, which is consistent with the conclusion reached by several authors like Murakami et al. [2] and Minemura et al. [4]. A liquid flow degradation of 10% was obtained at α

_{i}= 3.5% for the lowest flow rate at 1000 r/min (Figure 8b), whereas this amount progressively reached 5% for the design flow coefficient at 1450 r/min (Figure 8a). The pump started to be quite unstable for a flow coefficient of 0.08 and around α

_{i}= 7% at 1450 r/min. When the rotational speed was lower, the same behavior could be found with a more limiting value of the maximum allowable inlet void fraction due to the reduced rotational speed.

#### 3.2.2. Changes in Theoretical Pump Degradation for Two Different Flow Rates

_{tp}. This parameter is very often used to characterize pump degradation level. It is defined as the actual two-phase head coefficient ψ

_{tp}divided by the head coefficient ψ

_{0}obtained from only pure water, namely ψ*

_{tp}= ψ

_{tp}/ψ

_{0}. It is represented in Figure 9a for both rotational speeds and for the flow coefficient value of φ = 0.06, already referred to in the previous section. Figure 9b gives the corresponding changes for a lower flow coefficient φ = 0.04. Each curve exhibits quite a sharp degradation at a high inlet void fraction depending on the rotational speed. In Figure 9a, one can observe two different slope modifications. The first one occurs between inlet void fractions from 2.5% to 3%. The second one corresponds to the sharp performance degradation, which leads to the pump shut-off conditions. This was related to the visualization patterns and is discussed in the last section of the paper.

_{tp}versus inlet void fraction (all assumptions and development can be found in [2]). C

_{i}is constant and equal to 0 for the present case. The value of k depends on the number of blades. Correlation proposed by Murakami leads to k = 2 and 3 for six blades:

_{tp}and head degradation ratio ψ*

_{tp}could also be used, assuming affinity laws hold true, which leads to Equation (6):

## 4. Physics of Flow Pattern Inside the Impeller and RSI Area

#### 4.1. Flow Visualization Results under Different Inlet Air Void Fraction

_{i}increases and the flow remains as a bubbly flow regime up to 3% inside the impeller passage. This has been already found by Shao et al. [14], but the amount of bubbles was more important for the present case. In the volute section after the tongue, a bubbly flow situation could be observed for all void fractions.

_{i}reaches a value of 1%, the flow pattern looks better for the lower flow rate with a lesser bubble amount. This corresponds to a smaller reduction in the flow coefficient ratio that was been experimentally observed in Figure 8b compared with Figure 8a. Up to 2% of α

_{i}, the head degradation ratio followed the suggested homogeneous model proposed by Murakami et al. [2]. The curve fit the model up to 4% for n = 1450 r/min (see Figure 9a) and 2% (see Figure 9b). This can be related to the flow pattern observed in Figure 10c and Figure 11c for both rotational speeds. When α

_{i}= 3%, the flow pattern looked almost the same, but with less accumulation when rotational speed was high. The head degradation ratio was the same for both flow coefficients, but did not follow the homogeneous flow model any more.

_{i}= 4%. When α

_{i}= 4.2%, the flow pattern suddenly changed, as shown in Figure 11f. A segregated pattern was detected near the volute tongue with a clear separation of gas accumulation near the impeller outlet section, covering the whole space between the impeller outlet throat and its outlet radius. Fewer bubbles remained close to the shroud suction side due to the leakage flow (due to the axial gap between the open impeller shroud and the casing) and a clear transparent liquid zone was detected inside the impeller passage with few isolated bubbles. This zone was blocked by the air accumulation. It was experimentally observed that, for increasing values of α

_{i}, and after a few seconds of operation, the pump could no longer provide sufficient head and shut down.

_{i}. The flow pattern was similar for α

_{i}= 3.5%, as seen in Figure 10f, when compared with the pattern for α

_{i}= 4.2% and the higher flow rate. This flow pattern looked different compared to what is usually observed. For the present case, strong blockage to liquid flow was not located close to the first 20% of the impeller passage (as it is generally), but close to the end part of it due to the RSI effect. For better understand this effect, it has to be relate to the two previously described different degradation slopes that were detected. The first slope corresponded to a slight slope modification that occurred just before α

_{i}= 3%, which corresponded to a local blockage effect at the impeller inlet section, as already observed by Murakami and Minemura [1]. The second slope modification, which was quite larger, was located at the impeller outlet and was responsible for pump shut off at α

_{i}= 4.2%.

#### 4.2. Unsteady Characteristics of the Flow Structure

## 5. Conclusions

_{d}), the same trend is observed but with a decrease in the maximum admissible inlet void fraction, i.e., 4.2% and 3% for n = 1450 r/min and n = 1000 r/min, respectively.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

b | impeller blade width |

D | diameter |

H | pump head |

LVF | local void fraction |

M | shaft torque |

n | rotational speed |

p | local static pressure |

P | shaft power |

Q | volume water flow rate |

R | radius |

R_{e,imp} | impeller Reynolds number, ${R}_{e,imp}={u}_{2}\cdot {R}_{2}/v$ |

t | time |

T | time period |

u | circular velocity |

v | absolute velocity |

z | height level |

Z | impeller blade number |

## Greek Symbols

α | inlet air void fraction |

η | global efficiency of the pump, $\eta =\rho g{Q}_{l}H/P$ |

v | water kinematic viscosity |

φ | flow coefficient, $\phi =Q/(2\pi \cdot {R}_{2}\cdot {b}_{2}\cdot {u}_{2})$ |

ρ | density of fluid mixture, $\rho ={\rho}_{l}\cdot (1-\alpha )+{\rho}_{g}\cdot \alpha $ |

ω | angular velocity |

Ωs | specific speed, $\mathsf{\Omega}s=\omega \cdot \frac{{Q}^{0.5}}{{(gH)}^{0.75}}$ |

ψ | Head coefficient, $\psi =gH/{({u}_{2})}^{2}$ |

## Subscripts

B | bubble |

d | design condition |

g | gas |

i | relative to inlet condition |

imp | relative to impeller |

l | liquid |

tp | related to two-phase condition |

th | related to two-phase condition |

0 | related to α equal zero |

1 | impeller pump inlet |

2 | impeller pump outlet |

* | non dimensional value |

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**Figure 2.**Views of the experimental set up and the transparent pump model. (

**a**) Test scene and (

**b**) drawing of the pump assembly dimensions (mm).

**Figure 3.**Pump head coefficients for two rotational speeds: (

**a**) n = 1450 r/min and (

**b**) n = 1000 r/min.

**Figure 5.**Pump theoretical head coefficients for two rotational speed: (

**a**) n= 1450 r/min and (

**b**) n= 1000 r/min.

**Figure 8.**Flow coefficient degradation ratio for two rotational speed: (

**a**) n = 1450 r/min and (

**b**) n = 1000 r/min.

**Figure 9.**Changes in theoretical pump degradation for two different flow rates: (

**a**) φ = 0.06; (

**b**) φ = 0.04.

**Figure 10.**Flow pattern under φ = 0.04 for different α

_{i}: (

**a**) 0.7%; (

**b**) 1%; (

**c**) 2%; (

**d**) 2.5%; (

**e**) 3%; and (

**f**) 3.5%, pump shut off condition.

**Figure 11.**Flow pattern under φ = 0.06 for different α

_{i}: (

**a**) 0.5%; (

**b**) 1%; (

**c**) 2%; (

**d**) 3%; (

**e**) 4%; (

**f**) 4.2%, pump shut off condition.

**Figure 12.**Instantaneous flow pattern for φ = 0.06 at α

_{i}= 4.2% at different time: (

**a**) t

_{0}; (

**b**) t

_{0}+ T/4; (

**c**) t

_{0}+ T/2; and (

**d**) t

_{0}+ 5T/6.

Reference | R_{2} (m) | R_{2}/R_{1t}(-) | n (r/min) | u_{2}(m/s) | u_{1}(m/s) | b_{2}/R_{2}(-) | W_{1}(m/s) | Z (-) | β_{2}(°) | β_{1}(°) | Φ_{d}(-) |
---|---|---|---|---|---|---|---|---|---|---|---|

Murakami et al. [2] * | 0.112 | 2.24 | 1750 | 20.6 | 9.2 | 0.16 | 9.7 | 5 | 18.1 | 19.4 | 0.084 |

Sato et al. [10] ** | 0.125 | 2.083 | 1100 | 14.4 | 6.9 | 0.144 | 7.34 | 8 | 25 | 20 | 0.069 |

Stel et al. [11] *** | 0.1021 | 2.55 | 1150 | - | - | - | - | 8 | - | - | 0.09 |

Mansour et al. [12] * | - | 2 | 650 | - | - | 0.15 | - | 6 | 24.7 | 19.5 | - |

Verde et al. [13] *** | 0.0557 | 2.52 | 900 | 5.25 | 2.08 | 0.1077 | 3.0 | 7 | 46.8 | 45 | 0.098 |

Shao et al. [14] ** | 0.125 | 3.125 | 1450 | 19.0 | 6.08 | 0.072 | 7.71 | - | 32 | 38 | 0.098 |

Present pump * | 0.087 | 2.351 | 1000 | 9.11 | 3.87 | 0.138 | 8.175 | 6 | 30 | 28 | 0.08 |

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**MDPI and ACS Style**

Si, Q.; Zhang, H.; Bois, G.; Zhang, J.; Cui, Q.; Yuan, S.
Experimental Investigations on the Inner Flow Behavior of Centrifugal Pumps under Inlet Air-Water Two-Phase Conditions. *Energies* **2019**, *12*, 4377.
https://doi.org/10.3390/en12224377

**AMA Style**

Si Q, Zhang H, Bois G, Zhang J, Cui Q, Yuan S.
Experimental Investigations on the Inner Flow Behavior of Centrifugal Pumps under Inlet Air-Water Two-Phase Conditions. *Energies*. 2019; 12(22):4377.
https://doi.org/10.3390/en12224377

**Chicago/Turabian Style**

Si, Qiaorui, Haoyang Zhang, Gérard Bois, Jinfeng Zhang, Qianglei Cui, and Shouqi Yuan.
2019. "Experimental Investigations on the Inner Flow Behavior of Centrifugal Pumps under Inlet Air-Water Two-Phase Conditions" *Energies* 12, no. 22: 4377.
https://doi.org/10.3390/en12224377