# Method for the Calculation of the Underwater Effective Wake Field for Propeller Optimization

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Calculation Method

#### 2.1. Basic Formula

_{T}and K

_{Q}are propeller thrust coefficient and torque coefficient, η is the efficiency of the propeller, T and Q represent the propeller’ thrust and torque, J is the advance coefficient, ρ is the fluid density, D is the propeller’s diameter, and n is propeller’s rotational speed.

#### 2.2. Numerical Calculation of the Unsteady Propeller-Induced Velocity Field

_{t}, the time is ${k}_{t}\Delta t$, and the first blade’s angle position is ${k}_{t}\Delta \theta $. The blades are numbered along the direction of ${\theta}_{1}$, and the number k blade is in the position of ${k}_{t}\Delta \theta -2\pi (k-1)/Z$.

_{W}is the panel number along the trail vortex line. It should be infinite, but the number is usually very large.

_{t}, the induced velocity Equation (15) at the flow field point P

_{i}can be described as follows:

#### 2.3. Iterative Calculation Process

_{T}and the torque coefficient K

_{Q}of the propeller converge. The final wake gained is the effective wake. The iterative process is shown in Figure 2.

## 3. Instance Verification

#### 3.1. Model Introduction

#### 3.2. Effective Wake Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Apparent wake distribution. (

**a**) Axial wake distribution; (

**b**) Circumferential wake distribution; (

**c**) Radial wake distribution.

**Figure 5.**Induced velocity in tight front of the propeller. (

**a**) Axial-induced velocity; (

**b**) Circumferential-induced velocity; (

**c**) Radial-induced velocity.

**Figure 7.**Thrust and torque of propeller. (ECV and ACV represent effective wake calculated value and apparent wake calculated value, respectively).

Length between Perpendiculars (m) | Molded Breadth (m) | Draft (m) | Wetted Surface (m) | Block Coefficient | Advance Coefficient |
---|---|---|---|---|---|

7.2786 | 1.0190 | 0.3418 | 9.438 | 0.65 | 0.925 |

Number of Blades | Profile Type | Scale Ratio | Propeller Diameter (m) | Boss Ratio |
---|---|---|---|---|

5 | NACA66 + a = 0.8 | 31.599 | 0.25 | 0.18 |

Calculated Value | Experimental Value | Error | |
---|---|---|---|

Hull resistance (N) | 91.8 | 90 | 2% |

Propeller thrust (N) | 58.5 | 59.9 | 2.34% |

Propeller torque (N.m) | 2.47 | 2.53 | 2.47% |

K_{T} | 10K_{Q} | |
---|---|---|

ECV | 0.16554 | 0.2828 |

ACV | 0.14049 | 0.2453 |

Experimental value | 0.17030 | 0.2880 |

error of ECV | 2.7% | 1.80% |

error of ACV | 17.5% | 15.2% |

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**MDPI and ACS Style**

Li, J.; Zhao, D.; Wang, C.; Sun, S.; Ye, L.
Method for the Calculation of the Underwater Effective Wake Field for Propeller Optimization. *Water* **2019**, *11*, 165.
https://doi.org/10.3390/w11010165

**AMA Style**

Li J, Zhao D, Wang C, Sun S, Ye L.
Method for the Calculation of the Underwater Effective Wake Field for Propeller Optimization. *Water*. 2019; 11(1):165.
https://doi.org/10.3390/w11010165

**Chicago/Turabian Style**

Li, Jianing, Dagang Zhao, Chao Wang, Shuai Sun, and Liyu Ye.
2019. "Method for the Calculation of the Underwater Effective Wake Field for Propeller Optimization" *Water* 11, no. 1: 165.
https://doi.org/10.3390/w11010165