# Centrifugal Pump Monitoring and Determination of Pump Characteristic Curves Using Experimental and Analytical Solutions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}). In this study, the mixture head ${H}_{mix}$ was calculated with the relation:

_{2}in the CO

_{2}-diesel fuel mixture was 0.40, at which point the pumping height was about 90% of the height when only pumping diesel fuel.

- sound source localization (such as signal from a safety whistle [13]);
- real-time processing and intuitive visualization tools;
- robustness of the device in outdoor environments

## 2. Materials and Methods

## 3. Results

_{m}—mixture density; p

_{d}—pressure at the outlet of the pump; p

_{s}—pressure at the pump inlet; Q

_{a}—air flow rate.

_{a}) have been used: 1.28 m

^{3}

_{S}/h; 1.60 m

^{3}

_{S}/h; 1.92 m

^{3}

_{S}/h; 2.24 m

^{3}

_{S}/h; 2.56 m

^{3}

_{S}/h; 2.88 m

^{3}

_{S}/h; 3.2 m

^{3}

_{S}/h; and respectively 3.52 m

^{3}

_{S}/h.

^{3}/h; H water = 82 m) in Figure 3, is shown by the curve H82. By reading this curve from right to left, the switch from normal operation can be observed. Initially, the vibration velocities are close to the vibration values at normal operating conditions, shown in curve H. An increase in the amount of air amplifies the vibrations, which are strongest at the flow rate of 7.5 m

^{3}/h. This aspect is also maintained in high pressure and low flow scenarios (see lines H73, H62, H52 in Figure 4). The points on the pump characteristic curves H42, H38, H32, H25 (with low pressure and high flow) have initial speeds of vibration slightly higher than at normal operating conditions. The vibration level is almost unaffected by flow rate in the 22–55 m

^{3}/h interval. With the reduction of flow, vibrations decrease rapidly as the amount of air becomes important into the mixture, acting as a dampener.

^{3}/h, with higher values).

^{3}/h, after which the vibration velocities are constant and under normal operation values. However, the difference is small and we can say that air influx does not influence the pump operating condition. At flow rates above 38 m

^{3}/h, the vibration velocities are greater than those of normal operation. The situation is different for the introduction of large amounts of air A9%, A10% and A11%. In all these three cases, the recorded velocities exceeding the normal functioning values and their trend is accompanied by maximum and minimum values for certain flow rates. To conclude, the vibrations intensify with increasing air in the pump at levels above 5% of the nominal pump flow. The influence is strongest at low flow rates (up to 15 m

^{3}/h). As we approach the nominal flow rate, differences are reduced. At flow rates higher than 38 m

^{3}/h, the values corresponding to the normal operation are increasing again. All in all, the operation at the flow rates that differ from Q

_{n}(particularly under 0.6 of Q

_{n}and more than 1.2 of Q

_{n}), with an amount of air higher than 5% of Q

_{n}is characterized by velocities of vibration up to 60% larger, compared to values at normal operating conditions.

^{3}/h. The pump efficiency decrease is proportional with the amount of air introduced into the system. Efficiency is declining rapidly when the amount of air is over 10%, so the pump stops having an active role in the pumping system. Functioning with an air-water mixture indicates energy losses related to the lack of control over the fluid, which exhibits an eddy movement between the blades. From the vibration viewpoint, pump malfunctioning is observed outside of the 0.6–1.2 Q

_{n}range, where the two-phase mixture leads to stronger vibrations. It was observed that when the pump delivers near the nominal flow rate, vibrations are close to those of the normal functioning condition and therefore cannot be used as an indicator of a low efficiency. Hence, at these flow rates, the vibration measurement is not a measure of the capability of the pump.

## 4. Discussion

^{3}/h, and at a quantity of air ranging from 4 to 7%. If the amount of air is increasing, the correction method does not provide acceptable results. In the range of low flow rates (less than 25 m

^{3}/h), introducing a quantity of air sharply changes the characteristics of the pump, while the correction method indicates a very small change. In this case, the correction method gives results which unfortunately cannot be used in practice.

## 5. Conclusions

_{n}(in particular under 0.6 of Q

_{n}and larger than 1.2 of Q

_{n}), with more than 5% of Q

_{n}air is characterized by velocities of vibration up to 60% higher compared to the values of normal operation. It can be observed that the analytical method of correction cannot be used in practice. Differences between the experimental curves corresponding air-water mixture and those determined by the method of correction are important, as shown in Figure 8.

## Author Contributions

## Conflicts of Interest

## Nomenclature

${H}_{mixture}$ | Pump head, m |

${p}_{d}$ | Pressure at the outlet of the pump, bar |

${p}_{s}$ | Pressure at the pump inlet, bar |

${\rho}_{g}$ | Air density, kg/m^{3} |

${\rho}_{m}$ | Mixture density, kg/m^{3} |

${\rho}_{w}$ | Water density, kg/m^{3} |

a | acceleration, m/s^{2} |

b_{2} | Impeller outlet width, mm |

D_{1} | Impeller inlet diameter, mm |

D_{2} | Impeller outlet diameter, mm |

f | frequency, Hz |

g | Gravitational acceleration, m/s^{2} |

H_{n} | Designed head, m |

n | Rotating speed, RPM |

v | velocity, m/s |

x | Volumetric fraction, - |

Z | Blade number, - |

Q_{n} | Nominal flow rate, m^{3}/s |

Pump head | the maximum outlet pressure of the pump, in meters of fluid |

Pump efficiency | output hydraulic power versus input mechanical power |

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**Figure 2.**Stand images: (

**a**) speed transducer and vibration velocity transducer; (

**b**) sound level meter and acquisition system.

**Figure 4.**Vibration velocities corresponding to the point modification of the characteristic curve when introducing different amounts of air into the fluid circulated.

**Figure 5.**Vibration velocities corresponding to the points of the pump characteristic curve, at variable amounts of air in water. Air flow differs as shown in Table 2. Pump nominal flow 32 m

^{3}/h.

**Figure 6.**Amplitude and frequencies of sound at normal operating conditions (

**top**); and with air intake (

**bottom**). Green line—no air, red line—with air intake.

**Figure 8.**Comparison between experimental pump characteristic curves and those obtained through the correction method.

**Figure 9.**The influence of the suction pressure: (

**a**) concerning the pump flow; (

**b**) concerning the vibration velocity.

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

Nominal flow rate—Q_{n} | 32 m^{3}/h |

Designed head—H_{n} | 60 m |

Rotating speed—n | 2950 RPM |

Impeller inlet diameter—D_{1} | 70 mm |

Impeller outlet diameter—D_{2} | 130 mm |

Impeller outlet width—b2 | 12 mm |

Blade number—Z | 7 |

Stages number | 10 |

Vertical distance between flanges | 150 mm |

Flanges nominal diameter | 50 mm |

Engine power | 5.5 kW |

Curves | Air Flow Rate (m^{3}_{S}/h) | Curve | Water Flow Rate (m^{3}/h) | Water Head (m) | ||
---|---|---|---|---|---|---|

C0 | A0% | E0% | 0 | H82 | 14 | 82 |

C1 | A4% | E4% | 1.28 | H73 | 28 | 73 |

C2 | A5% | E5% | 1.6 | H62 | 31 | 62 |

C3 | A6% | E6% | 1.92 | H52 | 41 | 52 |

C4 | A7% | E7% | 2.24 | H42 | 45 | 42 |

C5 | A8% | E8% | 2.56 | H38 | 48 | 38 |

C6 | A9% | E9% | 2.88 | H32 | 50.5 | 32 |

C7 | A10% | E10% | 3.2 | H25 | 53.5 | 25 |

C8 | A11% | E11% | 3.52 |

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**MDPI and ACS Style**

Stan, M.; Pana, I.; Minescu, M.; Ichim, A.; Teodoriu, C.
Centrifugal Pump Monitoring and Determination of Pump Characteristic Curves Using Experimental and Analytical Solutions. *Processes* **2018**, *6*, 18.
https://doi.org/10.3390/pr6020018

**AMA Style**

Stan M, Pana I, Minescu M, Ichim A, Teodoriu C.
Centrifugal Pump Monitoring and Determination of Pump Characteristic Curves Using Experimental and Analytical Solutions. *Processes*. 2018; 6(2):18.
https://doi.org/10.3390/pr6020018

**Chicago/Turabian Style**

Stan, Marius, Ion Pana, Mihail Minescu, Adonis Ichim, and Catalin Teodoriu.
2018. "Centrifugal Pump Monitoring and Determination of Pump Characteristic Curves Using Experimental and Analytical Solutions" *Processes* 6, no. 2: 18.
https://doi.org/10.3390/pr6020018