# Seakeeping Analysis of Planing Craft under Large Wave Height

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Numerical Method

#### 2.1. RANS Equation

#### 2.2. Turbulence Model

#### 2.3. Boundary Conditions

#### 2.4. Wall y^{+}

^{+}value near the hull should be controlled between 30 and 300. The wall y

^{+}value is dimensionless quantity, and the formula for calculating the y

^{+}value is as follows:

^{+}value will greatly affect the accuracy, the value of y

^{+}should be larger.

#### 2.5. Volume of Fluid Method

#### 2.6. Overset Method

## 3. Towing Tank Experiments

## 4. Numerical Simulation Validation

#### 4.1. Computational Domains

#### 4.2. The Verification of Overset Method

#### 4.2.1. Grid Parameter

#### 4.2.2. Value of y^{+}

^{+}has influence on the accuracy of calculation, under normal conditions the value of y

^{+}ranges from 30 to 300.

^{+}, the values of 50, 100, 200, 250, and 300 were adopted, the boundary layer grid generated according to different values of y

^{+}are presented in Figure 10.

^{+}value of hull less than the theoretical value during the sailing.

^{+}are presented in Table 6 and Figure 11, respectively.

^{+}are all less than 10%, but the deviation which y

^{+}= 250 is the smallest. Due to the intense motion of the planing craft, the waterline length sharply reduces. A low y

^{+}value greatly affect the accuracy. In subsequent numerical simulations, the y

^{+}value was set at 250.

#### 4.2.3. Time Step of Iteration

^{+}are presented Figure 12.

^{+}, and the time step of iteration on the accuracy and computational efficiency are verified. The results show that the numerical method has good convergence and high accuracy in simulating of the sailing of USV01 in calm water. Based on the overset method which has been verified, the numerical simulation validation for the seakeeping test of USV01 will be carried out.

#### 4.3. Validation of Numerical Method

^{+}is set at 250, the ∆t is set at 0.002 s. In this way both the accuracy and computational efficiency are guaranteed.

## 5. Numerical Simulation of Planing Craft in Regular Wave with Large Wave Height

## 6. Results

#### 6.1. The Influence of Wave Length on the Navigation Configuration

#### 6.2. The Influence of Speed on the Navigation Configuration

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 10.**Boundary layer grid: (

**a**) y

^{+}= 50, (

**b**) y

^{+}= 100, (

**c**) y

^{+}= 200, (

**d**) y

^{+}= 250, (

**e**) y

^{+}= 300.

**Figure 13.**Calculation grids: (

**a**) Domain grids; (

**b**) Medium-profile local grids; (

**c**) Surface grid on the hull; (

**d**) Grid near free surface; (

**e**) Free surface of regular wave.

**Figure 14.**Comparison of the numerical and tested results: (

**a**) Amplitudes of the heave; (

**b**) Amplitudes of the pitch; (

**c**) Amplitudes of the acceleration of the CG; (

**d**) Amplitudes of the acceleration of the bow; (

**e**) Average values of the resistance.

**Figure 16.**The comparison of the RAOs of the prototype and improved vessel: (

**a**) Amplitude of the acceleration of the CG; (

**b**) Amplitudes of the acceleration of the bow; (

**c**) Amplitudes of the heave; (

**d**) Amplitudes of the pitch.

**Figure 17.**The simulation of the sailing of the improved vessel in the wave-piercing status: (

**a**) Free surface; (

**b**) Gas–liquid phase diagram; (

**c**) Free surface representation of the hull.

**Figure 18.**The simulation of the sailing of an improved vessel in the hull-borne status: (

**a**) Free surface; (

**b**) Gas–liquid phase diagram; (

**c**) Free surface representation of the hull.

**Figure 19.**Comparison of the RAOs at two speeds: (

**a**) Amplitudes of the acceleration of the CG; (

**b**) Amplitudes of the acceleration of the bow; (

**c**) Amplitudes of the heave; (

**d**) Amplitudes of the pitch.

**Figure 20.**Comparison of the RAOs under different navigation configurations: (

**a**) Amplitudes of the acceleration of the CG; (

**b**) Amplitudes of the acceleration of the bow; (

**c**) Amplitudes of the heave; (

**d**) Amplitudes of the pitch.

Main feature | Symbol | Value |
---|---|---|

Model scale | k | 1:4 |

Length overall | L | 2.75 m |

Beam overall | B | 0.78 m |

Mouded depth | h | 0.325 m |

Displacement | Δ | 125.4 kg |

Draft | d | 0.1325 m |

Longitudinal position of the centre of gravity | ${L}_{CG}$ | 1.048 m |

Rotational inertia | J | 58.6 (kg·m^{2}) |

Deadrise angle | β | 18 deg |

No. | U (m/s) | Fn | H (m) | λ/L | λ(m) | $\mathsf{\omega}(\mathbf{rad}/\mathbf{s})$ | H/λ |
---|---|---|---|---|---|---|---|

1 | 6 | 1.16 | 0.21 | 1.5 | 4.125 | 13.031 | 0.051 |

2 | 6 | 1.16 | 0.21 | 2.25 | 6.1875 | 9.261 | 0.034 |

3 | 6 | 1.16 | 0.21 | 3 | 8.25 | 7.301 | 0.025 |

4 | 6 | 1.16 | 0.21 | 3.5 | 9.625 | 6.446 | 0.022 |

5 | 6 | 1.16 | 0.21 | 4 | 11 | 5.787 | 0.019 |

6 | 6 | 1.16 | 0.21 | 5 | 13.75 | 4.816 | 0.015 |

Boundary | Distance | Boundary Conditions |
---|---|---|

Inlet | 2.5 L | Velocity inlet |

Outlet | 4 L | Pressure outlet |

Top | 2 L | Velocity inlet |

Bottom | 1 L | Velocity inlet |

Side | 1.5 L | Symmetry plane |

Inlet of overset region | 1.25 L | Overset grid |

Outlet of overset region | 0.25 L | |

Top of overset region | 0.25 L | |

Bottom of overset region | 0.25 L | |

Side of overset region | 0.3 L |

Grid parameters | Grid 1 | Grid 2 | Grid 3 | Grid 4 | |
---|---|---|---|---|---|

Total | 150 k | 280 k | 650 k | 1400 k | |

Grid on hull | Relative Size (% L) | 1 | 1 | 1 | 0.5 |

Refinement grid on the boundary of overset region | Relative Size (% L) | 4 | 2. | 1.5 | 1 |

Refinement Grid around overset region | Relative Size (% L) | 4 | 2.5 | 1.5 | 1 |

Refinement Grid around free surface | Relative Size of grid in X Y Z direction (% L) | N | 4 4 2 | 2.5 2.5 0.8 | 1.5 1.5 0.5 |

**Table 5.**Numerical results of four grids. CFD, computational fluid dynamics; EFD, experimental fluid dynamics.

Grid | Resistance/N | Deviation (%) | |
---|---|---|---|

CFD | EFD | ||

1 | N | 235.8 | N |

2 | 206.52 | 235.8 | 12.41 |

3 | 229.41 | 235.8 | 2.71 |

4 | 230.24 | 235.8 | 2.35 |

y^{+} | Resistance/N | Deviation (%) | |
---|---|---|---|

CFD | EFD | ||

50 | 223.06 | 235.8 | 5.4 |

100 | 220.82 | 235.8 | 6.35 |

200 | 221.78 | 235.8 | 5.95 |

250 | 229.41 | 235.8 | 2.71 |

300 | 228.56 | 235.8 | 3.14 |

∆t (s) | Resistance/N | Deviation (%) | |
---|---|---|---|

CFD | EFD | ||

0.001 | 228.84 | 235.8 | 3.11 |

0.002 | 229.41 | 235.8 | 2.71 |

0.006 | 209.72 | 235.8 | 11.06 |

0.01 | 200.82 | 235.8 | 14.83 |

0.02 | 180.66 | 235.8 | 23.38 |

**Table 8.**Numerical and test results of the response amplitude operators (RAOs) and resistance: (

**a**) Heave and pitch; (

**b**) Acceleration; (

**c**) Resistance.

(a) | ||||||

Heave/mm | Pitch/deg | |||||

λ/L | EFD | CFD | Deviation (%) | EFD | CFD | Deviation (%) |

1.5 | 3.844 | 3.48 | 9.33 | 2.261 | 2.21 | 2.25 |

2.25 | 8.517 | 8.66 | 1.75 | 3.844 | 4.16 | 8.22 |

3 | 12.964 | 13.02 | 0.43 | 5.35 | 5.44 | 1.68 |

3.5 | 13.492 | 14.19 | 5.24 | 5.502 | 5.8045 | 5.49 |

4 | 13.341 | 13.98 | 4.8 | 5.051 | 5.151 | 1.97 |

5 | 11.456 | 12.39 | 8.15 | 3.915 | 4.273 | 9.14 |

(b) | ||||||

Acceleration of Center of Gravity (CG)/g | Acceleration of Bow/g | |||||

λ/L | EFD | CFD | Deviation (%) | EFD | CFD | Deviation (%) |

1.5 | 0.905 | 0.825 | 8.83 | 2.11 | 1.931 | 8.48 |

2.25 | 0.98 | 1.003 | 2.34 | 2.355 | 2.205 | 6.36 |

3 | 0.829 | 0.849 | 2.41 | 1.809 | 1.705 | 5.74 |

3.5 | 0.678 | 0.637 | 6.04 | 1.356 | 1.351 | 0.36 |

4 | 0.527 | 0.494 | 6.26 | 0.979 | 0.925 | 5.51 |

5 | 0.301 | 0.310 | 2.99 | 0.527 | 0.485 | 7.97 |

(c) | ||||||

Resistance/N | ||||||

λ/L | EFD | CFD | Deviation (%) | |||

1.5 | 240.806 | 213.993 | 11.13 | |||

2.25 | 255.584 | 225.988 | 11.58 | |||

3 | 246.725 | 223.342 | 9.47 | |||

3.5 | 227.517 | 199.802 | 12.18 | |||

4 | 221.607 | 193.844 | 12.52 | |||

5 | 217.178 | 190.169 | 12.43 |

Main Feature | Symbol | Value |
---|---|---|

Model scale | k | 1:3 |

Length overall | L | 2 m |

Beam overall | B | 0.54 m |

Mouded depth | h | 0.256 m |

Displacement | Δ | 66.67 kg |

Draft | d | 0.147 m |

Longitudinal position of the center of gravity | LCG | 0.82 m |

Deadrise angle | $\beta $ | 24 deg |

Main Feature | Symbol | Value |
---|---|---|

Length overall | L | 2 m |

Beam overall | B | 0.67 m |

Mouded depth | h | 0.23 m |

Displacement | Δ | 66.67 kg |

Draft | d | 0.118 m |

Longitudinal position of the center of gravity | LCG | 0.82 m |

Deadrise angle | $\beta $ | 18 deg |

No | U (m/s) | Fn | H (m) | λ/L | λ (m) | $\mathsf{\omega}(\mathbf{rad}/\mathbf{s})$ | H/λ |
---|---|---|---|---|---|---|---|

7 | 2 | 0.46 | 0.45 | 2 | 4 | 7.316 | 0.1125 |

8 | 2 | 0.46 | 0.45 | 3 | 6 | 5.391 | 0.075 |

9 | 2 | 0.46 | 0.45 | 4 | 8 | 4.390 | 0.05625 |

10 | 2 | 0.46 | 0.45 | 5 | 10 | 3.749 | 0.045 |

11 | 2 | 0.46 | 0.45 | 6 | 12 | 3.324 | 0.0375 |

(a) | ||||

Amplitude of Heave (m) | Amplitude of Pitch (deg) | |||

λ/L | prototype | improved vessel | prototype | improved vessel |

2 | 0.103 | 0.118 | 6.825 | 7.895 |

3 | 0.213 | 0.209 | 8.764 | 10.685 |

4 | 0.228 | 0.209 | 9.653 | 9.44 |

5 | 0.233 | 0.208 | 8.942 | 7.835 |

6 | 0.235 | 0.207 | 7.483 | 6.195 |

(b) | ||||

Amplitude of Acceleration of CG (g) | Amplitude of Acceleration of Bow (g) | |||

λ/L | prototype | improved vessel | prototype | improved vessel |

2 | 0.574 | 0.651 | 1.017 | 1.278 |

3 | 0.677 | 0.659 | 1.411 | 1.309 |

4 | 0.531 | 0.503 | 0.871 | 0.783 |

5 | 0.398 | 0.367 | 0.617 | 0.549 |

6 | 0.272 | 0.251 | 0.451 | 0.347 |

No | U (m/s) | Fn | H (m) | λ/L | λ (m) | $\mathsf{\omega}\text{}(\mathbf{rad}/\mathbf{s})$ | H/λ |
---|---|---|---|---|---|---|---|

12 | 3 | 0.69 | 0.45 | 2 | 4 | 8.897 | 0.1125 |

13 | 3 | 0.69 | 0.45 | 3 | 6 | 6.440 | 0.075 |

14 | 3 | 0.69 | 0.45 | 4 | 8 | 5.177 | 0.05625 |

15 | 3 | 0.69 | 0.45 | 5 | 10 | 4.392 | 0.045 |

16 | 3 | 0.69 | 0.45 | 6 | 12 | 3.845 | 0.0375 |

**Table 14.**RAOs of the improved vessel at different speeds and with different wave lengths: (

**a**) Heave and pitch; (

**b**) Acceleration.

(a) | ||||

Amplitude of Heave (m) | Amplitude of Pitch (deg) | |||

λ/L | Fn = 0.46 | Fn = 0.69 | Fn = 0.46 | Fn = 0.69 |

2 | 0.118 | 0.097 | 7.895 | 6.597 |

3 | 0.209 | 0.232 | 10.685 | 10.434 |

4 | 0.209 | 0.246 | 9.44 | 10.225 |

5 | 0.208 | 0.244 | 7.835 | 8.673 |

6 | 0.207 | 0.242 | 6.195 | 7.465 |

(b) | ||||

Amplitude of Acceleration of CG (g) | Amplitude of Acceleration of Bow (g) | |||

λ/L | Fn = 0.46 | Fn = 0.69 | Fn = 0.46 | Fn = 0.69 |

2 | 0.651 | 0.771 | 1.278 | 2.059 |

3 | 0.659 | 0.918 | 1.309 | 2.709 |

4 | 0.503 | 0.752 | 0.783 | 1.403 |

5 | 0.367 | 0.612 | 0.549 | 0.783 |

6 | 0.251 | 0.481 | 0.347 | 0.574 |

No | U (m/s) | Fn | H (m) | λ/L | λ (m) | $\mathsf{\omega}\text{}(\mathbf{rad}/\mathbf{s})$ | H/λ |
---|---|---|---|---|---|---|---|

17 | 2 | 0.46 | 0.45 | 3 | 6 | 5.391 | 0.075 |

18 | 3 | 0.69 | 0.45 | 3 | 6 | 6.440 | 0.075 |

19 | 4 | 0.92 | 0.45 | 3 | 6 | 7.489 | 0.075 |

20 | 5 | 1.15 | 0.45 | 3 | 6 | 8.539 | 0.075 |

21 | 6 | 1.39 | 0.45 | 3 | 6 | 9.594 | 0.075 |

22 | 2 | 0.46 | 0.45 | 6 | 12 | 3.324 | 0.0375 |

23 | 3 | 0.69 | 0.45 | 6 | 12 | 3.845 | 0.0375 |

24 | 4 | 0.92 | 0.45 | 6 | 12 | 4.367 | 0.0375 |

25 | 5 | 1.15 | 0.45 | 6 | 12 | 4.888 | 0.0375 |

26 | 6 | 1.39 | 0.45 | 6 | 12 | 5.411 | 0.0375 |

**Table 16.**The RAOs of the improved vessel at different speeds: (

**a**) Heave and pitch; (

**b**) Acceleration.

(a) | ||||

Amplitude of Heave (m) | Amplitude of Pitch (deg) | |||

Fn | λ/L = 3 | λ/L = 6 | λ/L = 3 | λ/L = 6 |

0.46 | 0.209 | 0.207 | 10.685 | 6.159 |

0.69 | 0.232 | 0.242 | 10.434 | 7.465 |

0.92 | 0.196 | 0.255 | 8.745 | 7.651 |

1.15 | 0.171 | 0.2704 | 6.951 | 8.408 |

1.39 | 0.142 | 0.3035 | 6.115 | 9.483 |

(b) | ||||

Amplitude of Acceleration of CG (g) | Amplitude of Acceleration of Bow (g) | |||

Fn | λ/L = 3 | λ/L = 6 | λ/L = 3 | λ/L = 6 |

0.46 | 0.659 | 0.251 | 1.309 | 0.347 |

0.69 | 0.918 | 0.481 | 2.709 | 0.574 |

0.92 | 1.583 | 0.557 | 4.022 | 0.766 |

1.15 | 2.193 | 0.712 | 4.788 | 1.276 |

1.39 | 2.436 | 1.038 | 4.871 | 2.381 |

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**MDPI and ACS Style**

Bi, X.; Zhuang, J.; Su, Y.
Seakeeping Analysis of Planing Craft under Large Wave Height. *Water* **2020**, *12*, 1020.
https://doi.org/10.3390/w12041020

**AMA Style**

Bi X, Zhuang J, Su Y.
Seakeeping Analysis of Planing Craft under Large Wave Height. *Water*. 2020; 12(4):1020.
https://doi.org/10.3390/w12041020

**Chicago/Turabian Style**

Bi, Xiaosheng, Jiayuan Zhuang, and Yumin Su.
2020. "Seakeeping Analysis of Planing Craft under Large Wave Height" *Water* 12, no. 4: 1020.
https://doi.org/10.3390/w12041020