# Optimization Research on the Space-V-Type Biomimetic Surface Grooves of a Marine Centrifugal Pump

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Response Surface Experimental Design

#### 2.1. Space-V Groove Layout

^{+}) and width (s

^{+}) are h

^{+}≤ 25 and s

^{+}≤ 30, respectively. Using these results as a basis, we chose both h

^{+}and s

^{+}values to be 12, which corresponds to s = h = 0.3 mm based on Equations (1) and (2). In order to generate an accurate comparison between the two designs of biomimetic groove structures, we standardized the dimensions of the Space-V groove to s = h = b = 0.3 mm while minimizing the impact of variables.

_{f}represents the frictional resistance coefficient.

#### 2.2. Selection of Experimental Factors and Changes in Coding Levels

#### 2.3. Experimental Design

## 3. Response Surface Optimization Results Analysis

#### 3.1. Analysis of Parameter Significance

_{α}(f

_{U}, fQ

_{E}), where α = 0.05. If M > M

_{α}(f

_{U}, fQ

_{E}), the regression equation is significant; if M ≤ M

_{α}(f

_{U}, fQ

_{E}), the equation is not significant [22].

_{j}in the regression equation can be judged using Equation (4).

_{j}represents the partial sum of squares of factor x

_{j}.

_{j}and M

_{α}(1, fQ

_{E}). If M

_{j}>M

_{α}(1, fQ

_{E}), the variable factor x

_{j}is significant for the response value; if M

_{j}≤ M

_{α}(1, Q

_{E}), the factor is not significant for the response value.

^{2}has a significant effect, while other effects are not significant.

^{2}(coefficient of determination) can also be used to verify the reliability of the model. The closer R

^{2}is to 1, the better the fit of the regression model. The R

^{2}in this model is 0.8554 and the R

^{2}

_{adj}in this model is 0.8012, indicating a relatively good fit of the regression equation, and the prediction of the total sound pressure level has a high level of reliability. Meanwhile, C.V (general coefficient of variation) and Adeq precision (accuracy) can also measure the reliability of the experiment. A small C.V value indicates higher reliability and accuracy of the experiment. The C.V value of this experiment is 0.31%, indicating high reliability. Adeq precision is considered reasonable if it is greater than 4.0. The precision of this experiment is 6.114, indicating a precise experimental design. Equation (5) represents the regression model of the total sound pressure level.

#### 3.2. Interaction Effects of Parameters on Total Sound Pressure Level

## 4. Comparison of Performance of Biomimetic Marine Centrifugal Pump before and after Optimization

#### 4.1. Hydraulic Performance Comparison Analysis

#### 4.2. Analysis of In-Field Noise Comparison

## 5. Conclusions

- (1)
- The BBD method was used to experimentally design the height, width, and spacing of the biomimetic grooved structure, and a multivariate regression equation was established between the total sound pressure level of the marine centrifugal pump and the three geometric parameters of the grooves. The significance of the model was verified through a variance analysis.
- (2)
- With the increase in groove height, the total sound pressure level first decreases and then increases; with the increase in groove width, the total sound pressure level first decreases and then increases; and with the increase in groove spacing, the total sound pressure level increases.
- (3)
- The optimization scheme for the groove parameters was determined to be height: h = 0.65 mm, width: s = 0.6 mm, spacing: b = 0.8 mm.
- (4)
- The comparative analysis conducted on the Space-V groove model before and after optimization revealed notable improvements in the head and efficiency under various operating conditions. Additionally, the optimized model effectively reduced broadband noise and discrete noise at various characteristic frequencies. Specifically, the optimized Space-V groove model exhibited an increased head of 0.27 m, an increased efficiency of 1.21%, and a drag reduction rate higher than the unoptimized model by 0.87% under the rated condition. Furthermore, in comparison to the smooth model at the rated condition, the optimized Space-V groove model displayed an efficiency improvement of 4.51%, a resistance reduction of 3.73%, and a decrease in the overall sound pressure level by 1.81%.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Influence of groove height and width interaction on total sound pressure level for two-dimensional (

**a**) and three-dimensional response surface (

**b**).

Coding | Experimental Factor | Coding Level | ||
---|---|---|---|---|

−1 | 0 | 1 | ||

A | Groove height/mm | 0.2 | 0.6 | 1.0 |

B | Groove width/mm | 0.1 | 0.45 | 0.8 |

C | Groove spacing/mm | 0 | 1.2 | 2.4 |

Number | A | B | C | Total Sound Pressure Level (dB) |
---|---|---|---|---|

1 | 0.2 | 0.1 | 1.2 | 184.13 |

2 | 1 | 0.1 | 1.2 | 182.11 |

3 | 0.2 | 0.8 | 1.2 | 183.12 |

4 | 1 | 0.8 | 1.2 | 182.56 |

5 | 0.2 | 0.45 | 0 | 182.73 |

6 | 1 | 0.45 | 0 | 182.21 |

7 | 0.2 | 0.45 | 2.4 | 183.65 |

8 | 1 | 0.45 | 2.4 | 182.86 |

9 | 0.6 | 0.1 | 0 | 181.56 |

10 | 0.6 | 0.8 | 0 | 182.11 |

11 | 0.6 | 0.1 | 2.4 | 181.98 |

12 | 0.6 | 0.8 | 2.4 | 182.43 |

13 | 0.6 | 0.45 | 1.2 | 181.76 |

14 | 0.6 | 0.45 | 1.2 | 181.70 |

15 | 0.6 | 0.45 | 1.2 | 181.21 |

16 | 0.6 | 0.45 | 1.2 | 180.53 |

17 | 0.6 | 0.45 | 1.2 | 180.37 |

Factor | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | Prob (P) > F | Significance |
---|---|---|---|---|---|---|

Model | 13.34 | 9 | 1.48 | 4.60 | 0.0283 | Significant |

A | 1.89 | 1 | 1.89 | 5.87 | 0.0459 | Significant |

B | 0.024 | 1 | 0.024 | 0.075 | 0.7920 | Not significant |

C | 0.67 | 1 | 0.67 | 2.07 | 0.1935 | Not significant |

AB | 0.53 | 1 | 0.53 | 1.65 | 0.2394 | Not significant |

AC | 0.018 | 1 | 0.018 | 0.057 | 0.8189 | Not significant |

BC | 0.0025 | 1 | 0.0025 | 0.007756 | 0.9323 | Not significant |

A^{2} | 7.72 | 1 | 7.72 | 23.96 | 0.0018 | Significant |

B^{2} | 1.10 | 1 | 1.10 | 3.42 | 0.1068 | Not significant |

C^{2} | 0.65 | 1 | 0.65 | 2.03 | 0.1972 | Not significant |

Q/Q_{d} | Torque/N∙m | Drag Reduction Rate/% | |||
---|---|---|---|---|---|

Smooth Model | Unoptimized Space-V Groove Model | Optimized Space-V Groove Model | Unoptimized Drag Reduction Rate | Optimized Drag Reduction Rate | |

0.6 | 3.19 | 3.24 | 3.20 | −1.56 | −0.31 |

0.8 | 3.45 | 3.41 | 3.38 | 1.16 | 2.03 |

1.0 | 3.85 | 3.74 | 3.71 | 2.86 | 3.73 |

1.2 | 4.31 | 4.27 | 4.23 | 0.93 | 1.86 |

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**MDPI and ACS Style**

Li, H.; Yu, Z.; Hua, R.; Li, C.; Guo, C.; Liu, H.; Dong, L.
Optimization Research on the Space-V-Type Biomimetic Surface Grooves of a Marine Centrifugal Pump. *Water* **2023**, *15*, 4031.
https://doi.org/10.3390/w15224031

**AMA Style**

Li H, Yu Z, Hua R, Li C, Guo C, Liu H, Dong L.
Optimization Research on the Space-V-Type Biomimetic Surface Grooves of a Marine Centrifugal Pump. *Water*. 2023; 15(22):4031.
https://doi.org/10.3390/w15224031

**Chicago/Turabian Style**

Li, Hua, Zifeng Yu, Runan Hua, Chenqi Li, Chao Guo, Houlin Liu, and Liang Dong.
2023. "Optimization Research on the Space-V-Type Biomimetic Surface Grooves of a Marine Centrifugal Pump" *Water* 15, no. 22: 4031.
https://doi.org/10.3390/w15224031