^{1}

^{1}

^{2}

^{1}

^{3}

^{1}

^{1}

^{2}

^{3}

To research the effects of the blade outlet angle on the performance and the radial force of the marine pump, the unsteady numerical simulation of the four different models is carried out. The radial forces on the impeller and the blades are obtained under different flow rate conditions. The time and frequency domain characteristics of radial resultant force on the impeller and the blades are analyzed and those of the impeller torque are researched. The results show that the radial forces of the impeller and the blades increase with the increase of the blade outlet angle at the same flow rate. With the same blade outlet angle, the radial forces decrease with the increase of the flow rate. The roundness of radial force vector diagram becomes more obvious with the decrease of the blade outlet angle. The root mean square (RMS) of radial force on the blades is about 30% of that on the impeller. The main frequency of radial force on the impeller and the blades is the axial passing frequency (APF), and that of impeller torque is the blade passing frequency (BPF), and there are peaks at the blade frequency multiplier. At the same flow rate, the main frequency and maximum fluctuation amplitudes on the impeller and the blades increase with the increase of the blade outlet angle. Meanwhile, the impeller torque increases with the increase of the blade outlet angle. With the same blade outlet angle, the main frequency, maximum fluctuation amplitudes, and the impeller torque decrease with the increase of the flow rate. The amplitude difference decreases with the increase of the flow rate. The blade outlet angle has an obvious greater influence on the radial forces and fluctuation at the small flow rate. The vibration test shows that the vibration intensities of model 25 and model 35 are less than 2.5 mm/s, and the vibration intensity of model 25 is about 0.2 mm/s less than that of model 35.

The marine pumps are commonly used in complex environments, which need to have the characteristics of small vibration, low noise, and high reliability. The liquid medium dynamic reaction force on the impeller in the centrifugal pump produces radial force, and the fluctuation of radial force makes the pump shaft subject to alternating stress, which results in pump vibration of different degrees.

At present, there are many research studies on the internal flow pressure fluctuation, radial force, and vibration mechanism in the centrifugal pump and pump as turbine. The reduction of noise is significant by increasing the gap between the impeller and the tongue [

In addition, the time domain and frequency domain of pressure fluctuation at monitoring point on diffuser and outlet elbow are analyzed in mixed flow pump, and the pressure fluctuation peak decreases gradually with the increase of the flow rate [

The blade outlet angle of research on the influence of radial force in the centrifugal pump is less, so the effect of different blade outlet angles on radial force of the marine pump is necessary for research. The internal flow field in the magnetic drive pump is analyzed with the numerical calculation method. The radial force on the impeller and the blades, and impeller torque at various flow rates are obtained. The time domain and frequency domain characteristics of radial force and impeller torque are analyzed. The hydraulic performance and vibration tests are carried out on the real pump, which provided a reference for further research on radial force and vibration of the pump.

The marine magnetic drive pump is researched as an object; its design parameters are rated flow ^{3}/h, head _{s} = 133.5. The main geometric parameters of the pump are shown in Table

Main geometric parameters of the designed magnetic drive pump.

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

Impeller outlet diameter _{2} (mm) | 102 | |

Impeller outlet diameter _{2} (mm) | 194 | |

Impeller outlet width _{2} (mm) | 21.6 | |

Impeller hub diameter dh (mm) | 48 | |

Blade inlet angle _{1}/(°) | 15–20 | |

Impeller 25 | Blade outlet angle _{2}/(°) | 25 |

Impeller 30 | Blade outlet angle _{2}/(°) | 30 |

Impeller 35 | Blade outlet angle _{2}/(°) | 35 |

Impeller 40 | Blade outlet angle _{2}/(°) | 40 |

Blade wrap angle Φ/(^{°}) | 106 | |

Blade number | 6 | |

Volute base circle diameter _{3} (mm) | 210 | |

Tongue angle | 32.7 |

The structure of the magnetic drive pump is shown in Figure

Structure of the magnetic drive pump. 1. Volute. 2. Impeller. 3. Motor cooling pipe. 4. Pump cooling pipe. 5. Motor. 6. Outside magnetic rotor. 7. Isolator. 8. Inside magnetic rotor. 9. Connecting body. 10. Guide bearing.

The cavities between the front shroud, the back shroud, and the volute are taken into account in the modeling. The flow field with minimal gaps between the impeller rings and the volute can also be effectively captured. The model includes inlet pipe, outlet pipe, volute, impeller, front cavity, back cavity, and balance holes. Therefore, the full-flow field numerical simulation analysis is adopted, and the calculation results include volume loss and disc friction loss.

The structured hexahedral mesh of components in the model is generated with ICEM software. It can be better divided as the small area of impeller rings and tongue. The mesh independence of the model is checked, and the mesh is finally exported in cfx5 format. The impeller mesh and schematic diagram of the pump is shown in Figure

(a) Impeller mesh and (b) schematic diagram of pump.

The mesh independence of the model is studied with model 35 as an example. The relation curve between the head of the pump and the mesh number under the design flow rate is shown in Figure

Variation of head with mesh number in model 35.

The steady and unsteady flow fields inside the pump are calculated with Ansys CFX. The inlet of the pump model is set as static pressure inlet and the outlet as mass flow outlet. The wall roughness of the pump is set at 50 ^{−5}.

Model 35 is analyzed by using the standard

Diagram of simulation values with different turbulence models.

The RNG _{,}

The frozen rotor interface is set for steady calculation, while the unsteady calculation uses the transient rotor interface in the CFX. The results of steady analysis are used as the initial conditions for unsteady calculation. In the unsteady calculation, the time step setting is considered as follows. If the time of 2° rotation of the impeller is taken as the time step, the sampling points per revolution are 180, and the sampling resolution is slightly lower. Meanwhile, considering the pump speed and the resources of the computer, the time of 1° rotation of the impeller is set as the time step, which is 5.649 × 10^{−5}·s. When the transient analysis runs for 15 revolutions, the flow field presents periodic change and that is stable. The result of the 15th revolution is taken as the analysis. The time domain and frequency domain analysis of radial forces on the impeller and blades and impeller torque are carried out.

The

The vector diagram of radial force on the impeller under different flow rate conditions is shown in Figure

Vector diagram of radial force on the impeller under different flow rate conditions. (a) 0.8Q. (b) 1.0Q (c) 1.2Q.

With the same blade outlet angle, the radial force on the impeller decreases with the increase of the flow rate. The radial force vector diagram gradually tends to be circular and concentric, and the roundness becomes more obvious with the decrease of the blade outlet angle. At each flow rate, the radial force vector diagrams in the four groups of models present obvious sidelobes. The number of sidelobes is 6 and the same as the number of leaves, which is mainly caused by the rotor and stator interference generated by the blade passing through the tongue region. It is shown that the fluctuation frequency of radial force is related to the number of blades and mainly to the blade frequency.

The time domain of radial resultant force on the impeller under different flow rate conditions is shown in Figure

Time domain of radial resultant force on the impeller under different flow rate conditions. (a) 0.8Q. (b) 1.0Q. (c) 1.2Q.

At the flow rate of 0.8Q, the radial resultant force has a large variation amplitude, and the variation amplitude of the resultant force obviously decreases with the increase of the flow rate. At the same flow rate, the radial resultant force increases with the increase of the blade outlet angle. The main reason is that the absolute velocity at the impeller outlet increases as the blade outlet angle increases, and the dynamic pressure increases. The increase of the pressure will lead to the increase of the radial force.

The formula of Fast Fourier Transform (FFT) is as shown formula (

Frequency domain of radial resultant force on the impeller under different flow rate conditions. (a) 0.8Q. (b) 1.0Q. (c) 1.2Q.

The amplitude of frequency domain and maximum fluctuation of radial resultant force on the impeller are shown in Table _{max} and _{min} are, respectively, the maximum and minimum values of the radial resultant force on the impeller (N) and ^{3}). The amplitude difference is the difference between the maximum and the minimum values of the maximum fluctuation amplitude under the same flow rate condition. The influence degree of different blade outlet angles on the radial resultant force can be seen from amplitude difference value.

Amplitude of frequency domain and maximum fluctuation of radial resultant force on the impeller.

Flow | Model | Main frequency amplitude (N) | Maximum fluctuation amplitude (%) | Amplitude difference (%) |
---|---|---|---|---|

0.8Q | 25 | 33.4 | 0.4153 | 0.1716 |

30 | 35.7 | 0.5173 | ||

35 | 38.4 | 0.5401 | ||

40 | 40.6 | 0.5869 | ||

1.0Q | 25 | 22.8 | 0.2461 | 0.1529 |

30 | 26.3 | 0.2757 | ||

35 | 27.9 | 0.2993 | ||

40 | 31.5 | 0.3990 | ||

1.2Q | 25 | 12.7 | 0.1405 | 0.1308 |

30 | 16.5 | 0.1684 | ||

35 | 20.1 | 0.2023 | ||

40 | 22.6 | 0.2713 |

As can be seen from Figure

The amplitude difference decreases with the increase of the flow rate. It indicates that the blade outlet angle has the more significant effect on the radial force and fluctuation on the impeller at the small flow rate. The main reason is that the impeller runner is designed according to the hydraulic model under the design flow rate condition. When the flow rate is small, the back flow and flow separation appear in the internal pump so that the radial force on the impeller is not in balance, thus increasing the radial force on the impeller and reducing the hydraulic efficiency.

The pressure contour maps on the front side of blades with different blade outlet angles are shown in Figure

Pressure contour maps on the front side of blades with different blade outlet angles. (a) 0.8Q (_{2} = 25°). (b) 1.0Q (_{2} = 25°). (c) 1.2Q (_{2} = 25°). (d) 0.8Q (_{2} = 30°). (e) 1.0Q (_{2} = 30°). (f) 1.2Q (_{2} = 30°). (g) 0.8Q (_{2} = 35°). (h) 1.0Q (_{2} = 35°). (i) 1.2Q (_{2} = 35°). (j) 0.8Q (_{2} = 40°). (k) 1.0Q (_{2} = 40°). (l) 1.2Q (_{2} = 40°).

Time domain of radial resultant force on the blades under different flow rate conditions. (a) 0.8Q. (b) 1.0Q. (c) 1.2Q.

The vector diagram of radial force on the blades under different flow rate conditions is shown in Figure

Vector diagram of radial force on the blades under different flow rate conditions. (a) 0.8Q. (b) 1.0Q. (c) 1.2Q.

At the flow rate of 1.2Q, the difference becomes more uniform. There are 6 obvious sidelobes in the radial force vector diagram on the blades at different flow rates, and the radial force on the blades is significantly smaller than that on the impeller. That is mainly the influence of radial force on the front and back shrouds of the impeller is more significant.

The time domain of radial resultant force on the blades under different flow rate conditions is shown in Figure

RMS of radial resultant forces on the impeller and the blades.

Flow | Model | _{i} (N) | _{b} (N) | _{b}/_{i} × 100 |
---|---|---|---|---|

0.8Q | 25 | 309.1 | 84.5 | 27.3 |

30 | 321.9 | 86.9 | 27.0 | |

35 | 349.1 | 108.5 | 31.1 | |

40 | 356.6 | 110.6 | 31.0 | |

Δ | — | 47.5 | 26.1 | — |

1.0Q | 25 | 261.4 | 79.0 | 30.2 |

30 | 274.3 | 84.8 | 30.9 | |

35 | 295.2 | 93.5 | 31.7 | |

40 | 305.6 | 100.4 | 32.8 | |

Δ | — | 44.2 | 21.4 | — |

1.2Q | 25 | 199.2 | 54.4 | 27.3 |

30 | 210.4 | 63.7 | 30.3 | |

35 | 226.3 | 70.5 | 31.2 | |

40 | 239.9 | 71.6 | 29.8 | |

Δ | — | 40.7 | 17.2 | — |

_{i} is the RMS of radial force on the impeller and _{b} is the RMS of radial force on the blades in Table

The frequency domain of radial resultant force on the blades under different flow rate conditions is shown in Figure

Frequency domain of radial resultant force on the blades under different flow rate conditions. (a) 0.8Q. (b) 1.0Q. (c) 1.2Q.

As can be seen from Figure

Amplitude of frequency domain and maximum fluctuation of radial resultant force on the blades.

Flow | Model | Main frequency amplitude (N) | Maximum fluctuation amplitude (%) | Amplitude difference (%) |
---|---|---|---|---|

0.8Q | 25 | 14.7 | 0.1890 | 0.0657 |

30 | 16.8 | 0.2065 | ||

35 | 18.9 | 0.2346 | ||

40 | 20.4 | 0.2547 | ||

1.0Q | 25 | 10.5 | 0.1680 | 0.0562 |

30 | 12.2 | 0.1346 | ||

35 | 14.6 | 0.1631 | ||

40 | 16.3 | 0.2242 | ||

1.2Q | 25 | 5.4 | 0.0623 | 0.0445 |

30 | 6.5 | 0.0910 | ||

35 | 7.3 | 0.0986 | ||

40 | 7.9 | 0.1068 |

As can be seen from Table

The time domain of torque on the impeller under different flow rate conditions is shown in Figure

Time domain of torque on the impeller under different flow rate conditions. (a) 0.8Q. (b) 1.0Q. (c) 1.2Q.

Frequency domain of torque on the impeller under different flow rate conditions. (a) 0.8Q. (b) 1.0Q. (c) 1.2Q.

The main frequency amplitude and maximum fluctuation amplitude of the impeller torque are shown in Table _{max} and _{min} are, respectively, the maximum and minimum values of the impeller torque (N·m).

Amplitude of frequency domain and maximum fluctuation of torque on the impeller.

Flow | Model | Main frequency amplitude (N) | Maximum fluctuation amplitude (%) | Amplitude difference (%) |
---|---|---|---|---|

0.8Q | 25 | 5.63 | 0.0309 | 0.0124 |

30 | 5.96 | 0.0347 | ||

35 | 6.47 | 0.0374 | ||

40 | 6.92 | 0.0433 | ||

1.0Q | 25 | 4.51 | 0.0258 | 0.0112 |

30 | 5.20 | 0.0300 | ||

35 | 5.80 | 0.0319 | ||

40 | 6.63 | 0.0370 | ||

1.2Q | 25 | 2.93 | 0.0184 | 0.0108 |

30 | 3.61 | 0.0213 | ||

35 | 4.49 | 0.0244 | ||

40 | 5.45 | 0.0292 |

As can be seen from Figure

Numerical analysis is carried out on four groups of models to obtain the external characteristic curve. Taking the pump head and efficiency into consideration, model 35 is selected as the experimental prototype to verify the hydraulic performance, which is measured on the closed pump test system. The external characteristic curves of the marine magnetic drive pump test and simulation are shown in Figure

Experimental and numerical performance curves.

It can be seen that the simulation results of model 35 are in great agreement with the trend of the head, efficiency, and shaft power curves of the test results. Under the design flow rate condition, the simulation precision of the pump head is controlled within 1.2%, which indicates that the model can accurately simulate and predict the pump hydraulic performance. By comparing the simulation results of four different blade outlet angles, it can be seen that the head is obviously improved, and the efficiency has a decreasing trend with the increase of the blade outlet angle. The main reason is that the impeller runner gets shorter with the increase of the blade outlet angle. The medium diffusion in the impeller runner gets larger, and the fluid hydraulic loss increases. Meanwhile, the hydraulic efficiency of the pump decreases at small flow rate.

According to ISO 10816 vibration evaluation standard for rotating machinery, the vibration test is carried out for pump prototypes with blade outlet angles of 25° and 35°. Considering the periodicity of the radial force and the sensitivity to the vibration of the pump unit, the acceleration sensor is arranged at the connection between the volute and the connecting body, as shown in Figure

Schematic diagram of pump measuring point. 1. Inlet pipe. 2. Volute. 3. Outlet pipe. 4. Measuring point. 5. Connecting body.

The formula between vibration velocity and vibration intensity is as shown formula (_{rms} is the vibration intensity (mm/s). The vibration intensity indicates the severity of vibration, and it is expressed by the RMS of vibration velocity at the specified point. The results of vibration intensity test on the prototypes of model 25 and model 35 are shown in Figure

Vibration intensity test of the pump.

The main frequency of the radial resultant force on the impeller and the blades are the APF. There are peaks at the BPF and blade frequency multiplier. The main frequency of impeller torque fluctuation is the BPF. There are peaks at blade frequency multiplier, and the peak value gradually decreases.

The radial forces of the impeller and the blades increase with the increase of the blade outlet angle at the same flow rate. With the same blade outlet angle, the radial forces decrease with the increase of the flow rate. The roundness of radial force vector diagram becomes more obvious with the decrease of the blade outlet angle.

The RMS of radial resultant force on the blades is about 27%–33% of that on the impeller, which is mainly distributed around 30%.

At the same flow rate, the main frequency and maximum fluctuation amplitudes on the impeller and the blades increase with the increase of the blade outlet angle. Meanwhile, the impeller torque increase with the increase of the blade outlet angle.

With the same blade outlet angle, the main frequency, maximum fluctuation amplitudes, and the impeller torque decrease with the increase of the flow rate. The amplitude difference decreases with the increase of the flow rate.

The blade outlet angle has an obvious greater influence on the radial force of the impeller and the blades under the small flow rate condition than other flow rate conditions.

The simulation precision of model 35 pump head is controlled within 1.2% under the design flow rate condition, and the model can accurately simulate and predict the pump hydraulic performance.

The vibration test of model 25 and model 35 prototype shows that the vibration intensities of the pump unit are less than 2.5 mm/s under 0.8Q, 1.0Q, 1.2Q, and 1.4Q flow rate conditions. The vibration intensity of model 25 is about 0.2 mm/s less than that of model 35.

_{2}:

Impeller outlet width

_{h}:

Impeller hub diameter

_{1}:

Impeller inlet diameter

_{2}:

Impeller outlet diameter

_{3}:

Volute base circle diameter

Natural constant

_{b}:

RMS of radial force on the blades

_{i}:

RMS of radial force on the impeller

Difference between the maximum and minimum values of the RMS

Pump head

Pressure

Shaft power

Rated flow

Rotation

_{s}:

Specific speed

_{max}:

Maximum value of the radial resultant force

_{min}:

Minimum value of the radial resultant force

Time

_{max}:

Maximum value of the impeller torque

_{min}:

Minimum value of the impeller torque

Vibration velocity

_{rms}:

Vibration intensity

Blade number

_{1}:

Blade inlet angle

_{2}:

Blade outlet angle

Blade wrap angle

Tongue angle

Density

Pump efficiency

Frequency.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

Fan-yu KONG was in charge of the whole project, Hong-li ZHANG proposed the analysis methodology and wrote the manuscript, Ai-xia ZHU proofread the manuscript, and Fei ZHAO and Zhen-fa XU assisted with laboratory analyses. All authors read and approved the final manuscript.

This project was supported by the National Natural Science Foundation of China (no. 11602097) and Scientific Research Project of Wuxi Institute of Technology, China (no. ZK201804).